Spatiotemporal imputation of missing rainfall values to establish climate normals

Abstract

Spatial kriging interpolation has been a widely popular geostatistical method for decades, and it is commonly used to predict both gridded and missing climatic variables. Climate data is typically monitored across a variety of timescales, from daily measurements to thirty-year periods, known as long-term averages (LTAs). LTAs can be constructed from daily, monthly, or annual measurements so long as any missing values in the data are infilled first. Although spatial kriging is an available method for the prediction of missing data, it is limited to a single moment in time for each imputation. Not only can missing values only be predicted with observations measured at the same instance in time, but the entire imputation process must be repeated up to the number of timesteps in which missing data is present. This study investigates the imputation performance of spatiotemporal regression kriging, an extension of spatial regression kriging which simultaneously accounts for data across both space and time. Hence, missing data is predicted using observations from other points in time, and only a single imputation process is required for the entire data set. Spatiotemporal regression kriging has been evaluated against a variety of geostatistical methods, including spatial kriging, for the imputation of monthly rainfall totals for the Republic of Ireland. Across all tests, the spatiotemporal methods presented have outperformed any purely spatial methods considered. Furthermore, three different regression methods were considered when de-trending the data before interpolation. Of those tested, generalized least squares (GLS) was shown to provide the best results, followed by elastic-net regularization when GLS proved computationally unavailable. Finally, the data set has been infilled using the best performing imputation method, and precipitation LTAs are presented for the Republic of Ireland from 1981–2010.