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Anomaly Compensation and Cloud Clearing of AIRS Hyperspectral Data
Presented at IEEE GRSS
Boston Section Meeting
August 24, 2005
Choongyeun (Chuck) Cho
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Overview I Problem statement
Definition of anomaly
Background Atmospheric InfraRed Sounder (AIRS), Advanced
Microwave Souding Unit (AMSU), and Humidity Sounder for Brazil (HSB) instruments
Signal characterization and reduction of artifacts Principal component analysis (PCA) and its variants Artifacts in AIRS data
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Overview II Stochastic cloud-clearing
Background and prior work Description of stochastic-clearing (SC) algorithm
Validation of stochastic-clearing algorithm ECMWF Physical clearing
Conclusion Summary / contributions Future work
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Where Are We? Problem statement
Definition of anomaly Background Signal characterization and reduction of artifacts Stochastic cloud-clearing Validation of SC algorithm Conclusion
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Problem Statement
What is hyperspectral data? Hundreds or thousands of contiguous channels
What is anomaly? Defined as an unwanted spatial or spectral signature,
statistically distinct from its surrounding: Given X and a priori information about Δ, what is best
estimate of Δ or X? A priori info about anomaly can have different forms:
• Spectral statistical description, or usually ensembles• Spatial structure or texture• Joint spatial/spectral description
XX~
˜
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Examples of Anomalies
Anomalies of AIRS data discussed in this talk Instrumental noise Noisy channels
• AIRS data exhibits consistently noisy channels Scan-line miscalibration
• Resulting in striping patterns Cloud contamination
• Clouds generally make IR observations colder• Compensation for cloud impact is critical for accurate
retrieval
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Where Are We? Problem statement Background
AIRS/AMSU/HSB instruments Signal characterization and reduction of artifacts Stochastic cloud-clearing Validation of SC algorithm Conclusion
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AIRS/AMSU/HSB Instruments on Aqua
Atmospheric InfraRed Sounder (AIRS) 2378-channel infrared spectrometer covering
3.7-15.4μm 1.1˚ FOV (13.5km at nadir)
Advanced Microwave Sounding Unit (AMSU) 15 microwave channels 3.3˚ FOV (40.5km at nadir)
Humidity Sounder for Brazil (HSB) 1.1˚ FOV (13.5km at nadir, same as AIRS) 4 microwave channels (150,190 GHz) Scan motor failure since Feb 2003
AIRS/HSB
AMSU
“golfball”
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Sample AIRS Brightness Temperatures
AIRS sample spectra for 3-by-3 FOVs AIRS sample image
Data: August 21, 2003 near Great Lakes
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Where Are We? Problem statement Background Signal characterization and reduction of artifacts
Principal component analysis (PCA) and its variants Artifacts in AIRS data
Stochastic cloud-clearing Validation of SC algorithm Conclusion
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Principal Component Analysis Useful to characterize multivariate signal, and reduce
dimensionality
Can be defined recursively (x: m-dim multivariate signal):
Solution: y = WTx where W = [w1|w2|…|wn], wi are eigenvectors of CXX which is often estimated
To reduce dimension, n << m The resulting reconstructed signal: (PC filter)xWWx Tˆ
xwyxww
xwyxww
kkT
kiwwwk
Tw
k
),var(maxarg
),var(maxarg
1,...,1,1
1111
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Noise-Adjusted Principal Component
Principal components are sensitive to arbitrary scaling
Noise-adjusted PC (NAPC) Normalize data before applying PCA: Guarantees maximum SNR
What if noise variances are not known? Need to be estimated using blind signal separation (BSS)
technique such as Iterative Order and Noise (ION) estimation
XGX 2
1
na
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Noise-Adjusted Principal Component
Typical “variances versus PC index” plot (truncated at 400)
NAPC shows sharper break than PC 6 NAPCs explain 99.8% of variances
Cumulative explained varianceScree plot for AIRS data
Var
ian
ce
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Artifacts in AIRS Data
Measurements from a sensor can have different sources of artifacts
AIRS data has different types of unwanted artifacts Instrumental noise Noisy channels Scan-line miscalibration
Each dot in the image is:
K 2.0|ˆ| ,, jiji xx
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Instrumental Noise
Instrumental white noise is unavoidable NAPC filtering provides adaptive noise filtering
NAPC filtering is extensively used in our stochastic clearing algorithm and noisy channel detector.
Before
After
Histogram of difference
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Noisy Channels I
Some channels are consistently noisy These channels need to be excluded for further analysis and
retrieval of physical parameters Noisy channel detection is done with NAPC filtering such
that a channel having 5σ even once is flagged “noisy”
Block diagram of noisy channel detector
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Noisy Channels II
AIRS science team has their own list of bad channels.
Detection rates for noisy and popping channels:
Type of bad channel Number of NASA compiled bad channels
Number detected by proposed algorithm
% detected
High noise 5 5 100%
Detector response exhibits unexpected steps (Popping)
2 2 100%
Total 7 7 100%
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Scan-line Artifacts I
Miscalibrated scan-line results
in stripes
A simple low-pass filter (in along-track direction) in NAPC domain corrects this artifact efficiently
Block diagram of removing-stripe algorithm
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Scan-line Artifacts II Results Original Images Processed Images
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Where Are We? Problem statement Background Signal characterization and reduction of artifacts Stochastic cloud-clearing
Background and prior work Description of stochastic-clearing (SC) algorithm
Validation of SC algorithm Conclusion
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Background and Prior Work
What is cloud-clearing? Cloudy radiances (or TB) cause inaccurate retrieval Cloud-cleared radiances: radiances which would have
been observed if FOV contains no clouds
Prior work on cloud-clearing Ignore cloudy FOVs: only ~5% of AIRS FOVs are clear! Physical cloud-clearing: iterate between estimation of
physical parameters and calculation of observed radiance Adjacent-pair clearing: use adjacent FOVs which have
different fractional cloud cover Purely spatial processing: restore 2-D temperature field
from sparse clear data
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Stochastic Clearing (SC) How does stochastic clearing (SC) work?
SC estimates cloud contaminations solely based on statistics without using any physical models
Hyperspectral measurements may contain sufficient information about clouds in an obscured manner
Robust and stable training is necessary Nonlinearity is accommodated using stratification
(sea/land, latitude, day/night), multiplicative scan angle correction, etc.
Advantages of SC approach Simple: SC does not require physical models (retrieval or
radiative transfer). Fast: Based on matrix addition and multiplication
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Block Diagram of SC Algorithm
Linear Operator A
3x3 AIRS
TB’sSelect/average
FOV’s
5 microwave ’sLand fraction
Secant
Linear Operator B
Linear Operator C
Linear Operator D
CloudyTest
Morecloudy
Less cloudy
N
1 PC-cloud 2 TB’s1
7
N
1 PC
Cleared AIRS TB’s
N = 314 channels
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Operators for SC AlgorithmECMWF + SARTA (v1.05)
clear TB’sN AIRS TB’s
AMSU ch.5,6,8,9,10
secant Land fraction
AIRS-cloudPC’s
TB’s
AIRS Cleared
TB’s
Find warmest † among 9 pixels*
Find coldestamong 9 pixels*
Noise-Adjusted
PC’s
Noise-Adjusted
PC’sLINEAR
ESTIMATOR PC-1
N
7
3
5 4
TB-
+
++
Trained with >1000 golfballs
N
N
N
Operator A
Select & avg FOV’s
Trained with >1000 golfballs
Operator B Operators
C, D
* Warmest/coldest based on 11 4-m channels peaking 1-3 km
†Average 4 warmest pixels for 5-10 km WF, 9 for WF >10 km
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Clearing Corrections vs ECMWF ’s
-10 0 10 20 30 40 50 60oK
AIR
S c
lear
ed –
EC
MW
F/S
AR
TA
(oK
)
10
5
0
-5
-10
10
5
0
-5
-10
Weighting function peak ~0.47 km, 2217.4 cm-1
1oK threshold
2oK threshold
Red circles are best 37 percent
“good golfballs” for nighttime ocean,
all angles (operator C)
Blue circles are cloudy golfballs
(operator D)
Classification Algorithm: “good
golfballs” are below both 1K
and 2K thresholds at operator B
Weighting function peak ~2.7 km, 2231.5 cm-1
-10 0 10 20 30 40 50 60 70oK
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AIRS-ECMWF for 827 Channels
Weighting function peak height (km)
314 good channels
Best 22 percent of golfballs
(operator C)
Thresholds were 0.8K and 3K
Nighttime ocean, all scan angles
Includes all 4- and 15-m
channels plus one-fifth of the
rest
0 1 2 3 4 5 7 9 19 29 39
314 good channels
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Where Are We? Problem statement Background Signal characterization and reduction of artifacts Stochastic cloud-clearing Validation of SC algorithm
ECMWF Physical clearing
Conclusion
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ECMWF Data Set Used ECMWF profiles are used to simulate cloud-cleared TB’s via
SARTA v1.05 radiative transfer, for all scan angles, 314 channels
Global, 3 days: 8/21, 9/3, 10/12/03 (L1B v3.0.8)
AIRS instrument noise reduced by averaging 1, 4, or 9 of the warmest* 15-km pixels for weighting function peaks 0-5, 5-10, and >10 km, respectively
Used 1000 golf balls to regress each of 10 categories based on day/night, land/sea, and |lat|<40 or 40<|lat|<70
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RMS Difference (AIRS-ECMWF) for Ocean
For best 28%: sea + |lat|<40º + day (best for sea)
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RMS Difference (AIRS-ECMWF) for Land
For best 28%: land + |lat|<40º + night (best for land)
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Cloud-cleared AIRS vs. ECMWF (best 28%)
RMS difference (oK) between cloud-cleared AIRS and ECMWF/SARTA, 10 different estimators
RMS > 0.7 K are boxed Excellent agreement for ocean and equatorial regions Degradation over daytime land near surface
Weighting function
peak height (km)
Ocean|Lat|<40 30<|Lat|<70
Day Night Day Night
Land|Lat|<40 30<|Lat|<70
Day Night All Day Night All
0 – 1
1 – 2
4 – 5
6 – 7
10 – 11
0.38 0.4 0.86 0.91 1.68 0.77 1.36 1.48 0.78 1.19
0.27 0.29 0.54 0.57 0.94 0.38 0.75 0.84 0.44 0.70
0.28 0.30 0.45 0.45 0.34 0.29 0.33 0.41 0.33 0.39
0.23 0.27 0.34 0.36 0.25 0.24 0.28 0.34 0.26 0.31
0.24 0.27 0.33 0.35 0.23 0.25 0.26 0.24 0.28 0.27
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Global Cloud-Clearing Images (2392.1cm-1)
SC applied to 8/21/2003 descending orbits (L1B v4.0.9) 2392.1cm-1, WF peak=0.23 km
Observed AIRS Cloud-cleared (best ~78%)
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Global Cloud-Clearing Images (2392.1cm-1)
CC Residual = Spatially high-pass filtered version of CC WF peaks at 0.23 km
Observed AIRS CC residual
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Cloud-Clearing Images and Sea Surf. Temperature
Angle-corrected TB images at window channels
Clearing works well even if there is no hole (clear FOV)
Ob
serv
ed
Cle
ared
SS
T
AIRS 2390.1cm-1: near Hawaii AIRS 2399.9cm-1: near SW Indian Ocean
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Validation with Physical Clearing Visible vs. AIRS 8.15-m Data
Visible Ch 3
Granule 91(9/6/02)
(solar reflection)
1227.7 cm-1
Channel 1284(H2O)
5
15
25
35
45
140
120
100
80
60
40
20
5
15
25
35
45
290
285
280
275
270
265
260
270
265
260
255
250
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Determination of AIRS Cloud-Cleared Brightness Temperature Baselines
Channel 1284 (H2O) (1227.7 cm-1)Granule 91 (9/6/02) Indian Ocean, LAT -26.3, LON 70.2
Stochastic CC Clear Mask † Fitted ‡
† Clear mask determined from Visible Ch 3, Brown being clear‡ Polynomial fit: 4th order in scan angle, 3rd order downtrack
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Stochastic versus Physical Cloud-Cleared8.15-m Brightness Temperatures
Channel 1284 (H2O) (1227.7 cm-1)Granule 91 (9/6/02) Indian Ocean, LAT -26.3, LON 70.2
Filter subtracts cloud-cleared baseline and convolves with 33 boxcar
-Visible Ch 3Stochastic Clearing Physical Clearing
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Correlation Coefficients: Visible (v3) vs. Cloud-Cleared 8.15-m AIRS TB’s
AIRS channel 1284(1227.7 cm-1)(water vapor)September 6, 2002
Lon -26.3/Lat 70.2Indian Ocean
Lon -12.5/Lat -106.1Eastern Southern Pacific
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Stochastic and Physics-BasedCloud-Cleared Window Channel TB
Channel 2121 (2399 cm-1), WF peak ~200m9/6/02 North of Bermuda
* Note that the physical clearing is most recent version (PGE v4.0.0), calculated this week.
Stochastic Clearing Physics-Based Clearing*
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Where Are We? Problem statement Background Signal characterization and reduction of artifacts Stochastic cloud-clearing Validation of SC algorithm Conclusion
Summary / contributions Future work
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Summary
Anomaly compensation techniques are discussed based on signal processing techniques (NAPC and ION) and nonlinear estimators
Anomalies: Gaussian instrument noise, noisy channels, scan-line miscalibration, and cloud contamination
Stochastic clearing (SC) algorithm tested to be successful using different validation schemes: ECMWF Sea surface temperature (SST) Physical algorithm
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Contributions: Methodology We developed “architected nonlinear estimators”, taking
advantage of simplicity of linear estimator and robustness of general nonlinear estimator
NAPCs are used to reduce dimension and suppress noise, making more robust and stable estimation
Prior knowledge (either spectral or spatial) about anomaly is utilized to meaningfully structure a nonlinear estimator
Linear
Estimator
GeneralNonlinearEstimator
ArchitectedNonlinearEstimator
Dimensionreduction
Prior infoabout anomaly• Stable
• Simple/Fast• Less powerful
• May be unstable • Complex/Slow • Most powerful
• Stable• Simple/Fast• Sufficiently powerful
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Contributions: Stochastic Clearing
SC algorithm developed based on anomaly compensation and nonlinear estimation techniques: Enjoys excellent agreement with numerical weather
prediction model (ECMWF) Performs superior to physical clearing Very fast: depends on matrix addition and multiplication;
consists of 664 lines of Matlab code, ~20 minutes to cloud clear an entire day of AIRS data on ordinary PC
Clearing at extreme scan angles is good; hole-hunting using high spatial resolution may not be essential for cloud-clearing
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Future Work
Anomaly compensation theory Optimization of combining spectral and spatial processing More extensive spectral processing techniques
SC algorithm Joint cloud-clearing and retrieval Better model for nonlinearities Optimum architecture for SC algorithm using efficient
design-of-experiment approach
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Where Are We? Problem statement Background Signal characterization and reduction of artifacts Stochastic cloud-clearing Validation of SC algorithm Conclusion
That’s all, folks.
Any questions?
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Back-up Slides
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Global Cloud-Clearing Images (2392.1cm-1)
Zoom-in images in Southeastern Pacific WF peaks at 0.23 km
AIRS CC CC residual
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Determination of AIRS Cloud-Cleared Brightness Temperature Baselines
Channel 1284 (H2O) (1227.7 cm-1)Granule 91 (9/6/02) Indian Ocean, LAT -26.3, LON 70.2
Stochastic CC Cloud Mask † Fitted ‡
† Brown being clear (accepted)‡ Polynomial fit: 4th order in scan angle, 3rd order downtrack
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SC Validation w.r.t. SST
NCEP sea surface temperature
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AIRS Stratified Stochastic Cloud ClearingFirst-pass results Multiplicative Scan-angle Stratified results
(AIR
S c
lear
ed r
adia
nce)
– (
EC
MW
F/S
AR
TA
) (o K
)
46% golfballs good
54% rejected
46% golfballs good
54% rejected
0.8K threshold
3K threshold
Estimate of cloud-clearing radiance correction (oK)
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AIRS Stratified Stochastic Cloud Clearing
Altitude of weighting function peak (km)
RM
S:
clea
red
AIR
S r
adia
nce
s vs
. EC
MW
F/S
AR
TA
First pass, all golfballs, all scan angles
Second pass, multiplicative scan angle
Third pass, best 46% golfballs (all scan angle)Third pass’, best 46% golfballs using |θ|<16○
0.5K
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AMSU Contributions for Land
For land + 30º<|lat|<70º + night
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Iterative Order and Noise (ION) Estimation
To apply NAPC, the noise variances need to be estimated
Signal model: x = Ap + Gn, where A is a mixing matrix, p is signal of unknown dimension k, G is diagonal noise covariance matrix, n is unit-variance white Gaussian noise.
ION iteratively estimates signal order (k), mixing matrix (A) and noise variances (G): Estimate order (k): using scree plot Estimate A and G: using Expectation-Maximization
algorithm
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Blind Signal Separation
Observation model: x = Ap + G1/2w- A, p, G, w and k (dimension of p) are unknown.- A: mixing matrix (n×k), p: source signal vector (k×1)- G: diagonal cov matrix (n×n), w: white Gaussian noise vector (n×1)- Use matrix X, P and W to denote concatenated samples of x, p and w: X = AP + G1/2 W
Given X, how to estimate A, G and k.
Previous signal separation techniques assume either k or G is known
Iterative Order and Noise (ION) estimation:- First, estimate signal order, k, using eigenvector decomposition- Estimate A and G using Expectation-Maximization algorithm
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Blind Signal Separation II
Estimation of signal order, k:
- Selected based on scree plot, sorted eigenvalue vs.
eigenvalue index
Knee point separates
signal from noise
X = AP + G1/2W
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Blind Signal Separation III
Expectation-Maximization (EM) algorithm iteratively finds maximum likelihood (ML) estimate of parameters where model depends on hidden (latent) variable
Expectation step: estimate unobserved data (P and PTP) using estimate of A and G
Maximization step: compute ML estimate of A and G using estimates of P and PTP
X = AP + G1/2W
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ION Algorithm Block Diagram
i iˆ ˆG ,Z
ii, AG
1-i1,-i AG
X, optionally normalize rows to zero mean and unit variance
oG I, i 1 Set imax, e.g. imax = 10
Noise Normalization
1 2n i 1
ˆX G X
nX
Order Estimation
Scree Plot
SVD
EM Algorithm
Expectation
Maximization
1k
i<imax
Yes
No
ii, AG
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Physics of Radiative Transfer
Radiative transfer links environmental parameters to hyperspectral data
For a black body, spectral brightness is defined as:
For microwave channels (hf << KT) , this is linear with temperature:
1-1-2-/2
3
HzsterWm)1(
2),(
KThfec
hfTfI
Tc
kfTfI
2
22),(
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Physics of Radiative Transfer
Upwelling radiation received at a sensor at altitude L has four contributions:
Can be rewritten as:
)sec(2
0
)sec(),()sec(
)sec(
0
)sec(),(
0
00
0
)(
),(),()sec()(
))(1(
),(),()sec(),(
eIf
dzezfzfIef
eIf
dzezfzfILfI
cosmic
L dzzf
surface
L dzzf
z
Lz
L
s dzzfIzfWfILfI0
),(),()(),(
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Physics of Radiative Transfer
Weighting functions for AIRS/AMSU
AIRS Weighting function peaks
AMSU Weighting functions
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Physics of Radiative Transfer Microwave/IR atmospheric absorption spectrum
MW: Water vapor absorption lines at 22, 183, 325 GHz, O2 absorption at 118, 368 GHz, etc.
IR: distinct water vapor, O3, CO2 absorptions
Microwave Infrared