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On the Assessment of Nonlocal Climate Feedback. Part II: EFA-SVD and Optimal Feedback Modes

Zhengyu LiuDepartment of Atmospheric and Oceanic Science, Center for Climatic Research, University of Wisconsin—Madison, Madison, Wisconsin

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Na WenPhysical Oceanography Laboratory, The Ocean University of China, Qingdao, China

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Abstract

The equilibrium feedback assessment (EFA) is combined with the singular value decomposition (SVD) to assess the large-scale feedback modes from a lower boundary variability field onto an atmospheric field. The leading EFA-SVD modes are the optimal feedback modes, with the lower boundary forcing patterns corresponding to those that generate the largest atmospheric responses, and therefore provide upper bounds of the feedback response. The application of EFA-SVD to an idealized coupled ocean–atmosphere model demonstrates that EFA-SVD is able to extract the leading feedback modes successfully. Furthermore, these large-scale modes are the least sensitive to sampling errors among all the feedback processes and therefore are the most robust for statistical estimation. The EFA-SVD is then applied to the observed North Atlantic ocean–atmosphere system for the assessment of the sea surface temperature (SST) feedback on the surface heat flux and the geopotential height, respectively. The dominant local negative feedback of SST on heat flux is confirmed, with an upper bound of about 40 W m−2 K−1 for basin-scale anomalies. The SST also seems to exert a strong feedback on the atmospheric geopotential height: the optimal SST forcing has a dipole pattern that generates an optimal response of a North Atlantic Oscillation (NAO) pattern, with an upper bound of about 70 m K−1 at 500 hPa. Further issues on the EFA-SVD analysis are also discussed.

Corresponding author address: Z. Liu, CCR, 1225 W. Dayton St., Madison, WI 53706. Email: zliu3@wisc.edu

Abstract

The equilibrium feedback assessment (EFA) is combined with the singular value decomposition (SVD) to assess the large-scale feedback modes from a lower boundary variability field onto an atmospheric field. The leading EFA-SVD modes are the optimal feedback modes, with the lower boundary forcing patterns corresponding to those that generate the largest atmospheric responses, and therefore provide upper bounds of the feedback response. The application of EFA-SVD to an idealized coupled ocean–atmosphere model demonstrates that EFA-SVD is able to extract the leading feedback modes successfully. Furthermore, these large-scale modes are the least sensitive to sampling errors among all the feedback processes and therefore are the most robust for statistical estimation. The EFA-SVD is then applied to the observed North Atlantic ocean–atmosphere system for the assessment of the sea surface temperature (SST) feedback on the surface heat flux and the geopotential height, respectively. The dominant local negative feedback of SST on heat flux is confirmed, with an upper bound of about 40 W m−2 K−1 for basin-scale anomalies. The SST also seems to exert a strong feedback on the atmospheric geopotential height: the optimal SST forcing has a dipole pattern that generates an optimal response of a North Atlantic Oscillation (NAO) pattern, with an upper bound of about 70 m K−1 at 500 hPa. Further issues on the EFA-SVD analysis are also discussed.

Corresponding author address: Z. Liu, CCR, 1225 W. Dayton St., Madison, WI 53706. Email: zliu3@wisc.edu

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