Cordero-Fuentes, Marangelly

Evans, Frank

McCarty, William

Moradi, Isaac

NASA Technical Reports Server

Assimilation of Microwave Cloudy Radiances into NASA
GEOS Model Using a Novel Bayesian Monte Carlo
Technique
Isaac Moradi1,2 Frank Evans3,
William McCarty1, Marangelly Cordero-Fuentes1
1. GMAO/GSFC/NASA, 2. ESSIC, University of Maryland,
3. U. of Colorado
17th JCSDA Technical Review Meeting and Science Workshop,
May 29 - 31, 2019
Washington, DC, USA
May 29, 2019
https://ntrs.nasa.gov/search.jsp?R=20190029105 2019-09-26T19:52:21+00:00Z
This work is supported by the NASA Data for
Operation and Assessment program, grant#
NNX17AE89G. Many thanks to NDOA Program
Manager, Dr. Tsengdar Lee.
Outline
Definitions
Motivation of the work
Bayesian Monte Carlo Integration (BMCI) technique
Implementation into NASA GEOS
Results
All-weather radiative transfer calculations
Cost function for 3D-Var Data Assimilation:
J(~x) =
Jb︷ ︸︸ ︷
1
2
(~x − ~xb)T ~B−1(~x − ~xb) +
Jo︷ ︸︸ ︷
1
2
(H(~x)− ~y)T ~R−1(H(~x)− ~y)
Relation between the observations (y) and the forward operator (H) can be expressed
as: y = H(~x , ~pb, ~ps) + 
~x state vector, ~pb parameters such as shape and size distribution of hydrometers, ~ps
indicates the scattering parameters (e.g., phase function)
dIν
dx
= −(αν + Sν)Iν + ανBν(T ) + SνJν
Jν =
∫
pν(Ω)IνdΩ
Limitations of direct assimilation of cloudy radiances
Inaccuracy in the first-guess: the models do not provide a close first guess for cloud
parameters or clouds are often displaced.
Lack of required RT inputs: ~ps neither provided by the model nor fully measurable
thus estimated from limited in-situ/aircraft measurements.
Non-linearity in the forward model: ~x is the mean value of the model variables
within grid-box and because H is non-linear: H(~x) 6= H(~¯x).
Limitations of direct assimilation of cloudy radiances
Inaccuracy in the first-guess: the models do not provide a close first guess for cloud
parameters or clouds are often displaced.
Lack of required RT inputs: ~ps neither provided by the model nor fully measurable
thus estimated from limited in-situ/aircraft measurements.
Non-linearity in the forward model: ~x is the mean value of the model variables
within grid-box and because H is non-linear: H(~x) 6= H(~¯x).
Limitations of direct assimilation of cloudy radiances
Inaccuracy in the first-guess: the models do not provide a close first guess for cloud
parameters or clouds are often displaced.
Lack of required RT inputs: ~ps neither provided by the model nor fully measurable
thus estimated from limited in-situ/aircraft measurements.
Non-linearity in the forward model: ~x is the mean value of the model variables
within grid-box and because H is non-linear: H(~x) 6= H(~¯x).
Limitations of direct assimilation of cloudy radiances
Inaccuracy in the first-guess: the models do not provide a close first guess for cloud
parameters or clouds are often displaced.
Lack of required RT inputs: ~ps neither provided by the model nor fully measurable
thus estimated from limited in-situ/aircraft measurements.
Non-linearity in the forward model: ~x is the mean value of the model variables
within grid-box and because H is non-linear: H(~x) 6= H(~¯x).
Simplified RT models: Operational RT models that use a simplified RT framework,
such as spherical hydrometeors, which is not appropriate at higher microwave
frequencies where ice scattering is important.
Assuming Gaussian Errors: DA systems assume Gaussian error statistics, examined
using the departures, but in the case of cloudy radiances the departures are likely
to be non-Gaussian.
Limitations of direct assimilation of cloudy radiances
Inaccuracy in the first-guess: the models do not provide a close first guess for cloud
parameters or clouds are often displaced.
Lack of required RT inputs: ~ps neither provided by the model nor fully measurable
thus estimated from limited in-situ/aircraft measurements.
Non-linearity in the forward model: ~x is the mean value of the model variables
within grid-box and because H is non-linear: H(~x) 6= H(~¯x).
Simplified RT models: Operational RT models that use a simplified RT framework,
such as spherical hydrometeors, which is not appropriate at higher microwave
frequencies where ice scattering is important.
Assuming Gaussian Errors: DA systems assume Gaussian error statistics, examined
using the departures, but in the case of cloudy radiances the departures are likely
to be non-Gaussian.
The BMCI technique
The BMCI technique can be summarized in three steps:
I generation of a retrieval database of atmospheric state and cloud variables
using a-priori information. The database should also include extreme cases
as the extrapolation is not allowed.
I the atmospheric state and cloud variables are fed into the RT model to gen-
erate the synthetic observations. In addition to the state variables such as
temperature, water vapor, and cloud profiles, cloud microphysics and param-
eterization such as particles’ shape and size distribution are also utilized as
input.
I real measurements along with the generated database are given to the re-
trieval package, then the retrieval package will select the cases which are
close to the real measurements and integrate them according to the Bayes’
theorem to give the estimate of the mean and uncertainty of the state and
cloud variables.
The BMCI technique
The BMCI technique can be summarized in three steps:
I generation of a retrieval database of atmospheric state and cloud variables
using a-priori information. The database should also include extreme cases
as the extrapolation is not allowed.
I the atmospheric state and cloud variables are fed into the RT model to gen-
erate the synthetic observations. In addition to the state variables such as
temperature, water vapor, and cloud profiles, cloud microphysics and param-
eterization such as particles’ shape and size distribution are also utilized as
input.
I real measurements along with the generated database are given to the re-
trieval package, then the retrieval package will select the cases which are
close to the real measurements and integrate them according to the Bayes’
theorem to give the estimate of the mean and uncertainty of the state and
cloud variables.
The BMCI technique
The BMCI technique can be summarized in three steps:
I generation of a retrieval database of atmospheric state and cloud variables
using a-priori information. The database should also include extreme cases
as the extrapolation is not allowed.
I the atmospheric state and cloud variables are fed into the RT model to gen-
erate the synthetic observations. In addition to the state variables such as
temperature, water vapor, and cloud profiles, cloud microphysics and param-
eterization such as particles’ shape and size distribution are also utilized as
input.
I real measurements along with the generated database are given to the re-
trieval package, then the retrieval package will select the cases which are
close to the real measurements and integrate them according to the Bayes’
theorem to give the estimate of the mean and uncertainty of the state and
cloud variables.
Beam filling
Beam filling was calculated as the difference between the brightness temperatures weighted
according to an elliptical Gaussian beam pattern and Tbs calculated using the average profiles.
The profiles were generated with 5km resolution using stochastic statistics derived from GPM
DPR and central profiles IWP and rain rate.
Top: SkinTemp (left), IWP (right), Bottom: Rain WP (left), Surface Wind Speed (right)
Correlated observation errors
SST Analysis
180°W 120°W 60°W 0° 60°E 120°E 180°E
60°S
45°S
30°S
15°S
0°
15°N
30°N
45°N
3.0
1.5
0.0
1.5
3.0
4.5
6.0
7.5
9.0
SST Analysis
66°W 60°W 54°W 48°W 42°W 36°W 30°W 24°W
9°N
12°N
15°N
18°N
21°N
24°N
27°N
30°N
2.0
1.6
1.2
0.8
0.4
0.0
0.4
0.8
1.2
66°W 60°W 54°W 48°W 42°W 36°W 30°W 24°W
9°N
12°N
15°N
18°N
21°N
24°N
27°N
30°N
0.15
0.30
0.45
0.60
0.75
0.90
1.05
1.20
Mean
obs minus forecast
Std
obs minus forecast
Analysis Intensity Error
Forecast Intensity Error
Forecast Track Error
Irma Track in GEOS-5 Forecast
NoSatellite C360C
Irma Track in GEOS-5 Forecast
GEOSOper C360C
Irma Track in GEOS-5 Forecast
GBATMSGBGMI thin C360C
Wind speed (km/h) profiles
GEOSOper C360C GBATMSGBGMI thin C360C
Temperature anomaly
GEOSOper C360C GBATMSGBGMI thin C360C
Conclusions
I Conventional data assimilation schemes cannot properly assimilate satellite
radiances in the rainband of tropical cyclones due to inaccuracy in RT
scattering parameters as well as inaccuracy in the first guess provided by
NWP models
I A new technique is proposed that does not depend on the minimization of
the cost function.
I Preliminary results from BMCI technique are encouraging but require
extensive validation, though validation itself is challenging
I These retrieved profiles are valuable for both analyzing the structure of the
hurricanes as well as to provide more accurate initial conditions for the NWP
models
Thank you for
your attention!


Assimilation of Microwave Cloudy Radiances into NASA GEOS Model Using a Novel Bayesian Monte Carlo Technique

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