This paper is about the statistical correction of systematic errors in dynamical sea surface temperature (SST) prediction systems using linear regression approaches. The typically short histories of model forecasts create difficulties in developing regression-based corrections. The roles of sample size, predictive skill, and systematic error are examined in evaluating the benefit of a linear correction. It is found that with the typical 20 yr of available model SST forecast data, corrections are worth performing when there are substantial deviations in forecast amplitude from that determined by correlation with observations. The closer the amplitude of the uncorrected forecasts is to the optimum squared error-minimizing amplitude, the less likely is a correction to improve skill. In addition to there being less "room for improvement," this rule is related to the expected degradation in out-of-sample skill caused by sampling error in the estimate of the regression coefficient underlying the correction.Application of multivariate [canonical correlation analysis (CCA)] correction to three dynamical SST prediction models having 20 yr of data demonstrates improvement in the cross-validated skills of tropical Pacific SST forecasts through reduction of systematic errors in pattern structure. Additional beneficial correction of errors orthogonal to the CCA modes is achieved on a per-gridpoint basis for features having smaller spatial scale. Until such time that dynamical models become freer of systematic errors, statistical corrections such as those shown here can make dynamical SST predictions more skillful, retaining their nonlinear physics while also calibrating their outputs to more closely match observations.
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