CMG Research: Enhanced Empirical Orthogonal Function (EOF) Representations and Time-varying Statistical Models for Climate Patterns

University Of California-Irvine, Irvine CA

Investigators

Abstract

This project seeks to develop statistical methods to identify and analyze patterns of large-scale climate variability. Climate dynamicists have traditionally relied on Empirical Orthogonal Function (EOF) analysis (equivalent to principle component analysis) to characterize and study climate variability patterns, yet EOF analysis has several known limitations, particularly the assumption that the patterns do not change over time, and the lack of error analysis accompanying the method. The PIs would use modern statistical methods to develop alternative representations of the climate patterns to address both of these limitations. The core of the approach is a parameterized model for the covariance of a meteorological field (e.g., the covariance of mean sea level pressure, or MSLP, that is typically used to define the North Atlantic Oscillation, or NAO) based on a relatively small number of parameters. The low-dimensional parameterization offers a number of advantages when compared to traditional EOF/principal component analysis. The parameters of the model correspond to important features of the climate pattern, e.g., locations of centers of action. Statistical inference using the model naturally produces estimates of variability, which can be used to evaluate apparent movement in the climate pattern over time. Also, the model can be generalized to allow for variation in key climate pattern features over time. The primary method consists of expressing the covariance matrix of meteorological variables (e.g. MSLP over a set of gridded locations) in terms of specified spatial basis functions (e.g. "Mexican hat" functions) which are dependent on a small set of parameters whose values can be adjusted to maximize a log-likelihood function. Bayesian methods would also be used to obtain parameter estimates and uncertainty estimates, in order to relax the assumption of normally distributed variance. The parameters of the model would have clear physical interpretations, like the locations of centers of action. The initial application of the new statistical analysis will be to the variability of the NAO, motivated by recent papers which claim that 1) the NAO pattern in MSLP is nonstationary as the northern center of action drifted northeastward during the 1980s and 1990s, 2) the pattern varies depending on seasonality, and 3) the negative phase of the NAO is more persistent than the positive phase. The implications of these effects for the interaction between the NAO and other climate system components, particularly Arctic sea ice, will be explored. Similar issues will be explored for the Southern Hemisphere annular mode (SAM), which has nonstationary behavior generally ascribed to changes in the Antarctic ozone hole. EOF analysis is ubiquitous in climate studies, so progress in developing alternatives which do not suffer from the lack of error analysis and the stationarity assumption could have extensive use throughout the field of climate dynamics, and perhaps more generally in the geoscience community. The work will also support two graduate students, one in a statistics program and the other in an atmospheric science program, who will benefit from exposure to interdisciplinary research in mathematical geoscience.