Statistical Interpolation Using Cyclostationary EOFs

Abstract

Investigated here is the space?time estimation or statistical interpolation of a global variable based on a few observations. Estimation of a global data field is essentially a problem of optimally estimating spherical harmonic expansion coefficients. The optimal estimation technique used here is similar to that in Kim et al. An important exception is that cyclostationary empirical orthogonal functions (CSEOFs) are used to develop the estimation technique instead of regular empirical orthogonal functions (EOFs). The use of CSEOFs is motivated by the fact that many climatic variables are (approximately) cyclostationary. That is, the statistics of a climatic variable vary periodically with a distinct nested periodicity. The developed technique is applied to estimating the global field of monthly surface temperature anomalies, which is a notable example of cyclostationary processes. The CSEOFs, an essential ingredient for formulating a cyclostationary estimation technique, account for the monthly variation of the surface temperature statistics, namely much larger variance in the winter than in the summer. Further, cyclostationary statistics contain information on how different months are correlated. This allows one to use all 12 months of measurements, thereby optimizing the estimation technique both in space and time. As the test results indicate, estimation error is much reduced when using the cyclostationary technique.