Reduced Dimension of Linear Empirical Dynamical Model to Forecast Pacific Sea Surface Temperatures

Low order empirical dynamical models have been widely applied to reduce the dimensionality of nonlinear climate system while realistically represent the key dynamical processes. One such approach is the Linear Inverse Model (LIM), a linear stochastically forced dynamical system that builds on the dominant patterns of climate variability, identified through Empirical Orthogonal Function (EOF) or variants, and determines the predictable dynamics from the time-evolving amplitudes of those patterns. As EOFs seek to find the coordinates that explain the most variance of the data, the EOF-based truncation may retain the dominant large-scale climate variability. However, key precursor dynamics with relatively small-scale anomalies may not be adequately identified. A possible solution is the Hankel reduced model, by conducting the balanced truncation through transforming the dynamical system into the Hankel space spanned by both the precursor dynamics and the large-scale response. This has mainly been tested on theoretical level. In this study, we apply the Hankel-based and the EOF-based approach to reduce the dimension of the observationally based empirical dynamical system (i.e., high dimensional LIM) constrained by the monthly Pacific Sea Surface Temperatures (SSTs). This experimental design provides us a baseline full dynamical system, which allows us to examine the effectiveness of the two reduced models in approximating the Pacific system dynamics and generating skillful seasonal Pacific SST forecasts. We find that the Hankel-based approach, by capturing the precursor dynamics and the large-scale response, provides better forecast than the EOF-based approach. Our findings suggest balanced truncation could potentially be useful for many linear and nonlinear systems, for improving the computational efficiency involving a high-dimensional dynamical system, such as data assimilation of global climate models or serving as an emulator to obtain multiple realizations for probability forecasts.