Abstract
This study makes use of a simple stochastic energy balance climate model that resolves the land–sea distribution and that includes a crude upwelling-diffusion deep ocean to study the natural variability of the surface temperature in different frequency bands. This is done by computing the eigenfunctions of the space-time lagged covariance function. The resulting frequency-dependent theoretical orthogonal functions (fdTOFs) are compared with the corresponding frequency-dependent empirical orthogonal functions (fdEOFs) derived from 40 years of data. The computed and modeled eigenvalues are consistent with the difference mainly explained by sampling error due to the short observational record. The magnitude of expected sampling errors is demonstrated by a series of Monte Carlo simulations with the model. The sampling error for the eigenvalues features a strong bias that appears in the simulations and apparently in the data. Component-by-component pattern correlations between the fdEOFs and the fdTOFs vary from 0.81 to 0.28 for the first ten components. Monte Carlo simulations show that the sampling error could be an important source of error especially in the low (interannual) frequency band. However, sampling error alone cannot satisfactorily explain the difference between the model and observations. Rather, model inaccuracy and/or spatial bias of observations seem to be important sources of error. The fdTOFs are expected to be useful in estimation/prediction/detection studies.
