A linear stochastic emulator of the California Current system using balanced truncation

Abstract

A downscaled reanalysis for the California Current system is used to construct a low-dimensional linear stochastic emulator of the 3-dimensional time evolving ocean circulation. The approach used is based on balanced truncation which simultaneously draws on information from the Empirical Orthogonal Functions (EOFs) and stochastic optimals of the ocean state-vector. In this way, balanced truncation faithfully preserves the inherent stability properties of the data, unlike the more traditional approaches based on truncation using EOFs alone. Since balanced truncation is predicated on singular value decomposition, formal error bounds on the accuracy of the reduced-dimension system can be computed. In addition, linear stochastic emulators that target different physical processes can also be constructed, and examples that focus on a region dominated by coastal upwelling are presented. Linear stochastic emulators, such as that developed here, can be exploited to generate very long simulations (or large ensembles) at high resolution that can be used to establish a statistical baseline for important oceanic processes, calculations that would otherwise be very challenging by direct numerical integration. An example is presented.