Graph-guided regularized regression to improve predictive skill of precipitation at seasonal timescales

Abstract:

Early and reliable prediction of seasonal precipitation remains a challenge with important socioeconomic implications for many regions around the world. Recently, data-driven machine learning (ML) methods have been proposed for seasonal prediction, some of them demonstrating progress. However, ML methods often exhibit two important limitations. First, they are prone to overfitting due to the largely underdetermined nature of the prediction problem and the limited observational record. Second, they lack a formalism by which they can explicitly incorporate structural dependencies of the covariates learned from observations or physics-based simulations. Here, we introduce a predictive model based on a graph-guided regularizer (called Graph Total Variation, GTV) which selects predictors “aligned” with an underlying graph representing dependencies of the covariates. We use large ensemble simulations from a climate model (CESM-LENS) to construct the dependency graph, thus, reducing the structural uncertainty in the estimation. Based on this approach, we are able to drastically decrease the dimensionality of the problem, explicitly honor the spatio-temporal structure of the covariates, and identify the most predictive features without specifying them a-priori. As a first application, we use the proposed GTV to predict winter precipitation in the southwestern US using sea surface temperatures over the entire Pacific basin. First, we show that the GTV explains more than 40% of the interannual precipitation variability in a strict train-test setting, outperforming all other regularization approaches and also models based on pre-specified teleconnection indices. Moreover, using a bootstrapping approach, we demonstrate that the GTV performance and the identified predictive features are quite insensitive to random perturbations in the dependency graph.