AT737 Temperature Sounding Oct. 4, 2010. AT737 Temperature Sounding2 Sounding sounding n (15c) 1 a : measurement of depth esp. with a sounding line b

AT737

Temperature Sounding

Oct. 4, 2010

AT737 Temperature Sounding 2

Sounding

sounding n (15c) 1 a : measurement of depth esp. with a sounding line b : the depth so ascertained c pl : a place or part of a body of water where a hand sounding line will reach bottom 2 : measurement of atmospheric conditions at various heights 3 : a probe, test, or sampling of opinion or intention

Merriam Webster’s Collegiate Dictionary, tenth edition


Schwarzchild’s Equation

TBLd

dL

,

Assume no scattering. Thenthe Radiative Transfer Eq. becomes:

Solution:

d

TBLLo

0

000 expexp

surface term

atmospheric term

depth optical where dzd a


Weighting Function

dTBLL

o

0

000 expexp

0exp

d

d

0

1

exp

Vertical transmittance

Th

hdhhWTBLL

0

,1

00

etc. ,,),ln(,,coordinateheight ppzh

dh

dz

dh

dhW a

11 1,

Weighting

Function

1

dza


Weighting Function

aa q

dh

dz

dh

dhW a

11 1,

If you know the mixing ratio of the absorbing gas, you can calculate the atmospheric temperature

tcoefficien absorption mass

gas absorbing of ratio mixing

density catmospheri

a

q


Weighting Function Shape

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1

Transmittance

Hei

ght(

km)

0

10

20

30

40

50

60

70

80

0.00E+00 1.00E-03 2.00E-03 3.00E-03

Vol. Absorption Coef. (1/m)

Hei

ght

(km

)

0

10

20

30

40

50

60

70

80

0.00E+00

1.00E-05

2.00E-05

3.00E-05

4.00E-05

5.00E-05

Weighting Function (1/m)

Hei

ght (

km)

x W

Transmittance to satellite

For a well-mixed gas, the absorption coefficient is dominated by atmospheric density

Product has a definite peak

q


Properties of the Weighting Function

0

10

20

30

40

50

60

70

80

0.00E+00

1.00E-05

2.00E-05

3.00E-05

4.00E-05

5.00E-05

Weighting Function (1/m)

Hei

ght (

km)

Th

hdhhWTBLL

0

,1

00

• Weighting function weights the Planck radiance

• Measured radiance is a weighted average of Planck function plus a surface term

• Weighting function is unavoidably broad

1

01,0

dhhWTh

h


Sampling the Atmosphere

0

10

20

30

40

50

60

70

80

0.00 0.01 0.02 0.03 0.04 0.05

Weighting Function (1/km)

Hei

ght (

km)

Create a family of weighting functions by changing the wavelength/spectral resolution (mass absorption coefficient)

But…


The Real World is Messy

1 2

3

4

GOES Sounder Channels

Transmittance above 40 km


GOES Sounder Weighting Functions

Not as “regular” as one would like


AMSU Weighting Functions


Spectrometers

IASI (Four Adjacent Spectra Red, black, blue, green)

AIRS (1528 Retrieval Channels in Red)

10 5 (m) 78 69 412.5


AIRS Weighting Functions

2378 Channels!


Sounding Retrieval

Lots of ways to do it. One way:

1. Make a first guess (the better the first guess, the better the result)

2. Calculate radiances

3. Compare with satellite-observed radiances

4. Adjust temperatures to better match radiances

5. Repeat until satisfactory convergence is achieved.


Sounding Retrieval

Because weighting functions are broad, retrieved soundings are smooth.


Limb Sounding

Great vertical resolution…

…but poor horizontal resolution.


Soundings for NWP

Direct Radiance Insertion Model ingests radiances Retrieval done inside model Big advantage: retrieved temps consistent with

other model fields, so the results persist, rather than radiating away as gravity waves.

Volume of satellite data much larger than volume of conventional data even though only a fraction of satellite data are used


CIRA 1DVAR Optimal Estimator (C1DOE) Data Flow

C1DOE Retrieval

AMSU-A AMSU-B

SST / LST(GDAS)

Dynamic Data

Land Emissivity (MEM - AGRMET)

Outputs

• Mixing ratio profile, temperature profile, cloud liquid water profile

• 6 Emissivity bands

• TPW

• Integrated CLW

• Many diagnostics!

Errors and Correlations

(Sa and Sy)

InstrumentProperties

(Capability for SSMIS)

T(p), RH (p), Tsfc (GDAS)

Cloud mask(optional)

First Guess and a priori data

Near real-time system has

been demonstrated


Bias Correction for RTM Vital

Channel

-4

-2

0

2

4

windows

DT

b O

bs

– M

od

el (

K)

26

leve

l – 7

leve

l RT

M

1 2 3 4 5 6 7 8 16 17 18 19 20

Channel

0

-2

-4

2

4

1 2 3 4 5 6 7 8 16 17 18 19 20

Model Bias for 26 vertical RTM levels Minus 7 Levels

CH 1 = 23.8CH 2 = 31.4CH 3 = 50.3

CH 4-8 = T(p)CH 16 = 89

CH 17 = 150 CH 18-20 = 183

window windows

window

• Simulated TB’s calculated from pristine, clear sky, island sonde matchups and compared to AMSU TB’s.

• Further refinement in progress

All zenith angles


C1DOE Retrieval Methodology

First guess atmosphere and surfaceCalculate weighting functions (sensitivity)Forward problem solved to yield estimates of the radiance in each channel

Millimeter Wave Propagation (MPM92) Model (Liebe et al. 1993)

Rayleigh cloud droplet absorption (Liebe et al. 1991) assuming a plane parallel, non-scattering atmosphere

Match observed and modeled radiancesIterative process

Additional details in Rodgers (2000)


Inverse problems

Satellites provide measurements of radiation (i.e. brightness temperatures).The user must make use of models in order to extrapolate atmospheric parameters from these measurements. This is known as an inverse problem. The nature of inverse problems can be understood using the “footprint”

analogy.


Inverse problems (cont.)

The relationship between the measured radiances, and the state vector is given by:

where x is the state vector, b

contains the model parameters, y is the measurement error, and f is the forward model.

ybxfy ,


Inverse problems (cont.)

Linearizing about the real state vector and the real model parameters leads to:

where x contains the estimated water vapor

profiles, temperature profiles and 5 emissivities, and b is the estimated model parameter vector.

The derivative terms are important for determining sensitivities of the radiances to both the model parameters and the water vapor profiles.

ybbb

Fxx

x

FbxFbxy

ˆˆ,ˆ,ˆ


Optimal Estimation

OE is a method used to introduce constraints to a systemA cost function must be minimized in order to find the optimal solution for the atmospheric state


Cost function

The cost function used in the C1DOE is given by:

The first term is a penalty for deviating from the first guess (first guess and a priori are equivalent in this retrieval). This limits the outcome to only physical solutions.The second term is a penalty for deviations of the simulated radiances from the forward model output. This is a way to constrain the forward model and observational errors.

xFySxFyxxSxx yT

aaT

a ˆˆ 11


C1DOE cost function (Φ):

2 TERM

1A

T

1 TERM

1Y

T )x(xS)x(xb))f(x,(ySb))f(x,(yΦAA

Model and

tsMeasuremen in Errors SY

*Error per channel (<= 3.5 K)•NEDT (noise)•Forward Model error•Biases: sensor - model

Minimize Differences between Observed and Simulated Tbs

Minimize Differences between a priori and retrieved states

T(p) and q(p) between

nscorrelatio and xin Errors S aA

*A priori errors•q(p): 25-50% RH•w(p): 0.15 mm •T(p): 1.5 K, ε: 0.01

A priori ensures solution is physical and acts as a virtual measurement to further constrain the problem.


Data – The Advanced Microwave Sounding Unit (AMSU)

Two modules: AMSU – A and AMSU – B (MHS)

20 channels: 23.8 to 183 GHz

Spatial resolution from 16 – 48 km at nadir

NEDT values ranging from 0.11 to 1.06 K (very low)

On NOAA satellites and Aqua Microwave Transmittance Spectrum

183 GHz used for moisture sounding


AMSU

Data came from the Advanced Microwave Sounding Unit (AMSU)20 channel microwave radiometerCh. 1-15 used for temperature (AMSU-A)Ch. 16-20 used for water vapor

(AMSU-B)


AMSU-A Channelization

Table 3.3.2.1-1. Channel Characteristics and Specifications of AMSU-A

Documents

AT737 Temperature Sounding Oct. 4, 2010. AT737 Temperature Sounding2 Sounding sounding n (15c) 1 a : measurement of depth esp. with a sounding line b