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A fast physical algorithm for hyperspectral sounding retrieval Zhenglong 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 316 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 n th iteration is the vector of retrieval parameters in n th 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 v i is the i th Eigenvector, f i is the i th 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 technique The 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 u i is the i th Eigenvector, g i is the i th 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 matrix The 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 plan By 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. Acknowledgement This 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. New old

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