EOFs of Climate Variability in Finite Interval and its Application in Climate signal Detection

Empirical orthogonal function (EOF) analysis is an important tool for climate studies. An important use of EOF analysis is in representing climate variability in terms of an orthogonal basis set. Many recent studies have employed EOF basis sets in conjunction with the development of climate signal detection and estimation methods.

With an infinitely long temporal segment, space-time EOFs associated with a stationary process can be factored into a product of spatial and temporal parts; EOFs associated with a periodically correlated process may be factored into a product of Bloch functions and Fourier components. In other words, each frequency component has attached a distinct string of spatial EOFs or Bloch functions. In most climate studies, observations are not sufficiently long and sampling errors contaminate the observational records. When the time interval is finite, the space-time EOFs can no longer be factored and the above Fourier series approximation will not hold.

This study presents a computational method of computing the eigenvalues and eigenfunctions of the lagged covariance matrices for both stationary and periodically correlated processes but with both taken on a finite interval for univariate and multivariate time series. Our numerical results show that the eigenfunctions are similar to their sine/cosine counterparts with some distortion, especically near the ends of the interval. The results may be applied to a variety of estimation and detection problems.

As an example, we calculate the EOFs and periodic EOFs of global scale climate variability on a 50 year interval and apply them in detecting anthropogenic climate signals in the surface temperature field from 1943 to 1993. We find that (1) all climate models in this study, including UK Hadley Center GCM, Germany ECHAM3/LSG GCM and Texas A&M University EBM, tend to overpredict the response to greenhouse-gas forcing by 20-40%; (2) The utilization of this periodic variation of globally cliamte variability statistics enhances our chances of detecting anthropogenic signals and improves detection performance. For the anthropogenic aerosol signal, the signal-to-noise ratio can be increased at least 30% by using periodic EOF representation of climate variability than EOF representation.