Estimating the Observed Atmospheric Response to SST Anomalies: Maximum Covariance Analysis, Generalized Equilibrium Feedback Assessment, and Maximum Response Estimation

Abstract

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.

Maximum covariance analysis to identify intraseasonal oscillations over tropical Brazil

“…It is a robust method to investigate dominant modes of interaction, because it favors a better understanding of the relationship between groups of variables (Frankignoul et al 2011). It consists of constructing a covariance matrix between two datasets and then performing the Singular Value Decomposition (SVD) of the resulting matrix (Levine et al 2013).…”

Assessing Atmospheric Response to Surface Forcing in the Observations. Part I: Cross Validation of Annual Response Using GEFA, LIM, and FDT

“…The feedback matrix B can be obtained in GEFA (Frankignoul et al 1998; LWL08) with a covariance of Eq. (1.3) with earlier SST y(t 2 t) as…”

“…In line with the quasiequilibrium response, often a simultaneous regression is used. However, a simultaneous regression tends to mix the atmospheric response (to SST) with the atmospheric forcing (on SST) (Frankignoul 1999). Instead, the atmospheric response to the simultaneous SST forcing should be identified with the SST leading the atmosphere, as first proposed by Frankignoul et al (1998).…”

“…However, a simultaneous regression tends to mix the atmospheric response (to SST) with the atmospheric forcing (on SST) (Frankignoul 1999). Instead, the atmospheric response to the simultaneous SST forcing should be identified with the SST leading the atmosphere, as first proposed by Frankignoul et al (1998). This SST-led regression is the essence of the so-called generalized equilibrium feedback analysis (GEFA) method (Frankignoul et al 1998;Liu et al 2008, hereafter LWL08; see section 2 for more discussion).…”

“…Instead, the atmospheric response to the simultaneous SST forcing should be identified with the SST leading the atmosphere, as first proposed by Frankignoul et al (1998). This SST-led regression is the essence of the so-called generalized equilibrium feedback analysis (GEFA) method (Frankignoul et al 1998;Liu et al 2008, hereafter LWL08; see section 2 for more discussion). Another type of method to study the atmospheric response to multiple SST forcings (e.g., a SST field) has been based on the singular value decomposition (SVD; Bretherton et al 1992) of the covariance matrix between the atmosphere and ocean.…”