Estimating the observed atmospheric response to SST anomalies : maximum covariance analysis, generalized equilibrium feedback assessment, and maximum response estimation

Three multivariate statistical methods to estimate the influence of SST or boundary forcing on the atmosphere are discussed. Lagged maximum covariance analysis (MCA) maximizes the covariance between the atmosphere and prior SST, thus favoring large responses and dominant SST patterns. However, it does not take into account the possible SST evolution during the time lag. To correctly represent the relation between forcing and response, a new SST correction is introduced. The singular value decomposition (SVD) of generalized equilibrium feedback assessment (GEFA-SVD) identifies in a truncated SST space the optimal SST patterns for forcing the atmosphere, independently of the SST amplitude; hence it may not detect a large response. A new method based on GEFA, named maximum response estimation (MRE), is devised to estimate the largest boundary-forced atmospheric signal. The methods are compared using synthetic data with known properties and observed North Atlantic monthly anomaly data. The synthetic data shows that the MCA is generally robust and essentially unbiased. GEFA SVD is less robust and sensitive to the truncation. MRE is less sensitive to truncation and nearly as robust as MCA, providing the closest approximation to the largest true response to the sample SST. To analyze the observations, a 2-month delay in the atmospheric response is assumed based on recent studies. The delay strongly affects GEFA SVD and MRE, and it is key to obtaining consistent results between MCA and MRE. The MCA and MRE confirm that the dominant atmospheric signal is the NAO-like response to North Atlantic horseshoe SST anomalies. When the atmosphere is considered in early winter, the response is strongest and MCA most powerful. With all months of the year, MRE provides the most significant results. GEFA SVD yields SST patterns and NAO-like atmospheric responses that depend on lag and truncation, thus lacking robustness. When SST leads by 1 month, a significant mode is found by the three methods, but it primarily reflects, or is strongly affected by, atmosphere persistence