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# An Assessment of Microwave Moisture Retrievals over Land and Ocean

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```									 An Assessment of AMSU-A
Moisture Retrievals over Land
and Ocean

Stan Kidder
20 June 2006

1
Purpose of Study

To determine how accurately atmospheric
water vapor and liquid water can be
1. A simplified forward model and
2. Rodger’s (2000) maximum a posteriori
(MAP) solution

2
In Other Words

• To use a simplified atmosphere (in which
everything is known) to determine the
best that one can hope for in moisture
retrieval accuracy and how various factors
(especially surface emittance) influence
this accuracy.

3
The Forward Model

TB(n) = enTstn                                          surface emission

+ TA(1 - tn)                        atmospheric emission

+ TA tn(1 - tn)(1 – en)                 surface reflection

TB = brightness temperature (K)     tn = atmospheric transmittance (unitless)
n = frequency (GHz)                 TS = surface temperature (K)
en = surface emittance (unitless)   TA = constant atmospheric temp (K)

4
The Forward Model (cont.)
tn = to(n)                                 oxygen

 exp[−bL(n)L]                        cloud liquid water

 exp[−bV(n)V]                       water vapor

to(n) = 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)
bL(n) = liquid water mass absorption coefficient (m2 kg-1)
bV(n) = water vapor mass absorption coefficient (m2 kg-1)

5
Forward Model Constants*

n    (GHz)            23.8               31.4      50.3         52.8

to                   0.9746             0.9588    0.5937       0.1639

bL   (m2 kg-1)       0.0600             0.1035    0.2575       0.2822

bV    (m2 kg-1)    5.18510−3      2.78910−3    4.77710−3   5.03410−3

*Determined using Liebe (1992).
6
The Measurement Vector

Se = se2I4

se = 0.5 K
(“noise”)

7
The State Vector

8
A Priori

9
A Priori Covariance

10
Surface Emittance

• Treated as a forward model parameter,
that is, as a random variable which is not
retrieved and thus adds error to the
retrieved quantities
• The standard deviation of surface
emittance is varied to evaluate the
accuracy with which it must be known to
achieve the desired accuracy of retrieval
11
Mean Emittance

Channel             23.8             31.4              50.3              52.8
Ocean*             0.421            0.443             0.482             0.488
Land               0.950            0.950             0.950             0.950
*From Kohn (1995). TS = 300 K, WS = 5 m s-1, salinity = 35 ppt, zenith angle = 0

12
The Retrieval Scheme
• K = analytic Jacobian [Kij = ∂TB(νi)/ ∂xj]
• Rodgers’ iterative solution (eq. 5.8) with K
being recalculated at every iteration:

• Convergence is achieved (eq. 5.29) when

13
Retrieval Error Covariance

• At convergence (Rodgers eq. 5.30):

14
Model Parameter-Caused Error
• Rodgers eq. 3.16 & 3.27:

Note that in the Dx equation, e stands for surface emittance, whereas, in
the Gy equation, Se is the measurement covariance matrix.

15
Procedure
1. Choose a state vector, and an emissivity
vector, approximating the values as Gaussian
variables
2.   Calculate the measurement vector with noise
3.   Retrieve the state vector using e0
4.   Repeat steps 1-3 1000 times
5.   Calculate the retrieval statistics as functions of
emittance noise

16
Results

• Presented as a series of graphs showing
the bias, standard deviation, and RMS
error of retrieving TS, TA, L, and V.

17
TS Ocean
TS Ocean

45
40
35
30
25                                                                    Bias
Kelvins

20                                                                    Std Dev
15                                                                    RMS

10
5
0
-5   0.000   0.005     0.010     0.015     0.020      0.025   0.030

Std. Dev. of Surface Emittance

18
TS Land
TS Land

10
9
8
7
6                                                                     Bias
Kelvins

5                                                                     Std Dev
4                                                                     RMS
3
2
1
0
0.000   0.005     0.010     0.015     0.020      0.025   0.030
Std. Dev. of Surface Emittance

19
TA Ocean
TA Ocean

10

8

6
Bias
Kelvins

4                                                                     Std Dev
RMS
2

0
0.000   0.005     0.010     0.015     0.020      0.025   0.030
-2
Std. Dev. of Surface Emittance

20
TA Land
TA Land

10

8

6
Bias
Kelvins

4                                                                     Std Dev
RMS
2

0
0.000   0.005     0.010     0.015      0.020     0.025   0.030
-2
Std. Dev. of Surface Emittance

21
L Ocean
L Ocean

0.25

0.20

0.15
kg/m^2 or mm

0.10                                                                     Bias
Std Dev
0.05                                                                     RMS

0.00
0.000   0.005     0.010     0.015     0.020      0.025   0.030
-0.05

-0.10
Std. Dev. of Surface Emittance

22
L Land
L Land

0.60
0.50
0.40
0.30
kg/m^2 or mm

0.20                                                                     Bias
0.10                                                                     Std Dev
0.00                                                                     RMS

-0.10   0.000   0.005     0.010     0.015     0.020      0.025   0.030

-0.20
-0.30
-0.40
Std. Dev. of Surface Emittance

23
V Ocean
V Ocean

14

12

10
kg/m^2 or mm

8
Bias
6                                                                     Std Dev
RMS
4

2

0
0.000   0.005     0.010     0.015     0.020      0.025   0.030
-2
Std. Dev. of Surface Emittance

24
V Land
V Land

80
70
60
50
kg/m^2 or mm

40                                                                     Bias
30                                                                     Std Dev
20                                                                     RMS

10
0
-10   0.000   0.005     0.010     0.015     0.020      0.025   0.030

-20
Std. Dev. of Surface Emittance

25
Conclusions
• Atmospheric temperature (TA) is accurately
retrieved over land or ocean
•   Surface temperature (TS) is accurately retrieved
over land, but poorly retrieved over ocean
•   Liquid water (L, CLW) is marginally retrieved
over ocean, but lost in the noise over land
•   Water vapor (V, TPW) is accurately retrieved
over ocean, but probably not retrievable over
land with AMSU-A channels

26
Conclusions (cont.)
• Retrieving surface emittances instead of treating
them as model parameters is unlikely to help
•   Adding AMSU-B channels would possibly help
with land retrievals
•   Experiments with C1DOE should be performed
to see if they support these results

27
References
Rodgers, C. D., 2000: Inverse Methods for Atmospheric
Sounding: Theory and Practice. World Scientific, 238 pp.
Kohn, D. J., 1995: Refinement of a semi-empirical model
for the microwave emissivity of the sea surface as a
function of wind speed, M.S. thesis, meteorology dept.,
Texas A&M University.
Liebe, H. J., 1992: Atmospheric Attenuation and Delay
Rates from 1 to 1000 GHz. Institute for
Telecommunication Sciences, NTIA/ITS.S1, 325