Model Tree and Regularization Approaches for Estimation of Missing precipitation Records

Missing precipitation records occur for several reasons, and their estimation is a significant challenge due to the spatial-temporal variability of precipitation. In this study, model tree (MT), regression tree (RT) approaches, and different variations of optimization formulations combined with three regularization schemes (i.e., ridge regression and Elastic net) are proposed and used to estimate missing precipitation data. Concepts of objective selection of sites for estimating missing data using correlations and distributional similarity are also used. The MT and RT models based on optimization and regularization approaches were developed and tested to estimate missing daily precipitation data from 1971 to 2016 at twenty-two rain gauges in Kentucky, U.S.A. The models were analyzed and evaluated using multiple performance and error measures. Results indicate that MT-based and regularization models provided the best estimates considering the performance measures. Regularization models provided better estimates of missing data than the optimization models while reducing the complexity of the model and improving performance. Objective selection of the sites for estimation also improved missing data estimation.