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: zhenglong.li@ssec.wisc.edu

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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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