A Comparison Study of EOF Techniques : Analysis of Nonstationary Data with Periodic

Identi cation of independent physical/dynamical modes and corresponding principal component time series is an important aspect of climate studies for they serve as a tool for detecting and predicting climate changes. While there are a number of di erent eigen techniques their performance for identifying independent modes varies. Considered here are comparison tests of eight eigen techniques in identifying independent patterns from a dataset. A particular emphasis is given to cyclostationary processes such as deforming and moving patterns with cyclic statistics. Such processes are fairly common in climatology and geophysics. Two eigen techniques that are based on the cyclostationarity assumption| cyclostationary empirical orthogonal functions (EOFs) and periodically extended EOFs| perform better in identifying moving and deforming patterns than techniques based on the stationarity assumption. Application to a tropical Paci c surface temperature eld indicates that the rst dominant pattern and the corresponding principal component (PC) time series are consistent among di erent techniques. The second mode and the PC time series, however, are not very consistent from one another with hints of signi cant modal mixing and splitting in some of derived patterns. There also is a detailed di erence of intraannual scale between PC time series of a stationary technique and those of a cyclostationary one. This may bear an important implication on the predictability of El Ni~ no. Clearly there is a choice of eigen technique for improved predictability. 1