1
Retrieval of Atmospheric Water Vapor and Temperature
1
Profiles
over Antarctica
through Iterative Approach
2
3
Zhimeng Zhang
1
, Shannon Brown
2
, Andreas Colliander
2
4
1
California Institute of Technology, Pasadena, CA, USA
5
2
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA
6
Correspondence to
: Zhimeng Zhang (zhimeng@caltech.edu)
7
Abstract
.
Retrieving atmospheric water vapor and temperature profiles presents considerable challenges over land
8
surfaces
using microwave radiometry
due to uncertainties associated with estimating background surface emissions.
9
In response, we have devised an approach that integrates the atmospheric retrieval algorithm with the background
10
emission algorithm, establishing an iterative loop to refine the accuracy of atmospheric profiles. Leveraging optimal
11
estimation techniques with sounding channels spanning from Ka
-
to G
-
band obtained from ATMS, we successfully
12
retrieved atmospheric temperature and humidity profiles
across space and time
. These retrieved atmospheric profiles
13
undergo continual updates throughout each iteration, exerting influence on subsequent surface retrievals. This iterative
14
process persists until convergence is achieved in the atmospheric retrieval. The algorithm's novelty lies in its fusion
15
of surface retrieval with atmospheric retrieval, thereby enhancing overall accuracy.
We
validated the retrievals
against
16
radiosonde data.
Our iterative algorithm proved to
be
efficient and accurate in retrieving temperature profiles
with
17
surface emissivity and in detecting melting events. Though our algorithm
was
able to capture the water vapor
18
variations,
the results showed that
to obtain accurate absolute values of the water content
an
independent
ly retrieved
19
surface emissivity
is required
.
20
21
1
Introduction
22
23
The Greenland and Antarctica ice sheets play a crucial role in the ongoing global sea level rise due to the
increasing
24
melting of these vast ice reserves
[Rignot et al. 2011]
. This emphasizes the pressing need to closely monitor and
25
comprehend the mechanisms driving the accelerated melt events taking place
[Noble et al. 2020]
.
To
effectively
26
monitor and analyze the ice sheets, it becomes paramount to have a deep understanding of the atmospheric conditions
27
that directly impact these regions
[Le clec’h et al. 2019]
. This understanding is vital for accurately predicting the future
28
evolution of these ice masses
[Le clec’h et al. 2019]
.
29
T
he current atmospheric retrievals encounter certain challenges, particularly concerning uncertainties in
30
estimating the surface emission background. These uncertainties are further compounded by the unique characteristics
31
of the polar ice sheets, which typically
have a
dry atmosphere, rapidly changing surface emissivity during the melting
32
seasons, and
a
relatively high background emission, all of which contribute to the complexity of the problem
[
Miao
33
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2
et al., 2001]
.
Traditional retrieval
s are hindered by the lack of independent surface emissivity and the uncertainties in
34
estimation of the background surface emission.
35
To address these challenges, we propose implementing a strategy that involves integrating the atmospheric
36
retrieval process with a surface emission estimation within an iterative loop. This approach aims to enhance the
37
accuracy and reliability of the
retrieved atmospheric temperature and humidity profiles
, leading to a
better
38
understanding of the mechanisms influencing the melting of the Greenland and Antarctica ice sheets.
39
The Advanced Technology Microwave Sounder (ATMS)
instruments
on board polar orbiting satellites serve the
40
essential function of conducting temperature and water vapor sounding in the atmosphere
[Goldberg et al. 2006, Muth
41
et al. 2005]
. With a total of 22 channels, they are equipped to receive and measure radiation from various layers of the
42
atmosphere. These spectral positions include the oxygen band spanning 50
–
58GHz, the two distinctive water vapor
43
lines at 22GHz and 183 GHz, and specifically designed transparent window channels.
44
W
e implemented our iterative retrieval algorithm to analyze the ATMS data collected specifically from 17
45
r
adiosonde stations in the Antarctica region throughout the year 2016
. We chose 2016 because of the
extensive
melt
46
anomaly over
the Ross Ice Shelf
during the 2015
-
2016 austral summer
(e.g.,
Nicolas et al., 2017;
Mousavi et al., 2022;
47
de Roda Husman et al., 2024;
Hansen et al., 2024)
that provides a particularly suitable
conditions for testing the effect
48
of changing surface emissivity on the atmospheric retrievals
. This
analysis allowed us to examine the validity and
49
limitation
s
of the iterative algorithm.
50
51
2
Observations
52
2.1
Observation Data
-
ATMS data
53
54
The Advanced
Technology
Microwave Sound
er (ATMS)
onboard polar
-
orbiting satellites
are
meant for the
55
atmosphere’s
temperature and water vapor sounding
[Goldberg et al. 2006, Muth et al. 2005,
K
im et al. 2014, 2020].
56
It
ha
s
2
2
channels
to receive and measure radiation from different layers of the atmosphere to obtain global data on
57
tropospheric humidity and temperature
at either quasi
-
vertical or quasi
-
horizontal polarization
.
Table 1 lists t
he
58
channels’
radiometric characteristics
,
and Figure
3
shows
the spectral p
ositions of these channels
with respect to the
59
atmospheric opacity caused by oxygen and water vapor.
The cross
-
track scanning microwave sensors measure
60
microwave thermal emission from the Earth and its atmosphere in the
oxygen band of 50
–
58GHz, the two water vapor
61
lines at 22
GHz and 183 GHz, and window
channels
(see Fig.
3
), with a swath width of approximately 2600 km. The
62
temperature information
of the atmosphere
is
obtained from Channels
3
-
15
.
Channels 18
-
22
are centered
at
the 183.31
63
GHz water vapor line
but with
a
successively narrower bandwidth from
±
7GHz
to
±
1GHz,
giv
ing
humidity
64
information on
the
successively higher
troposphere.
The beam width of the ATMS varies across its frequency channels:
65
it is 1.1
degrees for channels in the 160
-
183 GHz range, 2.2 degrees for the 80 GHz and 50
-
60 GHz channels, and 5.2
66
degrees for the 23.8 and 31.4 GHz channels
[
K
im et al. 2014, 2020]
. Both SNPP
(Suomi National Polar
-
orbiting
67
Partnership
)
and the
NOAA
-
20
(National Oceanic and Atmospheric Administration
20, also known as Joint Polar
68
Satellite System 1, JPSS
-
1
) satellite
s
orbit at an altitude of approximately 830 km. This results in instantaneous spatial
69
resolutions on the ground at nadir of about 16 km, 32 km, or 75 km, depending on the channel.
Due to the cross
-
track
70
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3
scanning approach, t
he instrument provides observations at a wide range of
incidence
(off
-
nadir)
angles. To ensure
71
accuracy, we only use observations with an incidence angle less than 60°, as the instrument footprint increases
72
proportionally to
1
푐표푠
!
휃
⁄
.
The ATMS data used in this work were obtained from the Comprehensive Large Array
-
73
data Stewardship System (
CLASS
) of NOAA.
74
75
Fig
ure
1
shows the zenith opacity of a typical polar dry atmosphere for the ATMS frequency range. The opacity is
76
dominantly caused by water vapor and oxygen in the atmosphere. The contribution of nitrogen, orders of magnitude
77
smaller and without any spectral line at this frequency range, can be neglected. The total opacity is computed by
78
integrating the opacity per unit length from the top of the atmosphere toward the surface
[Meeks and Lilley 1963]
.
79
Channels 1, 2
, 16
,
and
1
7
are located at transparent window regions, where the opacity is low.
T
he atmosphere
80
becomes opaque to a channel at the layer of the atmosphere where the integral of the total opacity reaches the value
81
of one [Petty 2004]. The
Jacobian
s
of the
temperature and water vapor
channel
s
peak whe
n
the opacity becomes one.
82
For the window channels
, the overall opacity is much less than one.
These
c
hannels can see through the atmosphere
83
and are sensitive to Earth’s surface emission
; therefore,
they
can
b
e used
for deriving surface emissivity
.
However, at
84
oxygen (58
GHz) and water vapor (183
GHz) absorption bands, the observed brightness temperature
is
not
very
85
sensitive to the surface emission. The
surface
emissivity
at these frequencies
will be derived using
the
adjacent
86
c
hannels that have relatively low opacity: CH3 at 50.3
GHz will be used to derive the emissivity in the range of 50.3
-
87
57.29
GHz (CH3 to CH15) at QH polarization; CH18 at 183.31
±
7 GHz for the emissivity near 183.31
GHz (CH18
88
to CH22
) at QH
polarization.
In all, we derive surface emissivity for the window channels 1 (23.8 GHz), 2 (31.4 GHz),
89
3 (50.3 GHz), 16 (88.2 GHz), 17 (165.5 GHz), and 18 (183.31
±
7GHz) and
assume the emissivity variation is linear
90
between the frequencies.
91
92
Figure
1
.
Spectra positions
of 22 ATMS channels, on top of zenith opacity due to oxygen and water vapor.
93
94
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4
Table.1
95
Channel Number
Central frequency [GHz]
푁퐸
∆
푇
[K]
Polarization
1
23.8
0.7
QV
2
31.4
0.8
QV
3
50.3
0.9
QH
4
51.76
0.7
QH
5
52.8
0.7
QH
6
53.596 ± 0.115
0.7
QH
7
54.4
0.7
QH
8
54.94
0.7
QH
9
55.5
0.7
QH
10
57.290344
0.75
QH
11
57.290344 ± 0.217
1.2
QH
12
57.290344 ± 0.3222 ± 0.048
1.2
QH
13
57.290344 ± 0.3222 ± 0.022
1.5
QH
14
57.290344 ± 0.3222 ± 0.010
2.4
QH
15
57.290344 ±
0.3222 ± 0.0045
3.6
QH
16
88.2
0.5
QV
17
165.5
0.6
QH
18
183.31 ± 7.0
0.8
QH
19
183.31 ± 4.5
0.8
QH
20
183.31 ± 3.0
0.8
QH
21
183.31 ± 1.8
0.8
QH
22
183.31 ± 1.0
0.9
QH
96
97
Figure
2
shows t
he
temperature (third column) and
w
ater vapor
(fo
u
rth column)
Jacobians
at
all 22
ATMS
c
hannels
98
for
June (
austral winter;
upper row)
and
December (
austral summer;
lower row)
atmospheres
, representative
of
99
Antarctica atmosphere
.
The
Jacobians are
calculated by increasing the water vapor
and
temperature at each vertical
100
layer to the orange dashed line. Therefore, a positive value implies that adding water vapor or increasing temperature
101
will increase the radiance observed by the instrument and vice versa.
The Jacobian shows the sensitive altitudes of
102
each channel. Near
the
oxygen absorption band, CH3 to CH15 are sensitive to successively higher altitudes, up to ~60
103
km above the sea level.
Channels 18
–
22 are located
near
the water vapor line at
183.31 GHz. The atmospheric opacity
104
for these channels differs significantly, mak
ing
these channels sensitive to different layers of the atmosphere. The
105
bandwidth of these channels decrease
s
with the channel number,
with
Channel 22 being the narrowest and Channel
106
18 being the broadest. Water vapor Jacobians for Channels 18
–
22 show that the channels are sensitive to different
107
layers of the atmosphere with a sensitivity
of
about a few kilometers.
For
the
atmosphere above ~10 km, the water
108
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vapor content drops so low that common perturbations cannot be detected by ATMS. The Jacobians shown
are
from
109
the
nadir view (0
o
incidence
angle).
Jacobians corresponding to off
-
nadir angles peak at slightly higher altitudes
110
because of the longer path length the radiation
must
travel.
111
112
113
Figure
2
.
Typical Antarctica
atmospheres for
winter (upper row)
and
summer (lower row) weathers at WAIS DIVIDE
114
(79.5
o
S, 112
o
W)
.
The plots show t
he temperature
profile
(left column) and
the
specific humidity
profile
(second
115
column)
, the t
emperature
Jacobian
(third column)
,
and
the
water vapor
Jacobian
(forth column) for all 22 ATMS
116
Channels.
The
Jacobians are based on nadir view (0
o
incidence
angle).
117
118
2.2
The
Prior
–
MERRA
-
2
119
120
With ATMS capturing microwave thermal emission, our approach involved using Optimal Estimation (OE) to
121
transform these observations into the desired variable of interest.
OE
, as outlined by Maahn et al.
(
2020
)
, acts as a
122
widely accepted physical retrieval method that takes into account various factors such as measurements, prior
123
information, and associated uncertainties. By leveraging Bayes’ theorem,
OE
aims to derive the most efficient solution
124
for determining the atmospheric state, particularly when retrieving temperature and humidity profiles from Microwave
125
Radiometer (MWR) data. The role of the prior information in this process
is crucial
. We chose to use
the
Modern
-
Era
126
Retrospective analysis for Research and Applications, version 2 (
MERRA
-
2
)
[17]
atmospheric reanalysis
as the prior
127
for the pressure, temperature, water vapor
,
and liquid water profiles (e.g., Rosenkranz. 2001).
This dataset, known as
128
"tavg3_3d_asm_Nv," provides a comprehensive overview
of the atmosphere
with its
three
-
hour averaged structure
129
comprising 72 vertical layers and a spatial resolution of 0.625 degrees in longitude and 0.5 degrees in latitude. To
130
account for surface characteristics such as skin temperature, temperature/wind speed at
two
meters, and surface
131
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pressure, we integrated MERRA
-
2 single
-
level diagnostics data labeled as "tavg1_2d_slv_Nx". By merging the three
-
132
dimensional assimilated meteorological data with the single
-
level diagnostics data, our analysis extends across 73
133
vertical layers starting from
two
meters above the surface and extending beyond 70 kilometers into the atmosphere.
134
135
2.3
Radiosonde data
136
137
In the Antarctica region, a network of radiosonde stations
is strategically positioned to capture in
situ measurements
138
of atmospheric profiles. These stations
contribute to the Integrated Global Radiosonde Archive (IGRA), collected
139
once per day, albeit at
a
relatively low time resolution
[Durre et al. 2006]
. However, efforts such as the
Atmospheric
140
Radiation Measurement (
ARM
)
West Antarctic Radiation Experiment (AWARE) have bolstered observational
141
capabilities by providing high t
emporal
resolution radiosonde data at key locations such as the West Antarctica Ice
142
Sheet (WAIS) and McMurdo
[Lubin et al. 2017]
. During 2016, AWARE collected atmospheric profiles every minute,
143
offering unprecedented insights into the dynamic atmospheric processes in this critical region.
Observing stations in
144
Antarctica that measure ground
-
based meteorological data are located mostly around lower elevations and coastal
145
areas. We only found two stations on the high plateau (above 2500 m), including South Pole Station (90
o
S)
[Xu et al.
146
2019]
and WAIS DIVIDE (79
o
S)
[Lubin et al. 2017]
, that have measurements during 2016.
The radiosonde
147
measurements reveal detailed features in temperature and humidity profiles at high altitude resolution ranging from
148
20
m to
a
few hundred meters.
149
150
In our study, a
n
evaluation of our iterative retrieval algorithm was conducted across the network of
nine
radiosonde
151
stations in the Antarctica region throughout 2016. This testing allowed us to assess the algorithm's validation and
152
limitations under diverse atmospheric conditions, ice sheet melting conditions
,
and geographical settings.
W
e
153
compared the retrievals with the
temperature and humidity
profiles
gathered from the radiosondes. This comparative
154
analysis served as a benchmark for evaluating our iterative retrieval approach. Through this validation process, we
155
gained insights into the algorithm's efficacy in capturing the atmospheric properties and ice sheet conditions across
156
the Antarctica region. Furthermore, the validation results guid
ed
refining and optimizing our retrieval methodology
157
for enhanced accuracy and utility in atmospheric studies and
ice sheet melting events
assessments.
158
159
Table.2
160
IGRA Daily
AMUNDSEN
-
SCOTT
90.0
o
S
0
o
NOVOLAZAREVSKAJA
70.7678
o
S
11.8317
o
E
SYOWA
69.0053
o
S
39.5811
o
E
DAVIS
68.5744
o
S
77.9672
o
E
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161
162
3
Iterative Retrieval Algorithm
163
3.1 Iterative Process
164
165
We developed a channel
-
selective iterative approach to retrieve surface emissivity along with the atmospheric
166
temperature and humidity profiles
,
as illustrated in Figure
3
. The procedure begins with an initial estimation of surface
167
emissivity, which is then used to derive temperature and humidity profiles. Next, these profiles are utilized to refine
168
the surface emissivity in a continuous loop until the update in emissivity reaches a margin of 0.01. The final
169
discrepancy between observed and modeled brightness temperatures (the residual) is compared against the noise
170
equivalent
delta
temperature to assess the accuracy.
The noise equivalent delta temperature (NE
D
T) indicates the level
171
of instrument noise, which can be defined using the ideal noise equation for a total power radiometer such as ATMS
172
[Ulaby et al. 1981]:
173
∆
푇
=
푇
"#"
.
$
%&
+
0
∆
(
(
1
!
2
!
"
.... [1]
174
w
here
푇
"#"
is the system noise temperature (including atmosphere contribution),
퐵
is the bandwidth,
휏
is the
175
integration time and
∆
퐺
퐺
⁄
represents instrument gain fluctuations.
Any residual falling within 1.5 times the noise
176
equivalent temperature is deemed successful.
177
The outcome of the routine comprise
s
the profiles of temperature and humidity as well as the surface emissivity
178
for all frequency channels (23GHz to 183GHz). Choosing an initial emissivity value of
휀
0
as 0.8 across all frequencies
179
aligns with the average AMSU
-
A surface emissivity data in the Antarctic region
used in the past
[Spencer and William
180
1999]
. In
Figure
4
, we show the histogram of the AMSU
-
A recorded surface emissivity at 23GHz, 31GHz
,
and 50GHz
181
(
Ferraro et al. 2016
)
, with a median
value n
ear 0.8.
The AMSU
-
A emissivities are directly calculated from the satellite
182
observations in clear
-
sky conditions.
Typically, the iterative process converges within
six
iterations, enabling efficient
183
retrieval of the atmospheric temperature and humidity profiles along with the surface emissivity.
184
185
186
MIRNYJ
66.5519
o
S
93.0147
o
E
CASEY
66.2825
o
S
110.5231
o
E
MARIO ZUCHELLI STATION
74.6958
o
S
164.0922
o
E
MCMURDO
77.85
o
S
166.6667
o
E
ARM per minute
McMurdo Station
77.85
o
S
166.66
o
E
WAIS Divide
79.468
o
S
112.086
o
W
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187
Figure
3
.
Flow diagram of the iterative retrieval process.
The process start
s
with an initial guess of surface emissivity
188
to retrieve temperature and humidity profiles, which are then utilized to adjust the surface emissivity for subsequent
189
iterations. Residuals are determined as the disparity between observed and modeled brightness temperature and
190
assessed against the observation noise equivalent temperature. Any outcomes with residuals surpassing 1.5 times the
191
noise are regarded as unsuccessful and discarded. The final outcomes are the temperature and humidity profiles
192
alongside the surface emissivity.
193
194
195
196
Figure
4
.
In the iterative retrieval process, the starting value of
휀
0 is set at 0.8 for all frequencies based on AMSU
-
A
197
surface emissivity data in the Antarctic region. The histogram depicting AMSU
-
A surface emissivity records at 23GHz,
198
31GHz, and 50GHz shows a median value
near
0.8.
199
200
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3.2
Forward
M
odel
-
Radiative Transfer Model
201
202
RTTOV (Radiative Transfer for TOVS
1
) is a radiative transfer code widely used in atmospheric remote sensing
203
research
[Saunders et al. 2018]
. The model incorporates detailed representations of atmospheric properties, including
204
temperature, humidity, pressure,
and optionally, trace gases, aerosols, and hydrometeors, together with surface
205
parameters and viewing geometry
, allowing for accurate simulations of radiative transfer processes in diverse
206
atmospheric conditions.
RTTOV is
a fast radiative transfer model for passive visible, infrared
,
and microwave
207
downward
-
viewing satellite radiometers, spectrometers, and interferometers. RTTOV computes the top
-
of
-
208
atmosphere radiances in each of the
sensor
channels being simulated.
We incorporate a
P
ython interface written for
209
RTTOV v11.3.
The r
equired geophysical inputs of the model are humidity and temperature profiles, the surface skin
210
temperature, and the surface emissivity
.
The model was not only used to calculate radiances but also
to calculate the
211
associated Jacobians
:
212
퐾
)
(
휃
)
=
*
+
#
(
-
)
*
/
$
...[
2
a]
213
where j is the vertical grid index and
푥
)
can be
the water vapor
mass
mixing ratio (
Q
) i
n
fractional units
or temperature
214
(T) in Kelvin
215
푥
)
=
0
$
%
"
&
0
$
'()
or
푥
)
=
푇
...[
2
b]
216
The
푄
)
123
are identical to the profile for which the Jacobian is calculated.
This type of Jacobian shows the sensitivity
217
of
푇
%
to relative
changes in the humidity
/temperature
at each vertical grid
point. The profile is
assumed to be linear
218
between the
vertical
grid
points. The grid used
is equidistant in the logarithm of the pressure
;
hence
,
it is
approximately
219
equidistant in altitude.
220
221
3.3 Re
trieved Profiles
222
223
We utilized our iterative retrieval method
,
as
described
in Section
3
.1
,
on the ATMS data collected over the Antarctica
224
region
during 2016
. Fig
ure
5
displays an instance of the evolution of the retrieved
profiles
through multiple iterations
,
225
including
the temperature profiles (top left), specific humidity profiles (top right), and frequency
-
dependent surface
226
emissivity (bottom left) acquired after
six
iterations. The bottom right panel shows the residual divided by the
227
observation error.
As discussed in Section
3
.1, i
f the residuals for all frequencies/channels are under 1.5 times the
228
uncertainty, the model is considered to fit well. Following
six
iterations, we observe convergence in the iterative
229
process.
230
1
TOVS:
Television InfraRed Observation Satellite (
TIROS
)
Operational Vertical Sounder, a suit
e
of three
instruments that measure upwelling radiation from the atmosphere from which surface properties, clouds, and the
vertical structure of the atmosphere can be determined.
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10
The graphs show temperature profiles up to 20
km above sea level and specific humidity profiles up to 10
km above
231
sea level, where radiosonde data is accessible.
In the upper two panels, the purple curves display the radiosonde
in
232
situ
measurements, used to validate the iterative retrieval algorithm.
The radiosonde measurements reveal more
233
detailed features in temperature and humidity profiles at higher altitude resolution
s
ranging from 20
m to
a
few
234
hundred meters, which
the microwave
radiometer based
algorithm
s
are
unable to retrieve.
Despite these fine features,
235
the temperature profile obtained through iterations closely matches the radiosonde measurements
.
The specific
236
humidity below
6
km also shows a good agreement with the measurements. However, our retrieval method is not as
237
sensitive to specific humidity above
6
km, align
ing
with the contribution function in Fig.
2
and the lower humidity
238
levels observed above
6
km.
239
240
The brightness
temperature
coming from both atmospher
ic
and surface emission can be calculated using Equation
3
:
241
퐿
(
휈
)
=
∫
퐵
(
휈
,
푇
)
푑휏
$
&
*
+
[
1
−
휀
"
(
휈
)
]
∙
휏
"
!
(
휈
)
∙
∫
%
(
4
,
+
)
&
"
푑휏
$
&
*
+
휀
"
(
휈
)
∙
휏
"
(
휈
)
∙
퐵
(
휈
,
푇
"
)
,
...[
3
]
242
243
where
퐿
is the radiance at frequency
휈
;
퐵
(
휈
,
푇
)
is
P
lan
c
k
’s
law
;
휏
is the transmittance from
the
top of
the
atmosphere
,
244
and
휏
"
is the transmittance from
the
top of
the
atmosphere to
the
surface, both of which depend mostly on oxygen and
245
water vapor absorption;
휀
"
is the surface emissivity
,
while
1
−
휀
"
is the
respective
surface reflecti
vity
, and
푇
"
is the
246
surface skin temperature. The three terms
on the right
-
hand side
correspond to
the
upwelling atmospheric emission,
247
the
downwelling atmospheric emission reflected by
the
surface
,
and
the
surface emission respectively.
248
249
When the atmospher
ic
profiles are known, the observed brightness temperature from the top of the atmosphere can be
250
represented as a linear function of the surface emissivity. Therefore, by utilizing the atmospher
ic
profiles measured
251
by
the
radiosonde
s
and the brightness temperature observed by ATMS, we can
solve
the surface emissivity at the
252
ATMS observation frequencies
. This
is considered
as
the
reference
surface emissivity
here
(the black
dotted
line in
253
the lower left panel in Fig
ure
5
). Upon comparison with our iteratively retrieved surface emissivity (red curve), we
254
discovered that our retrieved results are highly consistent with the
reference
values. However, at 183
GHz (water
255
vapor absorption band), the surface emission becomes closely intertwined with the emission from near
-
surface water
256
vapor, making it challenging to accurately determine the value using our iterative algorithm
.
Consequently, our
257
iterative algorithm may not always provide accurate results at 183 GHz
(see Section 4.1)
.
By using the
reference
258
surface emissivity, the retrieved profiles displayed in the black
dotted
lines in the upper panels of Fig
.
5
represent the
259
best atmosphere profiles achievable with the ATMS 22 channels observations (optimal profile). The comparison
260
between the optimal profile and the iterative retrieved profile in the upper panel
s
indicated a high level of consistency.
261
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11
262
Figure
5
.
Retrieved temperature profiles (top left), specific humidity profiles (top right)
,
and frequency
-
dependent
263
surface emissivity (lower left)
over
six
iterations
(for
clarity
, only iteration
s
1, 3,
and
6 are
displayed
)
.
The l
ower right
264
panel shows the residual divided by
the
observation
error
(t
he model
’s fit
is considered good when the
absolute
265
residuals at all frequencies are less than
1.5
times the uncertainty
, indicated by the dashed lines)
. The iteration process
266
converges
within
six
iterations.
The gray curve shows the prior for
the
temperature
and
humidity profiles. In the
267
bottom two figures, the oxygen and water vapor absorption
frequency band
s
/channels are shaded in gray. In the upper
268
two panels, the purple curve shows the
r
adiosonde
in
situ
measurements. The black
dotted
line shows the
r
etrieved
269
profiles using the radiosonde
-
derived emissivity.
270
4
Validation and Discussion
271
272
4.1
McMurdo Station
273
274
The findings
over the radiosonde
stations
highlight
ed
the changes in surface and atmospheric conditions over the year
275
and their connections. We
compare
d
the
retriev
ed profiles
with
the
radiosonde measurements to demonstrate the
276
effectiveness and constraints of our iterative retrieval method.
277
278
The McMurdo Radiosonde Station is located on Ross Island at coordinates 77.85
o
S, 166.66
o
E. In 2016, radiosonde
279
observations
were obtained
with high time resolution at this station. The
Figure 6
histogram
display
s
the variance
280
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12
between the
atmospheric profiles derived by our iterative algorithm and the optimal profiles (as explained in Section
281
3.1). The left panel depict
s
the
temperature
difference
below 70
km height, while the right panel show
s the
specific
282
humidity
difference
below 10
km height, spanning the entire year of 2016.
E
ach panel
shows
the median value and
283
the
68%
confidence intervals (one
standard deviation
, or sigma
)
. The accuracy of
the
temperature
profile
retrieval was
284
high, with 68% falling within ±0.5K of the
reference
value. However, in the right panel, while most humidity
285
variations were detectable (to be further discussed in the next paragraph), the absolute value was not precise compared
286
to the measurement, with only 68% showing a difference within 30% of the actual profile. The humidity was strongly
287
linked to the surface emissivity at 183
GHz.
Fig.
7
shows
the histogram displaying the difference between the surface
288
emissivity retrieved
iteratively
and the
reference
value. The surface emissivity retrieved iteratively is highly accurate
289
within a range of ±0.01 for clear
-
sky transparent window channels like 23.8
GHz, 31.4
GHz, and 88.2
GHz. In the
290
oxygen absorption band between 50 and 58
GHz, most of the retrieved
surface
emissivity values fall within ±0.02 of
291
the
reference
value, aligned with the fact that retrieved temperatures have a
one
-
sigma difference within ±0.5K from
292
the actual value.
The c
hannels with frequencies exceeding 165
GHz are impacted by the water vapor absorption band
;
293
specifically, at 165GHz, only 68% of the emissivity values differ from the actual value within 0.03, and at 183GHz,
294
only 68% of the emissivity values differ from the
reference
value within 0.1
.
T
hese discrepancies are too significant
295
to
con
sider the retrieved
humidity profile
satisfactorily accurate
.
It appears that
an independent estimation of
the
ice
296
sheet surface emissivity
would be needed
to separate the effects of ice sheet emissions and atmospheric humidity.
297
298
Figure
6
.
Histogram of the difference between the atmospheric profiles retrieved by our iterative algorithm and the
299
optimal profiles based on true surface emissivity from Radiosonde measurements. The left panel showed temperature
300
below 70
km
and the right panel showed specific humidity below 10
km for the entire year of 2016. Dashed black
301
lines represented the median value and
the
68%
confidence intervals (one
standard deviation
)
in each panel.
302
303
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13
304
Figure
7
.
Histogram of the surface emissivity retrieved in our study compared to the
reference
value.
The d
ashed
305
black lines represented the median value and
the
68%
confidence intervals (
one
standard deviation
)
in the lower middle
306
and lower right panels.
307
308
The changes in
surface emissivity over the year
can
provide information about melting events on the ice sheet.
Fig
.
309
8a
present
s
surface
emissivity from
November
2015 to the end of 2016 at three transparent window frequencies and
310
near the oxygen absorption band. The blue curve represents values obtained from
our
iterative algorithm, while the
311
red dashed line shows the
reference
values. These values are in good agreement with each other. Two melting events
312
were observed around mid
-
December and mid
-
January, as indicated by the black arrows. The melting event in mid
-
313
January was more significant. Following the melting event, the emissivity decreased due to
an ice
crust form
ed
within
314
the
surface snow
during the refreezing
. The formation of
an
ice crust
within
the surface snow increases scattering and
315
depresses brightness temperature, resulting in reduced effective emissivity. The increase in surface emissivity during
316
the melting event was more pronounced in
the
high
-
frequency
channels (corresponding to emissivity from a more
317
shallow
surface layer)
,
suggesting
minor melting near the surface
.
Fig.
8b
displays temperature and specific humidity
318
perturbations from December 2015 to March 2016, encompassing the time frame of the melting event
s
. These
319
perturbations show deviations of the profiles from the average values during the specified period. The top row shows
320
results from our iterative algorithm, while the bottom row shows profiles measured using radiosonde. Despite the
321
higher altitude resolution in radiosonde measurements, our iterative algorithm captures
the
temperature and humidity
322
variations effectively. The two melting events in mid
-
December and mid
-
January corresponded with increases in near
-
323
surface temperature and humidity, as indicated by the black arrows. The temperature and humidity changes during
324
mid
-
January were more significant, corresponding to a more substantial melting.
Temperature increased by over 10
325
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14
K during the mid
-
January melting event, while a temperature rise of approximately 5
K was observed during the mid
-
326
December melting event.
327
328
329
Figure
8a
.
McMurdo Radiosonde Station (77.85
o
S, 166.66
o
E). Surface emissivity from November 2015 to the end of
330
2016 at three window frequencies (23.8GHz, 31.4GHz and 88.2GHz) and the
oxygen absorption band (50GHz
–
331
58GHz). The blue curve represents values from our iterative algorithm and the red dashed line shows values derived
332
from the radiosonde measurements. Two melting events occurred in mid
-
December and mid
-
January
,
pointe
d
out by
333
the
black arrows. The X
-
axis shows the month of the year, from 2015/11/1 to 2016/12/31.
334
335
336
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