11

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

22

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

33

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.

44

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)

55

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)

66

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).

77

The Measurement VectorThe Measurement Vector

S = I4

= 0.5 K (“noise”)

88

The State VectorThe State Vector

99

A PrioriA Priori

1010

A PrioriA Priori Covariance Covariance

1111

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

1212

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

1313

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

1414

Retrieval Error CovarianceRetrieval Error Covariance

• At convergence (Rodgers eq. 5.30):At convergence (Rodgers eq. 5.30):

1515

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.

1616

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

1717

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.

1818

TTSS Ocean Ocean

TS Ocean

-5

0

5

10

15

20

25

30

35

40

45

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

1919

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

2323

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

2424

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

2626

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

2727

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

2828

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