Towards data-driven approaches for simulating rainfall in climate models

Climate model simulations of rainfall in the tropics suffer from pervasive biases, and that can lead to degraded climate simulations in other regions as well. Over the past two decades, high-resolution satellite measurements of tropical rainfall have become available. These data are most commonly used to constrain physics-based climate models by validating statistical properties of rainfall such as means and variances. However, the satellite data contain a wealth of spatiotemporal information on sub-diurnal timescales that can be used to construct predictive models. This study explores the feasibility of predicting rainfall from atmospheric state using a hierarchy of empirical models.

Our empirical approach is similar to the physics-based approach in that vertical profiles of atmospheric state at a particular instant of time serve as the predictors, and rainfall over a subsequent time period is the predictand. However, we allow the empirical model to "learn" from data to determine the model parameters. Empirical Orthogonal Function (EOF) decomposition is applied to vertical profiles from NASA MERRA-2 reanalysis to select the dominant predictor modes at analysis time 00 UTC. Rain predictions for the subsequent 6-hour period (00-06 UTC) are separated into different types from TRMM satellite data: stratiform, deep convective, and shallow convective. For each rain type, two generalized linear statistical models (logistic regression for rain occurrence and gamma regression for rain amount) are trained on 2003 data and used to predict during 2004. The results show that the statistical approach can predict spatial patterns and amplitudes of tropical rainfall in the time-averaged sense. The first EOF of humidity and the second EOF of temperature contribute most to prediction. In addition to generalized linear models, other common machine learning techniques (support vector machine and random forest) are compared. Furthermore, marginal nonlinear relationships between predictand and individual predictor are explored via a nonparametric regression technique. Interestingly, incorporating the identified marginal nonlinear relationship into the generalized linear model does not improve the prediction, suggesting that these marginal nonlinear effects are explained by other predictors in the model.