Assessment of Atmospheric Profiles Retrieved from...
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Assessment of Atmospheric Profiles Retrieved from Satellite Theory and Case Study Nikita Pougatchev Gail Bingham, Stanislav Kireev, and David Tobin ITSC-15 Acquafredda Maratea, Italy October 3 - 10, 2006
Transcript of Assessment of Atmospheric Profiles Retrieved from...
Assessment of Atmospheric Profiles Retrieved from Satellite
Theory and Case Study
Nikita PougatchevGail Bingham, Stanislav Kireev, and David Tobin
ITSC-15Acquafredda Maratea, Italy
October 3 - 10, 2006
Assessment=End-to-End Error Modeling Atmosphere, Signal, Retrieval and Validation
Assessment Model SDR & EDR Assessment
y
TrueProfile
xsat
Radianceysat
Parameter Error Noise
Instrument SDR
SmoothingParameter
Forward modelNoise
Retrieval EDR
TrueProfile
xval
xvalyval
Validation System
ˆ
valy valx
x
SDR - Sensor Data Records – Radiances/SpectraEDR – Environmental Data Records – Retrieved Profiles (in this presentation)
Linear Assessment ModelConcept
• Atmospheric, Instrument, Forward Model, and Retrieval parameters and their errors are random variables
• Variations and errors are characterized by Covariances
• Vertical resolution is characterized by Averaging Kernels
• Variations and errors propagate Linearly through Atmosphere – Instrument – Signal – Retrieval-Validation
EDR Assessment Model – EDRAM• Linear mathematical error model for the Post-launch/Validation
assessment of atmospheric profile retrievals.• Assessment Comparison/Book-Keeping• Assessment = Scientifically accurate relation between true state of
the atmosphere and measurements• Validated and validating data differ by:
– Time and location– vertical resolution and grid– absolute accuracy and noise level
•EDRAM makes the assessment accurate by allowing for the difference.
x2
x1
x2x1
x1
x2
d
d
d
≠
EDRAM Concept
• The validated system performs a set of measurements on an ensemble of true states x
• r(x) is a nominal retrieval with the absence of any errors in the measured signal and in the forward model
• e represents retrieval errors characterized by its mean value (Bias) and covariance (retrieval Noise)
• The goal of the EDRAM is to assess actual Bias and Noise of validated system by simulating its nominal retrieval based on validating data and to estimate the error of the assessment.
x = r(x) + e
{e} = ΔEeS
Linear Assessment Model Atmosphere, Signal, Retrieval and Validation
Assessment Model SDR & EDR Assessment
y
= − −
+
+
+
a
y b
y
y
ˆδx (A I)(x x )G K δb
G ΔFM
G ε
TrueProfile
xsat
Radianceysat
Parameter Error - δbNoise – ε
Instrument SDR
ˆδy = Kδb + εSmoothingParameter
Forward modelNoise
Retrieval EDR
TrueProfile
xval
xvalyval
Validation System
expectedˆδy expectedˆδx
ˆ
valy valx
x
Clive Rodgers
EDRAM – Data Flow
1x
Statistical Characteristicsof true states
Validated RetrievalCharacterization
Validating DataCharacterization
1 21 x 2 x 12{x S }; {x S }; S
1
a1 εA ; S
Estimation of
Bias
Noise
1ˆΔx Err±
1εS
2x22 εA ; S
EDRAM -Theoretical backgroundRetrieval Model
i ai i i ai i iˆ ˆx = x + A (x - x ) + Δx ε+Retrieval/Measurements
NoiseBias
TruestateAveraging
KernelA priori
i=1 Validated datai=2 Validating Data
The goal of the EDRAM is to assess actual Bias and Noise of validated system.
1ˆΔx1ε
S
EDRAM - Theoretical backgroundRelation between Atmospheric States
i=1 Validated datai=2 Validating Data
and1 1 2 2x δx x δx Mean and variation about mean of true states
T12 21S = S Cross-covariance between true states
1 2δx Bδx + ξ=Relation between true states
2cov(x ,ξ) = 01 2
Tx x ξS = BS B + S
1 2x xS S Auto-covariance of true states
Variation atvalidated point
Un-CorrelatedCorrelated
2
-112 xB = S S
Theoretical background(Continued)
12 1 2ˆ ˆx = A Bx1x 2xSimulating
with
11 2ˆ ˆ ˆδx x - x≡Analyzed DifferenceSimulated Validated Measurement!
1 1 2 11 2 1 a1 1 2 a2 1 1 2ˆ ˆ ˆ ˆδx x - x [(I - A )x - A B(I - A )x ]+ A x A BA x Δx≡ = − +
Mean DifferenceMean Expected Difference e ˆδx Bias
1 12 1 2
T T Tˆδx 1 2 x 1 2 ξ ε 1 ε 1S = (A B(I - A ))S (A B(I - A )) + A S A + S + (A B)S (A B)
Covariance of the Analyzed Difference
Validated Measurement
21 2 a 1 2 2 1 2= A B(I - A )x + A BA x + A Bε
Case Study
• Validation Data Set – radiosondes at ARM Southern Great Plain (SGP) site; July –December 2002 (416 sondes).
• Validated parameter – Atmospheric Temperature Vertical Profile.
• Validated System – characterized by AIRS* averaging kernels.
Log P
100 1000
Log
P
100
1000
-10 -5 0 5 10 15 20 25 30
Sx2 (auto-covariance) matrix
72 ev profTemperature
K2
S12 matrix 0-3 h bin 72 ev prof
Temperature
Log P
100 1000
Log
P100
1000
S12 matrix 0-6 h bin 72 ev prof
Temperature
Log P
100 1000
Log
P
100
1000
S12 matrix 0-12 h bin 72 ev prof
Temperature
Log P
100 1000
Log
P
100
1000
S12 matrix 0-24 h bin 72 ev prof
Temperature
Log P
100 1000
Log
P
100
1000
S12 matrix 0-48 h bin 72 ev prof
Temperature
Log P
100 1000
Log
P
100
1000
S12 matrix 0-120 h (5 days) bin 72 ev prof
Temperature
Log P
100 1000
Log
P
100
1000
S12 matrix 0-96 h (4 days) bin 72 ev prof
Temperature
Log P
100 1000
Log
P
100
1000
TE=2x 2 2 2 2S {(x - x )(x - x ) }
Auto- and Cross-Correlation
Auto-Covariance Sx23 hours 6 hours 12 hours
24 hours 2 days 4 days 5 days
12 1 1 2 2S {(x - x )(x - x ) }TE=
K
0 1 2 3 4 5 6 7
Log
P
200
300
400
500
600
700800900
100
1000
K
0 1 2 3 4 5 6 7
Log
P
200
300
400
500
600
700800900
100
1000
K
0 1 2 3 4 5 6 7
Log
P
200
300
400
500
600
700800900
100
1000
K
0 1 2 3 4 5 6 7
Log
P
200
300
400
500
600
700800900
100
1000
Non-Coincidence ErrorUncorrelated/Residual error
Sξ =Sx1-BSBT
12 hours 24 hours
( )a n d d ia g o n a l s2ξ xS S
ξSξSξSξS 2xS
2xS2xS
2xS
1 2δx Bδx + ξ=
2cov(x ,ξ) = 01 2
Tx x ξS = BS B + S
Variation atvalidated point
Un-CorrelatedCorrelated
Log P
100 1000
Log
P
100
1000
-2 0 2 4 6 8 10 12
Log P
100 1000
Log
P
100
1000
Log P
100 1000
Log
P
100
1000
Log P
100 1000
Log
P
100
1000
6 hours3 hours
K2
1 2
Tξ x xS = S - BS B
Non-Coincidence Error(continued)
Non-Coincidence Error400 - 800 mb
Time bin τ (h)0 20 40 60 80 100 120
RM
S Er
ror σ
ξ (K
)
0
1
2
3
4
Non-Coincidence Error
RMS Error σξ (K)0 1 2 3 4 5 6
Log
P
200
300
400
500
600
700800900
100
1000
3 hors6 hors12 hors24 hors2 days5 days
Non-Coincidence Error400 - 800 mb
Time bin τ (h)0 3 6 9 12
RM
S Er
ror σ
ξ (K
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 22 0 14( . . ) Kξσ τ= +AIRS global estimate 0.8 KChahine et al., 2006
( 3 , 100 )hour km± ±
Averaging Kernels
Averaging Kernel-0.2 0.0 0.2 0.4 0.6 0.8 1.0
H (k
m)
0
2
4
6
8
10
12
14
16
Averaging Kernel-0.2 0.0 0.2 0.4 0.6 0.8 1.0
Log
P
200
300
400
500
600700800900
100
1000
Averaging Kernels for Temperature ProfileAIRS Spectral Channels, ILS, and SNR
Optimal Estimation (Clive Rodgers)
“Satellite Retrievals” vs. RadiosondesRMS
Log P
100 1000
Log
P
100
1000Log P
100 1000
Log
P
100
1000
Non-Coincidence 6 hours ErrorNon-Coincidence 6 hours
&Smoothing Error
Square RootDiagonals - RMS
K0 1 2 3 4 5 6
Log
P
200
300
400
500
600700800900
100
1000
Smoothing & Non-Coincidence RMS Non-Coincidence RMSAuto-Covariance RMS
= 1 1 1 2ˆδx A x - A Bx= 1 2ˆδx x - Bx
Conclusions
•Non-Coincidence Error analysis is applicable to Radiances (SDR) and retrievals (EDR) assessment.
•EDRAM provides scientific basis and practical tool for accurate comparison of atmospheric profiles of different vertical resolution and taken at different times and locations.
•EDRAM estimates retrieval bias and noise as well as statistical significance of the estimates based on the comparison.
•EDRAM can be used for evaluation of a satellite EDR for Earth System and Climate studies by accurately referencing them to other data sets with known accuracy and precision.
