Practical Approximations to Seasonal Fluctuation–Dissipation Operators Given a Limited Sample

Abstract

his paper studies operators inspired by the fluctuation?dissipation theorem that consider the seasonality (nonstationarity) of the climate system under conditions of limited sample size relevant to application of the method to observational records. The approach is used to predict the steady-state response of an atmospheric general circulation model to localized temperature perturbations.A seasonal operator nominally requires a much larger data sample than a stationary operator; the authors study some strategies to overcome this. First, two methods for approximating the seasonality of the system are examined. Second, an alternative ?transpose approach? to the standard dimension reduction is considered that is more efficient and accurate for small sample sizes and additionally enables the use of a kernel, which provides a convenient way to incorporate prior physical understanding into the operator.All operators show considerable skill in predicting seasonal responses for a variety of variables (temperature, winds, rainfall, and cloud cover) and better skill in predicting the annual-mean ones. A comparison of these predictions to ones done on the same system with temporally fixed boundary conditions shows unexpectedly that skill is, if anything, improved by the presence of a seasonal cycle. The authors suggest that the extra complexity due to a seasonal system is outweighed by the added information due to the seasonal forcing and the effect of seasonality in smoothing out prediction errors.