This paper proposes a regularized regression procedure for finding a predictive relation between one variable and a field of other variables. The procedure estimates a linear prediction model under the constraint that the regression coefficients have smooth spatial structure. The smoothness constraint is imposed using a novel approach based on the eigenvectors of the Laplace operator over the domain, which results in a constrained optimization problem equivalent to either ridge regression or least absolute shrinkage and selection operator (LASSO) regression, which can be solved by standard numerical software. In addition, this paper explores an unconventional procedure whereby regression models are estimated from dynamical model output and then verified against observations-the reverse of the traditional order. The methodology is illustrated by constructing statistical prediction models of summer Texas-area temperature based on concurrent Pacific sea surface temperature (SST). None of the regularized regression models have statistically significant skill when estimated from observations. In contrast, when estimated from dynamical model output, the regression models have skill with respect to dynamical model data because of the substantially larger sample size available from dynamical model output. In addition, the regression models estimated from dynamical model data can predict observed anomalies with significant skill, even though no observations were used directly to estimate the regression models. The results indicate that dynamical models had no significant skill because they could not accurately predict the SST itself, not because they could not capture realistic SST teleconnections.
Bibliographical noteFunding Information:
We thank Michael K. Tippett, Andrew Rhines, acting as reviewer, and another reviewer for insightful comments that led to substantial improvements in methodology and clarifications in the final paper. T.D. was supported by the National Science Foundation (AGS-1338427 and CCF-1451945), the National Aeronautics and Space Administration (NNX14AM19G), and the National Oceanic and Atmospheric Administration (NA14OAR4310160). A.B. was supported by the National Science Foundation (CCF-1451945 and IIS-1447566). The views expressed herein are those of the authors and do not necessarily reflect the views of these agencies.
- Forecasting techniques
- Principal components analysis
- Regression analysis
- Seasonal forecasting
- Statistical forecasting
- Statistical techniques