Objective and Optimal Spatial Interpolation Approaches for Imputing Missing Precipitation Records

Spatial and temporal interpolation methods are generally used for estimation of missing data. Objective selection of control points (sites) with available data in a region for use in spatial interpolation to estimate missing data in space and time is always a challenge. The numerical weights derived through spatial and temporal interpolation approaches attached to data available at different sites have an impact of the estimation of missing data. Parsimonious and robust interpolation models can be developed using schemes that objectively select optimal number of sites and methodologies that eliminate redundant sites and regulate the weights. In this study regularization schemes, mathematical programming model formulations and different feature selection methods used in machine learning field are developed and evaluated for optimal and objective selection of sites for estimation of missing precipitation records. Variants of regularization schemes such as ridge regression, lease absolute shrinkage selection operator (LASSO) and elastic net are experimented. Mixed integer nonlinear optimization programming (MINLP) models with binary variables and multiple feature selection methods are adopted in this work. A case study using precipitation data at several rain gauges in a temperate climatic region of Kentucky, USA is used to demonstrate the benefits of using regularization schemes and optimization with binary variables to select an optimal subset of control points. Results point to improved estimations when these approaches are used for estimation of missing precipitation data.