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.
