1 an assessment of amsu-a moisture retrievals over land and ocean stan kidder 20 june 2006
TRANSCRIPT
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An Assessment of AMSU-A An Assessment of AMSU-A Moisture Retrievals over Land Moisture Retrievals over Land
and Oceanand Ocean
Stan KidderStan Kidder
20 June 200620 June 2006
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Purpose of StudyPurpose of Study
To determine how accurately To determine how accurately atmospheric water vapor and liquid atmospheric water vapor and liquid water can be retrieved from AMSU-A water can be retrieved from AMSU-A data using data using 1.1. A simplified forward model andA simplified forward model and
2.2. Rodger’s (2000) Rodger’s (2000) maximum a maximum a posterioriposteriori (MAP) solution (MAP) solution
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In Other WordsIn Other Words
• To use a simplified atmosphere (in To use a simplified atmosphere (in which everything is known) to which everything is known) to determine the best that one can determine the best that one can hope for in moisture retrieval hope for in moisture retrieval accuracy and how various factors accuracy and how various factors (especially surface emittance) (especially surface emittance) influence this accuracy.influence this accuracy.
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The Forward ModelThe Forward Model
TB() = Ts surface emission
+ TA(1 - ) atmospheric
emission+ TA (1 - )(1 – ) surface reflection
TB = brightness temperature (K)
= frequency (GHz)
= surface emittance (unitless)
= atmospheric transmittance (unitless)
TS = surface temperature (K)
TA = constant atmospheric temp (K)
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The Forward Model (cont.)The Forward Model (cont.)
o oxygen
exp[−L()L]cloud
liquid waterexp[−V()V]water
vapor
o() = vertical transmittance of dry, cloud-free atmosphere
L = vertically integrated cloud liquid water (kg m-2 or mm)
V = vertically integrated water vapor (TPW, kg m-2 or mm)
L() = liquid water mass absorption coefficient (m2 kg-1)
V() = water vapor mass absorption coefficient (m2 kg-1)
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Forward Model Constants*Forward Model Constants*
(GHz)(GHz) 23.823.8 31.431.4 50.350.3 52.852.8
oo 0.97460.9746 0.95880.9588 0.59370.5937 0.16390.1639
LL (m(m22 kg kg-1-1)) 0.06000.0600 0.10350.1035 0.25750.2575 0.28220.2822
VV (m(m22 kg kg-1-1)) 5.1855.1851010−3−3 2.7892.7891010−3−3 4.7774.7771010−3−3 5.0345.0341010−3−3
*Determined using Liebe (1992).
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The Measurement VectorThe Measurement Vector
S = I4
= 0.5 K (“noise”)
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The State VectorThe State Vector
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A PrioriA Priori
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A PrioriA Priori Covariance Covariance
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Surface EmittanceSurface Emittance
• Treated as a forward model parameter, Treated as a forward model parameter, that is, as a random variable which is that is, as a random variable which is not retrieved and thus adds error to the not retrieved and thus adds error to the retrieved quantitiesretrieved quantities
• The standard deviation of surface The standard deviation of surface emittance is varied to evaluate the emittance is varied to evaluate the accuracy with which it must be known to accuracy with which it must be known to achieve the desired accuracy of retrievalachieve the desired accuracy of retrieval
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Mean EmittanceMean Emittance
Channel Channel 23.823.8 31.431.4 50.350.3 52.852.8
Ocean*Ocean* 0.4210.421 0.4430.443 0.4820.482 0.4880.488
LandLand 0.9500.950 0.9500.950 0.9500.950 0.9500.950
*From Kohn (1995). TS = 300 K, WS = 5 m s-1, salinity = 35 ppt, zenith angle = 0
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The Retrieval SchemeThe Retrieval Scheme
• KK = analytic Jacobian [ = analytic Jacobian [KKijij = = ∂∂TTBB((ννii)/ ∂)/ ∂xxjj]]
• Rodgers’ iterative solution (eq. 5.8) with Rodgers’ iterative solution (eq. 5.8) with KK being recalculated at every iteration: being recalculated at every iteration:
• Convergence is achieved (eq. 5.29) whenConvergence is achieved (eq. 5.29) when
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Retrieval Error CovarianceRetrieval Error Covariance
• At convergence (Rodgers eq. 5.30):At convergence (Rodgers eq. 5.30):
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Model Parameter-Caused Model Parameter-Caused ErrorError• Rodgers eq. 3.16 & 3.27:Rodgers eq. 3.16 & 3.27:
Note that in the x equation, stands for surface emittance, whereas, in the Gy equation, S is the measurement covariance matrix.
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ProcedureProcedure
1.1. Choose a state vector, and an emissivity Choose a state vector, and an emissivity vector, approximating the values as vector, approximating the values as Gaussian variablesGaussian variables
2.2. Calculate the measurement vector with Calculate the measurement vector with noisenoise
3.3. Retrieve the state vector using Retrieve the state vector using 00
4.4. Repeat steps 1-3 1000 timesRepeat steps 1-3 1000 times
5.5. Calculate the retrieval statistics as Calculate the retrieval statistics as functions of emittance noisefunctions of emittance noise
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ResultsResults
• Presented as a series of graphs Presented as a series of graphs showing the bias, standard deviation, showing the bias, standard deviation, and RMS error of retrieving Tand RMS error of retrieving TSS, T, TAA, L, , L, and V.and V.
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TTSS Ocean Ocean
TS Ocean
-5
0
5
10
15
20
25
30
35
40
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0.000 0.005 0.010 0.015 0.020 0.025 0.030
Std. Dev. of Surface Emittance
Kel
vin
s Bias
Std Dev
RMS
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TTSS Land Land
TS Land
0
1
2
3
4
5
6
7
8
9
10
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Std. Dev. of Surface Emittance
Kel
vin
s Bias
Std Dev
RMS
2020
TTAA Ocean Ocean
TA Ocean
-2
0
2
4
6
8
10
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Std. Dev. of Surface Emittance
Kel
vin
s Bias
Std Dev
RMS
2121
TTAA Land Land
TA Land
-2
0
2
4
6
8
10
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Std. Dev. of Surface Emittance
Kel
vin
s Bias
Std Dev
RMS
2222
L OceanL OceanL Ocean
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Std. Dev. of Surface Emittance
kg/m
^2
or
mm
Bias
Std Dev
RMS
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L LandL LandL Land
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Std. Dev. of Surface Emittance
kg/m
^2
or
mm
Bias
Std Dev
RMS
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V OceanV OceanV Ocean
-2
0
2
4
6
8
10
12
14
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Std. Dev. of Surface Emittance
kg/m
^2
or
mm
Bias
Std Dev
RMS
2525
V LandV LandV Land
-20
-10
0
10
20
30
40
50
60
70
80
0.000 0.005 0.010 0.015 0.020 0.025 0.030
Std. Dev. of Surface Emittance
kg/m
^2
or
mm
Bias
Std Dev
RMS
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ConclusionsConclusions
• Atmospheric temperature (TAtmospheric temperature (TAA) is accurately ) is accurately retrieved over land or oceanretrieved over land or ocean
• Surface temperature (TSurface temperature (TSS) is accurately ) is accurately retrieved over land, but poorly retrieved retrieved over land, but poorly retrieved over oceanover ocean
• Liquid water (L, CLW) is marginally retrieved Liquid water (L, CLW) is marginally retrieved over ocean, but lost in the noise over landover ocean, but lost in the noise over land
• Water vapor (V, TPW) is accurately retrieved Water vapor (V, TPW) is accurately retrieved over ocean, but probably not retrievable over ocean, but probably not retrievable over land with AMSU-A channelsover land with AMSU-A channels
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Conclusions (cont.)Conclusions (cont.)
• Retrieving surface emittances instead of Retrieving surface emittances instead of treating them as model parameters is treating them as model parameters is unlikely to helpunlikely to help
• Adding AMSU-B channels would possibly Adding AMSU-B channels would possibly help with land retrievalshelp with land retrievals
• Experiments with C1DOE should be Experiments with C1DOE should be performed to see if they support these performed to see if they support these resultsresults
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ReferencesReferences
Rodgers, C. D., 2000: Rodgers, C. D., 2000: Inverse Methods for Inverse Methods for Atmospheric Sounding: Theory and Practice. Atmospheric Sounding: Theory and Practice. World Scientific, 238 pp.World Scientific, 238 pp.
Kohn, D. J., 1995: Refinement of a semi-empirical Kohn, D. J., 1995: Refinement of a semi-empirical model for the microwave emissivity of the sea model for the microwave emissivity of the sea surface as a function of wind speed, M.S. thesis, surface as a function of wind speed, M.S. thesis, meteorology dept., Texas A&M University.meteorology dept., Texas A&M University.
Liebe, H. J., 1992:Liebe, H. J., 1992: Atmospheric Attenuation and Atmospheric Attenuation and Delay Rates from 1 to 1000 GHzDelay Rates from 1 to 1000 GHz. Institute for . Institute for Telecommunication Sciences, NTIA/ITS.S1, 325 Telecommunication Sciences, NTIA/ITS.S1, 325 BROADWAY, Boulder, CO 80303BROADWAY, Boulder, CO 80303