A Bayesian Approach to Regional Decadal Predictability: Sparse Parameter Estimation in High-Dimensional Linear Inverse Models of High-Latitude Sea Surface Temperature Variability
The parameters of a Linear Inverse Model (LIM; i.e., the drift and diffusion matrices) must be inferred from data, and the traditional approach is to use simple point estimates. Here, we use Bayesian methods to estimate these parameters for sea surface temperature (SST) distributions from the Community Earth System Model (CESM).
We find that the use of Bayesian methods with informative priors for LIM parameter estimation is significantly more skillful in forecasts than traditional ML point estimates, and can better estimate the underlying probability distribution of the data. Moreover, the choice of prior distribution has an appreciable impact on estimation outcomes, and priors that emphasize physically relevant properties enhance the model’s ability to capture the variability of SST anomalies.
We advocate for a Bayesian approach to LIMs as a way to 1) address the ill-conditioned nature of high-dimensional parameter estimation by providing a formal way to regularize the parameter distributions and 2) produce well-calibrated predictive uncertainties. This strategy has been tested and compared to traditional LIM modeling at recovering LIM parameter values and at forecasting high-latitude SST anomalies. We find that the Bayesian approach to statistical forecasting may produce significant recovery and calibration benefits, especially in terms of regional predictability, when compared to simple ML-based point estimation.