A fast physical algorithm for hyperspectral sounding retrievalZhenglong Li#, Jun Li#, Timothy J. Schmit@ and M. Paul Menzel#
#Cooperative Institute for Meteorological Satellite Studies (CIMSS), University of Wisconsin-Madison@Center for Satellite Applications and Research, NESDIS
Email: [email protected]
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1. Introduction
Hyperspectral infrared (IR) radiance measurements from polar
orbiting satellite have been shown useful in weather forecasting and
nowcasting. However, current use of Hyperspectral IR (HIR) radiance
measurements is not optimal due to massive data volume. In order for
HIR measurements to have real-time impacts on weather forecasting
and nowcasting, data thinning and channel selection are the two most
commonly used methods to speed up the process. Both methods
essentially lose some fine scale information, which is very important for
meso-scale applications.
This study presents a fast physical algorithm to simultaneously
retrieve temperature, moisture and ozone profiles along with surface
temperature and emissivity using HIR radiance measurements. By
performing retrieval in Eigenvector space of radiances, the computation
is about 6 times faster than before. With this technique, the HIR
sounding retrieval on single field-of-view (SFOV) basis using more
channels may be realized in real-time, which further improves the
capability of nowcasting. This technique may also benefit the
assimilation community. Modelers may have an option to assimilate the
real-time HIR sounding retrievals using this technique with more
channels of radiance measurements.
2. 1-Dvar HIR sounding retrieval technique
The 1-Dvar technique is a commonly used physical retrieval
technique:
(1)
where
is the vector of retrieval parameters in (n+1)th iteration
is the Jacobian matrix
is the covariance matrix of satellite measurements
matrix is the inverse of the background covariance matrix
is the regularization factor
is the BT difference (DBT) between the satellite measurements and
the radiative transfer (RT) calculation in nth iteration
is the vector of retrieval parameters in nth iteration
Eq (1) is almost impossible to use with all channels because of
the huge amount of matrix operation. Usually, the retrieval state
parameters, including atmospheric profiles and surface emissivities, are
represented by Eigen Vector coefficients
(2)
where vi is the ith Eigenvector, fi is the ith expansion coefficient, L is the
number of Eigenvectors, V is the Eigenvector matrix, and F is the
expansion coefficient vector. With Eq (2), Eq (1) can be written as:
(3)
where a variable with a ^ is the variable in Eigen Vector space:
By retrieving the Eigen Vector coefficients instead of the state
parameters, the process is not only much faster, but also more stable.
Eq (3) works well for traditional sounders, such as the
Geostationary Operational Environmental Satellite (GOES) Sounder
and the High-Resolution Infrared Radiation Sounder (HIRS), because
they both have limited channels (<20). For HIR sounders, such as the
Infrared Atmospheric Sounding Interferometer (IASI) and the
Atmospheric Infrared Sounder (AIRS), there are thousands of channels.
Even after channel selection, there are still hundreds of channels. The
computation of Eq (3) is still significant.
3. The fast HIR sounding retrieval techniqueThe key to the fast HIR sounding retrieval algorithm is to perform
the retrieval in radiance Eigen Vector space instead of normal radiance
space. The observation vector can be expressed in Eigenvector space
(4)
where ui is the ith Eigenvector, gi is the ith expansion coefficient, K is the
number of Eigenvectors, U is the Eigenvector matrix and G is the
expansion coefficient vector.
With Eq (4), Eq (3) can be written as
(5)
where a variable with a ~ is the variable in radiance Eigen Vector space
Eq (5) is different from Eq (3) in that the observation is in radiance
Eigen Vector space instead of radiance space. The advantages of this
include:
1) increased computation efficiency
2) increased iteration stability
4. Application to IASI measurements
The fast physical algorithm was applied to IASI observation for
Hurricane IKE from Sep 1 2008 to Sep 14, 2008. 1649 out of 8641 IASI
channels are used. A simple linear regression technique is used to
generte the first guess. Figure 1 shows the time need to process the
granule of 20080901003559 using the old and the new algorithms.
Figure 1. Time to process the granule of 20080901003559 using the old and
the new techniques.
Figure 2 and 3 shows the validation of the IASI sounding
retrieval using collocated ECMWF analysis over land and ocean.
Land
Figure 2. IASI temperature and moisture sounding retrievals validated using
ECMWF analysis over land
Ocean
Figure 3. IASI temperature and moisture sounding retrievals validated using
ECMWF analysis over ocean
From Figure 1, 2 and 3:
1. The fast algorithm reduces the processing time by 83 %.
2. The new technique is effective in improving the first guess in both
temperature and moisture profiles.
5. Application to AIRS measurements and
background covariance matrixThe fast physical algorithm was also applied to AIRS
observations for Hurricane IKE from Sep 1 2008 to Sep 14, 2008. 1453
out of 2378 AIRS channels are used. Granule 176 on Sep 6 2008 was
randomly picked for testing the algorithm. The ECMWF analysis is used
for validation. Figure 4 and 5 shows the comparison between the old
and the new retrieval algorithm.
Figure 4. AIRS temperature and moisture sounding retrievals validated
using ECMWF.
Figure 5. AIRS TPW retrievals validated using ECMWF.
From Figure 4 and 5, the new algorithm after tuning the background
covariance matrix, improves the moisture retrieval near the surface. As
a result, the TPW STD error is reduced by 0.05 cm, and the bias error
is reduced by 0.1 cm.
6. Summary and future planBy converting the HIR radiance spectrum to Eigen Vector
expansion coefficients, the new HIR physical retrieval algorithm is
effective in reducing the computation by 83 % compared with the old
method. The application to AIRS measurements show that the new
algorithm also slightly improves moisture profile after tuning the
background covariance matrix.
Future plan focuses on two areas:
1) Application of the retrieval products. Besides validating the retrieval
products, we will focus on if the HIR retrieval products may improve
the weather forecasting, especially hurricane forecasting. With the
increased computation efficiency and more channels used, the new
physical algorithm has a potential to provide real-time high quality
retrieval products for weather forecasting.
2) Transition to CrIS. CIMSS is currently working on implementing the
HIR algorithm to CrIS onboard NPP. The successful demonstration
of CrIS is very important to JPSS program.
6. AcknowledgementThis work is partly supported by NOAA GOES-R/JPSS
programs. The views, opinions, and findings contained in this report are
those of the authors and should not be construed as an official National
Oceanic and Atmospheric Administration or U.S. government position,
policy, or decision.
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