Using Spacetime Geostatistical Analysis to Improve Precipitation Isoscape Interpolation in Australia

Abstract

Precipitation isoscapes are a valuable tool in the application of water isotopes in hydrology, ecology, provenance, and forensics. To date, although many different spatial interpolation methods have been developed, spatio-temporal geostatistical interpolation has not been attempted. The objective of this research is to develop an interpolation method that identifies both the spatial and temporal correlation structure of isotopic signatures. This method will allow for interpolation on a month-to-month basis, which is an improvement in temporal resolution compared to previous long-term averages for annual or monthly isoscapes. This is particularly useful for isotope applications that require data on short-term variability, such as isotope forensics and food provenance. An algorithm for universal spacetime cokriging (USCo) was developed, and universal spacetime kriging (USK) and USCo were compared to linear models calculated using generalised least squares (GLS). A case study demonstrating the methodology has been presented, which is located in the southeastern region of Australia. When compared to GLS and USCo, USK had the lowest root mean square error (RMSE), mean absolute error (MAE), predicted residual error sum of squares (PRESS), Akaike information criterion (AIC) and Bayesian information criterion (BIC) for predicting both δ^2 H and δ^18 O values. These proved USK to be the best interpolation method. Both USK and USCo clearly identified the existence of spatial and temporal correlations. USCo required a much longer processing time than USK, however, appeared to improve prediction accuracy when more data were added to the model. Pearson’s correlation coefficients for total precipitation (-0.22, -0.19); evapotranspiration (0.27, 0.29); relative humidity (-0.45, -0.41); temperature (0.50, 0.45); distance from the coast (0.22, 0.15); altitude (-0.22, -0.18); and latitude (0.21, 0.17); for δ^18 O and δ^2 H respectively, indicated that the climatic covariates were better predictors than purely spatial covariates. Therefore, the methods and models discussed in this paper can greatly improve the temporal resolution of isoscape models for precipitation isotopes. This is particularly useful in regions where isotope ratio data is sparse, and direct observations are available to enable the statistical filling of these spatial gaps.

Keywords: isoscapes, kriging, cokriging, precipitation, precipitation isotopes