Investigation of mass balance parameters on the Greenland ice sheet using passive microwave satellite data

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Investigation of Mass Balance Parameters
on the Greenland Ice Sheet
Using Passive Microwave Satellite Data
by
Waleed Abdalati
B.S. Syracuse University, 1986
M .S. University o f Colorado, 1991
A thesis submitted to the Faculty o f the Graduate School of the
University o f Colorado in partial fulfillment o f the requirements for the degree of
Doctor o f Philosophy
Department of Geography
1996
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This thesis for the Doctor o f Philosophy degree by
Waleed Abdalati has been approved for the
Department o f Geography
by
'f
Dr. Konrad Steffen
Dr. Roger G. Barry
Date
7 - /7 - ^
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To my father, for the example,
my mother, for the foundation,
my sister for the encouragement,
and to Drew, for the promise o f things to come.
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iv
Abdalati, Waleed (Ph.D., Geography)
Investigation of Mass Balance Parameters on the Greenland Ice Sheet Using Passive
M icrowave Satellite Data
Thesis directed by Professor Konrad Steffen.
The Greenland ice sheet is an integral part o f the Earth system, and this barren
expanse is intimately linked with the climate both within, and far beyond, its borders.
This research seeks to improve our understanding o f the role o f the ice sheet both in
response to and as a contributing factor to changes in the climate. One means of
studying such a large and remote area is with the use of satellite data. In this investiga­
tion passive microwave satellite data are used to assess the melt characteristics o f the
ice sheet, and a microwave radiative transfer model is developed to investigate the
effects of accumulation and hoar development on the m icrowave emission. In addi­
tion, the relationships between accumulation, melt, and coastal temperatures are
assessed.
The analyses shows that there are significant links between regional tempera­
tures, the extent of melt, and the snow accumulation characteristics. A melt signal is
identified in the microwave emission, which enables the classification o f dry and wet
snow. Based on this melt signal, the spatial extent o f snowmelt on the ice sheet was
observed to increase at a rate o f 4.5% per year for the years 1979-1991. At the same
time, regional air temperatures along the coast showed a strong correlation and
increased by approximately 1.1°C over the 12 year period. Following the eruption of
Mt. Pinatubo in 1991, both the melt extent and regional temperatures dropped to
nearly their lowest levels in the 1978-1994 coverage period o f the passive microwave
data set.
In addition to the melt effects in the ablation zones o f the ice sheet, changes in
accumulation rates impact the microwave emission in the dry snow zones, but they are
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V
only secondary effects. O f m uch greater significance is the development o f hoar dur­
ing the summer months. These large crystals, with their high scattering characteristics
reduce the microwave emission by almost 3% (which translates to almost 5 K). They
are nearly an order o f magnitude more effective in altering the emission than are
changes of accumulation. Thus identification of accumulation variations requires suc­
cessful parameterization o f hoar characteristics.
Finally, a comparison between temperatures, m elt assessments, and accumula­
tion estimations shows that under conditions o f warming, the amount o f melt (mass
loss) increases by approximately 49% o f the current value per 1°C air temperature rise
while the amount of accumulation (mass gain) decreases by about 7%. The result is an
expected negative mass balance which is estimated to be approxim ately -200 Gt (or
km water equivalent). This corresponds to a 0.5 mm sea level rise.
Understanding the interactions betw een the Greenland ice sheet and the Arctic
and global climates is an ongoing process. Through the analysis of passive microwave
satellite data, this research address some of the important issues and provides insight
into these complex interactions. As a result, our understanding of the behavior of the
ice sheet in the changing climate is improved.
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VI
Acknowledgments
Many people have contributed to this thesis in various ways. First, I would
like to thank my principal advisor, Konrad Steffen, for his guidance, support, and
encouragement, for providing me with the opportunity to do this work, and for always
keeping his door open. I would also like to thank Roger Barry, who in addition to
being an indispensable resource, helped provide the necessary perspective. Also the
efforts o f my other committee members, Jim M aslanik, Richard Armstrong, and Judy
Curry who provided useful insight and suggestions which improved the work are
greatly appreciated. The contribution o f Jeff Key, who helped me with the DISORT
code is also very much appreciated. I am grateful as well to Jay Zwally for his helpful
discussions over fish dinners at the ETH/CU camp. I would also like to acknowledge
the contributions of all of my officemates, John Heinrichs, Julienne Stroeve, Jason
Box, and Jeral Estupinan, who on numerous occasions helped me brainstorm and see
the answers to problems that ranged from basic climatology to IDL graphics. In addi­
tion I would like to acknowledge the absolutely indispensable contributions of John
Kauzlauric and Scott Grigsby who kept the computer systems up and running at all
hours. They were very accommodating and I am grateful. This work was supported
under NASA grant NAWG-2158, and for that I would like to thank Bob Thomas. It
was also supported under Swiss Science Foundation grants 21-27449.89 and 2036396.92. Finally, I would like to express my deepest appreciation for the support,
understanding, and patience o f Cheri, who aside from me, sacrificed more than any­
body in support o f the completion of this work.
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Table of Contents
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1.0 INTRODUCTION
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1.1 The Greenland ice sheet
1
1.2 Climate and the ice sheet
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1.3 Objective
2.0
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INSTRUMENTS AND DATA DESCRIPTION
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2.1 W hy passive microwave remote sensing?
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2.2 Passive microwave instruments
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2.3 Satellite data
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2.4 In situ data
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3.0 SATELLITE DATA CONTINUITY: INSTRUM ENT CROSSCALIBRATION
3.1 Introduction
3.2
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Method of comparison
17
3.3 Results and discussion
18
3.4 Conclusion
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4.0 SNOW MELT IDENTIFICATION AND CLASSIFICATION
27
4.1 Introduction
27
4.2 M icrowave emission and brightness temperature (Tj,)
28
4.2.1 Surface-emitting and isothermal media
28
4.2.2 Volume-emitting non-isothermal media
29
4.3 Passive m icrowave melt signal
31
4.4 Previous m elt algorithms
33
4.4.1 Single-channel difference technique
33
4.4.2 37 GHz emission model
38
4.4.3. Gradient ratio
38
4.5 M ethod o f melt determination in this study
39
4.5.1 Improved melt signal
39
4.5.2 S S M /IF 8 analysis
42
4.5.3 SM M R analysis
45
4.5.4 SSM /I F l l analysis
46
4.5.5 M elt/Threshold relationship
46
4.5.6 Atmospheric variability
47
4.5.7 Additional error sources
50
4.6 Results and discussion
51
4.6.1 Seasonal melt cycle
51
4.6.2 M elt extent
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4.6.3 Interannual variations
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4.7 Conclusion
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5.0
ACCUMULATION AND HOAR: EFFECTS ON MICROWAVE
EM ISSIVITY
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5.1 Introduction
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5.2 Observed passive microwave brightness temperature trends
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5.3 History o f microwave modeling of polar fim
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5.2
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Hoar formation
5.5 Radiative transfer model development
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5.5.1 The equation o f radiative transfer
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5.5.2 Discrete ordinate radiative transfer method
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5.5.3 M odel description
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5.6 Results and Discussion
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5.6.1 Emissivity and accumulation
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5.6.2 Emissivity and hoar layer thickness
88
5.6.3 Accumulation and hoar: combined effects
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5.6.4 Assumption validity for hoar layer
90
5.7 Conclusion
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6.0 ACCUMULATION, HOAR FORMATION AND Tb: CASE STUDY SUMM IT
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6.1 Introduction
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6.2 M odel adjustment to Summit conditions
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6.2.1 Em ission sensitivity to grainsize distribution
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6.2.2 Estimation o f grainsize distribution
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6.2.2.1 Surface grain size
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6.2.2.2 Growth rate
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6.3 H oar parameterization
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6.4 In situ accumulation estimates: ice core interpretation
98
6.5 Accounting for Temperatures
103
6.6 Results and discussion
105
6.6.1 M odel run for Summit
105
6.6.2 Comparison to observed brightness temperatures
105
6.7 Conclusion
7.0 MELT, ACCUMULATION, AND TEMPERATURE RELATIONSHIPS
108
109
7.1 Introduction
109
7.2 M ethod
112
7.3 Results and discussion
113
7.4 Conclusion
116
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8.0 SUMMARY AND CONCLUSIONS
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8.1 Data continuity
117
8.2 M elting o f the snowpack
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8.3 Accumulation, hoar, and microwave brightness temperature
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8.4 Application to Summit, Greenland
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8.5. Temperature, accumulation, and melt relationships
121
8.6. Future work
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9.0 REFERENCES
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List of Tables
Table 1.1. Estimates of Mass Balance of the Greenland Ice Sheet. Units
are in km3 water equivalent per year.
Table 2.1. History of microwave radiometry on spacecraft.
Table 3.1. Greenland Ice Sheet Regression Coefficients. The slopes (Pi)
and intercepts (Pq) of the regression lines are given for two cases,
one in which the error is assumed attributable to the F8 data
(denoted by the subscript “x=Fl 1”), and one in which the error
is attributable to the F8 data (denoted by the subscript “x=F8”).
Table 3.2. Antarctic Ice Sheet Regression Coefficients. As in table 3.1,
the subscript x = F ll attributes all error to the F8 data, and x=F8
attributes all error to the F I 1 data.
Table 3.3. Recommended linear regression coefficients for Greenland and
Antarctica to relate the FI 1 data to the F8. The corrected FI 1
brightness temperatures, Ti,(Fl 1/), are related to the uncorrected
ones, T b(Fl 1), by the following relationship:
Tb(Fl l ^ P i T ^ F l l)+ p0.
Table 4.1. Days of melt per year calculated using the single-channel
difference threshold technique of Mote et al. (1993), for a typ­
ically cold and a typically warm (locations A and B respectively
in Figure 4.3) area on the Greenland ice sheet. Also shown are
the mean annual winter brightness temperatures based on
averages from Dec. 1 through Feb. 28 (as suggested by Mote
et al., 1993).
Table 5.1. Model assumptions and characteristics for nominal conditions on
the ice sheet (mean annual accumulation o f 100 mm w.e.
(Ohmura and Reeh, 1991), and 1.5 cm thick hoar layer). Also
given are the sources of the assumptions made and the sensitivity
of the emissivity to each assumption or characteristic. Each
assumption (1-17) are discussed following the table.
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List of Figures
Figure 1.1. M ap o f Greenland and surrounding areas. The thick line within
Greenland represents the ice sheet perimeter. Also shown are
several coastal towns and various locations on the ice sheet
referenced throughout this dissertation.
2
Figure 1.2. Contour map of the Greenland ice sheet showing the high central
region and the South Dome (the mountain in the vicinity o f Dye 3).
This topography acts as a barrier to high-latitude circulation.
3
Figure 2.1. Histogram showing the distribution o f brightness temperatures
within 1 pixel (25 km) o f the ETH/CU camp based on orbital
data for the period May 1 - December 31, 1991. The variations
within a day can easily be +/- 15 K from the m ean for a day.
Though not used in this study, the 22 GHz channel is included
for completeness.
13
Figure 3.1. Scatter plots and regression lines for the Greenland F8 and FI 1
data: Dec. 8 -D ec. 18,1991. Because the data are for the
northern hemisphere winter, diurnal variations are minimal.
Thus the scatter is more attributable to instrument differences
rather than surface differences. Though not used in this study,
the 22 GHz channel is included for completeness.
19
Figure 3.2. Scatter plots and regression lines for the Antarctica F8 and FI 1
data: Dec. 8 - Dec. 18, 1991. Because the data are for the austral
summer, there is a significant diurnal cycle, which causes more
scatter about the regression lines than is the case for the Green­
land ice sheet (Figure 3.1). Though not used in this study, the
22 GHz channel is included for completeness.
20
Figure 4.1. 1988-1992 Time series of 19 GHz brightness temperatures across
the Greenland ice sheet at the latitude o f the ETH/CU camp
(69.5°). The plot is much rougher near the edges o f the ice sheet
w here snowmelt occurs, while it is much smoother in the center,
w here the snow remains dry. This rough/smooth relationship is
attributable to sharp changes in microwave emissivity under
conditions of melt.
32
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Figure 4.2. 1988-1992 T b time series of brightness temperatures at the
ETH/CU camp for (a) 19V, (b) 37V, (c) 19H, and (d) 37H.
The drastic increase and decrease in Tb at the onset o f melt
and refreeze respectively result from the dependence o f emiss­
ivity on snow wetness.
Figure 4.3. Location map o f Greenland showing ETH/CU camp and the
coastal stations from which atmospheric data were obtained for
comparisons to melt estimates. Also shown are a typically cold
location o f the ice sheet (Location A: 79°N, 25°W) and a typically
warm area (Location B: 62°N, 43°W ) for which comparisons are
made.
Figure 4.4. SSM/I T b time series o f 19 GHz vertical polarization for a
typically cold region o f the ice sheet (Location A, 79°N, 25°W )
and a typically warm area o f the ice sheet (Location B, 62°N,
43°W ). Both Locations A and B are shown in Figure 4.1. Also
shown are the melt thresholds for each hear and location as
derived by the method o f Mote et al., (1993).
Figure 4.5. SSM/I time series o f the horizontally polarized gradient ratio for
the location of the ETH/CU camp. The large increases at the
onset o f melt occur because the water in the snow affects the 19
GHz channel more than the 37 GHz channel. Similarly, there is a
drastic decrease in gradient ratio during the refreeze condition.
Figure 4.6. SSM /I time series o f the 19 GHz polarization ratio (4.5a) and 37
GHz polarization ratio (4.5b) for the location of the ETH/CU
camp. The depolarization effects become evident as the ratio
approaches zero in the summer months.
Figure 4.7. Cross-polarized gradient ratio (XPGR) time series for the ETH/CU
cam p pixel for the dates o f available SSM/I data. Also shown are
the dates on which melt was observed to begin at the camp, and
the corresponding XPGR threshold associated with melt. There
are two thresholds: XPGR = -0.158 for the F8 SSM/I and XPGR =
-0.0265 for the F I 1 SSM/I. Two thresholds are necessary in part
because o f instrument differences, but primarily because of the
different crossover tim es of the two instruments.
Figure 4.8. Sensitivity of melt techniques to increased atmospheric extinction.
For increased atmospheric losses, the single-channel approaches
show a decrease in signal (underestimate o f melt) while the XPGR
method shows an increase (overestimate o f melt). The XPGR is
also least affected by the increased extinction. The slopes are such
that a positive slope indicates a reduced signal and a negative slope
means the signal is enhanced.
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Figure 4.9.
The average spatial melt extent for the years 1979-1994 (solid
line), mean melt +/- 1 standard deviation (dotted line), and melt
area for 1°C temperature change (dashed line) in km2 for the
melt months o f June, July and August. The extent was calculated
by determining the mean area coverage for these months in each
year and then averaging these values over the entire coverage
period.
52
Figure 4.10. M onthly maps o f areal m elt extent. The shaded areas are areas
that experience m elt in the month shown at least once in the
period from 1979-1994, and the darkness indicates what per­
centage of the month (averaged over the time series) the pixel
was wet. Light shading indicates a low wetness frequency, and
dark shading indicates a high frequency of melt. The white areas
represent the dry snow areas, and the black areas are regions of
Greenland that are not fully covered by the ice sheet.
54
Figure 4.11. 1979-1994 composite of melt. The shaded areas are areas that
experience melt in the month shown at least once in the period
from 1979-1994. The different shades of gray indicate the per­
centage of time throughout the coverage period, the pixels exper­
ienced melt for the month shown. The white areas represent the
dry snow areas, and the black areas are the locations of pixels that
are not fully covered by the ice sheet.
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Figure 4.12. Facies classification map o f the Greenland ice sheet (from
Benson, 1962).
57
Figure 4.13. Interannual variations in mean melt extent (average area for
the months o f June, July, and August of each year) as determined
by the XPGR classification technique for the years 1979-1994
(solid line). The years 1978-1991 show a 4.5% increase in areal
m elt extent. In 1992, following the eruption of Mt. Pinatubo, the
melt area decreased considerably, before continuing to rise again
in 1993 and 1994. Also shown (dashed line) are the coastal temp­
erature anomalies from the six climate stations in Figure 1.1.
They are well correlated with the melt extent.
59
Figure 5.1.
Location m ap o f various SMMR T b time series in the dry snow
regions of the ice sheet. The 18V signal was examined for loc­
ations A-J (labeled with a “*”), and they are plotted in Figure 5.2.
Also shown are other places on the ice sheet referred to in this
chapter (labeled with a “+”). These indicate areas from which
data either were collected in the past or will be collected in the
future. Location B is also the site o f the Inge Lehman camp
referred to in the text.
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Figure 5.2. SMMR 18V brightness temperature trends for the areas shown
in Figure 5.1. M ost regions show some increasing trend between
the years 1980 and 1986.
66
Figure 5.3. Locations of 18V
trends of varying magnitude. The strongest
trends are located in the northeast region of the ice sheet, which is
the low accumulation zone.
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Figure 5.4. Accumulation map o f the Greenland ice sheet (Ohmura and Reeh,
1991). The lowest accumulation rates are found in the areas that
exhibit the strongest brightness temperature trends.
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Figure 5.5. Firn temperature profiles as a function of time of surface max­
ima for Maudheim, Antarctica (71°03’S, 10°56’W). These are
typical of the seasonal variations of snow temperature with the
deeper temperatures showing less range and a time lag compared
with those closer to the surface.
72
Figure 5.6. Snow structure used in the radiative transfer model. The struc­
ture represents winter conditions at Inge Lehman, in which the
summertime hoar is sandwiched between the spring and fall snow.
80
Figure 5.7. Dependence of microwave emissivity on accumulation and hoar
thickness at Inge Lehman (77°57’N, 39°11’W). The isolines in (a)
are at 2 mm intervals, while those in (b) are at 10 cm intervals,
with the exception of the 2 cm line. The sensitivity is greatest
when accumulation is low and for thick hoar layers. Furthermore,
the emission is more strongly dependent on hoar formation than
accumulation variations.
87
Figure 6.1. Dependence of microwave emissivity on grain growth rates (6.1 a)
for varying surface grain sizes, and on grain sizes (6.1b) for
varying growth rates. The emissivity is nearly twice as affected
by the grain growth rate (S) than the surface grain size (r03).
94
Figure 6.2. Plots of the 37V/37H ratio for the Summit pixel for 1979-1994.
Also shown are the hoar indices for each year calculated by
dividing the magnitude o f the sustained decrease in the ratio in
a given year, by the average for the full period. The x-axis is the
days past SMMR launch, while the y-axis is the 37V/37H ratio.
99
Figure 6.3. Plot of SO18 for an ice core near Summit Greenland (Bolzan and
Strobel, 1994). The peaks and troughs indicate the summer and
winter levels respectively.
100
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XVII
Figure 6.4. 37V brightness temperature time series for 1978-1994 showing the
dates o f m inim um T b based on a 30 day running mean (dashed
line). Also shown are the winter solstices of each year (solid line)
for comparison. The average date o f minimum T b value is January
17, and the standard deviation is 31 days. The x-axis is the days
past SM M R launch, while the y-axis is the 37V brightness temper­
ature.
102
Figure 6.5. Dependence o f microwave emissivity on accumulation and hoar
layer thickness at Summit (72°N, 38°W). The isolines in (a) are
at 2 mm intervals, while those in (b) are at 10 cm intervals, with
the exception o f the 2 cm line. As with Inge Lehman, the sensit­
ivity to hoar formation is much greater than to accumulation
variations.
106
Figure 6.6. 19V brightness tem peratures before and after adjusting for the
hoar development. The presence or absence o f hoar can change
the Tb by several K. Also shown for comparison are the accum ­
ulation rates as derived from icecore analysis. W ithout including
tem perature effects, there is essentially no correlation between the
accumulation and the brightness temperatures.
107
Figure 7.1. Relationships between temperature at 5 cm depth (a), and albedo,
and snow depth (b) at the ETH/CU camp. Immediately after a
snowfall, albedo values rose considerably and temperatures
dropped significantly, suggesting a possible feedback between the
snow deposition, and temperature/melt conditions.
111
Figure 7.2. Relationships between accumulation and melt extent (a) and
precipitation and annual temperature anomaly (b). There is no
correlation between m elt extent and snowfall, however, there is
a slight negative correlation between temperature and accum ­
ulation (R=-0.49).
114
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1. Introduction
1.1 The Greenland ice sheet
Bound on the west by Baffin Bay and the Davis Strait, and on the east by the
Greenland Sea and Denmark Strait, the Greenland ice sheet (Figure 1.1) extends from
approximately 60°N latitude, well into the Arctic Circle to approximately 83°. A mys­
terious and remote place, the Greenland ice sheet is currently uninhabitable to humans
except on finite terms. These include the expeditions of the scientists who seek to
understand it, as well as those of explorers and adventurers, past and present. Despite
its inhospitable characteristics, the ice sheet is a unique, complex, and important com­
ponent o f the Earth system with important links to the climate conditions that extend
well beyond its borders.
Rising to an elevation in excess o f 3000 m above sea level (a.s.l.), the Green­
land ice sheet plays an important role in the Arctic as well as global climate. Its topog­
raphy (Fig. 1.2) presents a major barrier to high-latitude circulation (Ohmura et al.,
1991), while its albedo characteristics significantly impact the regional radiation bal­
ance (Dickinson et al., 1987). A remnant o f the Pleistocene, the Greenland ice sheet is
estimated to have been between 2.92 and 5.59 x 105 km 3 during the last ice age (Ohm­
ura and Reeh, 1991). Currently, however, the ice sheet has a surface area of 1.75 x 106
km2 and a volume of 2.65 x 106 km3. These correspond to 11 and 8% of the global
glacier surface area and volume respectively (Thomas, 1993), and the equivalent of 7
m of water relative to the global sea level (Warrick and Oerlemans, 1990). At its high­
est point, 3210 m a.s.l. (72.3°N and 38.9°W ), the ice is estimated to be approximately
3000 m thick, but on average the thickness is believed to be 1515 m (Steffen et. al,
1993).
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Figure 1.1. M ap of Greenland and surrounding areas. The thick line within Greenland
represents the ice sheet. Also shown are several coastal towns and various locations
on the ice sheet referenced throughout this dissertation.
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Figure 1.2. Contour map of the Greenland ice sheet showing the high central region
and the South Dome (the mountain in the vicinity o f Dye 3). This topography acts as a
barrier to high-latitude circulation.
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4
Presently, the equilibrium line (the line at which the mass gain, is equal to the
mass loss) descends from 1800 m a.s.l. at the southern end of the ice sheet to 750 m
a.s.l in northern Greenland (Ambach and Kuhn, 1985). The accumulation and ablation
area occupy 82% and 18% of the ice sheet respectively (Steffen et al, 1993), and the
dry snow zone, the borders of which range from 1650 m in the north to 3100 m (a.s.l.)
in the south (Steffen et al., 1993), is believed to occupy approximately 35% of the ice
sheet (estimated from Benson, 1962). Thus nearly 65% of this vast expanse is
believed to experience some melt.
Associated with this melt are changes in albedo, and energy, moisture, and
momentum exchanges with the atmosphere. Albedo is significantly reduced by the
melt process because the water film on the grain surface effectively increases the grain
size and hence the absorption cross section of the grain (Warren, 1982). Moisture and
momentum fluxes vary with melt because the energy required for formation of water
vapor from snow differs between dry and wet snow. This difference is due to the fact
that the latent heat of vaporization is about 13% less than the latent heat of sublima­
tion; thus less energy is required evaporate water from the surface of wet snow, than to
convert the solid ice crystals directly into water vapor.
Two semi-permanent cyclones, the Baffin Bay low and the Icelandic low, dom ­
inate the winter circulation, with Greenland lying under a weak saddle between the
two depressions. In the summer, a pressure ridge extends from the northeast toward
the center o f the ice sheet which controls the summer circulation (Ohmura and Reeh,
1991). These characteristics, along with radiative forcing and cloud cover are inti­
mately related to the climate of the Greenland ice sheet.
Annual total precipitation and accumulation for Greenland have been calcu­
lated by Ohmura and Reeh (1991) based on accumulation measurements of 251 pits
and cores and precipitation measurements made at 35 meteorological stations in the
coastal regions. They estimate the annual precipitation to be 340 mm water equivalent
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(mm w.e.) and the annual accumulation to be 310 mm w.e., with an increasing gradient
from north to south. Similar precipitation rates were calculated by Bromwich and oth­
ers (1993) based on analyses o f synoptic activity, and Robasky and Bromwich (1994)
did the same by analyzing the atmospheric moisture flux convergence. These accum u­
lation values are largely dependent on atmospheric parameters such as water vapor
content and circulation.
1.2 Climate and the ice sheet
Snow and ice, particularly when they cover an expanse as large as Greenland,
are critical components of the global climate system. In surface - atmosphere interac­
tion, they influence the heat, moisture, and momentum exchange (Dickinson et. al,
1987). Also the high latitude ice-covered areas of the world are of particular interest
because they are highly sensitive to global climate change (Mitchell et al., 1993) due
to their unstable positive feedback nature. With their high albedo, they reflect a large
portion o f incoming solar radiation, but because the albedo decreases as snow melts,
any associated change in albedo becomes a self compounding change. Considering
this positive feedback mechanism, an understanding of the behavior of the ice sheet
and its variations is desirable for the monitoring and detection of climate changes.
One additional feature that is intimately related to the Greenland climate is the
ice sheet mass balance, yet it is not well understood. Recent work by Zwally et al.
(1989) has reported a thickening o f the Greenland ice sheet south of 72° N latitude at a
rate o f 0.23 m/year, based on satellite radar altimetry measurements. Unfortunately,
due to its orbital inclination, the satellite did not make measurements north o f 72°N;
thus the growth of the northern portion of the ice sheet has not been assessed.
Zw ally’s estimates are inconclusive, however, due to the large relative errors in the
altimetric measurements. Consequently, it is not known with any certainty whether
the ice sheet thickness is increasing or decreasing. A summary of mass balance esti-
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6
mates is given in Table 1.1.
In addition, little is known about the melt characteristics o f the ice sheet. Recent
estimates based on passive microwave data (Mote and Anderson, 1995) suggest that the
mean areal surface melt extent of the ice sheet has increased by 3.8% between the years
1979 and 1991. However, the relationship between the ice sheet thickness, the melt
extent, and the regional climate is still unclear.
Table 1.1. Estimates of Mass Balance o f the Greenland Ice Sheet. Units are in km3 water
equivalent per year.
Source
Accumulation
Ablation
Calving
Total
Loewe (1936)
+425
-295
-150
-20
Bauer (1955)
+446
-154
-155
-84
Bader (1961)
+630
-120 to -270
-215
+145 to +295
Benson (1962)
+500
-272
-215
+ 13
Bauer (1966)
+500 ± 250
-3 3 0 ± 165
-2 8 0 ± 140
-110 + 555
Radok et al. (1982)
576
69
139
0
Weidick (1985)
+ 5 0 0 ± 100
-295 ± 100
-205 ± 60
0 ± 260
1.3 Objective
A means of remotely sensing variations in the ice sheet mass balance would be of
considerable value in developing an understanding of the behavior of this integral com po­
nent of the global climate system, both in response to and as a contributing factor to global
change. This research examines two essential components of the mass balance equation:
1) snow accumulation, which is the prevailing component of the mass input, and 2) snow
melt, which comprises approximately 60% of the mass loss (Weidick, 1985). The primary
objective o f this research has been to use passive microwave satellite data to develop
methods of estimating and monitoring these parameters and to relate them to each other as
well as the regional and global climate.
A melt signature in the passive microwave signal has been identified (Abdalati and
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7
Steffen, 1995), and it is used to estimate ice sheet melt extent on time scales ranging
from daily to annual. In addition, a radiative transfer model is developed and applied
to the winter signal to estimate impacts of accumulation rates and hoar formation on
the brightness temperatures (T^) in the dry snow regions o f the ice sheet. These results
are compared to the limited amount of available climate data for the region. Their
relationships are examined and discussed, and finally, recommendations for directions
o f future research efforts are made based on the insight gained throughout this work.
The Greenland ice sheet is not only a critical component o f the global climate
system, but this sensitive and volatile region also provides an early indicator of climate
changes to come. Yet little is know about it. This research effort is intended to charac­
terize the impact of snow accumulation, metamorphism, and melt on the microwave
emission of the firn. Furthermore, it seeks to improve the characterization of mass bal­
ance in a changing climate. In doing so, it provides a significant step toward a com­
prehensive understanding o f the Greenland ice sheet, the state of its mass balance, and
its unique relationship with the regional and global climates.
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8
2. Instrument and Data Description
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2.1 W hy passive microwave remote sensing?
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Satellite remote sensing provides data on scales that were once impossible to
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achieve for the remote regions of the earth, such as the Arctic. Passive microwave sat-
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ellite data are particularly well suited for Arctic studies for several reasons. First,
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microwaves are capable of penetrating clouds. This occurs because their wavelengths
are long in comparison to the cloud particle size, and as such, there is little signal
extinction. Cloud penetration capabilities are especially significant in remote sensing
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of the Arctic where the frequent presence o f clouds is a major obstacle in the use of the
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higher resolution visible and thermal infrared instruments (Schweiger and Key. 1992).
1
Equally as important is the fact that passive microwave instruments can pro-
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vide information during the polar night, because they measure thermally emitted radiation, and do not rely on the sun as a source of illumination. Similarly, passive
microwave data can be collected at times when the sun angle may be too low for opti-
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cal sensors.
With specific regard to the Greenland ice sheet, passive microwave data hold
information not only about surface characteristics, but about some subsurface condi­
tions as well. By measuring emission from the snowpack volume rather than the sur­
face, an additional dimension of information is added to what can be remotely sensed.
Thus, when used in conjunction with visible and infrared sensors, passive microwave
instruments can contribute to a more complete understanding of the conditions of the
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ice sheet.
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Finally, the lower spatial resolution of the passive microwave data, in compari­
son to data from other sensors, significantly reduces the data volume, thus making
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9
analysis o f long time series more computationally feasible. All of these features col­
lectively m ake passive microwave measurements well suited for the study of the cli­
mate and mass balance of the Greenland ice sheet.
2.2 Passive microwave instruments
A comprehensive history of spacebome microwave radiometers through the
SSM/I instrument is given in Table 2.1. The first space-borne m icrowave radiom eter
was on the 1962 Venus flyby of the M ariner 2. Operating at 15.8 GHz and 22.2 GHz it
measured lim b darkening o f planetary emission (Ulaby et al, 1981). Terrestrial appli­
cations of microwave radiometry to the polar regions of the earth began with the
Soviet U nion’s launch of Cosmos 384 in 1970 which measured sea surface tem pera­
ture and sea ice concentration. Soon after, in 1972, the United States launched the
Electrically Scanning Microwave Radiometer (ESMR) on Nimbus 5. Operating at
19.3 GHz, ESM R provided information on rain rate, seaice type and concentration,
and snow cover. It was from information obtained by ESMR that the role o f volume
scattering within the medium and its impact on the ice sheet microwave signal began
to be understood (Gloersen et al., 1974). The Nimbus 5 ESMR was later followed by
a 37 GHz dual polarized instrument of the same type on Nimbus 6.
W hile useful information was obtained by these single-channel radiometers,
the advantages of multiple frequencies and polarizations were soon realized. The first
multi-channel passive microwave satellite instrument that was used heavily in polar
surface research was the Scanning Multi-channel Microwave Radiometer (SMMR).
Other multi-channel radiometers did exist, namely the Nimbus E M icrowave Spec­
trometer (NEM S) on Nimbus 5, and the Scanning Microwave Spectrom eter (SCAMS)
on Nimbus 6, but they were not applied very extensively to polar surfaces. The
SMMR was launched into sun-synchronous near polar orbit on the Nimbus 7 satellite
in October o f 1978. A linearly polarized passive microwave instrument, it operated at
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10
T able 2.1. History o f microwave radiometry on sp acecraft
Year o f
fjuunch
1962
SpoeecrojiJ
instrum ent
acronym
frequencies
(G H z)
A n ten n a
type
M anner 2
(V enus flyby)
15 8. 22 2
M echanically sca n n ed
p arab o la
C osm os 2*3
3.5. 8 8
2 2 .2 .3 7
N a dir-view ing
S w e th -m d th
o f scan
(k in )
Sm allest-resolution
elem ent
(k m )
P la n etary
1300*
13
h o rn s
N im b u s 3
ESM R
E lectrically
sca n n ed
array
22 2. 31 J
53 6. 54 V
5K8
1974
M eteor
37
D u a l p o la n z a u o n
35* from n a d ir
1975
N im b u s 6
ESM R
37
D ual p o lariz atio n
electrically
sc a n n e d array
A tm o s p h e re - W a ter-v ap o r c o n te n t,
liq u id -w aier co n te n t
180
16
115
A tm o sp h ere : R a in rate
S urface: Sca-ice c o n c en tra tio n
ice cla ssific atio n . snow cover
A tm o sp h ere T em p e ratu re profile
w ate r-v a p o r co n te n t,
b q u id -w a te r co n te n t
S urface: Ic e classification,
snow covet
S urface: Soil m o istu re, oce an wind-.
A tm o sp h ere R am rate
S urface: Soil m oisture
A tm o sp h ere . L iq u td -w a te t content
1300
20x43
S am e as N im b u s 5 ESM R
22 2 .3 1 6.
52 R. 53 8.
55 4
T h re e ro tatin g
hy p erb o lic
m irro rs
Sam e as N im b u s 5 N E M S
D M SP
S S M /T
50.5. 53.2.
54 3 .5 4 9.
58 4 .5 8 8.
59 4
S ingle
ro ta tin g
m irro r
A tm o sp h ere . T em p e ra tu re profile
tiro s
N /M S U
(2 satellites)
50.3. S3.7.
55 0. 57 9
D u a l ro tatin g
m iiTors
N im b u s 7
SM M R
6 6. 10 7.
1 8 .2 1 .3 7
Single
o s d lla u n g -o ffs e t
p ara b o lic reflector
S casat I
SM M R
1982
(p la n n e d )
25
200
Five
lens-ioadcd
h o rn s.
nadir-view ing
M echanically
scanned
p arab o la
Skytab
S I93
3000
N adir-view ing
p h ase d arra y
1978
L im b d a rk e n in g o f plan e ta ry
em ission
S urface: S ea te m p e ra tu re , sea-ice
c o n c e n tra tio n
C osm os
1973
Principal param eters
m easured or inferred
DM SP
S S M /I
19.4.22.3
37.0.85.5
C o n tin u o u sly
r o ta tin g offset
p a ra b o lic re flec to r
1986
TIROS-0
(p la n n e d )
AM SU
18 .5 .2 2 .2 .
3 1 .6 .5 0 .3 -5 7 .9
(7 ch). 9 0 .1 5 0 .
183.3 (3 ch )
C o n tin u o u sly
sca n n ed
m irro rs
110
A tm o sp h ere T em p e ratu re profile
IK x 2 7 b
A tm o sp h ere : W a ter-v ap o r co n te n t,
liq u id w a te r c o n te n t,
ra in rate
14 x 2 l b
S u rfa ce. S ea s ta te (w in d speed).
sea te m p e ra tu re , sca-icc
c o n c e n tra tio n , ice
c la ssific atio n , snow
cover, soil m oisture
I6 X 14
P rec ip itatio n ra te over o c e a n /la n d ,
o c e a n w ind s p e e d ,
ice ty p e /c o n c e n tra tio n s ,
soil m oisture
15
A tm o sp h eric te m p e ra tu re a n d
w a te r v a p o r profiles
• C o u rte s y o f L. K ing. N A S A /G S F C .
b R eso lu tio n a t h ig h est frequency only.
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five frequencies, 6.6, 10.7, 18.0, 21.0, and 37.0 GHz, each o f which had a vertically polar­
ized channel, and a horizontally polarized channel. The SMMR scanning angle was 50.3°,
and it provided nearly eight years o f coverage every other day until its failure in August
1987.
The Special Sensor M icrowave Imager (SSM/I), which was the follow up instruI
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ment to the SMMR, was first launched into sun-synchronous near polar orbit on the
Defense M eteorological Satellite Program (DMSP) F8 satellite in June of 1987. In
December, 1990, a second SSM/I instrument for sensing the polar regions was also
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launched into a sim ilar orbit on the DM SP F I 1 satellite, providing redundant coverage.
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Both SSM/I instruments operate at four frequencies, 19.35, 22.24, 37.0, and 85.0 GHz,
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and they too have vertically and horizontally polarized channels at all operational frequen-
I
cies, except the 22.24 GHz which only has a vertically polarized channel. The scan angle
for both SSM /I instruments is 53.1°.
2.3 Satellite data
For this research, the SMMR data used were from the 18 GHz horizontally and
vertically polarized channels (18H and 18V respectively), and the 37 GHz horizontally
and vertically polarized channels (37H and 37V respectively). The SSM/I data used were
19 GHz horizontal and vertical polarization (19H and 19V respectively) data and the 37V
and 37H data. The overlap in coverage between the SMMR and the SSM/I instruments
results in a continuous data set which dates back to October 1978.
Three different types o f microwave data were examined in this study. The first
was the binned and gridded product produced by the National Snow and Ice Data Center
(NSIDC) in Boulder, Colorado. In this data set, the satellite data are arranged on a 25 km
x 25 km grid scale and binned into daily averages using what is called a “drop in the
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bucket” approach. Both the northern and southern hemispheres are laid out in a 25 km x
25 km grid, and each radiom eter scan for each orbit is assigned to the grid cell containing
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12
the scan center. An average o f all scans in a given day is then computed for each grid
cell. In this way, daily images o f the northern and southern hemispheres are generated.
For this research, 4097 images were analyzed, one for nearly each day o f SMMR and
SSM /I coverage, and it is this data set on which a vast m ajority o f the
analyses are based.
The second type o f data examined was the orbital satellite data. Rather than
being binned and gridded, and output as images, the data are archived as latitude, lon­
gitude, time of scan, and brightness temperatures. A comparison between the NSIDC
product (daily average gridded values) and an orbital data test set show that while
binned and gridded data represent the daily averages for a region, there is a large vari­
ance throughout the day which gets smeared out in the average. Hence some impor­
tant information contained in the orbital signal m ay be lost due to averaging. For the
comparison, a single location on the ice sheet was chosen, the location o f the ETH/CU
climate station (shown in Figs. 1.1 and 1.2, and discussed in Section 2.4). The study
was conducted for the dates May 1, 1991 - December 31, 1991, and all satellite passes
that were within 25km (1 SSM/I pixel) of the camp were selected and averaged over
each entire day. The results, which are shown in Figure 2.1, indicate that there is a
broad range in brightness temperature throughout the day of more than ±15 K in some
cases with a standard deviation as high as 6.5 K. Thus for accurate comparisons on
sub-daily time scales, and for retrieval of parameters which have a diurnal cycle (such
as the snow melt), the orbital data are preferable. However, data volume, and lack of
availability for the full coverage period makes a complete analysis with orbital data
impossible.
The third type o f data examined was sample EASE-Grid (Equal A rea SSM/I
Earth Grid) brightness temperatures. Like the standard NSIDC product, the EASEGrid format is on a 25km x 25km grid scheme. However, the EASE-Grid processing
incorporates a method to interpolate from swath space to Earth-gridded coordinates
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1
°)
b)
Tb Anomolies (19V)
60
S td . Dev.
b
Tb Anomalies (19H)
60
4 .5 3
S td . Dev. « 5 .5 6 K
g 50
40
40
30
30
20
-2 0
-1 0
0
10
20
-2 0
Difference From Mean (K)
c)
Tb Anomalies (22V)
60
S td . Dev. -
4 .6 1 K
-1 0
0
10
20
Difference From Meon
d)
Tb Anomalies (37V)
60
S td . Dev. ■= 6 .2 2 K
40
30
30
20
20
20
e)
0
10
20
Difference From Meon
10
-----
•20
10
20
10
0
D ifference From Meon
Tb Anomalies (37H)
60
S td . D ev. « 6 .5 3 K
40
30
20
10
0
10
20
Difference From Meon
Figure 2.1. Histogram showing the distribution of brightness temperatures within 1
pixel (25 km) of the ETH/CU camp based on orbital data for the period May 1 December 31, 1991. The variations within a day can easily be ±15 K from the mean
for a day. Though not used in this study, the 22 GHz channel is included for complete
ness.
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14
which uses weighting functions based on the actual antenna pattern. By means of this
interpolation, every observation is slightly modified to the brightness temperature that
would have been observed had the antenna been pointing directly at the center o f the
EASE-Grid pixel. In addition, the EASE-Grid data are resolved into ascending and
descending pass averages (which are approximately 12 hours out of phase) rather than
into daily averages. A s a result, sub-daily variations in temperature can be resolved
which is important for studying areas in which a large diurnal brightness temperature
variations exist. The processed data currently exist for August 1, 1987- November 20,
1988. The processing involved in the generation o f the EASE-Grid product is describe
in more detail Arm strong and Brodzik, (1995).
The objective o f this study was long term monitoring of the ice sheet (over the
full coverage period), and this objective is what drives the data format selection.
Because EASE-Grid data and quality controlled orbital data were not available for
most o f the coverage period, the long term analyses were done with the binned and
gridded product. Some peripheral short term analyses were done with the other data
types, but they were prim arily used for interpretation and clarification of the long term
studies. In all cases, regardless o f the data set used, this research has primarily been
based on the 18 and 37 GHz channels for the SMMR data, and the 19.35 and 37 GHz
channels for the SSM /I data.
2.4 In situ data
In Spring, 1990 scientists from the Swiss Federal Institute of Technology
(ETH) in Zurich installed a semi-permanent research camp at the equilibrium line of
the Greenland ice sheet near Jakobshavn (see Figs. 1.1 and 1.2). The exact location of
the camp is at 69° 34/ N latitude and 49° 1 7 'W longitude, and 1150 m above sea level.
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15
Since its establishment the station has provided a full suite of climatological data
including temperatures below and above the ice, radiation data, atmospheric data,
information on snow properties throughout the transition from dry to wet snow, radio­
sonde data, measurements pertaining to the ice flow dynamics, and other useful infor­
mation about this data-sparse area. These measurements are expected to continue
beyond 1996. W hile all of the data provide critical pieces to the complex puzzle of the
Greenland climate, of particular interest in this study is the snow wetness data col­
lected during the 1990, 1991, 1993, 1994, and 1995 field seasons. These data sets
were collected at the critical times of transition from dry to wet snow, and they provide
the reference on which the melt algorithm, described in Chapter 4, is based.
There is a limited amount o f data available for the dry snow areas of the ice
sheet, where the accumulation effects are modeled (Chapters 5 and 6), however Bolzan and Strobel (1994) have published accumulation estimates based on oxygen-isotope and gross (3 activity analyses of shallow ice cores near Summit (shown in Fig.
1.1). In addition, John Bolzan has provided me with supplemental unpublished analy­
ses of the ice cores. These data provide a basis for comparison with the accumulation
model.
Additional comparisons are made using the data and calculations of Bromwich
et al. (1993) who have done precipitation analyses for Greenland based on a parame­
terization o f the synoptic activity at the 500 mbar level. Their studies combine coastal
climate station data with National M eteorological Center (NMC) model data to arrive
at precipitation estimates. Finally, some in situ data from the Humboldt Site (78°30'
N, 56°50' W) are used (K. Steffen, unpublished data) to provide insight into the snow
stratigraphy and metamorphism processes in the firn.
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16
!
3.0 Satellite Data Continuity: Instrument Cross-Calibration
3.1 Introduction
The transition from one instrument to another is a critical period in the
collection o f data, because it establishes the relative calibrations between instruments.
The multi-channel microwave data sets provide extended coverage back to 1978;
however, in order for these extended time series to be consistent, it is necessary that the
relationships between different passive microwave instruments be well understood. As
one generation of instruments is replaced by another, the changes in signal due to the
instrument characteristics themselves must be accurately assessed. Such a
determination requires that comparisons be made for large homogeneous areas with
weak diurnal cycles. The spatial homogeneity is essential, because the instruments,
with their slightly different orbits, will not contain the exact same areas within each
pixel. The weak diurnal cycle is important because the instruments do not cross the
same area at the same time o f day. Compared to other parts o f the world, the Greenland
and Antarctic ice sheets satisfy these criteria, particularly during their respective winter
seasons; therefore, they provide the best locations for such calibrations. By using these
large homogeneous areas and examining overlapping periods of coverage, the
relationships between the different instruments can be studied.
The relationships between SMMR and SSM/I brightness temperatures have
already been investigated (Jezek, et al., 1991; Steffen et al., 1993; Mote and Anderson,
1995). In this chapter I will develop and discuss the relationships between the two
different SSM /I instruments: the one launched on the DMSP F8 satellite, and one on the
DM SP F I 1 satellite. The ultimate objective is to determine what corrections, if any, are
necessary for the data sets in order to insure that they are consistent with one another.
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17
The DM SP F8 satellite was launched into sun-synchronous near polar orbit on
June 20, 1987, and it flies at a nominal altitude o f 848 km. With an inclination angle
of 98.8 degrees, its orbital period is 101.7 minutes. The F I 1 satellite was launched on
December 1, 1990, also into sun-synchronous orbit, and it flies at 837 km and a 98.7
degree inclination angle. Its orbital period is 100.5 minutes. It is these orbital
differences that are largely responsible for the differences in data values between the
two instruments as discussed below.
3.2 M ethod of comparison
The SSM/I orbital data were processed at the National Snow and Ice Data
Center (NSIDC) in Boulder, Colorado, where they were then binned and gridded into
daily averages and 25 km x 25 km pixels. The product is a series of daily maps of the
northern and southern hemispheres on a 25 km x 25 km grid. NSIDC provided a
common data set for the two different SSM/I instruments for the month of December,
1991. It is this common data set on which the analysis was performed.
The method o f analysis applied here to the two SSM/I instruments was based on
the comparison made by Jezek et al. (1991) at the Byrd Polar Research Center (BPRC)
between the SMMR and SSM/I for their overlap period in 1987. The analyses for this
study were carried out for the dates of December 8 through December 18, 1991. This
time period was chosen because it provided the longest and most consistent data set
available for the overlap period in which there were no erroneous scans.
For the Greenland comparison, an icemask was produced by digitizing the
margins o f the ice sheet from the Geological Survey of Greenland Quaternary Map of
Greenland (1:2,500,000 scale). This map was further modified by reducing the mask
by two pixels around the perimeter of the ice sheet. This conservative approach was
taken in order to insure that no land-contaminated pixels were included when the
icemask was applied due to the large instantaneous field of view (IFOV) of the channels
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18
(19 GHz -70 x 45 km; 22 GHz - 60 x 40 km; 37 GHz - 38 x 30 km (Carsey, 1992)). The
modified mask was then applied to the northern hemisphere data, and the ice sheet
brightness temperatures were retrieved for all channels on the dates specified. After the
mask was applied, approximately 22,000 data points were retrieved for each channel and
each instrument over the eleven day period (roughly 2000 points per day). Scatter plots
were made from the data, and the correlation and linear regression coefficients were
calculated.
For the Antarctic data, the same dates were used, along with the Antarctica land
mask provided by NSIDC. In this case as well, two pixels around the perimeter o f the ice
mask were removed to eliminate contamination effects. Approximately 215,000 data
points were retrieved for each channel (roughly 19,500 points per day). From these data
sets scatter plots were generated, and the regression and correlation coefficients were
calculated. Any point outside o f the mask was not considered. Also, data points with
brightness temperature values o f 0 K or in excess of 300 K were assumed to be erroneous
and were not included in the analysis.
3.3 Results and discussion
The results for the Greenland ice sheet comparison are shown in Figure 3.1 and
listed in Table 3.1. Those from Antarctica are shown in Figure 3.2 and summarized in
Table 3.2. Each of the tables shows two sets o f coefficients: one set in which the FI 1
brightness temperatures are taken as the independent variable, and the F8 values are the
dependent, and another using the F8 data as the independent variable and the FI 1 data as
the dependent. It is evident that the two data sets are highly correlated, with correlation
coefficients greater than 0.985 in all cases. As expected, since the instruments are so
similar, the slope of the regression lines are close to 1.0 for all channels, and the intercepts
are mostly positive and very low in magnitude. When the axes are switched, however, the
slope and intercepts are not even qualitatively transposed about the line F8 = FI 1, as would
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°)
b)
19V
240
200
220
180
200
>- 160
19H
u.
180
140
160
1201-
160
180
c)
200
220
F8 T. (K)
120
240
d)
22V
140
160
180
F8 T. (K)
200
37V
240
240
220
220
200
i-* 2 0 0
^
180
180
160
160
160
e)
180
200
220
F8 T. (K)
240
160
180
200
F8 T. (K)
220
240
37H
220
200
-
180
i- 160
140
140
160
180
F8 T. (K)
200
220
Figure 3.1. Scatter plots and regression lines for the Greenland F8 and FI 1 data: Dec.
8 - Dec. 18, 1991. Because the data are for the northern hemisphere winter, diurnal
variations are minimal. Thus the scatter is more attributable to instrument differences
rather than surface differences. Though not used in this study, the 22 GHz channel is
included for completeness.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
°)
b)
19V
280
260
260
240
19H
240
u. 2 0 0
t-* 200
£ 180
180
160
160
140
220
160 180 200 220 240 260 280
P8 T. (K)
c)
22V
140 160 180 200 220 240 260
F8 T. (K)
d)
280
280
260
260
S' 240
240
£
220
i-
200
u- 2 0 0
180
180
160
160
160 180 200 220 240 260 280
F8 T. (K)
e)
37V
220
160 180 200 220 240 260 280
F8 T. (K)
37H
260
240
S' 220
200
lZ
180
160
140
140 160 180 200 220 240 260
F8 T. (K)
Figure 3.2. Scatter plots and regression lines for the Antarctica F8 and F I 1 data: Dec.
8 - Dec. 18, 1991. Because the data are for the austral summer, there is a significant
diurnal cycle, which causes more scatter about the regression lines than is the case for
the Greenland ice sheet (Figure 3.1). Though not used in this study, the 22 GHz chan­
nel is included for completeness.
Reproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
21
T able 3.1. Greenland Ice Sheet Regression Coefficients. The slopes (pj) and
intercepts (P q) o f the regression lines are given for two cases, one in which the error is
assumed attributable to the F8 data (denoted by the subscript “x= Fl 1”), and one in
which the error is attributable to the F8 data (denoted by the subscript “x=F8”).
Correl.
Coef. (R)
0.297
0.987
1.86
0.993
1.000
0.152
0.987
2.48
0.994
22V
1.001
0.076
0.986
2.69
0.993
37H
1.009
-1.67
0.977
4.12
0.993
37V
0.987
2.81
1.000
-.0523
0.993
19H
1.000
19V
il
X
(Po) x=F8
( P i ) x=FIl
'o
CO.
( P i ) x=F8
Channel
Table 3.2. Antarctic Ice Sheet Regression Coefficients. As in table 3.1, the subscript
x = F ll attributes all error to the F8 data, and x=F8 attributes all error to the FI 1 data.
Channel
( P i ) x=fi i
( P o ) x=Fl 1
( P i ) x=F8
(Po) x=F8
Correl.
Coef. (R)
19H
0.988
2.40
0.992
1.16
0.990
19V
0.984
2.91
0.998
0.930
0.991
22V
0.991
1.46
0.993
2.11
0.992
37H
0.995
0.992
0.982
3.53
0.988
37V
0.983
3.13
0.992
2.21
0.988
be expected with such highly correlated data. Thus there exist two sets of coefficients,
depending on which data set is regressed against which, resulting an ambiguity which
must be resolved. The reason is explained below:
A standard linear regression between two variables y and x is expressed in the
following form:
y =
P ,* + P 0
(3.i)
where:
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x is the independent variable which is assumed to be error free,
y is the dependent variable with which all errors or differences are associated.
P] is the least squares estimate of the slope o f the regression line.
Po is the least squares estimate of the intercept of the regression line.
Pi is calculated from the following formula:
_ £ [ ( * , - * ) (y,— y )]
(3.2)
where x and y are the mean values of x and y respectively. Pq is calculated as:
Po = y - M
(3-3)
W hen the dependent and independent axes are switched, the denominator o f Eq.
3.2 is replaced with the y values (yj and y) while the numerator remains the same; also
the y and x terms in Eq. 3.3 are switched. Thus for a linear regression model of
perfectly correlated sets of F8 and FI 1 brightness temperatures (Tb(F8) and T b(Fl 1)
respectively) the following relationship holds true:
If:
Tb ( F \ l ) = p, [Tfe( F 8 ) ] + p Q
(3.4)
then:
Tb (F 8 ) = ^ [Th ( F I 1) ] + ^
(3.5)
This relationship is simply algebraic, and would apply to perfectly correlated
data. It has two necessary features: First, if the slope (P1) is less than 1.0 in Eq. 3.4,
then the slope in Eq. 3.5 (after the axes are switched) must be greater than 1.0 by a factor
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of 1/Pj. The converse must also be true (i.e. if P] is greater than 1.0, then 1/Pj must be less
than 1.0). Second, the sign o f the intercept, when the axes are switched, must be opposite
of the sign o f the original intercept, and the magnitude o f the new intercept must differ from
that of the original intercept by a factor of 1/Pj.
The greater the departure from perfect correlation, the less exact these scaling
factors become, since a linear regression treats the independent variable as error free, and
assigns all error to the dependent variable. None-the-less, in most instances these
relationships should at least be qualitatively maintained. In the case of the F8 and FI 1 data,
however, these qualitative relationships do not hold true because of the nature of the data
spread around the FI 1 = F8 line. Each set of coefficients results in a different relationship
between the F8 data and the F I 1 data, thus leading to ambiguous calibration terms.
W ithout any additional knowledge, each set of coefficients is equally valid.
However, in order to compare data from different SSM/I instruments o f the past, present,
and future, as well as the SMMR instrument, it is necessary to establish a baseline data set
to which all others can be referenced. It does not matter which is considered to be the
baseline, but to optimally relate one to the other, a reference data set, m ust be chosen. Then
the regression coefficients calculated with that reference data set taken to be the
independent variable must be applied.
The reference data set is chosen to be that o f the F8 instrument for two reasons:
First, the F8 data set is the initial SSM/I data set. M any analyses have been performed and
rigorous algorithm validations have been done using this data without the application of
any coefficients. In order to relate sim ilar future analyses to the ones already done with F8
data, it would be much more practical to apply the correction coefficients to the newer data
sets rather than redoing the old analyses with new coefficients. Secondly, the complete set
of SSM/I vs. SM M R comparisons previously done for overlapping Antarctic coverage was
performed with the SSM/I F8 data set taken as the independent variable - i.e. the “true”
data set (Jezek, et al., 1991). In order to be consistent, future comparisons should follow
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24
the same convention, using the F8 values as the “true” data.
The appropriate coefficients for regressing the FI 1 data to the F8 baseline are
obtained by applying the relationships in equations 3.4 and 3.5 to the slopes (Pi) and
intercepts (Po) in Tables 3.1 and 3.2 for the x=F8 conditions. The resulting form of
Equation 3.5 becomes:
Th ( F 1 1 )' =
[T „ (F 1 1 )] + -
-8
(3.6)
In Eq. 3.6 Tb( F l l ) ' represents the adjusted F l l brightness temperatures, and the P]
and Po terms are those for which the F8 data are assumed to be error free. Hence a set
o f correction coefficients to be applied to the F l l data can be found by inverting the
coefficients in Tables 3.1 and 3.2, determined when F8 data are chosen as the
dependent variable. These coefficients are shown in Table 3.3, and when applied to
the F l l data, they result in brightness temperature changes on the order of 1 K.
T able 3.3. Recommended linear regression coefficients for Greenland and Antarctica
to relate the FI 1 data to the F8. The corrected F I 1 brightness temperatures, Tb(Fl l'),
are related to the uncorrected ones, T b(Fl 1), by the following relationship:
T b(Fl l /)= P ,T b(F l 1)+P0
G reen lan d
G reenland
A n tarctica
A n tarctica
Pi
Po
Pi
Po
19H
1.013
-1.89
1.008
-1.17
19V
1.013
-2.51
1.002
-0.932
22V
1.014
-2.73
1.007
-2.12
37H
1.024
-4.22
1.019
-3.59
37V
1.000
0.052
1.008
-2.23
C hannel
The application o f the regression coefficients allows the F I 1 data to be readily
related to the SMMR data by regressing back to the F8 baseline. Then by applying
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Jezek* s regression coefficients to the SMMR data, no correction to the F8 data, and
appropriate coefficients (shown in Table 3.3) to the F I 1 data, a consistent time series is
generated. Applying either set of coefficients does not insure any improvement in
accuracy, since the “true” values are not exactly known, but it does insure an
improvement in data consistency.
It should be noted that the regression coefficients for Antarctica and Greenland
differ slightly from each other. Similarly, the scatter about the regression line is
consistently greater for Antarctica than for Greenland (Figures 3.1 and 3.2). This is
most likely attributable to the fact that the analysis was done for the month of
December, when there is a comparatively large diurnal temperature cycle in
Antarctica, on the order of 10°C, and a very weak one in Greenland. In addition, there
should be m elt events occurring near the coast of Antarctica during December, which
do not occur in Greenland. These conditions result in varying brightness temperatures
in Antarctica throughout the day. Consequently, time differences in satellite orbits
result in a greater scatter of the data points about the regression line for Antarctica than
for Greenland, which causes minor differences in the regression coefficients. Thus for
instrument corrections to improve data consistency, the Greenland coefficients should
be applied in order to eliminate diurnal affects.
These coefficients (published in Abdalati et al., 1995) improve the relationship
between F8-derived ice concentration and FI 1-derived ice concentration by as much as
3.9% (D. Cavalieri, personal communication), and they are currently used by NSIDC
in their ice concentration products (NSIDC, 1996). In addition, a neural network wind
speed algorithm (Krasnopolsky et al., 1995) which shows a 1 m/s bias in wind speed
for the FI 1 observations, eliminates the bias and significantly reduces the RMS errors
by incorporating the coefficients in Table 3.3 (V. Krasnopolsky, personal
communication).
It is evident that the adjustment in brightness temperatures, though very slight.
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26
are useful in improving data consistency between the F8 and FI 1 data sets. When the
appropriate coefficients from Jezek et al., (1991) are applied to the SMMR data, and
those from Abdalati et al. (1995) are applied to the FI 1 data, a continuous and
consistent 17 year data set is produced dating back to 1978
3.4 Conclusion
Based on the high correlations between the F8 and FI 1 data sets, and the
proximity of the regression coefficients to the Tb(F8) = T b(Fl 1) line, an extended time
series which spans both data sets will be minimally impacted by the fact that the
brightness temperatures were derived from radiance measurements o f two different
instruments. These small variations are attributable to the different orbital
characteristics of the two satellites, most notably, the differences in the times of the
measurements, that are averaged into each grid cell. Fortunately, the differences in
gridded brightness temperatures are so small that the application of any regression
coefficients only impacts the data generally by little more than 1 percent and in most
cases, less than 0.5 percent.
However, to maximize the consistency o f algorithms and time series that
involve the two different sensors, a reference data set must be taken as the “true”
values and all other data must be corrected to correspond to the reference data.
Because past SSM/I algorithm development and calibrations have been based on F8
data, the differences are assumed to be attributable to the F l l data. Therefore the
coefficients in Table 3.3 are used to maximize the consistency between products
developed with the F8 and F I 1 data sets. When used in conjunction with the SMMR
coefficients (Jezek et al., 1991), these coefficients yield a consistent and continuous 17
year passive microwave data set on which long term time series analyses can be
performed.
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27
4. Snow Melt Identification and Classification
4.1 Introduction
W et snow, with an albedo o f approximately 0.7 (Konzelmann and Ohmura,
1995), absorbs much more solar radiation than dry snow, which has an albedo o f about
0.9 (Oke, 1987). In light of this relationship, and considering the vastness o f the
Greenland ice sheet, an understanding o f the ice sheet melt conditions can provide
essential insight to the energy and mass exchanges that occur between the ice sheet and
the atmosphere. This in turn can help create a clearer picture of the role of the ice sheet
in the regional and global climate.
Because o f the ice sheet’s gentle slope, small changes in air temperature will
result in large areal changes in the dry and wet snow facies. Assuming an adiabatic
lapse rate o f 0.6°C/100m (Putnins, 1970), a slope above the equilibrium line o f 0.4°
(Steffen, 1995), and a melt area perim eter of 3300 km, a 1°C temperature rise will
increase the melt area by 79,000 km 2. Thus it becomes evident that variations in melt
extent are a sensitive param eter in the Arctic climate and climate changes. A method
of monitoring the melt conditions o f the entire ice sheet is important for studying the
melt characteristics and assessing their variability over time.
O f additional significance is the parameterization of snow albedo in various
energy balance models. Given the vast difference between the albedo of wet and dry
snow, characterization of the state o f melt on the ice sheet is important for adequate
parameterization of the surface albedo for energy balance modeling.
In this chapter, a method for using passive microwave satellite data for
monitoring melt on the Greenland ice sheet is developed and discussed. The method is
then applied to passive microwave data from 1979 through 1994, and the melt
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28
characteristics of the ice sheet are analyzed.
4.2
4.2.1
Microwave emissivity and brightness temperature (Tb)
Surface-emitting and isothermal media
The radiance or intensity (the energy flux per unit wavelength per unit solid
angle) of an isothermal black body is given by the Planck function:
L “ ,5
- Tr
—, he
f --------.
,nn
X [eXp{U T p) - \
<4 -‘ >
L is the black body radiance; c, h and k are the speed of light, Planck’s constant, and
Boltzmann’s constant respectively; X is the wavelength; and Tp is the physical temper­
ature of the body.
Bodies and surfaces found in nature, however, are gray bodies, which do not
emit their energy with perfect efficiency. For these, the emitted radiance is defined as:
L ' = e'L
(4.2)
where 1 / is the gray body radiance, and £/ refers to the microwave emissivity. The
proportionality constant, e', accounts for the efficiency of emission of a gray body as
compared to a black body. By definition, it is the ratio of radiance emitted by a gray
body at a given temperature, to that which would be emitted by a black body at the
same temperature.
,
V
= X
(4.3)
Also by definition, the emissivity of a black body is 1.0.
At long wavelengths, on the order o f millimeters, the term (hcA kTp) in Eq. 4.1
is nearly zero and equation 4.1 approaches the Rayleigh-Jeans approximation:
9 ck
L = - ^ TP
(4-4)
which is valid for most microwave applications. Because of this approximation, emit­
ted radiance, is typically expressed in units of temperature. This form of expression of
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29
emittance, known as the brightness temperature (Tb), is:
I
tv
!
h ~ 2 ck
(4’5)
Substituting Eq. 4.5 into Eq. 4.3 yields the relationship between emissivity and T b:
2ckT .
e' =
(4.6)
XL
And applying the Rayleigh-Jeans approximation, and rearranging terms, the well
known linear relationship betw een brightness temperature and physical temperature is
established:
Tb = e ' Tp
(4.7)
The above derivation is a simple form that is only applicable to isothermal m edia or
media which em it only from the surface. Thus it does not apply to the polar fim.
4.2.2 Volume-emitting non-isothermal media
Shortly after the launch o f ESMR, it was recognized that the microwave
brightness temperatures on the Greenland and Antarctic ice sheets are significantly
lower than can be explained by the snow temperature and simple reflection at the airsnow interface; thus suggesting that a significant amount of scattering must occur
within the medium (Gloersen et al., 1974). This assumption was verified theoretically
by Chang et al. (1976), who demonstrated the significance of volume scattering in the
microwave emission o f polar firn. As a result, the observed microwave brightness
temperatures represent integrated values o f emission and extinction from within the
snowpack. Thus it follows that some information about the snow in the vertical
dimension can potentially be determined from the microwave brightness temperatures.
For a non-isothermal semi-infinite medium, such as the firn, the radiance from
the surface can be thought of as a weighted sum of radiances from infinitesimally thin
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30
isothermal horizontal layers spanning the depth of the medium. The weights for each
component of the sum are determined by the amount of extinction of upwelling radia­
tion from each layer, by those above it. This is sometimes referred to as the pointdirection gain (/(z)), and it is given numerically as:
_
(
L im it
\
1 I"
T ' /
\
L (z)
(4.8)
The term /lz) is the scaling factor which describes the amount of radiation emitted
from depth z that actually reaches the surface (z=0). It is also a function of azimuth
and zenith angles, but for illustration purposes, only depth is considered. L(z) and
e/(z) are the depth variant radiance and emissivity. Thus it can be shown that the emittance of a thermally varying gray body can be described as:
(4.9)
o
U sing/(z), an effective black body radiance (L*) can be defined as:
(4.9)
o
and an effective physical temperature can be given by:
(4.10)
o
The effective physical temperature can be thought of as an average temperature of the
medium that is weighted by its depth-dependent radiative transfer characteristics (size,
shape, orientation, and scattering characteristics o f the snow grains).
We can now describe the volumetric or bulk emissivity, e:
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31
which is analogous to Eq. 4.3, but for a non-isothermal medium. Similarly, the rela­
tionship between brightness temperature and effective physical temperature is:
Tb = e7*
(4.12)
The seemingly simple relationship in Eq. 4.12 holds considerable information
about the snow below the surface, and forms the basis for much of the interpretation of
passive microwave observations. M uch of the useful information obtained from
microwave radiometry is in how physical characteristics or processes in a medium are
manifested in the emissivity and consequently, the brightness temperature. One such
process is melting of the firn.
4.3 Passive m icrowave melt signal
For the dry snow condition, the snowpack is considered to consist of scattering
ice particles with an air background. As such, volume scattering is the dominant scat­
tering mechanism. At the onset of melt, however, water droplets begin to fill in the
background medium. This replacement of some of the background air with water
causes the volume scattering (and its associated losses) to diminish and surface scat­
tering to dominate. During the transition from volume to surface scattering, the micro­
wave emissivity increases sharply. In this way, the behavior of the wet snow at the
onset of melt approaches that of a black body (Matzler and Hiippi, 1989).
This phenomenon is illustrated for the 19.35 GHz SSM/I vertically polarized
channel in Figure 4.1. This 3 dimensional plot shows a time series of brightness tem­
peratures across the ice sheet (310°E to 335°E longitude) from January 1988 through
December 1991 at a latitude of 69.5°N. For the middle of the ice sheet, the plot
appears to level off in a plateau; whereas along the edges, (particularly around 317°E)
there are spikes along the time axis. These level areas are the locations at which the
j
i
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■
|
I
I
i
i
Figure 4.1. 1988-1992 Time series of 19 GHz brightness temperatures across the
Greenland ice sheet at the latitude of the ETH/CU camp (69.5°). The plot is much
rougher near the edges o f the ice sheet where snowmelt occurs, while it is much
smoother in the center, where the snow remains dry. This rough/smooth relationship is
attributable to sharp changes in microwave emissivity under conditions of melt,
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J.1
snow remains dry all year at that latitude, and the emissivity variation is minimal.
Near the coast the spikes exist because of the change in emissivity due to melt. As
shown in equation (4.1), changes in emissivity result in changes in brightness temper­
atures for a constant physical temperature. In the nearly level plateau areas, on the
plot, there is some variation in the time series due to seasonal temperature changes, but
they are not pronounced as they are in the m elt areas. The time series of the 19V chan­
nel for the pixel at the location of the ETH/CU camp (69°34/N 49°17'\V) is shown in
Figure 4.2a.
This phenomenon is not limited to the 19 GHz channel alone. A similar spike
is found in the 37 V channel as well (Fig. 4.2b), and also in the horizontally polarized
channels o f the same frequencies (Figs. 4.2c and 4.2d). Furthermore, the impact of
water content varies with polarization and frequency (Ulaby et al., 1986). These vari­
ations form the basis for the melt algorithm developed in this research and will be dis­
cussed in more detail in section 4.5.
4.4 Previous melt algorithms
4.4.1 Single-channel difference technique
A previous study which reported on melt region classification in Greenland
(Mote et al., 1993) made use of a single-channel difference threshold applied to SSM/I
data. In their study, Mote et al. used data from the SSM/I 19 GHz vertically polarized
channel to calculate for each pixel on the ice sheet, winter mean brightness tempera­
tures. They then applied a difference threshold to identify melt areas. When a pixel
exhibited a brightness temperature in excess o f the winter mean plus the difference
threshold on a particular day, that day was classified as experiencing melt. A similar
technique has been applied to Antarctic data by Ridley (1993) and Zwally (1994). The
difference threshold used by M ote et al. and Ridley was 31 K above the mean winter
temperature. The threshold used by Zwally was 30 K.
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34
a)
19 GHz (V)
b)
3 7 GHz (V).
280
260
S
^—' 240
CL
E 220
CD
1—
200
V_
180 •
UD
160 :
1988 1989 1990 1991 1992
Date
c)
19 GHz (H)
1988 1989 1990 1991 1992
Date
d)
37 GHz (H)
' 240
a.
E 220
CD
200
F
1988 1989 1990 1991 1992
Date
1988 1989 1990 1991 1992
Date
Figure 4.2. 1988-1992 Tb time series o f brightness temperatures at the ETH/CU camp
for (a) 19V, (b) 37V, (c) 19H, and (d) 37H. The drastic increase and decrease in Tb at
the onset o f melt and refreeze respectively result from the dependence o f emissivity on
snow wetness.
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35
W hile this method seems to exploit the brightness temperature increases that
are indicative of melt, the coupling o f the summer melt criterion to the winter mean
brightness temperature results in a cold region bias. In other words, cold areas have a
less stringent m elt criterion than warm ones. This point is illustrated by examining
two points on the ice sheet, a typically cold one (Location A in Figure 4.3), and a typi­
cally warm one (Location B in Fig. 4.3). As shown in Fig. 4.4, in the cold area the
melt signal at 19V is much more clearly pronounced than it is in the warmer region.
The winter signal is more stable, and the difference between summer and winter
brightness temperatures is much greater. The warm region, on the other hand, shows
an increasing brightness temperature trend during the winter and significantly higher
winter brightness temperatures than the colder area. As a result, the difference
between summ er and winter brightness temperatures is much less in the warmer area
than in the colder one. This leads to the prediction of more melt events in the cold area
than in the warm, and more melt events in years with cold winters than years with
warm ones (Table 4.1). These results are counter-intuitive and most likely due to the
direct coupling o f the melt criterion to the winter conditions.
Table 4.1. Days of melt per year calculated using the single-channel difference
threshold technique of Mote et al. (1993), for a typically cold and a typically warm
(locations A and B respectively in Figure 4.3) area on the Greenland ice sheet. Also
shown are the mean annual winter brightness temperatures based on averages from
Dec. 1 through Feb. 28 (as suggested by Mote et al., 1993).
L ocation
Y ear
M ean w in ter
N u m b e r o f predicted
m elt days
A
B
1989
1990
1991
1989
1990
1991
158
154
155
225
236
231
46
66
36
30
2
19
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36
.77
TjJule.-,
S u m m it
•ETH/CU: Comp.
69
65
•S n o d re .....;•
g C j)s tro m f jo rd
■Q
l - ■>■■■■<?.
I^SGodthob <-
80
57
70
.60
50
40.
Figure 4.3. Location map of Greenland showing ETH/CU camp and the coastal sta­
tions from which atmospheric data were obtained for comparisons to melt estimates.
Also shown are a typically cold location of the ice sheet (Location A: 79°N, 25°W)
and a typically warm area (Location B: 62°N, 43°W ) for which comparisons are made
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
37
280
Location B
Location A
266 K
260
263 K
256 K
240
a. 2 2 0
189
185 K
186 K
O' 180
QD
160
140
1988
1989
1990
1991
1992
Date
Figure 4.4. SSM/I Tj, time series of 19 GHz vertical polarization for a typically cold
region of the ice sheet (Location A, 79°N, 25°W) and a typically warm area o f the ice
sheet (Location B, 62°N 43°W ). Both Locations A and B are shown in Figure 4.1.
Also shown are the melt thresholds for each hear and location as derived by the
method of M ote et al., (1993).
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38
4.4.2 37 G Hz emission model
A more theoretical approach has been taken by M ote and Anderson (1995).
They developed a simple 37 GHz horizontal polarization emission model o f the polar
fim. With this empirically adjusted model, they simulated a condition of 1%
volumetric water content in the top m eter of snow in order to identify the 37H signal
that is consistent with such conditions. They then applied it to the ice sheet brightness
temperatures, and any pixels on a given day that exhibited a Tj, consistent with or in
excess of the modeled melt values were classified as wet, while those with brightness
temperatures below the “wet” value were classified as dry.
This method, while it is not subject to the cold region bias o f the single-channel
difference approach described above, does have certain limitations. Because o f the
shorter wavelength and the associated reduced penetration depth, it is highly sensitive
to surface melt and may overlook important subsurface conditions. This is particularly
true during the time of refreeze when frozen snow may exist. M ote and Anderson
acknowledge the relationship between their melt assessment and the ablation estimates
are weakest for the m onth o f August, when refreeze is beginning to take place. In
addition, the shorter wavelength of the 37 GHz signal is more affected by severe
atmospheric conditions and dense cloud cover than the 19 GHz. This may become most
problematic near the coast where the most melt events occur.
4.4.3 Gradient ratio
The changes in emissivity associated with m elt are frequency dependent, with
low frequencies (e.g. 19 GHz) being more responsive to melt than higher frequencies
(such as 37 GHz). It is this frequency dependence that formed the basis for a prelimi­
nary investigation by Steffen et al. (1993). Using the horizontally polarized gradient
ratio (GR), melt was classified for six months in 1990. The gradient ratio is defined
as:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
Tb ( l 9 H ) - T b (37H)
(4.13)
Tb (1 9 //) + Tb (3 7 //)
where Tb(19H) and Tb(37H) refer to the brightness temperatures of the 19.35 GHz
horizontal and 37.0 GHz horizontal channels of the SSM/I respectively. The GR time
series for the ETH/CU camp pixel is shown in Figure 4.5.
The signal in the gradient ratio is much less sensitive to spatial variations in
physical temperatures since it is a normalized difference. As such, it allows for the
definition of an absolute single threshold based on multiple channels. Furthermore,
the differing penetration depths of the different channels provide additional informa­
tion about the depth of the m elt and its subsurface characteristics. This will be
explained in detail in section 4.6.1.
4.5 Method of melt determ ination in this study
4.5.1. Improved melt signal
The GR melt signal can further be enhanced by exploiting the depolarization
effects that occur when snow melts. The differences between the vertically polarized
signal and the horizontally polarized signal diminish when the snow becomes wet
(Srivastav and Singh, 1991). As the dielectric interfaces change during melt, the bulk
reflection coefficient changes as well. In doing so, horizontally polarized brightness
temperatures increase more dramatically than those of vertical polarization. This
effect is illustrated for the ETH/CU camp pixel in the polarization ratio (Figure 4.6a),
defined for the 37 GHz channels as:
Tb {31V) - T b (37H)
Tb (37V) + T h (37H)
(4.14)
where Tb(37V) and Tb(37H) refer to the brightness temperatures of the 37 GHz vertical
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40
0. 15
o
0 .1 0
-
cr
c
_(U
x>
oL_
o
0 .0 5 -
c
o
_N
o
X
0.00
-0 .0 5 1988
1989
1990
1991
1992
1993
1994
1995
Date
Figure 4.5. SSM/I time series of the horizontally polarized gradient ratio for the loca­
tion of the ETH/CU camp. The large increases at the onset of melt occur because the
water in the snow affects the 19 GHz channel more than the 37 GHz channel. Simi­
larly, there is a drastic decrease in gradient ratio during the refreeze condition.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
a)
o
oc
c
o
X*
O
Nl
jo
o
CL
fsi
X
o
CT>
19 88
1989
1990
1991
1992
1993
1994
1995
1993
1994
19 95
Date
b)
O
CL
c
o
-*—•
o
N
O
o
CL
rsj
X
o
ro
19 88
1989
1990
1991
1992
Date
Figure 4.6. SSM/I time series o f the 19 GHz polarization ratio (4.5a) and 37 GHz
polarization ratio (4.5b) for the location of the ETH/CU camp. The depolarization
effects become evident as the ratio approaches zero in the summer m onths.
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12
and horizontal polarization respectively. The same relationship holds true for the 19
GHz polarization ratio (Fig 4.6b). It has been hypothesized that the PR could be used
to classify melt regions, however, the melt signal by itself is not quite distinct enough
for such an application.
Combining the ability of the gradient ratio to reduce the temperature effects
with the fact that the horizontal melt signal is stronger than the vertical melt signal, a
new combination of channels is established for the classification of wet and dry snow.
It is referred to as the cross-polarized gradient ratio (XPGR) and is given by:
v n z - a _ Tb ( l 9 H ) - T b (37V)
Tb ( \ 9 H ) + T b ( 31V)
(
}
Using this relationship, a threshold can be defined (see Figure 4.7) based on which ice
sheet melt extent is identified, mapped, and monitored in both space and time.
The XPGR overcomes the cold region bias, and the inconsistencies of the
single-channel difference technique (Abdalati and Steffen, 1995). Furthermore,
through the normalization, it is less sensitive to atmospheric variability than the single­
channel methods (see Section 4.5.6).
4.5.2. SSM/I F8 analysis
The analyses for the F8, FI 1, and SMMR data were done using the NSIDC
binned and gridded SSM/I data described in Section 2.2. To these data, the Greenland
ice mask (Sec. 3.2) was applied in order to isolate the ice sheet pixels. The analysis is
only carried out for pixels that lie entirely on the ice sheet (i.e. fully contained within
the perimeter) in order to eliminate land contamination. As a result, approximately 6%
of the ice sheet perim eter is omitted from the analysis, but the entire portion that is
omitted is assumed to experience summer melt, since it is all near the edge o f the ice
sheet.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
I I I I I I I I I I I | I I I I I I I I I I I | M
0 .1 0
O
cz
— -
I I I' I I I I I
I j I I I I
— Melt T h resh o ld
-
0 .0 5 -
c
a;
ToJ
0.00
"O
CD
o
0
1
1o(/)0
o
-
CL
-0 .0 5 -
-
0 .1 0
~
1988
1989
1990
1991
1992
1993
1994
1995
D a te
Figure 4.7. Cross-polarized gradient ratio (XPGR) time series for the ETH/CU camp pixel
for the dates of available SSM /I data. Also shown are the dates on which melt was observed
to begin at the camp, and the corresponding XPGR threshold associated with melt. There
are two thresholds: XPGR = -0.158 for the F8 SSM/I and XPGR = -0.0265 for the FI 1
SSM/I. Two thresholds are necessary in part because o f instrument differences, but
primarily because of the different crossover times of the two instruments.
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44
The data initially analyzed in this study were the SSM/I data from January 1,
1988 through December 31, 1991. For each of the ice pixels, the cross polarized
gradient ratios were calculated according to Equation 4.5, and a time series at the
location of the ETH/CU camp for the entire period was produced (Fig. 4.7). The time
series was then compared to the in situ data collected at the camp during the 1990, and
1991 field seasons.
The dates which correspond to sharp increases in XPGR are the same dates on
which the mean water content increased to approximately 1 percent. These were
identified as the dates of melt onset at the ETH/CU camp. According to the in situ
measurements, the melt threshold was found to be XPGR = -0.0158, which was
consistent for the period examined. Since the field data are only available for one site,
it is not known for certain whether these values are site specific. However, since the
metamorphic processes during melt are the same throughout the melt region, and the
XPGR is a normalized difference, it is assumed that the threshold does not vary with
location. This assumption is supported by comparisons of time series from several
locations on the ice sheet, which all show that the XPGR values during winter months
are clearly below the threshold, while those of summ er months are above it.
In previous applications o f the XPGR method, 0.5 percent water content was
used to define melt (Abdalati and Steffen, 1995). This was sufficient to provide a
classification based on SSM/I observations, but the signal/noise ratio for the SMMR
data was too low for the useful application of the 0.5 percent criterion. Additionally,
the ability of microwave radiometers to detect water at the time o f the development of
the SM M R instrument was nearly 1 percent water content (Stiles and Ulaby, 1980). For
the sake of consistent analysis over the entire time period, a threshold o f 1 percent was
used for the SSM/I as well as the SM M R data. Furthermore the same wetness level was
used by M ote and Anderson (1995) for their melt study, so the use of the same criterion
facilitates comparisons between the two techniques. Once the threshold was
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
established, all available SSM/I daily brightness temperatures for every pixel location
on the ice sheet were examined. Areas with XPGR values above the threshold on a
given day were classified as experiencing melt on that particular day. In this way, the
areal extent of melt for each day of SSM /I coverage was determined, and mean monthly
melt extent was calculated for the “m elt months” (June, July, and August) of each year.
Also determined were the interannual variations in melt extent.
4.5.3 SM M R analysis
The transition from one instrument to another requires careful analysis of the
relative calibrations between the two for data consistency. To account for operational
and instrumental differences between the SSM/I and SMMR instruments, the
calibration coefficients of Jezek et al. (1991) were applied. However, since ice sheet
melt has a diurnal cycle, and the two satellites have very different crossover times
(approximately local noon and midnight for SMMR and dawn and dusk for SSM/I at
the Equator), an additional step of geophysical parameter matching was taken. During
the overlapping coverage period (July 9, 1987 - August 20, 1987), and after applying
the SMMR/SSM/I regression coefficients, the XPGR was calculated for both the SSM /
I and SMMR observations. A new threshold for the SMMR data was then determined
which yielded the same m elt areas (to within 6 percent) as those identified by the SSM/
I data. In this way, the effects of diurnal differences are minimized. This new threshold
is XPGR = -.0265, and it is used as the melt criterion for the entire SMMR data set.
In addition, the signal to noise ratio of the SMMR instrument is not as that of
the SSM/I. The SMMR time series o f the XPGR shows much more variability for
consecutive coverage days than does the SSM/I. In order to reduce the effects of the
noisy signal, a smoothing function was applied to the SMMR data. This function was
a 5 day running mean, during two of which, the instrument was inactive. In other
words, the value of the brightness temperatures used on any given day is an average of
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
the scans on that day plus those on the two nearest days o f coverage - one from two days
before the day examined and one from two days after). Such a smoothing reduces the
temporal resolution, but has negligible impact on the seasonal and interannual studies.
4.5.4 SSM /I F l l analysis
The FI 1 instrument, like the SMMR, has day/night crossover times. Therefore,
after accounting for instrumental differences, the same threshold that is used for the
SM M R data, XPGR=-0.0265, should also be applicable to the F I 1 SSM/I data.
Comparisons between the in situ data from the ETH/CU camp for the years 1993 and
1994 show that this threshold is valid. This further increases confidence in the selection
of our SMMR and FI 1 melt threshold.
One slight discrepancy that does arise, however is that in the years 1993 and
1994, there are several brief incidents in which the m elt threshold is exceeded prior to
melt onset. In other words, there apparently exist a few false m elt signals. In 1993,
these occurred prior to our arrival and data collection the ETH/CU camp, but in 1994
these occurred during camp occupation. The 1994 dates on which the XPGR exceeded
the melt threshold were during the passage o f a severe weather system which deposited
snow. The presence of this system is believed to be the cause for this false melt signal,
and as explained section 4.5.6. these events are o f short duration and should not alter
the melt statistics significantly.
4.5.5. M elt/threshold relationship
It should be noted that these thresholds are somewhat arbitrary, primarily
because the spatial variability of the melt is very high even on small scales. Slight
topography variations result in uneven heating in areas of the snowpack and variable
temperature and density structure. As a result, melt is not horizontally uniform. The in
situ measurements were taken in a vicinity believed to be typical or representative of
the camp area; however, the variability of snow water content can be high within a
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47
pixel. Sample measurements in the field show variability as high as 3 percent water
content over as little as 10 meters distance; thus no exact correlation can be made
between the in situ point measurements and the 25 km pixel grid.
A second difficulty is that the depth and vertical stratification o f water within
the snowpack are also variable. Consequently, a particular value of brightness
temperature or combination thereof does not reflect a unique w ater content. In other
words, a deep snowpack may have a low water content on average, but the surface
could be very wet, as would be the case in the advent of a warm system passing through
a region of the ice sheet. Alternatively, a shallow snowpack may be more uniformly
wet, due to slower melt processes such as purely radiatively driven melt, and may
exhibit the same melt signal as in the previous example. Both can have very different
wetness characteristics and mean water content percentages, yet they may still give the
same signal.
However, the data do lend themselves to the definition o f a distinct threshold
which can be considered a boundary between dry and wet snow, and although the terms
dry and wet may not be specific, the ability to m onitor the areal extent of wet snow with
a consistent algorithm from year to year is a useful observational tool in Arctic climate
studies.
4.5.6 Atm ospheric variability
In remote sensing o f the high-latitude polar regions, atmospheric effects are
very small at microwave frequencies, and are often neglected (Massom, 1991). This is
especially true at the higher elevations of the ice sheet, where w ater vapor capacity is
low, and the clouds that form are generally more transparent than the optically thick
cumulus clouds near the coast. However, though it is only a very small part of the
signal, emission from and extinction by the atmosphere is a part of the apparent
microwave brightness temperature, and is convolved with the m elt signal.
None of the passive microwave melt methods to date included variability in the
atmosphere. M ote and Anderson (1995) explicitly incorporate the atmospheric
contribution in their model, but changes in the atmosphere are not considered; thus
large changes in atmospheric optical thickness (i.e. cloud cover) are not accounted for.
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48
This generally has a greater impact on the low elevation areas (coastal areas) than the
higher more cloud free areas, but in all o f these methods, atmospheric effects are
assumed to be small in comparison to the change in emission due to wetness.
Severe weather conditions can increase atmospheric extinction and lower the
brightness temperatures observed by the SSM/I and SM M R instruments. If melt exists
under an optically thick atmosphere, the lower Tj, can cause this melt to go undetected
by the single-channel approaches. In the case of the XPGR parameters, the 37 GHz
emission experiences more extinction than the 19GHz emission, because of its shorter
wavelength. Consequently, the normalized difference increases under optically thick
conditions such as those associated with clouds, water vapor and precipitation. The
normalization in the XPGR technique, however, is expected to mitigate the magnitude
o f this impact.
The relative effects of increased atmospheric losses are examined for nominal
melt area conditions (Figure 4.8). In the study, atmospheric losses for clear conditions
are used as a reference. The clear sky total column water vapor is assumed to be 0.24
g/cm (Grody, 1976), which is consistent with observations made at the ETH/CU camp.
The impact is expressed as a percentage of the melt signal (from dry to wet conditions).
For 19V, this signal is assumed to be 31 K (Mote et al., 1993). For 37H this signal is
taken to be 27K (estimated from M ote and Anderson, 1995). For the XPGR, the signal
is taken to be 0.0478 (the difference between the mean winter XPGR and the melt
threshold). The slopes in Figure 4.8 are such that a positive slope means the signal is
reduced by the atmosphere, thus allowing for a missed melt event under optically thick
skies, and a negative slope means that the melt signal is enhanced by the increased
optical thickness, thus allowing for false melt classification.
A doubling of the optical thickness has a moderate effect on the XPGR (10% of
the total melt signal), a higher effect on the 19V brightness temperature (20%), and an
even greater effect on the 37V Tj, (40%). An examination of the radiosonde data from
293 radiosonde launches at the ETH/CU camp during the 1990, 1991, and 1993 field
seasons shows that the total column water vapor varies in a season from a of 0.2 g/cm2
'7
to a maximum of 1.67 g/cm“, with an average value of approximately 0.7 g/cm- (one
percent of the values are well outside this range, but they were either beyond 5 standard
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49
200
150
CO
CO
o
o
c
zp 100
*1'
I
I
I"
I
I
l"'l"
I
|
I
T
I
I
I
I
I
I
I
j
I
I
l “ 'l
I
I 'I
I
I
|
I
As s um pt io n s :
T b ( l 9 v ) = 2 5 5 for c le a r sky conditions
Tb( 37h) = 2 2 0 for c le a r sky conditions
XPGR = —0 . 0 1 5 8 for clea r sky conditions
Sc on a n g l e = 5 3 . 1 d e g r e e s
Atm. loss f a c t o r varies with the
s q u a r e of t h e fre qu e nc y
Original c le a r sky loss f a c t o r s
19GHz: t a u = 0 . 0 2
37GHz: t a u = 0 . 0 3
1
I
I
I
I
I
I
3 7 GHz
CO
19 GHz
c
50
CD
<J
a;
Q_
XPGR
50
2
3
4
Multiples of Atm osp he ric Loss Factor
Figure 4.8. Sensitivity of melt techniques to increased atmospheric extinction. For
increased atmospheric losses, the single-channel approaches show a decrease in signal
(underestimate of melt) while the XPGR method shows an increase (overestimate of
melt). The XPGR is also least affected by the increased extinction. The slopes are
such that a positive slope indicates a reduced signal and a negative slope means the
signal is enhanced.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
deviations from the mean, or the product of low radiosonde launches; therefore they are
not used). Thus assuming water vapor is the primary contributor to optical thickness,
the ranges of optical thicknesses in Figure 4.8 ( lx to 5x the clear sky conditions) are
reasonable ones. It follows that the effects of atmospheric variability are of some
significance at the lower elevations, such as the ETH/CU camp. The atm ospheric water
content and its variability are expected to diminish further from the coast, where the
elevation is higher, temperatures are colder, and the distance to water sources is greater.
Finally, the contribution o f the atmosphere to brightness tem perature by virtue
o f its own emission also changes in a variable atmosphere. Under typical condition, the
sky brightness temperature at a 53° viewing angle is approximately 25 K (estimated
from Waters, 1976; M ote and Anderson, 1995). W hether this contribution increases or
decreases with cloud cover and w ater vapor content depends on the atm ospheric
temperature distribution, and the cloud heights and optical depths. T hus for the single­
channel techniques, the effects may either enhance or diminish the signal. Since the 19
and 37 GHz sky brightness temperatures are nearly equal for a w ater vapor-laden
atmosphere (Waters, 1976), the contribution of the sky emission to the XPGR cancels
out in the numerator of the XPGR and is essentially zero. Thus while it is an issue for
the single-channel methods, it is of negligible consequence for the X PG R method.
For the purposes o f this analysis, it is assumed (as with M ote and Anderson,
1995) that over large temporal and spatial scales, the atmospheric effects do not to
affect the trends significantly. A more complete analysis, would incorporate water
vapor and cloud cover estimates over the ice sheet, but considering the severely limited
means of estimating these parameters over the Greenland ice sheet, such analysis is not
yet feasible. However, of all of the proposed methods, the XPGR technique, by virtue
o f its normalization, is the least affected by these atmospheric factors.
4.5.7 Additional Error Sources
In addition to atmospheric considerations, a few other potential error sources
exist. The first is that the XPGR threshold is based on data from a single point, the
ETH/CU camp. This limitation arises from the lack o f available data. However, the
consistency of the threshold for every year of field observations, despite varying snow
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51
conditions, is encouraging. Furthermore, the effects of any site specific metamorphic
characteristics is mitigated by the fact that the index is normalized. For the most part,
the characteristics that effect the 19H emission, also effect the 37V, thus the division
by their sum (Eq. 4.15) minimizes their effects. Finally, a potential issue of concern is
the differing penetration/emission depths for the different frequencies. This difference
is very small during melt (Ulaby et al., 1986), and is o f no consequence during melt
onset. During refreeze, it can actually be a benefit by allowing the detection of wet
snow beneath a refrozen surface. This is discussed in more detail in section 4.6.1
below.
4.6. Results and discussion
4.6.1 Seasonal m elt cycle
The average daily extent o f snowmelt for the years 1979-1994 is shown in
Figure 4.9 along with the range of melt extent within 1 standard deviation o f the
average. Also shown are the melt areas associated with a heating or cooling o f 1°C,
which are discussed in the “Interannual Variations” section below. The locations of
melt for the primary melt months, June, July, and August, are depicted in Figure 4.10.
Melt onset begins at a limited number o f coastal pixels in April and May and is very
slight. In early June, the melt begins to spread, primarily around the region o f Sondre
Stromfjord and Jakobshavn but is still limited in areal extent. During mid-late June, and
the early part of July, the melt extent increases rapidly, as is indicated by the steep slope
of the curve in Figure 4.9. In late July, melt is at its maximum extent covering nearly
the entire perim eter of the ice sheet, and most of the southern portion of the ice sheet
(south o f 68°N latitude) with the exception of the high elevation South Dome. After
late July, refreeze begins to occur on the ice sheet and the areal extent of melt begins to
drop off steadily until mid-late September, and then more gradually through October.
The area showing the most melt throughout the summer is the region along the
west coast beginning at the southern tip of the ice sheet near Kap Farvel and extending
north past Jakobshavn. This region is the first to show melt, the last to show refreeze,
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5
j
4.0x10
3.0x10
E
D 2.0x10
d)
<
-t—<
1.0x10
May
Jun
Jul
Aug
Time of Year
Sep
Oct
Figure 4.9. The average spatial melt extent for the years 1979-1994 (solid line), mean
melt +1 standard deviation (dotted line), and melt area for 1°C temperature change
(dashed line) in km2 for the melt months o f June, July and August. The extent was
calculated by determining the mean area coverage for these months in each year and
then averaging these values over the entire coverage period.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
and remains wet, farther inland than most other locations (Fig. 4.10). This may most
likely be attributable to the gentle slope on the western side of the ice sheet, the greater
radiation intensity at the lower latitudes as compared to the higher ones, and possibly
the influence o f the warm dry continental air mass approaching from Canada, which
dominates the summ er circulation (Ohmura and Reeh, 1991). Another area of
extensive m elt is the northeast portion o f the ice sheet near Danmarkshavn and Nord.
This region also has a very gentle slope and is a low elevation (900 m above sea level).
Subsequently, more melt would be expected in this area.
A significant characteristic of Figure 4.9 is the positive skewness, or asymmetry
about the peak. This results from a combination o f two factors: 1) the differing
emission depths for the two frequencies and 2) the fact that melt and refreeze of the
snowpack both occur from the top down (i.e. first near the surface and then progressing
deeper into the snowpack).
For dry snow near its melting point, 19 GHz radiation is emitted primarily in the
top 2.5 m o f the snowpack and at 37 GHz, most of the emission is from the top 30 cm
(Ulaby et al., 1986). W hen melt begins near the surface however, the effective emission
depth decreases considerably to approximately 10 cm for a 1% water content (Ulaby et
al., 1986) for both 19 and 37 GHz. That is to say that more o f the signal comes from
the snow near the surface when the snow is wet, than when the snow is dry. During the
spring and early summer, the snowpack is absorbing incident radiation and undergoing
heating near the surface. The greater depths, which are primarily heated by conductive
heat fluxes from the surface, respond more slowly. Therefore, during this time of year,
the deeper snow is colder than the snow closer to the surface. W hen the snow becomes
wet, the change in emission depth o f the 19H results in a higher effective physical
temperature (Tp in Eq. 1) and therefore increases brightness temperature. Coupled with
sharp increase in emissivity o f wet snow, the effects on brightness temperature are
further increased. The same holds true for 37V, but the difference is not as great, since
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55
During refreeze, the differing penetration depths act to prolong the detection of
m elt until the subsurface snow has refrozen. When the surface begins to refreeze, more
o f the 19H emission comes from below the surface than does the 37V emission.
Consequently, when warmer wet snow lies beneath colder frozen snow, the XPGR
signal indicates melt. This becomes problematic when the melt state of the surface is
desired. For such application, the method of Mote and Anderson (1995) is better suited.
But for climatological investigations and snow structure modeling, knowledge of the
subsurface characteristics and the time of refreeze of the entire depth of the snowpack
is important. For example, the passing of a cold front in late summer, may act to
refreeze the surface while the subsurface remains wet. The snowpack will not be
classified as dry until the snowpack is frozen at greater depths. In this way, the climate
signal is more stable and less susceptible to surface variations and tracks wet snow
through its complete cycle.
The differing penetration depths and the “top down” occurrence of melt cause
the XPGR method to be highly sensitive to surface melt at the onset, yet not very
sensitive to surface refreeze. For these reasons, the full extent of melt, and a melt
climate signal can be closely monitored without much influence from short term
refreeze events.
4.6.2 M elt extent
A full composite o f the spatial melt extent and the percentage of melt days is
shown in Figure 4.11. The most active regions of the ice sheet are in the southern
portion of the ice sheet (south of 68°N). These show the greatest variability in areal
melt extent over the time period, while the more northern perim eter regions fluctuate
little. This area is influenced in the summer by the Atlantic Ocean (Ohmura and Reeh,
1991), and thus are affected by variations in circulation, temperatures and extent of the
Icelandic Low.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
Figure 4.10. M onthly maps o f areal melt extent. The shaded areas are areas that expe­
rience melt in the month shown at least once in the period from 1979-1994. and the
darkness indicates what percentage o f the month (averaged over the time series) the
pixel was wet. Light shading indicates a low wetness frequency, and dark shading
indicates a high frequency o f melt. The white areas represent the dry snow areas, and
the black areas are regions o f Greenland that are not fully covered by the ice sheet,
the change in emission depth is less. As a result, XPGR method is particularly sensitive
to the onset of m elt in spring, since it occurs near the surface.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
Figure 4.11. 1979-1994 composite of melt. The shaded areas are areas that experi­
ence melt in the month shown at least once in the period from 1979-1994. The differ­
ent shades o f gray indicate the percentage of time throughout the coverage period, the
pixels experienced melt for the month shown. The white areas represent the dry snow
areas, and the black areas are the locations of pixels that are not fully covered by the
ice sheet.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
i
ii
i
!
i
i
DIAGENETIC FACIES
ON THE
GREENLAND ICE SHEET
I
| DAT-SNOW
f
J PERCOLATION FADES
SOAKED
FACIES
facies
ABLATION FACIES
w ater
Figure 4.12. Facies classification map of the Greenland ice sheet (from Benson,
1962).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
58
The maximum melt areas depicted in Figure 4.11 follow the same general ,
contours as the facies classification map of Benson (1962) shown in Figure 4.12,
however, they are not as extensive. The Benson map indicates melt at higher elevations
than are detected by the XPGR method. This may be due to the fact that Benson’s
estimates were based on studies of numerous snowpits dug between 1952 and 1955
(Benson, 1962). The time period covered by Benson’s data, which dated back to 1937
(Benson, 1962), may have been anomalously warm, or in a different climate regime.
In addition, the binning into daily averages may prevent the detection of some
brief afternoon melt events by averaging them in with the night time brightness
temperatures of the refrozen surface. As a result, area melt extent may be slightly
underdetected. However, in the future, this analysis can be repeated using Equal Area
SSM/I Earth Grid (EASE-Grid) data, when they become available, which will be
divided into descending and ascending passes; thus eliminating the inclusion of the cold
nighttime brightness temperatures in the mean values.
It is also likely that the melt facies classification of Benson differs from the
satellite-derived estimate because the criterion for “melt” differs. Satellite observed
melt classification would not necessarily be identical to that determined from pits and
snow layers. What is most important for climate monitoring, however, is the
consistency of the technique, and the XPGR method provides a consistent long term
assessment of the melt conditions on the ice sheet. This monitoring technique will be
applicable as long as there are SSM/I (or similar) instruments in operation.
4.6.3 Interannual variations
The interannual variations of mean melt extent on the ice sheet are shown in
Figure 4.13. Also shown are the interannual variations in mean summer temperatures
based on climate data from several stations along the coast. These data sets were
obtained from the National Center for Atmospheric Research (NCAR) archives in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5C)
3.0x10'
C o a s t a l T e m p e r a t u r e A n o m a ly
M ean
M e lt E x t e n t
2.5x10'
x
o
E
o
c
0)
<
3
o
w.
ao>.
E
<u
f—
-2
-
1980
1985
1990
5.0x10'
1995
Y eor
Figure 4.13. Interannual variations in mean melt extent (average area for the months
of June, July, and August of each year) as determined by the XPGR classification
technique for the years 1979-1994 (solid line). The years 1978-1991 show a 4.5%
increase in areal melt extent. In 1992, following the eruption of Mt. Pinatubo, the
melt area decreased considerably, before continuing to rise again in 1993 and 1994.
Also shown (dashed line) are the coastal temperature anomalies from the six climate
stations in Figure 1.1. They are well correlated with the melt extent.
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60
i
i
i
!
]
i
Boulder, Colorado. The station locations are: Thule, Sondre Stromfjord, Godthab,
Julianehab, Danmarkshavn, and Angmagssalik (See Fig. 4.3). There were data sets
i
available from additional stations, but some were incomplete; therefore they were not
;
i
|
j
I
used. Three o f the stations, Sondre Stromfjord, Godthab, and Julianehab are located
close to one another in comparison to the others, along the Southwest coast of
Greenland. In order to avoid a bias to this area, the three were averaged and treated as
one value before being averaged in with the other coastal station temperatures.
Two features stand out in Figure 4.13. The first is the drastic increase in melt
|
extent between 1979 and 1991. This increase is 4.5% per year (± 3.2% at the 90%
confidence interval), which is slightly higher than the 3.8% per year reported by Mote
;
and Anderson (1995). This increased melt trend is consistent with the coincident
warming trend during the years 1979-1991, with a correlation coefficient between melt
extent and temperatures of R = 0.81. The correlation suggests that a 1°C temperature
|
i
rise is accompanied by an increase in melt area o f 72,000 km2, which compares quite
!
well to the 79,000 km2 estimated by the slope and lapse rate calculation. This
i
i
^
additional 72,000 km represents a 49% increase over the total average melt area.
As illustrated in Figure 4.9, the 49% increase results in a melt area that is within
:
t
l
the 1 standard deviation of the natural variability for the early and late parts of the melt
season (before the end of June, and after late September), but it is well outside of this
i
range in July, August and early September. Thus the melt associated with a warming
;
o f Greenland o f as little as 1°C nearly exceeds the natural variability of the ice sheet
m elt variation. Since an average increase o f more than 1°C was observed between 1979
1
I
and 1991, such a situation is not unlikely in the greenhouse scenario. Therefore,
j
j
greenhouse-related temperature increases will significantly increase the spatial extent
|
i
of melt on the ice sheet.
j
!
I
The second notable characteristic o f Figure 4.13 is the sharp drop in mean melt
extent in the year 1992 to nearly the lowest value o f the 16 year time period. In June
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61
1991 Mt. Pinatubo erupted spewing large amounts of aerosols (ash and sulfur dioxide)
into the atmosphere. For the months and even years following the eruption, the effects
o f the increased aerosols and “nuclear winter” have been felt worldwide, primarily as
changes in temperatures and the associated effects (Halpert, et al„ 1994). The melt
extent seem s to be no exception. The increased aerosols reduced the amount o f solar
energy reaching the surface of the earth. It is quite feasible that this is the cause of the
reduction in melt area. In the years following 1992, the increasing trend appears to
resume.
4.7 C onclusion
Satellite measurements enable consistent long-term climate studies of the
Greenland ice sheet. The XPGR technique identifies the seasonal cycle and interannual
variations m elt on the Greenland Ice sheet. The 16-year data set indicates that the melt
extent peaks in late July and recedes more slowly than it advances. This is primarily
due to the ability of the XPGR to detect wet snow beneath dry snow. This sub-surface
melt detection characteristic can potentially be used in conjunction with a method more
sensitive to surface conditions (e.g. M ote and Anderson, 1995) to provide more
information about the vertical wetness structure o f the snowpack. The results also
suggest that maximum melt occurs on the western coast, particularly in the southern
part of the ice sheet, and that the areas most sensitive to melt variations are the lower
latitude regions o f the ice sheet.
There is a significant increasing trend in melt area of 4.5% ± 3.2% per year from
1979 to 1991. The melt extent is well correlated with the observed increase in coastal
tem peratures between 1979 and 1991 in excess o f 1°C. In 1992, this trend was
disrupted, possibly by the eruption o f Mt. Pinatubo, and after 1992, the melt area
returned toward its higher levels. An additional two years o f data should provide
information as to whether the increasing melt trend observed prior to 1992 has resumed.
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62
Also, despite these post-Pinatubo variations, there appears to be a distinct relationship
between temperature and melt area such that melt area increases by 72,000 km2 (49%
of the 16-year average melt area) for a 1°C temperature increase. Such a melt area
increase is well outside 1 standard deviation of the natural variability of melt. Thus
small changes in the Greenland climate, are likely to result in large changes in the areal
melt.
Using the XPGR method, melt conditions on the Greenland ice sheet can be
monitored in space and time. Such capabilities are useful for understanding how the
Greenland ice sheet responds to our changing climate. In the future, these melt
conditions can be compared to such climatological conditions as atmospheric
circulation, temperature, seaice extent, etc., and they can be incorporated into climate
models, thus providing a better understanding of the intimate links between the
Greenland ice sheet, and the regional and global climates.
i
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63
5. Accumulation and Hoar: Effects on Microwave Emissivity
!
j
i
I
5.1.
Introduction
The extent o f volume scattering in the fim is largely dependent on packing den-
|
sity, temperatures o f the snow at various depths, and grain size distribution with depth,
|
which are all in turn closely linked to the accumulation rates (Chang et al., 1976,
j
Zwally, 1977). As a result, it has been hypothesized that accumulation rates on the ice
j
sheet can be derived from passive microwave brightness temperatures. However, the
;
development of hoar, which refers to large faceted crystals that often form at distinct
levels in the snowpack (Colbeck, 1991), complicates such retrievals. It w ill be shown
that the hoar formation within an annual layer contributes significantly to the overall
:
;
microwave emission.
The contribution of hoar to the microwave signal is strongly polarizationdependent, (Shuman et al., 1993), and the impact o f accumulation on the m icrowave
j
emission varies with frequency (Chang et al., 1976). It is these relationships which
|
can help deconvolve the contributions from accumulation, hoar form ation, and other
m etamorphic processes.
;
In this chapter, the relative contributions o f hoar and accum ulation are exam ­
ined. The objective is to assess the importance of hoar development in the detection of
;
snow accumulation using microwave radiative transfer theory, and observed bright-
|
ness temperatures. The investigation was motivated by observed trends in brightness
|
temperatures in certain areas o f the Greenland ice sheet which have been attributable
i
to possible changes in accumulation rates (Steffen et al., 1993).
I
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64
5.2. Observed Passive M icrowave Brightness Temperature Trends
Close examination of the SMMR time series of the 18 GHz vertically polarized
channel shows various brightness temperature trends in the dry snow areas of the ice
sheet. Depending on the location, these trends range from as little as 1K mean temper­
ature change over the coverage period (essentially no trend) to as much as 18 K over a
seven year period. The locations o f these time series are shown in Figure 5.1 and the
time series themselves are shown in Figure 5.2. Because they are located in the dry
snow region of the ice sheet, m elting and freezing factors need not be considered in the
interpretation of these trends.
A num ber potential factors could contribute to such trends. One is instrument
drift due to degradation, but this is refuted by the regional variability of the trend.
Another possible cause may be changes in the physical temperatures, but again, the
variability does not support this possibility; furthermore, analysis o f coastal climate
station data for the same periods shows no evidence of such temperature trends (Stef­
fen et al., 1993).
It has been shown by Zwally (1977) that changes in snow accumulation rate
directly affect emissivity. The relationship is such that an increase in accumulation
rate results in an increase in emissivity and subsequently (according to Eq. 4.1) an
increase in brightness temperature. This occurs because smaller snow grains have
higher emissivity values than larger ones (Chang et al., 1976). An increase in accumu­
lation rate reduces the snow grain growth rate at a fixed depth (Zwally, 1977), which
results in effectively smaller particles in the new accumulation regime. Since most of
the microwave emission occurs here, emissivities and brightness temperatures
increase. Conversely, reduced accumulation rates result in larger particles in the emit­
ting areas and thus lower brightness temperatures.
A close examination of the relationship between the strength of a trend and its
location on the ice sheet shows that the trends are strongest in the northeast region
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7.7
fumrrtlt'
•6.9
.6.5
73
rr5J
-4 3
Figure 5.1. Location map o f various SMMR Tj, time series in the dry snow regions of
the ice sheet. The 18V signal was examined for locations A-J (labeled with a
and
they are plotted in Figure 5.2. Also shown are other places on the ice sheet referred to
in this chapter (labeled with a “+” ). These indicate areas from which data either were
collected in the past or will be collected in the future. Location B is also the site o f the
Inge Lehman camp referred to in the text.
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66
D e lto
10 K
T
Ts ( I 8 v ) o t 7 6 N o n e 4C V.
f b (1 8 v j ot 7B N o n e 4 0 W
Tb ( 1 8 v ) c t 8 0 N o n e 4 0 W
D e lto
= 200
I
t
T = 5K
frig h t
= 200
D e lto
T
L o c o tio n A
1988
1982
1982
198;
Oo(«
Dot*
Dot*
Tb (1 8 v ) o t 7 4 N o n e 3 7 W
To ( I 8 v ) o t 7 2 N o n e 3 7 W
Tb { 1 8 v ) Ot 7 0 N o n e 3 7 W
T
D e lta
T
D e lto
T =
2K
T * ^ Pe,otjfe
(<)
D e lto
£
t
0«igM^»u
£
to
L o c o tio n D
1978
198*
Dou
1986
L O C O tio n
1988
1978
Tb (18w ) o t 7 8 N o n e 3 2 W
18K
i960
19B6
Dote
Dole
Tb ( I 8 v ) c t 7 8 N o n d 4 8 W
To ( 1 8 v ) c t 7 6 N o n e 3 2 W
D e ltc T
D e lto t
6*
T erypcolv'e
(«)
D e lto T
1962
E
nrigM«e«
t
£
c
to
L o c o tio n C
<980
1982
L o c o tio n H
1986
<980
1982
1988
1962
D ole
Tb (1 8 v ) Ot 7 4 N o n e 3 2 Vrf
T =
5K
Bi.qM«e«
I ff r rp r a l-'f
(«)
D e lto
L o c o tio n J
1982
Figure 5.2. SMMR 18V brightness temperature trends for the areas shown in Figure
5.1. Most regions show some increasing trend between the years 1980 and 1986.
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67
(Figure 5.3). The entire SMMR 18 GHz vertical polarization time series for every
other pixel on the ice sheet was examined, and the areas that showed mean tempera­
ture trends in excess o f 1 K/year, 2 K/year, and 3 K/year were identified and marked on
the map. The wet snow regions were then masked out, and the resulting areas are
shown in Figure 5.3. It is obvious that there is a convergence of trend strength in the
northeast of Greenland; i.e. the trends are stronger in the northeast (at approximately
78°N and 30°W) and become weaker further from that area.
A snow accumulation map based on Greenland climatology, (Ohmura and
Reeh, 1991), shows that this northeast section is the area with the lowest mean accu­
mulation on the entire ice sheet (see Figure 5.4). In fact, the farther one moves from
this area, the higher the accumulation rate in the dry snow regions seems to be. An
inverse correlation exists between strength of the trend, and the mean annual accumu­
lation rate. It has been suggested that these trends are directly related to changes in
snow accumulation rates (Steffen et al., 1993).
Intuitively, this inverse correlation seems reasonable because in higher accu­
mulation areas, more of the signal is already coming from new snow than in areas with
little accumulation. As a result, changes in accumulation should be of less conse­
quence in these high snowfall areas, and more significant in the places where precipi­
tation is less frequent. The relationship is more complex than that however, due to the
formation of hoar on or near the surface of the snowpack.
It will be shown that the formation and growth of hoar has a significant impact
on the microwave emissivity. It is hypothesized that the observed T b variations result
from a combination of accumulation variability and changes in the hoar development
from year to year. In order to understand the relative importance of each one, a radia­
tive transfer model of the polar fim is developed for the dry snow region of the Green­
land ice sheet. Accumulation and hoar layer thickness is made to vary, and the
sensitivity of microwave emissivity to these characteristics is examined. The model
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Figure 5.3. Locations of 18V Tb trends of varying magnitude. The strongest trends
are located in the northeast region of the ice sheet, which is the low accumulation
zone.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
I
I
\0'
30C
600
jo0®
^
• «lo’rtT*|»r\
1
800
'
,00
ISO O
Figure 5.4. Accumulation map of the Greenland ice sheet (Ohmura and Reeh, 1991).
The lowest accumulation rates are found in the areas that exhibit the strongest bright­
ness temperature trends.
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70
developed in this work is largely an extension o f previous microwave polar firn model­
ing, with the additional consideration of angle, polarization, and hoar effects.
5.3 History of microwave modeling o f polar firn
The first quantitative work in microwave radiative transfer modeling of the
polar firn was done by Chang et al., (1976). Using Mie scattering theory, they derived
the volumetric absorption, scattering, and reflectance characteristics of snow as func­
tions of grain size and wavelength for varying indices of refraction. In their model,
they made two m ajor assumptions, the first being that the snow particles are spherical,
and the second, that the grains scatter independently. Their research forms the basis of
most subsequent microwave emission modeling of the firn.
The work was followed up by Zwally (1977), in what is often regarded as the
landmark research on the effects of accumulation on microwave emissivity of polar
firn. Using the absorption, scattering, and reflectance characteristics derived by Chang
et al. (1976) for 19 GHz frequency, he developed a single scattering model of the firn
emission characteristics. In doing so, he conceded that there were significant prob­
lems with the model, in that scattering was most likely overestimated by his assump­
tions and approximations. However, by multiplying the scattering coefficients by an
empirically derived correction factor,/, good agreement could be obtained with the
observed emissivities at seven stations on the Greenland and Antarctic ice sheets. His
derived value o f /w a s 0.12. With this model, Zwally made the first calculations of
emissivity dependence on accumulation rates for different regions in Antarctica and
Greenland.
Rotman et al. (1982) extended Zw ally’s derivations by statistically determin­
ing scattering coefficients with a least squares fit to in situ data, for various locations in
Greenland and Antarctica. They applied these coefficients to Zwally’s single-scatter­
ing model, and used observed brightness temperatures from the Scanning Microwave
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71
Spectrometer (SCAMS) on the Nimbus-6 satellite to determine the accumulation rates
on the ice sheets. Their results are subject to the same limitations as Zwally’s, in that
they are derived with a single scattering model, and assume all error is attributable to
scattering estimates; however, it represents a logical “next step” to Zwally’s work.
Comiso et al. (1982) developed a multiple-scattering model in which the radi­
ative transfer equation (Eq. 5.2 in Section 5.4.1) was solved using the doubling or add­
ing method (Liou, 1980). The equation was solved iteratively for 1000 optically thin
layers of firn, and scattering from layer to layer was considered. In this way, a major
limitation of the Zwally model, i.e. the neglect of multiple scattering, was overcome.
An empirical correction factor for the scattering coefficients was still necessary, but
with their model, this factor, y=0.3, was larger (i.e. less o f a correction was required).
The above models calculated emissivity based on the assumption that the tem­
perature distribution in the snow is isothermal. This assumption is valid on average
for an entire year assuming that the temperature vs. depth curves are symmetrical over
one year’s time (Comiso et al., 1982). The governing equation for temperature as a
function of depth is (Dalrymple et al., 1966):
T ( z , t ) - Tm - A Re x p [ c lz] cos [0.99 ( t - c 2) - (c 3 + c4z )]
(5.1)
where T(z,t) is the temperature at depth z, and time o f year t in days (such that at day
zero, surface temperature is at a maximum); T m is the mean surface temperature; AR is
one half of the annual surface temperature range, and c j, C2, c3, and c4, are site specific
constants. A sample temperature distribution plot for Maudheim (V^OS’S, 10°56/W)
is shown in Figure 5.5.
However, van der Veen and Jezek (1993), showed that in central Antarctica,
the temperature distribution, and consequently the source term of the radiative transfer
equation, is asymmetric throughout the year. The reason is that in contrast to the
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7
TEMPERATURE (K)
235
250
3/8
1/ 2
TIME =
265
365
E
□c
t—
a .
LU
o
Figure 5.5. Firn temperature profiles as a function of time o f surface maximums for
Maudheim, Antarctica (71°03’S, 10°56’W). These are typical o f the seasonal varia­
tions o f snow tem perature with the deeper temperatures showing less range and a time
lag behind those closer to the surface (from Zwally, 1977).
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73
long winter, the short summer does not allow adequate penetration o f the warm tem­
perature wave to the full depth of emission. Thus a symmetrical equation^ such as Eq.
5.1. tends to overestimate both the winter minimum and summer m aximum tempera­
tures. The extent o f this forcing function asymmetry depends on the degree o f dispar­
ity between durations of the winter and summer seasons. Their work successfully
demonstrated the importance o f seasonal temperature variability in relating brightness
temperatures to snow accumulation through model inversion.
Finally, Zwally and Giovinetto (1995) combined a solution o f the radiative
transfer equation (Zwally, 1977) with the grain growth function o f Gow (1969) in
order to estimate mean annual accumulation rates. On average, they showed accumu­
lation estimates which exceeded field measurements by 12% and 39% for west and
east Antarctica respectively, and by 5% for Greenland. However, these derivations are
based on a hyperbolic function o f emissivity, and require significant in situ field data to
determine the coefficients of the function. As a result they represent averages on dec­
adal tim e scales, but they cannot account for interannual variations.
W hile all o f the above studies have brought research closer to accumulation
estimates in the firn, widely accepted satellite derived accumulation estimates have yet
to be realized. There is one significant factor which has been neglected in all o f the
studies, and that is the role of hoar development, the effects of which cannot be
ignored. These effects are modeled and studied in the following sections. As a result,
a more comprehensive and accurate understanding of microwave emission o f the firn
is achieved, which can ultimately improve accumulation estimates.
5.4 H oar form ation
Hoar forms in various ways, but what is essential for its developm ent in the
snowpack is the presence of a strong snow temperature gradient o f 10°C/m or larger
(Armstrong, 1985). These gradients cause sublimation at the w arm er deeper layers,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and recrystallization along the vapor diffusion gradient. Snow densities in excess of
350 kg/m3 are not conducive to such depth hoar formation (Sommerfeld, 1983), and a
tendency toward enhanced hoar formation at low densities (less than 200 kg/m3) has
been observed (Perla and Ommanney, 1985). Considering the density of snow in the
polar fim (consistently over 350 kg/m3 at the Humboldt Site, K. Steffen, unpublished
data), and the fact that 10°C/m is about the maximum temperature gradient in the
|
snowpack, (Dalrymple, 1963), conditions in the polar fim inhibit the formation of
depth hoar.
Hoar can also form near the surface in low density relatively new snow which
falls on a sufficiently metamorphosed crusty snow surface. After extended exposure,
an old snow surface can develop into a crust either through wind packing and erosion,
or radiative processes. This crust has a relatively low albedo compared to new snow,
and when the new snow falls, the radiative absorption at this crusty surface results in a
temperature and vapor gradient within the new snow layer. As the vapor diffuses
upward into the cooler snow, crystallization occurs, and hoar is formed at the interface
between the crust layer and the newer snow. Evidence of such a process has been
found at the Humboldt Site (K. Steffen, unpublished data). Such a formation is most
likely to occur during the summ er months when insolation is most intense, and strong
temperature and vapor gradients can develop.
Finally, hoar can form at or near the surface when the relatively intense insola­
tion warms the snow a centim eter below the surface as much as 5°C above the air tem­
perature (Alley et al., 1990). There is an upward diffusion o f vapor from the near
surface snow during which some of the vapor condenses forming a coarse-grained,
hoar layer of low density at or near the surface (Shuman and Alley, 1993). Such for­
mation requires intense insolation and is most likely to occur in the high elevation
areas such as Summit (Fig. 5.1), and areas of little cloud cover. Surface hoarcanalso
form during the advection of a m oist air mass over the cold fim where the vapor con-
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75
denses at the air-snow interface.
The scattering characteristics of these large hoar particles can reduce the
microwave emission significantly. In order to investigate these effects in conjunction
with those of accumulation, these parameters are varied in a radiative transfer model
of the fim.
5.5 Radiative transfer model development
5.5.1. The equation of radiative transfer
Emission in the snowpack is governed by the integro-differential radiative
transfer equation, given as (Comiso et al., 1982):
T
(5.2)
where 1(0) is the intensity (energy flux per unit wavelength per unit solid angle); 0
refers to the zenith angle; x is the optical depth; e is the volumetric emissivity, B is the
Rayleigh-Jeans approximation of the Plank function; (0o is the single-scattering
albedo; x’ and 0 ’ are the integration variables for depth and scattering angle respec­
tively; p. = cos(0); and P(0) is the scattering phase function, which describes the angu­
lar distribution of the scattered energy.
Each of the terms on the right side of the radiative transfer equation represents
a specific contribution to the upwelling intensity from the surface of the snowpack.
The first is simply the transmission of upwelling intensity from a given optical depth,
x, to the surface. This term accounts for the extinction o f upwelling intensity below
the depth o f a medium as it passes through the medium to the surface (by multiplica­
tion by the extinction term, e 'T/^). The second is the source term, which accounts for
I
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76
the contribution of thermally emitted radiation from within the medium. Included in
this term are the emissivity to account for the gray body nature of the medium, and the
extinction factor, to account for losses within the medium. Finally, the third term rep­
resents the directionally variable (anisotropic) scattering of radiation within the
medium. This term includes the phase function, single-scattering albedo, and expo­
nential extinction factor. Assuming independent scattering, the upwelling intensity is
simply the sum of all of these components.
Once intensity is calculated, the emissivity can be determined according to:
E
2 c kT m
(5.3)
W here X is the wavelength, c, k, and T m are the speed of light, Boltzm ann’s constant,
and the mean temperature of the snowpack respectively.
5.5.2 Discrete ordinate radiative transfer method
The discrete ordinate method is a method by which the radiative transfer equa­
tion (Eq 5.2) is solved by summing the intensities at discrete angular intervals. In its
simplest form, the two stream approximation, the total intensity is taken to be the sum
o f the upwelling and downwelling intensities (Iup and \down respectively):
i J 1 (x, p) (d p ) = i [l“p (x) + f own (x) ]
-l
(5.4)
More accuracy can be obtained by dividing the distributed intensity into a greater
number of angles or “streams” (not just two). This requires a more general form of
Eq. 5.4, a numerical quadrature:
m
(5-5)
-I
j=
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77
W here m is the num ber of streams, and w ’ are the quadrature weights, and (Oj are the
discrete ordinates, i.e. the cosines o f the angles into which the emitted intensity is
divided. By discretizing the problem, the integro-differential equation is broken down
into a system o f ordinary differential equations for which the eigenvalues and eigen­
vectors (i.e. the eigensolutions) can be found (Liou, 1973). Stamnes and Swanson
(1981) optimized the solution and were able to develop explicit expressions for inten­
sity at angles other than just the quadrature angels.
In this analysis, the Discrete Ordinate Radiative Transfer (DISORT) Code
developed by Stamnes et al. (1988) is used to solve the radiative transfer equation.
The input param eters are derived independently, and then incorporated into the DIS­
ORT model. In order to achieve sufficient accuracy a 16 stream approximation is used
(i.e. 0 is divided into 16 separate angles).
5.5.3 M odel description
Using DISORT to solve the radiative transfer equation, a model is constructed
which represents the firn at Inge Lehman on the Greenland ice sheet (77° 57’ N, 39°
11’ W; Location B in Figure 5.1). With this model, the dependence of emissivity on
accumulation and hoar development is assessed. This location was chosen for two
reasons: 1) Information is available on the grainsize/depth relationship (Gow, 1971);
thus scattering properties can be calculated (Zwally, 1977); and 2) It represents the
area in which the greatest interannual brightness temperature variability is observed
(3K/year, see Fig 5.3). In addition, it is near the site of the planned 1996 field cam ­
paign, from which comprehensive climatological and historical accumulation data will
be retrieved for comparisons and future model refinement. For these reasons, it is the
optimum location for the analysis.
The model consists of 20 multiple scattering layers where the only depthdependent variables are grain size, and single-scattering albedo. All assumptions and
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78
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characteristics of the model are either derived from or taken directly from Zwally
i
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(1977) and Comiso et al. (1982). They are summ arized in Table 5.1 and discussed in
more detail below.
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!
!
Table 5.1. Model assumptions and characteristics for nominal conditions on the ice
sheet (mean annual accumulation of 100 mm w.e. (Ohmura and Reeh, 1991), and 1.5
cm thick hoar layer). Also given are the sources of the assumptions made and the sensitivity o f the emissivity to each assumption or characteristic. Each assumption (1-17)
is discussed following the table.
Assumption/Characteristic
Sources3
Sensitivityb
1
horizontal homogeneity
1,2, 3 ,4
variable
2
isothermal snowpack
2 ,3
none
3
absorption coefficient
2
high
4
grainsize distribution
2 ,3
moderate
5
constant annual growth rate
2
low
6
19.35 GHz frequency
1,2, 3 ,4
model constraint
7
independent scattering
1,2, 3 ,4
empirically accounted
for (see 9 below)
8
Rayleigh scattering
1,2, 3, 4
none except for hoar
(discussed in results)
9
scattering coefficient
1,2, 3 ,4
moderate
10
optical thickness
2,3,4
moderate
11
single scattering albedo
1,2, 3 ,4
extreme
12
winter conditions
this study
model constraint
13
equal spring and autumn snowfall
this study
low
14
hoar radius
this study
moderate
15
hoar scattering characteristics
2, this study
discussed in results
16
emission angle ( 0 = 53°)
this study
model constraint
17
vertical polarization
this study
model constraint
a. Source references: 1. C hang e ta l.. 1976; 2. Zwally, 1977; 3. C om iso et al., 1982; 4. Van d er Veen and
Jezek. 1993.
b. Sensitivity term s are calculated based on the im pact o f a 20% change in the assumed value (w here
appropriate). T he convention is as follows: 0-2% change in calculated em ission - low: 2-6% change m oderate; 6-10% - high; 10-20% - extrem e.
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79
1) H orizontal homogeneity. The snowpack is assumed to be horizontally
homogeneous and structured as shown in Figure 5.6. There is some vertical variability
at different locations within the 25 km x 25 km passive microwave grid cells, but the
stratification is qualitatively maintained throughout (K. Steffen, unpublished data).
The extent of this variability is part of the ongoing research of the Program in Arctic
Regional Climate Assessment (PARCA). By assuming horizontal homogeneity, the
intensity is considered to be azimuthally independent.
2) Isothermal snowpack: While the snowpack is certainly not isothermal on
any given date, it is a close approximation for a full year average (Comiso et al.,
1982). Since emissivity is being calculated, not brightness temperature, the vertical
temperature distribution does not effect the results. If brightness temperatures were to
be calculated, or accumulation estimates were to be m ade by inverting the model, the
vertical tem perature profile would be necessary, but the scope of this study is to assess
the impact of changes in accumulation and hoar formation on the emissivity. Thus the
temperature distribution is not needed. This is discussed in more depth in Chapter 6.
3) Absorption coefficient: The absorption coefficient (ya) is equal to 0.038m '1.
Zwally (1977) uses a value of 0.15m '1, but Comiso et al. (1982) show that for the
polar firn, 0.038m"1 is more consistent with the theoretically derived values from the
Debye equation (Hobbs, 1974), and it also agrees with estimates made from a compi­
lation by Evans (1965) of measured loss tangents (Comiso et al., 1982). Furthermore,
Ya shows and excellent fit with empirical data for various sites in Greenland and Ant­
arctica, particularly for the Inge Lehman station.
4) Grainsize distribution: The cube of grain radius (r) varies linearly with
depth (z):
r3 = Tq + Sz
(5.6)
where, r03, the intercept of the regression line, is equal to 0.0278, and S, the slope of
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80
Direction of calculated emission
Snow surface
Layer 1: Second half o f current
year’s accumulation
Layer 2: hoar
Layer 3: First half of current year's
accumulation
^
Layers 4 - 2 0 : extending to 25 m depth.
The cube of the radius increases linearly with
depth.
Figure 5.6. Snow structure used in the radiative transfer model. The structure repre­
sents winter conditions at Inge Lehman, in which the summertime hoar is sandwiched
between the spring and fall snow.
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81
the regression line is equal to 0.0202 for z in m eters, and
tq3
in mm3 (Zwally, 1977).
The rate of grain growth with depth is primarily dependent on temperature, and accu­
mulation rates (Gow, 1969). Therefore, the model can be modified to represent any
location on the dry snow region o f the ice sheet if these values are known. This is dis­
cussed further in Chapter 6.
5) Constant annual grain growth rate: The size of the particle at the bottom
and top o f the current year’s snowfall is assumed not to vary from year to year; thus
with varying accumulation, the grainsize vs. depth relationship (S in Eq. 5.6) varies
inversely with the accumulation rate (Zwally, 1977).
6) 19.35 GHz frequency: As do most of the microwave models of the firn to
date (see Section 5.3) this model examines energy emitted at 19.35 GHz. This is the
frequency of an SSM/I channel; thus the radiative characteristics of polar firn at this
frequency are of great interest for interpretation o f microwave brightness tem pera­
tures. The closest channel on the SMMR instrument is 18 GHz, but through the appli­
cation of the correction coefficients (Jezek et al., 1991), they can be modified to
represent their 19.35 GHz equivalent.
7) Independent scattering: The snow grains are assumed to scatter indepen­
dently (Chang et al., 1976; Zwally, 1977; Comiso et al., 1982; van der Veen and Jezek,
1993). Because of the dense packing of the snow, however, there are some coherent
scattering effects, and the assumption results in an overestimate of the scattering
(Zwally, 1977, Comiso et al., 1982). This overestimate is one factor which is
accounted for by the empirical correction term ,/, discussed in item 9 below.
8) Rayleigh scattering: For 19.35 GHz (1.55 cm wavelengths), particles on the
order of 1.5 mm or less in diam eter satisfy the Rayleigh scattering criterion. Thus the
assumption is applicable to the snowpack. The Rayleigh criterion are not quite satisfied
by larger hoar particles, (in excess o f 1.5 mm in diameter), however, Rayleigh scatter­
ing is still assumed, with the acknowledgment that the amount of scattering is slightly
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!I
82
underestimated. The implications of this assumption are discussed in Section 5.6.4.
9) Scattering coefficient: The scattering coefficient (ys) varies with radius (r)
according to the formula:
Y,=/(1.8r)3
(5.7)
where the empirically derived correction factor,/, is assumed to be equal to 0.3
(Comiso et al., 1982). It accounts for the overestimating of scattering due to various
assumptions in the derivation o f the scattering coefficient, primarily that of indepen­
dently scattering, spherical particles. A comparison with 7 stations in Greenland and
Antarctica shows that forf= 0.3 the scattering term yields an excellent fit (R=0.986) to
empirical data (Comiso et al., 1982). Therefore, in this s tu d y /is assumed to be 0.3.
The cubic relationship between scattering and radius in Eq. 5.7 arises from the fact
that in the Rayleigh regime, scattering is dependent on r6 (Zwally, 1977), but the denj
sity o f the scattering particles N r is proportional to r
(Chang et al., 1976). The com ­
bined effect results in a dependence o f scattering on r3.
10) Optical thickness (%): The optical thickness of any given layer, the top and
bottom of which are at depths of z\ and Z2 respectively, is:
t ( z ) = JT [ya + ys { z ) ] d z
(5.8)
11) single scattering albedo (tss0): The single-scattering albedo, defined as the
probability that a particle will undergo scattering, vs. absorption, is given by:
ys
co = -------o
y +y
*a
(5-9)
*s
Table 5.1 indicates that the results are highly sensitive to single-scattering albedo; a
20% change in co0 alters the emissivity by 19%. Fortunately, the differences between
the magnitudes of ya (0.038 m '1) and ys (on the order of 0.3 m '1 for most of the em it­
ting area of the snowpack) are such that changes in ya are of little impact on co0, and
changes in ys tend to cancel out in the ratio. Therefore, despite the extreme sensitivity,
the single-scattering albedo is not likely to be very inaccurate.
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83
12) Winter conditions: The model stratification is as shown in Figure 5.6,
which is representative of winter conditions (The vertical position o f the hoar is dis­
cussed in item 13). Winter conditions are used because any effects attributable to inso­
lation, i.e. surface metamorphism, do not influence observed wintertime brightness
temperatures. Thus for comparisons of the model to observed values (as will be dis­
cussed in Chapter 6), the winter is the best time for comparison.
13) H oar at the center o f the annual layer: The situation of the hoar at the cen­
ter of the annual layer is based on two assumptions. The first is that the amount of
snow before the formation of hoar in a given year, is equal to the amount of snow that
falls after the formation of hoar. This assumption was based on an analysis of shallow
ice core data provided by John Bolzan of the Byrd Polar Research Center at The Ohio
State University. A 24 year comparison of winter-to-summer accumulation and summer-to-winter accumulation showed no bias one way or the other between early (win­
ter and spring) and late (summer and fall) snowfall over the period studied. There is
most likely some seasonal variation from year to year, but the ice core data suggest
that over long terms, they average out. The half year estimates were determined from
winter and summ er peaks in the stable oxygen-isotope ratios for the years 1964-1987
at 9 sites on a 150 x 150 km grid around Summit, Greenland (described in Bolzan and
Strobel, 1994). The conditions at Inge Lehman may be a little different than Summit,
but the Bolzan data are the best currently available. The PARCA 1996 field campaign
will improve this approximation.
The second assumption is that the hoar forms at or near the surface during the
summer. This is assumed to be the case because the most likely formation mecha­
nisms are that the hoar forms as surface hoar or near-surface depth hoar due to intense
insolation (Alley, 1990), or that it forms at the interface between a crust layer and
freshly deposited snow (see Section 5.2). Fortunately, the results are not influenced
much by where in the snow layer the hoar lies (a 20% error in this estimate results in
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84
less than 1% change in the snow emission).
14) H oar radius: The mean hoar radius is 1.5 mm. This value is typical for the
Humboldt Site, near Camp Century, and is assumed to be valid for Inge-Lehman. The
basis o f this assumption is the fact that Gow (1971) reported that the near surface par­
ticles at Inge Lehman are nearly the same size as those at Camp Century. Since it is of
moderate impact on the emission, additional data are required to validate this assump­
tion. These data will be collected during the 1996 PARCA field campaign.
15) H oar scattering characteristics: The dependence of scattering on the factor
(1.8r)3 in Eq. 5.7 is valid for grain sizes of less than 1mm radius, but for the larger hoar
particles, ys is taken to be (1.82r)3 (Zwally, 1977). The hoar is assumed to be in the
Rayleigh regime (the implications are discussed in section 5.6.4), and only a single
layer o f hoar is included near the surface of the model. Hoar layers may be present for
several years before metamorphism causes them to become nearly indistinguishable
from the surrounding snow, but this investigation is intended to assess the impact of
the most recently formed hoar (from the preceding summer). Subsequently, only one
layer was modeled. Furthermore, the contribution of deeper hoar layers is less than
that of the near surface layer by virtue of their depth.
16) Emission angle: Intensity is calculated for an angle of 53° from the zenith,
which is the scan angle of the SSM/I instruments. For estimates of accumulation from
brightness temperatures, the emission characteristics at the instrument observation
angle must be evaluated. The SMMR scan angle is closer to 50°, but as with wave­
length, the brightness temperatures can be adjusted to reflect their 53° equivalent with
the appropriate regression coefficients (Jezek et al., 1991).
17) Vertical polarization: The model examines vertically polarized electro­
magnetic radiation only. Vertical polarization is what is most useful for such a model
because 53° is near the Brewster angle for snow (Hollinger et al., 1987). At the Brew­
ster angle, which is the angle at which there is no reflection of vertically polarized
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85
radiation, the influence of layering in the snow structure in vertically polarized emis­
sion is minimal. Thus changes in brightness temperature are more linked to grain size
distribution, rather than stratification. This grain size distribution is presumed to be
closely related to accumulation and hoar development.
The phase function for vertically polarized radiation was determined by isolat­
ing the vertical component of the Rayleigh phase function for spherical particles. The
well known Rayleigh phase function is:
^ ( 0 ) = | [ 1 + ( c o s 0 ) 2]
(5.10)
where all of the terms are described above. Eq. 5.10 represents the combination of
vertically and horizontally polarized electromagnetic radiation. The product [ ?xl ] on
the right side of the equation comprises the horizontal component of the phase func­
tion, and the remainder represents the vertical component (Goody, 1964). Therefore,
the resulting phase function for vertical polarization is:
/>(6) = | [ ( c o s 0 ) 2]
(5.11)
This phase function is incorporated into the model as the coefficients of a Legendre
polynomial expansion.
The Rayleigh scattering phase function is based on the assumption that the
snow grains are spherical, which is just an approximation. To more accurately model
the firn, the moments of the phase function that account for the deviation from a true
sphere, should be applied. However, assuming the distribution and orientation to be
random, the moments would show no bias in one direction, or another. In this case the
Rayleigh phase function is still applicable.
In order to validate the model, it was run for the same input conditions as those
of Comiso et al.(1982), and yielded the same results to within a few tenths of a per­
cent. This is within the limits of the two different solution methods (doubling-adding
vs. discrete ordinates). An additional test case was run for a pure scattering medium
with a Rayleigh phase function (Chandrasekhar, 1960; Comiso et al., 1982), and again
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86
the results were within the limits o f the different solution methods.
A fter development and validation o f the model, it was run for various hoar
layer thicknesses and accumulation rates. The results o f these runs are presented in
Section 5.5, and the importance o f hoar, in addition to accumulation, in the microwave
emission is presented and discussed.
5.6 Results and discussion
The dependence o f emissivity on accumulation and hoar development are
shown in Figure 5.7. A number o f interesting and significant relationships are evident.
5.6.1 Em issivity and accumulation
The results indicate that an increase in accumulation results in an increase in
microwave emissivity. This is to be expected since greater accumulation rates result in
increased emission from the highly emissive sm aller grains of relatively new snow. In
addition, the sensitivity of emissivity to accumulation rate is greatest in the areas of the
lowest accumulation. This occurs because in high accumulation areas, snowfall from
the current year already comprises a large part o f the signal, and masks out much of
the contribution from previous year’s snow; thus changes in snowfall do not signifi­
cantly im pact the signal. Consider, for example, the extreme case of an area with 5 m
of snowfall per year. Each year, the 19 GHz microwave emission will be nearly totally
emitted from the current year’s snowfall. Thus a doubling o f snowfall will not result
in much o f a change in the signal.
Conversely, in areas with little accumulation a doubling o f snowfall will result
in much m ore o f the signal coming from the current year’s highly emitting snow than
in previous years. As a result, the sensitivity to accumulation variations is greater in
these low accumulation regions.
The accumulation-emissivity relationships are consistent with what has
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87
a)
0.74
No Hoor Loyei
0 .7 2
>N
1
u>
U}
0 .7 0
E
3 cm Hoar Layer
UJ
0.68
0.66
20
40
60
80
100
Annual Accumulation (cm)
b)
0 .7 4
2 m Accumulation
0 .7 2
% 0 .7 0
<n
E
LU
0 .6 8
2 cm Accumulation
0.66
0
10
20
Hoar Layer Thickness (mm)
30
Figure 5.7. Dependence o f microwave emissivity on accumulation and hoar thickness
at Inge Lehman (77°57’N, 390H ’W). The isolines in (a) are at intervals of 2 mm,
while those in (b) are at 10 cm intervals with the exception o f the 2 cm line. The sen­
sitivity is greatest when accumulation is low and for thick hoar layers. Furthermore,
the emission is more strongly dependent on hoar formation than accumulation varia­
tions.
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88
already been shown qualitatively by Zwally (1977). They also explain in part why the
observed brightness temperature trends (Section 5.2) are strongest in the low accum u­
lation areas. However, what is different and o f great importance to the future of
microwave modeling is the dependence and sensitivity of this relationship to the pres­
ence of hoar.
5.6.2. Em issivity and hoar layer thickness
The microwave emissivity is very sensitive to the hoar layer thickness itself.
According to the model, the presence o f a 1.5 cm thick hoar layer, which is typical for
Summit (C. Shuman, personal communication), reduces the emissivity, by 2.8 per­
cent. Assuming the mean wintertime 19 GHz vertically polarized brightness tempera­
ture is 170 K for a typical 1.5 cm hoar layer, the hoar is responsible for reducing that
by 5 K. In other words, if the hoar were not present, the brightness temperature would
be 175 K. The effect would be even greater in the summer, when the hoar is right at
the surface. Such a drop in the 19 V brightness temperature is consistent with was
observed at Summit during the m ajor hoar formation period of 1990 (Shuman et al.,
1993). Considering that hoar layers may vary from year to year from zero thickness to
greater than 4 cm (C. Shuman, personal communication) the impact of hoar on bright­
ness temperature can be tremendous.
Furthermore, according to the model, variations in hoar thickness of a millime­
ter have roughly the same impact on the emissivity as tens of centimeters of accumula­
tion changes. In terms of percentages, a 10% increase in hoar layer thickness may
impact the signal as much a 100% increase in accumulation. Again, the large optical
thickness and the high scattering characteristics result in a significant contribution to
the microwave emission. These relationships, which are strongly dependent on the
scattering and optical thickness properties o f the snow, are in turn driven by the grain
size distribution. The effects of varying grain size distribution are more thoroughly
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89
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examined in Chapter 6.
i
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Finally, the sensitivity o f microwave emissivity to hoar development is lowest
in the regions of maximum snowfall. This can beexplained by the fact that high accu-
|
mulation rates more effectively mask the hoar signal, and thus reduce the sensitivity of
I
the overall emission to the hoar development.
5.6.3 Accum ulation and hoar: combined effects
W hile the emissivity does show some variation with accumulation, the magni­
tude of the relationship is not enough to account for the differences observed in the
microwave brightness temperatures near the Inge Lehman location. According to Fig.
5.7 the relationship between the two increases significantly in the presence of a layer
of hoar. Without the consideration of hoar, it is impossible for accumulation variation
alone to cause the observed Tj, trend. W hen considered with a 2 cm hoar layer in the
snowpack, however, less than a 2 m change in accumulation will cause the observed 3
K rise in Tj,. W hile such large accumulation changes are still unlikely, the relationship
indicates that without the hoar, accumulation changes would be undetectable with the
19V channel. In addition, the thicker the hoar layer, the stronger the relationship
between accumulation and microwave emissivity.
This strengthened relationship and its dependence on hoar layer thickness is
most likely attributable to the high scattering characteristics and large optical thickness
of the hoar layer. These cause a significant extinction of the upwelling radiation from
the snow below. As a result, in the presence o f a thick hoar layer, more of the signal
comes from the near surface layers of snow than the deeper portions o f the snowpack;
thus the sensitivity of the signal to changes near the surface is greater.
Considering the m agnitude of the observed trends for the Inge Lehman region,
it is most likely that they are the result o f changes in both hoar development and accu­
mulation. The model suggests that the hoar development is a first-order factor, while
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90
the accumulation is a second-order cause.
5.6.4 Assumption validity for hoar layer
The validity of the assumptions made have been demonstrated by Zwally
(1977), and Comiso et al. (1982) for the polar firn. The issue that needs to be
addressed in this analysis is the extent o f applicability of these assumptions to a model
in which a hoar layer is present. One error source may be the far-field assumption, or
the treatment of the particles as independent scatterers. The applicability of the farfield approximation is dependent on the packing density o f the medium, or the ice/air
ratio. The lower this ratio, the more valid the far-field approximation. In the hoar
layer, the large particles actually result in reduced packing density as compared to the
rest o f the snowpack. Thus the far-field assumption, is in fact more valid for the hoar
layer than it is for the rest of the snowpack. S ince/accounts for some deviation from
the far-field conditions, the hoar effects are likely to be greater than predicted by the
model.
Another important consideration is the assumption of Rayleigh scattering in
the hoar layer. The scattering is actually somewhere between the Mie regime, where
particle size is on the order o f one wavelength, and the Rayleigh regime, where the
particle is less than one tenth of the wavelength. However, because the particle size is
approximately one fifth of a wavelength, the scattering is more closely related to Ray­
leigh then to Mie; associated errors are likely to be small.
Mie scattering is more in the forward direction than is Rayleigh which is more
symmetric about the horizontal plane, 0=90° (Henderson-Sellers and Robinson, 1991).
This effect would lead to an overestimate of scattering. However, calculation of the
Henyey-Greenstein asymmetry parameter (g), gives a result o f g=0.082. This param e­
ter is an factor which describes the symmetry (or lack thereof) of scattering character­
istics of a particle, and it is strongly dependent on wavelength and particle size. A
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91
positive value of g indicates that scattering is preferentially forward (for g=l , scatter­
ing is purely forward), and a negative value o f g indicates that scattering is preferen­
tially backward (for g= -1, scattering is purely backward). In the case of symmetric
scattering, g is equal to zero. The fact that the magnitude of the calculated value of g
is so low, means that scattering is only very slightly biased in the forward direction.
5.7 C onclusion
The radiative transfer model appears to represent the emission behavior of
snow under changing conditions of accumulation and hoar development. The link
between microwave emission and accumulation rates in the dry snow area of the
Greenland ice sheet is significant. However, the emissivity is even more dependent on
the extent o f hoar development. As a result, accumulation estimates based on passive
m icrowave observations require successful parameterization o f the hoar formation
characteristics.
Until this hoar development can be adequately parametrized, the detection of
interannual variations in accumulation will not be possible. The observed trends for
the Inge Lehman region are most likely due primarily to changes in hoar development,
and secondarily to changes in accumulation rates. The results o f the PARCA 1996
field campaign will add considerable insight to these issues.
Finally it is important to note that microwave modeling of the polar firn, is still
in its early stages. Slow progress has been made over the last 20 years. This work,
while subject to many of the limitations as those that have preceded it, demonstrates
the significance o f the hoar, and is the first m odeling effort which actually incorporates
hoar development.
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6. Accumulation, hoar formation, and Tb: Case Study - Summit
6.1 Introduction
The model described in Chapter 5 can be modified to reflect conditions at any
location on the Greenland ice sheet by incorporating the snow temperature and accu­
m ulation characteristics, and their impact on grain growth rates (Gow, 1969). Thus, if
hoar development can be adequately characterized and temperatures are known, accu­
m ulation estimates can potentially be made in the dry snow zones o f the ice sheet.
In this chapter, a m ethod for modifying the m odel to represent different loca­
tions in the dry snow areas o f the ice sheet is described, using Summit (72°N, 38°W)
as an example. Summit was chosen because there is a limited amount of in situ accu­
mulation data for comparison (Bolzan and Strobel, 1994). Unfortunately no sim ulta­
neous in situ accumulation and annual temperature m easurements were available,
because the AW S’s were set up around the tim e of the ice core extraction. At present
and in the future (e.g. at the Humboldt and TUNU sites and other parts of the PARCA
network) AW S’s equipped with snow height sensors and thermocouples will provide
the coincident measurements of the two parameters. Initially, it was hoped that sur­
face temperature estimates derived from AVHRR would be available for comparison
with ice core accumulation estimates, but they are not.
It is important to state up front that because snow temperature characteristics
are not yet known, actual accumulation estimates, cannot be made at present. W hat
follows is a description of the steps that need to be taken so that when tem perature data
become available, comparisons can be made. The exercise seems somewhat aca­
demic; however it does have merit, in that it addresses issues associated with interpre­
tation o f ice core accumulation estimates, and establishes a first-order characterization
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93
t
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|
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of hoar development. Both are accomplished with the use of passive microwave satellite observations, and the methods are presented here.
6.2.
6.2.1.
Model adjustm ent to Summit conditions
Emission sensitivity to grainsize distribution
In modifying the model to represent different regions on the ice sheet, the pri­
mary factor that affects the emissivity is the grain size distribution. Thus, before
attempting to model the local conditions at Summit, the sensitivity o f emission to
errors in grain size estimates are examined by running the model for various grainsize
:
profiles. Since the governing equation of the size distribution is (from Eq. 5.6):
I
3
3 , c
r = r0 + Sz
!
the variables in the sensitivity study are surface grain radius cubed (r03) and growth
i
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rate (S). A varying growth rate from 0.001 to 0.041 mm3/m was assumed, with r03
i
o
j
ranging from 0.001 to 0.041 mm . These limits were chosen because they sufficiently
i
j
bound the range of values observed in Greenland and Antarctica (compiled by Zwally,
1977), and they are roughly centered at the conditions found at Inge Lehman.
!
|
i
The results of the sensitivity study are shown in Figure 6.1. W hile the emissivity is dependent on both variables, it is approximately twice as sensitive to growth rate
as to surface grain size. For the conditions at Inge Lehman (Figure 1.1), a 25% under-
|
estimate of S results in a 2.7% overestimate of the emissivity (which translates to
approximately 4.8 K in Tj,). The same 25% underestimate in r03 overestimates the
i
I
emissivity by 1.3% (2.3 K). This higher sensitivity to growth rate is a direct result of
!
the volume scattering dependence on the grains below the surface. Regardless of the
i
grain sizes at the surface, a high growth rate will lead to large subsurface snow grains,
j
Since the emission depth at 19 GHz is approximately 5 m, rapidly growing subsurface
!
grains can have an effect on the emissivity that outweighs that of the grains at the top
j
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of the snowpack.
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94
a)
0.90
0.85
ir o.8o
>
cn
r„3=0.001 m m 3
(r,= 0 .1 m m )
E 0.75
Ld
0.70
r03=0.041 m m ;
0.65
0.000
0.010
0.020
0.030
Growth Rate (mmJ/m )
0.040
b)
0.90
0.85
>
S =0.001 m m 3/ m
0.80
*cn
co
E 0.75
LU
0.70
q
1 S = 0 .0 4 1 m m 3/ m
0.000
0.010
0.020
0.030
0.040
r„3 (mm3)
Figure 6.1. Dependence of microwave emissivity on grain growth rates (6.1a) for
varying surface grain sizes, and on grain sizes (6.1b) for varying growth rates. The
effect of grain growth rate (S) on emissivity is nearly twice that of surface grain size
(rG3)-
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95
W hat these results mean is that because of the depth of em ission, the slope of
the regression line in Eq. 5.6 is a more significant factor than the intercept; thus an
accurate estimate of S is more crucial than that of rG3. However, together they are
responsible for a substantial variation o f brightness temperature, and m ust be
accounted for when applying the model to different locations on the ice sheet.
6.2.2. Estimation o f grainsize distribution
6.2.2.1 Surface grain size (r03)
Comparing the conditions between Camp Century and Inge Lehman (Figure
1.1), the two areas have vastly different annual accumulation rates and slightly differ­
ent mean annual temperatures. Camp Century has more then twice the accumulation
of Inge Lehman (Ohmura and Reeh, 1991), and the mean annual tem peratures are 249
K at Camp Century versus 243 K at Inge Lehman (Zwally, 1977). Still, their surface
grain sizes differ by only 0.7% , while the growth rates at Inge Lehm an are nearly dou­
ble those of Camp Century (Gow, 1971). Though the size of these surface grains at the
time o f deposition is strongly dependent on the atmosphere in the snowflakes’ trajecto­
ries, on the Greenland ice sheet, these grains are largely affected by wind abrasion.
Based on the relationship between the two stations, it is assumed that for modeling the
dry snow areas of the firn, the surface snow is o f the same size at every location, and it
is the rate of metamorphism (as a function of depth) that varies.
6.2.2.2 Growth rate (S)
The rate at which grain sizes increase as a function of depth (z) is (from Zwally
and Giovinetto 1995):
(coPo)z
S = -----^ -----A e x p (-£ — )
m
(6.1)
where c0 is a constant; p0 is the average firn density in the top 10 m; A is the mean
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
annual accumulation rate; e is the activation energy of the growth process; R is the uni­
versal gas constant; and Tm is the mean annual temperature.
Assuming the first-order variables are the accumulation and mean temperature,
then the grain growth rate from Inge-Lehman can be adjusted to yield an approxim a­
tion for the value at Summit. Letting S represent the growth rate at Inge-Lehman, and
S ' represent that at Summit, the two can be related by dividing the equation for IngeLehman (Eq. 6.1), by the same equation for Summit (in which the varying parameters
are indicated with a “ ' ” superscript). The resulting expression is:
~\
5
S'
( C2p 2) z
(C\P\)z
A e x pl ,
AeXp{R T j
(6.2)
1
Assuming the products CjP] and C2P2 are both equal to 1010 (Zwally and Giovinetto,
1995), and after canceling constant terms, the resulting expression for growth rate at
Summit is:
S' = S
r e
A'
R
t
1
Tm
1
in
m
(6.3)
The correct value for A ', determined from the most recent 24 years of accumu­
lation data from the cores of Bolzan and Strobel (1994), is 208 mm w.e. Initial
attempts were made at calculating Tm' from AVHRR thermal infrared data for 19891993 (Julienne Stroeve, unpublished data); however, significant data gaps and the lack
of adequate cloud masking resulted in apparently cold-biased temperature. W hat was
actually used were the temperature relationships between Summit and Inge Lehman as
estimated by Diamond (1958) and Ohmura (1987). According to their calculations,
the mean annual temperatures are the same for the two places. This is further sup­
ported by Putnins’ (1970) adiabatic lapse rate estimates of nearly zero in the central
part o f the ice sheet. Fortunately, for the possible ranges o f temperature that may exist,
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97
S ' is a weaker function o f temperature than o f accumulation which is known with
more certainty. After setting Tm equal to T m' substituting the appropriate values for
each of the variables, Eq. 6.3 becomes:
S ' = (0.481) S
(6.4)
It is this value that is incorporated in the model for Summit.
It should be noted that assessment of this spatial variability in both temperature
and accumulation, as well as radiation and turbulent flux characteristics will be signif­
icantly enhanced by the network o f automatic weather stations (AWS’s) established as
part of the Greenland Climate network (GC-Net) (Steffen et al., in press). These sta­
tions, the first 5 of which were installed in 1995, and the next 4 of which will be
installed during the 1996 field season (one at Summit, and one near Inge Lehman),
will provide information on a of a num ber of climaiological variables and their spatial
variability. W hen the data are collected, they will provide a test of the above assump­
tions about accumulation and temperature differences.
6.3 Hoar param eterization
W hile the large size o f the hoar grains reduces the vertically polarized emis­
sion, their roughness and lower density increase the horizontal emission by reducing
the Fresnel reflection o f the upwelling radiation from below (Fung and Chen, 1981;
Remy and Minster, 1991). Based on this relationship, Shuman and Alley (1993)
showed that a sustained decrease o f the SSM /I 37V/37H ratio in the summertime is
often indicative of a hoar formation event. Such a sustained decrease is observed in
most summers o f the 1978-1994 coverage period, and were used to establish a proxy
for the extent of hoar formation.
Periods o f five days or more that show a sustained decrease in this ratio are
identified, and the cumulative change in the ratio for each summer is calculated. By
dividing the cumulative decrease in a given season by the mean annual decrease for
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98
the coverage period (1979-1994), an index for the amount of surface hoar formation is
obtained. This index is such that a value o f one indicates an average hoar formation
year; a value in excess of one indicates above average hoar formation, and a value less
than one is indicative o f below average hoar formation. The index is then weighted
and used to scale the brightness temperature, in order to account for the hoar effects.
Time series o f the 37V/37H ratios for each year of coverage are shown in Figure 6.2,
along with the hoar index for that year.
The weight of this scaling param eter is determined by running the DISORT
model for a typical case at Summit in which 1.5 cm o f hoar forms during the summer
(C.A. Shuman, personal communication). The percentage of contribution from this
“average” hoar layer as determined by the model is used to scale the hoar index, and
this scaled index is then applied to the observed brightness temperatures. In this way,
the variability is accounted for in the appropriate proportion, and a brightness temper­
ature more dependent on accumulation can be achieved. The method is crude, but
does provide the first attempt at accounting for the extent of surface/near-surface hoar
formation in the firn model.
6.4 In situ accumulation estimates: ice core interpretation
Ice cores have provided one o f the most commonly accepted bases for local
scale snow accumulation estimates on the ice sheet. In addition to their inherent value
for climatological investigations, they also help provide a basis for validating alterna­
tive methods for accumulation estimates (e.g. Bromwich et al., 1993). These esti­
mates are made by determining the mass o f firn that lies between various peaks and
troughs in oxygen-18 isotope concentrations (SO18) which indicate annual layers (dis­
cussed in Bolzan and Strobel, 1994; see Fig. 6.3). A significant problem arises in that
each winter isotopic trough is assumed to occur in December o f the given year, and
each summer peak is assumed to occur in June. These dates may be off by two months
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99
s
is
s
to
03
O)
o>
CO
tn
to
o>
0)
CO
Ol
o>
o
cn
is
IS
o
1s
CD
03
03
R
*
^
if
i
S <
x <r
8
o
^
8
K3
2
co
(T>
?
8
Figure 6.2. Plots of the 37V/37H ratio for the Summit pixel for 1979-1994. Also
shown are the hoar indices for each year calculated by dividing the magnitude sus­
tained decrease in the ratio in a given year, by the average for the full period. The xaxis is the days past SMMR launch, while the y-axis is the 37V/37H ratio.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
<5**0
- SO - 4 5 - 4 0 - 3 5 - 3 0 —25
15
SIT E
15
10
71
77
«
u
74
73
£
72
X
D.
•
0) r >
o 51
70
II
(B
15
55
1%=
52
10
C
500
A ctivity
10C 0
(cph
kg*’)
Figure 6.3. Plot of 8 0 18 for an ice core near Summit Greenland (Bolzan and Strobel,
1994). The peaks and troughs indicate the summer and winter levels respectively.
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101
in either direction (J. Bolzan, personal communication); thus resulting in an uncer­
tainty o f 4 months from one year to another - a time error o f 33%!
This uncertainty can be significantly reduced by determining the date of m ini­
mum and maximum brightness temperatures at the higher SSM/I frequencies, and
relating them to the time of minimum and maximum air temperature. The 37 GHz
vertical channel is best suited to such an application for primarily two reasons: First its
shallow penetration depth makes it highly responsive to surface conditions. The 37V
brightness temperature has been reported to respond within one day to surface tem per­
ature changes (Shuman et al., 1995). Second, the vertically polarized emitted intensity
is less sensitive to stratification than the horizontal (section 5.4.3). Therefore its varia­
tions are more closely related to temperature fluctuations than are those of the horizon­
tally polarized intensity.
To identify the actual dates represented by the observed 5 0 18 troughs or m in­
ima, the times of the lowest temperatures for which there was actually snow deposition
must be identified. A reasonable approximation to such a time can be made using a 30
day running mean and determining the center date of the coldest 30 day period. In
doing so. the coldest time period is identified, and assuming that there was precipita­
tion once in that time, the date of the trough can be identified to within approximately
± 15 days. Without in situ climate observations, there is no way o f knowing whether
or not there was precipitation in that time, but the estimate is still an improvement over
the December assumption by at least eliminating the temperature uncertainty.
Figure 6.4 shows time series of the 37V brightness temperatures at the Summit
for the entire SMMR-SSM/I coverage period. Also shown are two vertical lines, one
(solid) indicates the winter solstice of each year (originally assumed to be the approxi­
mate date of the 5 0 18 minimum), and the other (dashed) identifies the date of mini­
mum 37V brightness temperature. This minimum T^ is assumed to be a more accurate
estimate of the date of the 5 0 18 trough. Over the 16 year coverage period, the average
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10
Figure 6.4. 37V brightness temperature time series for 1978-1994 showing the dates
of minimum
based on a 30 day running mean (dashed line). Also shown are the
winter solstices of each year (solid line) for comparison. The average date o f m ini­
mum Tj, value is January 17, and the standard deviation is 31 days. The x-axis is the
days past SMMR launch, whiie the y-axis is the 37V brightness temperature.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
103
date of minimum temperature was January 17, and the standard deviation was 31 days.
By using the 37V signal to identify the dates of the annual horizons in the iso­
tope analyses, significantly more accurate estimates of the annual accumulation rates
can be made from the ice cores. Also, certain seasonal characteristics can be identified
such as how late or early temperature maxima and minima occurred each year; how
they varied from year to year; and how much snow fell between the summer and win­
ter. This simple method results in a substantial improvement in annual ice core inter­
pretation. It is applied to the ice core data from Summit (Bolzan and Strobel, 1994;
also discussed in Chapter 2, Section 4) for the years in which the core data overlap
with the was passive microwave data (1979-1987).
6.5 Accounting for temperatures
To compare model results adequately with observed brightness temperatures
from year to year, the interannual variability of snow temperatures must be removed
from the T b’s (i.e. eliminated as a variable). If mean annual snow surface tem pera­
tures are known, a modified version of Eq. 4.12 can be used to represent the associated
changes in brightness temperature. The relationship is:
A T b = eA Tm
(6.5)
W here ATb and ATm are the change in brightness and mean annual surface tempera­
tures respectively from year to year.
On annual scales, every degree Celsius of surface temperature change should
result in a T b drop o f e K. This assumes that the temperature drop propagates through­
out the emitting layers through the year. Even more accurate assessments of bright­
ness temperature/surface temperature relationships can be made by accounting for the
extinction characteristics o f the snowpack on smaller time scales (Sherjal, 1995).
Thus the effects of surface temporal variability on brightness temperature can be
accounted for if they are known.
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104
Because of its location near the center of the ice sheet and its high elevation,
the temperatures at Summit are largely radiatively driven (Barry and Kiladis, 1982).
However, there is convincing evidence that rapid warm events can occur frequently on
the ice sheet due to turbulent mixing in the inversion layer. This has been observed at
the ETH/CU camp and the Humboldt Site (K. Steffen, unpublished data) as well as at
Summit (C. Steams, unpublished data). Consequently, the temperature variability is
not only driven by the extent o f cloud cover which regulates the shortwave and long­
wave radiation, but also by the turbulent activity in the boundary layer.
W ork is currently underway to assess these surface temperatures (J. Stroeve,
work in progress), but presently, they are not available. As a result, comparisons
between microwave emission and observed accumulation for validation purposes can­
not be made. There is some merit, however, in comparing accumulation and hoar
development to brightness temperatures in order to see if their effects exceed the tem­
perature variability. In addition, though such an analysis is incomplete, the method
can still be established to which temperature effects can be added when they are
known.
In order to compare interannual T^, variations and accumulation estimates, the
brightness temperatures at Summit for the winter months, December, January, and
February were averaged for each year. A three month average was chosen in order to
dampen any interannual statistical variability and leave a more accumulation-depen­
dent and hoar-dependent brightness temperature. It is acknowledged that this approxi­
mation is not without errors, but in the absence of accurate surface temperature data, it
should minimize them. An analysis o f Summit data (C. Steam s, unpublished data)
shows that for the seven years from 1988-1994, the average winter (December - Feb­
ruary) showed approximately 5°C variability.
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105
6.6 Results and discussion
6.6.1 M odel run for Summit
The results o f the model run for Summit (Fig. 6.5) are very similar to those for
Inge Lehman. As expected the emissivity is higher, and the sensitivity to accumula­
tion variations and hoar development are less. These are both due to the fact that the
accumulation rate is more than twice as high at Summit as at Inge Lehman. For typi­
cal conditions at Summit, 200 mm w.e. accumulation (Ohmura and Reeh, 1991), and
1.5 cm hoar layer thickness (C. Shuman, personal communication), the hoar is
responsible for 2.6 percent of the emission. The hoar index is scaled accordingly (as
described in Section 6.3).
6.6.2 Comparisons to observed brightness temperatures
The comparison (Figure 6.6) shows that the effects of accumulation and hoar
development are most likely outweighed by the temperature component of the bright­
ness temperature. For the nine years o f overlapping accumulation and T b data (19791987), accumulation is loosely correlated to brightness temperature (R=0.55 at the
90% confidence level). The hoar index appears to have the same magnitude of corre­
lation, but inversely so (R=-0.51 at the 90% confidence level). This inverse correla­
tion is expected since extensive hoar development reduces the brightness temperature.
A fter applying the hoar index to the brightness temperatures, however, the correlation
disappears (R=0.07 at the 90% confidence level).
The observed relationship between hoar formation and brightness temperature
is reasonable and agrees with theory: as hoar development increases, the brightness
temperature decreases. The relationship between accumulation brightness tempera­
ture is also consistent as expected: increased accumulation raises the brightness tem­
perature. The fact that the two make sense, but then counteract one another to
eliminate any correlation, indicates that the dominant factor is the physical tempera-
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106
No Hoar Layer
0 .7 6
>
0 .7 4
’in
tn
tS 0 .7 2
cm Hoar Layer
0 .7 0
20
40
60
80
A n n u a l A c c u m u la tio n
0 .7 6
> ,
>
100
(c m )
2 m Accumulation
0 .7 4
'in
tn
0.72
0 .7 0
2 cm Accumulation
0
10
Hoar
L a y e r T h ic k n e s s
20
30
(m m )
Figure 6.5. Dependence o f microwave emissivity on accumulation and hoar layer
thickness at Summit (72°N, 38°W). The isolines in (a) are at 2 mm intervals, while
those in (b) are at 10 cm intervals, with the exception of the 2 cm line. As with Inge
Lehman, the sensitivity to hoar formation is much greater than to accumulation varia­
tions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
230
Accumulation Estimates from ice cores
Observed Mean Wintertime Brightness Tem perature
Brightess Temperature After Scaling By the Hoar Index
30
228
226
o 25
224
20
222
1980
1982
1984
1986
Date
1988
1990
1992
220
1994
Figure 6.6. 19V brightness temperatures before and after adjusting for the hoar devel­
opment. The presence or absence o f hoar can change the T^, by several K. Also shown
for comparison are the accumulation rates as derived from icecore analysis. Without
including temperature effects, there is essentially no correlation between the accumu­
lation and the brightness temperatures.
i
I
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108
ture. It most likely varies from year to the year to the extent that it overpowers the
effects o f the other factors.
6.7 Conclusion
The results indicate that the effects of hoar development and accumulation do
not exceed the temperature effects. Consequently, passive microwave based assess­
ments o f the accumulation rates cannot be made without the incorporation of tempera­
ture data. However, a method has been set up by which accumulation can be
compared to Tj, data once the surface temperature data become available.
In the establishment of this method, there have been two significant achieve­
ments. The first is an improvement in the interpretation of ice core data using 37V
brightness temperatures for annual interpretation. By determining the time of mini­
mum 37V brightness temperature each year, the date of minimum surface temperature
can be approximated; thus eliminating one o f the major uncertainties in ice core analy­
sis. The second achievement is an initial attempt at the characterization of hoar devel­
opment, by identifying sustained decreases in the 37V/37H T[, ratio, and calculating
the magnitude of these drops, a proxy for the hoar development is established. Such a
proxy is essential in the assessment of accumulation changes (as discussed in Chapter
5).
Since the observed T^ trend was only approximately 5 K in magnitude it is not
surprising that the temperature effects may be greater than the accumulation and hoar
effects. Unfortunately the analysis was limited to Summit because it is the only loca­
tion for which ice core data on accumulation were available. The observed trend near
the proposed TUNU North site (Figure 1.1) was approximately 18K during the SMMR
years, which exceeds any likely temperature effects. As a result, when core data are
obtained from TUNU-N, and surface temperature estimates are made, the model can
be validated and improved.
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109
7. Melt, accumulation, and temperature relationships
7.1 Introduction
The ice sheet mass balance is driven by climate conditions; however, there is
some uncertainty about its overall mass balance characteristics in a changing climate.
M elt is associated with conditions o f high temperatures, which, on the ice sheet, can be
enhanced by cloud cover and the accompanying downwelling longwave radiation.
These high tem peratures increase the atmospheric water vapor capacity and subse­
quently the hum idity gradient that can exist between the snow and the air. In addition,
less energy is required to convert wet snow to water vapor, since the latent heat of
vaporization is less than the latent heat of sublimation. These two effects combine to
increase the water vapor content in the air, and if precipitation follows, its amount will
be greater than under cooler conditions of little melt. The atmospheric water vapor
content can also be increased by enhanced evaporation by warm air over the nearby
water sources (Baffin Bay, Davis Strait, East Greenland Sea, and the Denmark Strait).
These air masses can advect more moisture onto the ice sheet than they would under
cooler conditions, which could increase the precipitation.
Alternatively, changes in temperature will induce changes in the synoptic
activity. The nature of these changes will also influence the precipitation and conse­
quently the mass balance conditions of the Greenland ice sheet. As a result, the accu­
mulation on the ice sheet could be reduced under conditions of warming, as suggested
by Ohmura et al. (in press).
Zwally et al. (1989) calculated a thickening of the ice sheet south o f 72°N lat­
itude of 0.23 m /yr from 1978-1986. Based on these calculations, Zwally (1989) sug­
gests that as temperatures increase, accumulation not only increases, but may increase
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
110
to the extent that it offsets any enhanced melt. Ohmura et al. (in press) on the other
hand suggest that in a warming scenario, accumulation on the ice sheet should in fact
decrease. These calculations are based on a high resolution general circulation model
(ECHAM3 with T106 horizontal resolution). In a CO 2 doubling (Scenario A, IPCC,
1991), they predict approximately a 5% accumulation reduction due to the weakening
of the Icelandic low in the east, and the reduced migration of cyclones from the Cana­
dian Arctic in the west.
To complicate the issue further, accumulation can impact m elt through albedo
feedbacks since fresh snowfall can have a very high albedo (0.95). The deposition of
fresh snow can significantly inhibit the melt processes by reflecting most of the incom ­
ing shortwave radiation, and reducing the solar heating of the snowpack. There has
been evidence of such an occurrence at the ETH/CU camp during the 1994 field sea­
son (Figure 7.1). On two occasions, when melt was just beginning, the deposition of
fresh snow interrupted the process. Immediately following the snowfall event, the
snow temperatures steadily dropped. This cooling of the snowpack continued until the
grains were sufficiently metamorphosed, the albedo was reduced, and increased
absorption led to a heating of the snowpack again.
Through changes in synoptic activity, and the feedbacks between melt and pre­
cipitation, the behavior of the ice sheet in a changing climate is uncertain. In this
chapter, the relationships between accumulation, melt, and regional temperatures are
investigated, and their impacts on one another are assessed. An understanding of these
relationships is important in determining whether Zwally's (1989) observations are
attributable to an increase in accumulation, which is in contrast with Ohmura et al., in
press), or some other phenomenon, such as a slowing of the ice sheet outflow. The lat­
ter has been suggested to have occurred at Dye 3 (65° 11' N , 43°49/ W, Fig. 1.1) as a
result o f the downward propagation of the stiffer post-Wisconsin ice (Reeh and Gundestrup, 1985).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ill
a)
p
-C
a.
(D
O
E
U
m
°
" 5
-10
Cl
E
<D
§ - 15
c
in
May 1C
Mc\ 17
May 24 May 31
Date
Jun 7
June 14
b)
£ 0.85
Snow Depth
Albedo
May 10
May 17
May 24 May 31
Date
Jun 7
80
Q
June 14
Figure 7.1. Snow temperature at 5 cm depth (a), and albedo and snow depth (b) at the
ETH/CU camp. Immediately after a snowfall, albedo values rose considerably and
temperatures dropped significantly, suggesting a possible feedback between the snow
deposition, and temperature/melt conditions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Finally, in contrast with the apparent thickening of the ice sheet, a warmer cli­
mate could bring with it enhanced basal melting at the outlet regions, which could has­
ten the glacial outflow (Iken, 1981). Therefore, if the ice sheet truly is thickening in
the southern portion, then the increased outlet flow is not adequate to offset either
increased accumulation or the slowed motion o f the stiffer ice. Although the ice sheet
mechanics are of significance to the mass balance, with calving accounting for roughly
40 percent o f the mass loss (Weidick, 1985), they are not directly manifested in melt or
accumulation, so they are not explicitly considered in this investigation. They are
implicitly considered, however, in the melt assessment by assuming that increased
m elt is associated with increased calving.
7.2 M ethod
M elt conditions are determined using the XPGR method discussed in Chapter
4, and the temperature data used are the annual averages of the six coastal stations also
discussed in Chapter 4. Accumulation estimates are taken from Bromwich et al.,
(1993) in which a parameterization of synoptic activity at 500 hPa and a simple oro­
graphic scheme are used to calculate precipitation. The assumption is made that there
is a strong direct correlation between precipitation and accumulation, with the two dif­
fering by approximately 9% due to evaporative losses (Ohmura and Reeh, 1991).
Bromwich et al. (1993) calculate precipitation as a sum of dynamic and oro­
graphic components of synoptic activity according to the following formula:
P = AQq1{M\VFI\ +Aj<77oo^850 '
(^.1)
where A0 and A] are empirically derived coefficients; q70o is the specific humidity at
the 700 hPa level; VFI is the vorticity flux index, which is a parameterization of verti­
cal velocity due to synoptic-scale cyclone activity (based on Chamey, 1949); Vg5g is
the geostrophic velocity at the 850 hPa level; and H is the terrain height of the Green­
land ice sheet. The first term on the right side of the equation is the dynamic compo­
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
nent, and the second is the orographic component (The method is described in
complete detail in Bromwich et al., 1993.). Using results from National M eteorologi­
cal Center (NMC) geopotential height analyses at the 500 and 850 hPa levels, they cal­
culated total annual precipitation in Greenland for the years 1964-1988.
The estimates by Bromwich et al., are large scale estimates, and have been well
supported by an independent atmospheric w ater budget analyses (Robasky and Bro­
mwich, 1994). Since the objective of this comparison is large scale accumulation and
melt relationships, the results from Bromwich et al., (1993) provide the best basis for
comparison. The common period for which there are accumulation, melt, and temper­
ature estimates is from 1979-1988; thus the analysis is based on a ten year data sample.
7.3 Results
The results are shown in Figure 7.2. There is a significant increasing trend in
the melt, which is strongly correlated with the summertime coastal temperature varia­
tions. These have been discussed thoroughly in Chapter 4 and will not be presented
here. Precipitation, however, exhibits no statistically significant trend for the ten years
examined. Furthermore, there is no correlation between melt and accumulation. Melt
does not seem to increase or decrease preferentially during years o f high accumula­
tion. nor does accumulation show any bias one way or the other under high or low melt
conditions.
The accumulation does show some slight, negative correlation with annual
temperature anomalies (R=-0.49 at the 80% confidence interval). The relationships
are not as highly correlated as those o f melt and temperature; however this is expected
since melt is an unstable, positive feedback, while accumulation is not, and small tem ­
perature perturbations are more clearly manifested in melt variability. The correlation
does, however, suggest that the effect of low temperatures is to increase precipitation,
while higher temperatures reduce precipitation. This may in part be due to the
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114
°)
1000
Annuol Accumulation
Mean melt extent
2.0x10 ,5
aj
s
800
E
c
600 _o
o
E
400 a
<j
1.5x10,5
X
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Figure 7.2. Relationships between accumulation and melt extent (a) and precipitation
and annual temperature anomaly (b). There is no correlation between melt extent and
snowfall, however, there is a slight negative correlation between temperature and
accumulation (R=-0.49)
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115
increased water vapor capacity of the air, but it is more likely a result of the suppres­
sion o f the synoptic activities that cause precipitation on the ice sheet, as Ohmura et al.
(in press) suggest.
Comparisons between the temperature and accumulation values in Fig. 7.2
suggest that a 1°C tem perature rise is associated with a 7%, or 49 km3w.e. (49 Gt)
increase in annual accumulation. However, the Brom wich et al. (1993) estimates do
not account for the enhanced sublimation due to the movement (shrinking) o f the 0°C
isotherm toward the center of the ice sheet. This retreat can increase the mass loss due
to sublimation, by 1.4%/°C (Steffen, 1995). By including this additional estimate, the
reduction in accumulation may be as much as 8.4% (59 km 3w.e.) for a 1°C warming.
This is greater than Ohm ura et al.’s 5% estimate for a 2-4°C warming in the CO 2 dou­
bling scenario (Ohmura et al., in press). The most likely reason for the large discrep­
ancy are the two different estimation methods; a high resolution long-term GCM
analysis, vs. a param eterization o f synoptic activity and observational relationships on
short time scales. Though they differ in exact magnitude, the two methods agree in
sign. Such agreement offers further credence to the idea that under conditions of
warming, the accumulation will decrease. It should also be stressed, however, that the
correlation, though significant, is fairly weak. To better understand the relationships, a
longer time series is required.
Considering the potential state o f mass balance in a warming scenario, it is evi­
dent that a warming will bring with it enhanced melting of the ice sheet (Chapter 4).
Assuming that calving and evaporation are directly related to melt extent, then the
mass loss will obviously increase in a warming scenario. In light of the observed neg­
ative correlation between accumulation and temperatures, it also appears that a warm­
ing scenario will bring with it a slight reduction in accumulation. With increased mass
output, and reduced mass input, a net loss is expected, even on short time scales.
Recalling (Ch. 4) that a 1°C temperature rise is associated with a 49% increase
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
in melt extent, and assuming that the total ablation is directly proportional to the melt
extent, it is possible to m ake a very rough estimate of the mass balance in a warming
climate. For a current ablation o f 295 Gt (Weidick, 1985), the loss for a 1°C increase
is 140 Gt, neglecting changes in calving, which should make the estimate even larger.
Combined with the 59 km3w.e. above, the net mass balance should be -200 Gt. This
is the equivalent of 0.5 mm of sea level rise. While these estimates are quantitatively
limited by the amount o f data, and uncertainties in the methods, they should at least be
qualitatively valid.
7.4 C onclusion
There appears to be no relationship between melt extent and accumulation,
which suggests that any feedback effects between the two are negligible on large
scales. There is, however, a slight negative correlation between temperatures and
accumulation. The relationship is such that a 1°C temperature rise would roughly
accompany an 8.4% reduction in accumulation. The combination of this reduced
accumulation along with increased melt for even small rises in temperatures, implies
that under conditions of greenhouse warming on the order of 1°C, the mass balance is
most likely negative. It further implies that the observed thickening of the ice sheet is
less likely due to accumulation increases, and more likely a result of slowed ice out­
flow, as suggested by Reeh and Gundestrup (1985).
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117
8. Summary and Conclusions
The Greenland ice sheet is an integral part of the Earth system. Many have
sought, and are seeking, to understand its behavior in our ever changing climate, and
as with any research of matters complex, convergence toward a complete understand­
ing is a continual process. The objective of this work has been to improve the under­
standing of the vital role o f the Greenland ice sheet in the Arctic and global climate.
Toward that end, a number of important results have come out of this investigation of
passive microwave remote sensing applications to mass balance studies of the Green­
land ice sheet.
8.1 Data continuity
The first simple, yet essential, result of the research has been the establishment
of instrument cross-calibration coefficients for long term SMMR and SSM/1 studies.
These do not apply simply to investigations of the ice sheet, but to studies of any sur­
face on the Earth. The relationships between SMMR and SSM/I F8 instruments have
been examined by Jezek et al. (1991), and have provided the necessary connection
between time series analyses that span the coverage period of both instruments, 19781991. Through this current research, the relationships and cross-calibration coeffi­
cients between the SSM/I F8 and FI 1 instruments have been determined. As a result,
more accurate analyses of passive microwave data that extends beyond 1991 to the
present can be conducted.
Furthermore, a scheme has been set up for all future passive microwave studies
using additional SSM/I or SSM/I-like sensors. The F8 instrument has been established
as a baseline instrument to which all subsequent SSM/I, and past SMMR can be refer-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
enced. This baseline was chosen because m any of the SSM /I algorithms, such as ice
concentration and wind speed algorithms, were developed and validated for the F8
instrument. Thus for the best consistency, with minimal impact on existing results and
data products, the F8 provides the best baseline, and any deviation between it and
other instruments should be attributed to the other instruments. This is an arbitrary
choice, but it is one that maximizes consistency between data sets. As long as there is
overlap between instruments, each can be cross-referenced to its predecessor until the
relationships between the sensor in question, and the F8 instrument is established.
8.2 M elting o f th e snow pack
In this work, m elt has been shown to exhibit a distinct signal in the cross-polar­
ized gradient ratio (XPGR), and by applying a sensor-varying threshold to the XPGR,
the spatial extent o f m elt can be determined. The XPGR m ethod is less sensitive to
spatial temperature variations, seasonal temperature effects, and atmospheric interfer­
ence than any of the existing single-channel algorithms (e.g. Mote et al., 1993; Zwally
and Fiegles, 1994; M ote and Anderson, 1995). In addition, because o f the varying
penetration depths of the two channels used, the XPGR method can detect some sub­
surface melt, and is less influenced by short-term surface signals than is the method of
Mote and Anderson (1995). The advantage o f such a phenomenon is that a truer cli­
mate signal is given, but a slight disadvantage is that surface freezing may go undetec­
ted. Thus it is best for climate studies, but is limited in application to albedo
parameterizations during refreeze. A combination o f methods, however, should yield
some information about the vertical extent o f snowmelt in adition to the spatial extent.
Using the XPGR technique, melt extent was examined for 16 years o f SMMRSSM/I coverage (1979-1994). M ean melt area was found to increase at a rate of 4.5%
per year during the years, 1979-1991 (Figure 4.12). This was correlated with an
increasing temperature trend o f 1.1 °C, which suggests that a temperature increase of
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119
1°C would be accompanied by a melt area increase o f 72,000 km 2. Such a value
exceeds ± 1 standard deviation for the 16 year time period. This increasing melt trend
appears to have been abruptly interrupted in 1992, however, following the eruption of
M ount Pinatubo.
In addition, the frequency and seasonal extent of melt has been identified for
each pixel on a month-by-month and composite basis (Figures 4.9 and 4.10 respec­
tively). M elt is most extensive in late July and early August (Figure 4.8). The areas
showing the most melt are those o f gentle slopes: the western slope o f the ice sheet
near Jakobshavn, and the northeastern region.
Using the XPGR method, melt conditions on the Greenland ice sheet can be
monitored in space and time. Such capabilities are useful for understanding how the
Greenland ice sheet responds to our changing climate. In the future, these melt
conditions can be compared to such climatological conditions as atmospheric
circulation, temperature, sea ice extent, etc., and they can be incorporated into climate
models, thus providing a better understanding of the intimate links between the
Greenland ice sheet, and the regional and global climates.
8.3. Accum ulation, hoar, and m icrowave brightness temperature
The impact of accumulation and hoar formation on the microwave signal has
been modeled with a m ultiple-scattering DISORT model. The model results (Figure
5.7) show that the presence o f hoar in the snowpack has a large effect on the micro­
wave emission. First, the presence o f hoar causes accumulation changes to have a
greater impact on the emissivity than they would in the absence o f hoar. This is
because the large scattering characteristics o f hoar tend to reduce the contribution of
deeper snow layers, thus making the emission more sensitive to surface variability.
Second, the hoar has a greater impact on the microwave emission than any
realistic accumulation changes. With hoar reducing the emission by approximately
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120
2.8%, a 10% change in hoar thickness can have as much impact as a doubling of accu­
mulation. Therefore, any application o f microwave observations to the assessment of
changes in accumulation requires the successful parametrization of the hoar.
Finally, the sensitivity of microwave emission to accumulation changes and
variations in hoar development is greatest in low accumulation areas. This explains
the strength of the observed trends (Figure 5.3) in the low accumulation areas of north­
eastern Greenland. In addition, the relationships between hoar, accumulation, and
microwave emission indicate that the observed trends are probably a combination of
changes in both hoar development and accumulation. The former is most likely firstorder effect, while the latter is second-order.
8.4. A pplication to S um m it, G reenland
In the comparison with ice core estimates of accumulation to Tb data, no real
relationships could be extracted due to the lack o f surface temperature data, however
some significant advances were m ade in the study. First, a comparison technique has
been developed by which the radiative transfer model o f the firn can be adapted to any
o f the dry snow areas o f Greenland, if temperature and accumulation characteristics
are known. In addition, the first initial attempt at the characterization of hoar develop­
ment has been made. By identifying sustained decreases in the 37V/37H Tb ratio, and
calculating the magnitude of these drops, a proxy for the surface hoar development is
established. Such a proxy is essential to the assessment o f accumulation changes.
Finally, an improvement has been made in the interpretation of annual ice core data
using 37V brightness temperatures. By determining the time of minimum 37V bright­
ness temperature each year, the date o f annual minimum surface temperature can be
approximated; thus eliminating one o f the m ajor uncertainties in ice core analysis.
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121
8.5. Temperature, accum ulation, and m elt relationships
The relationship between ice sheet melt extent and regional temperatures has
been clearly established: a 1°C temperature rise results in a 49% increase (+35% at the
90% confidence level) in the mean area m elt extent of the ice sheet. Temperature also
shows some slight negative correlation with accumulation (Figure 7.2), such that a
1°C rise is associated with a 8.4% decrease in accumulation (+8.1% at the 90% confi­
dence level). Although there are limits to quantifying the overall state of mass bal­
ance, the relationships do indicate that in a warming climate, ablation can be expected
to increase, and accumulation can be expected to decrease. Thus the overall mass bal­
ance of the ice sheet should be negative (-200 Gt). This is in accordance with the
model results of Ohmura et al. (in press), but in contrast to the suggestion of increased
accumulation made by Zwally (1989). Finally, the feedbacks between accumulation
and m elt do not appear to be significant.
8.6 Future work
W hile a number o f significant relationships have been established, there is still
much to do in the way of improving the use o f passive microwave observations for the
study of the climate and mass balance of the ice sheet. In the case of melt, a major
limitation to all passive microwave melt algorithms is that they are simply binary.
Either a pixel exhibits m elt characteristics or it does not. By combining methods, one
that is sensitive to surface conditions (Mote and Anderson, 1995), and one that is more
capable of detecting deeper melt, such as the XPGR technique, an understanding of
the depth of melt should be feasible. The result would be a more comprehensive
understanding of the melt conditions of the ice sheet. Such work has just begun
(Anderson, et al., in press), and shows promise for more complete melt assessment.
In the case of accumulation estimates and hoar formation characteristics, work
is really still in its infancy. Now that the significance of hoar has been demonstrated,
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122
more rigorous means o f detecting and modeling it m ust be developed if accumulation
estimates are ever to be obtained from brightness temperatures. It is unfortunate that
the only available ice core data was from Summit, where observed Tb variations were
slight, and there was limited information on the grain structure. The 1996 PARCA
field campaign at TUNU North will provide comprehensive data on the grain size dis­
tribution, grain shape and orientation, and accumulation rates, in the emitting layers of
the ice sheet. All of these are essential to the accurate modeling of the fim. When the
data are collected, the model can be refined and improved, and the fim accumulation
and metamorphic characteristics can be better assessed.
The Greenland ice sheet is a remarkable place - remote, pristine, and of great
importance to environments far beyond its borders. This thesis helps fit together some
pieces of the very complex puzzle of the role o f the Greenland ice sheet in our everchanging climate.
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123
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