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The authors systematically investigate two easily computed measures of the effective number of spatial degrees of freedom (ESDOF), or number of independently varying spatial patterns, of a time-varying field of data. The first measure is based on matching the mean and variance of the time series of the spatially integrated squared anomaly of the field to a chi-squared distribution. The second measure, which is equivalent to the first for a long time sample of normally distributed field values, is based on the partitioning of variance between the EOFs. Although these measures were proposed almost 30 years ago, this paper aims to provide a comprehensive discussion of them that may help promote their more widespread use. The authors summarize the theoretical basis of the two measures and considerations when estimating them with a limited time sample or from nonnormally distributed data. It is shown that standard statistical significance tests for the difference or correlation between two realizations of a field (e.g., a forecast and an observation) are approximately valid if the number of degrees of freedom is chosen using an appropriate combination of the two ESDOF measures. Also described is a method involving ESDOF for deciding whether two time-varying fields are significantly correlated to each other. A discussion of the parallels between ESDOF and the effective sample size of an autocorrelated time series is given, and the authors review how an appropriate measure of effective sample size can be computed for assessing the significance of correlations between two time series.

We examine the advances in our understanding of extratropical atmosphere-ocean interaction over the past decade and a half, focusing on the atmospheric response to sea surface temperature anomalies. The main goal of the paper is to assess what was learned from general circulation model (GCM) experiments over the recent two decades or so. Observational evidence regarding the nature of the interaction and dynamical theory of atmospheric anomalies forced by surface thermal anomalies are reviewed. We then proceed to examine three types of GCM experiments used to address this problem: models with fixed climatological conditions and idealized, stationary SST anomalies; models with seasonally evolving climatology forced with realistic, time-varying SST anomalies; and models coupled to an interactive ocean. From representative recent studies, we argue that the extratropical atmosphere does respond to changes in underlying SST although the response is small compared to internal (unforced) variability. Two types of interactions govern the response: One is an eddy-mediated process, in which a baroclinic response to thermal forcing induces and combines with changes in the position or strength of the storm tracks. This process can lead to an equivalent barotropic response that feeds back positively on the ocean mixed layer temperature. The other is a linear, thermodynamic interaction in which an equivalent-barotropic low-frequency atmospheric anomaly forces a change in SST and then experiences reduced surface thermal damping due to the SST adjustment. Both processes contribute to an increase in variance and persistence of low-frequency atmospheric anomalies and, in fact, may act together in the natural system.

Observations and sea surface temperature (SST)-forced ECHAM5 simulations are examined to study the seasonal cycle of eastern Africa rainfall and its SST sensitivity during 1979-2012, focusing on interannual variability and trends. The eastern Horn is drier than the rest of equatorial Africa, with two distinct wet seasons, and whereas the October-December wet season has become wetter, the March-May season has become drier.The climatological rainfall in simulations driven by observed SSTs captures this bimodal regime. The simulated trends also qualitatively reproduce the opposite-sign changes in the two rainy seasons, suggesting that SST forcing has played an important role in the observed changes. The consistency between the sign of 1979-2012 trends and interannual SST-precipitation correlations is exploited to identify the most likely locations of SST forcing of precipitation trends in the model, and conceivably also in nature. Results indicate that the observed March-May drying since 1979 is due to sensitivity to an increased zonal gradient in SST between Indonesia and the central Pacific. In contrast, the October-December precipitation increase is mostly due to western Indian Ocean warming.The recent upward trend in the October-December wet season is rather weak, however, and its statistical significance is compromised by strong year-to-year fluctuations. October-December eastern Horn rain variability is strongly associated with El Niño-Southern Oscillation and Indian Ocean dipole phenomena on interannual scales, in both model and observations. The interannual October-December correlation between the ensemble-average and observed Horn rainfall 0.87. By comparison, interannual March-May Horn precipitation is only weakly constrained by SST anomalies.Corresponding author address: Brant Liebmann, CIRES, University of Colorado,