Predictive statistical representations of observed and simulated rainfall using generalized linear models

Over the past two decades, high-resolution satellite measurements of tropical rainfall have become available. The most common approach to using these data for climate model validation is to compare the statistical properties of rainfall such as temporal means and variances, as well probability distributions. Temporal correlation properties of rainfall are also sometimes validated, but typically on daily or longer timescales, such as those associated with equatorial waves. However, satellite rainfall measurements contain spatio-temporal correlation information on sub-diurnal timescales that can be analyzed to validate and improve climate models. This study explores the feasibility of predicting sub-diurnal rain characteristics in the tropical Pacific from atmospheric profiles using a set of generalized linear statistical models.

Vertical profiles of temperature, humidity and wind and selected surface variables from either MERRA-2 reanalysis or Community Atmospheric Model (CAM5) simulations are used as predictors, with empirical orthogonal function (EOF) decomposition in the vertical. The rain predictions are separated into different types from TRMM satellite data (stratiform, deep convective, and shallow convective) and CAM5 output (large-scale and convective). For each rain type, two different statistical models (logistic regression for rain occurrence and gamma regression for rain amount) are trained on 2003 data and used to predict 2004 six-hourly rain occurrence and rate, respectively. The first EOF of humidity and the second EOF of temperature contribute most to the prediction for both statistical models. The logistic regression generally performs well for all rain types, but does better in the East Pacific compared to the West Pacific. The gamma regression predicts reasonable geographical rain amount distributions but rain rate probability distributions are not predicted as well, suggesting the need for a higher order model. Finally, the statistical models applied to TRMM observations and MERRA-2 environmental parameters perform better than the statistical models applied to CAM5 simulations. The results of this study suggest that there is statistical predictability and thus the potential for improved parameterization for tropical rain types based on empirical relationships.