at737 temperature sounding oct. 4, 2010. at737 temperature sounding2 sounding sounding n (15c) 1 a :...
TRANSCRIPT
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
AT737 Temperature Sounding 3
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
AT737 Temperature Sounding 4
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
AT737 Temperature Sounding 5
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
AT737 Temperature Sounding 6
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
AT737 Temperature Sounding 7
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
AT737 Temperature Sounding 8
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…
AT737 Temperature Sounding 9
The Real World is Messy
1 2
3
4
GOES Sounder Channels
Transmittance above 40 km
AT737 Temperature Sounding 10
GOES Sounder Weighting Functions
Not as “regular” as one would like
AT737 Temperature Sounding 11
AMSU Weighting Functions
AT737 Temperature Sounding 12
Spectrometers
IASI (Four Adjacent Spectra Red, black, blue, green)
AIRS (1528 Retrieval Channels in Red)
10 5 (m) 78 69 412.5
AT737 Temperature Sounding 13
AIRS Weighting Functions
2378 Channels!
AT737 Temperature Sounding 14
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.
AT737 Temperature Sounding 15
Sounding Retrieval
Because weighting functions are broad, retrieved soundings are smooth.
AT737 Temperature Sounding 16
Limb Sounding
Great vertical resolution…
…but poor horizontal resolution.
AT737 Temperature Sounding 17
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
AT737 Temperature Sounding 18
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
AT737 Temperature Sounding 19
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
AT737 Temperature Sounding 20
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)
AT737 Temperature Sounding 21
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.
AT737 Temperature Sounding 22
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 ,
AT737 Temperature Sounding 23
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
AT737 Temperature Sounding 24
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
AT737 Temperature Sounding 25
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
AT737 Temperature Sounding 26
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.
AT737 Temperature Sounding 27
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
AT737 Temperature Sounding 28
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)
AT737 Temperature Sounding 29
AMSU-A Channelization
Table 3.3.2.1-1. Channel Characteristics and Specifications of AMSU-A