Using spacetime geostatistical analysis to improve precipitation isoscape interpolation in Australia

Isoscapes are an invaluable tool for understanding the spatial patterning of stable precipitation isotopes around the world. Researchers have used many different interpolation methods to create isoscapes from simple deterministic models, using a weighted average, to stochastic methods like machine learning (ML), universal kriging (UK) and cokriging (CK). However, to the best of our knowledge, spatio-temporal geostatistical methods using universal spatio-temporal kriging (USK) or universal spatio-temporal cokriging (USCo) have not yet been applied. Additionally, there is no current function in the geostatistical packages for R programming software, which can implement USCo. This study aims to develop an interpolation method that identifies both the spatial and temporal correlation structure of isotopic signatures in data poor regions. This method will allow for interpolation on a month-to-month basis, improving temporal resolution when compared to previous long-term averages for annual or monthly isoscapes. An algorithm for USCo was developed for R. Historical stable precipitation isotope data (ẟ ¹⁸O and ẟ ²H) from southeastern Australia were analysed using these spatio-temporal geostatistical methods. Results from a leave-one-out analysis, compared generalised least squares regression analysis (GLS), USK and USCo. Metrics used were 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). Both USK and USCo consistently outperformed GLS, with the best MAE for ẟ ¹⁸O being 1.75 (GLS), 1.35 (USCo) and 1.32 (USK). For ẟ ¹⁸O USK outperformed USCo (MAE 1.32 vs 1.35) whereas in models for ẟ ²H USCo outperformed USK (MAE 10.44 vs 10.79). However, these differences were small, and the instability and the long processing time required for the USCo algorithm (480 min. vs 0.35 min. for USK) made USK the preferred method. Additionally, the isoscapes generated from USCo contained several ‘bullseyes’, detracting from the preferred smoothing effect expected from kriging. We found that the isotopic spatial patterning was similar for adjacent months but quite different as time progressed. Climatic covariates were better predictors than purely spatial covariates like distance from the coast and altitude. This was probably due to the strong spatial patterning of climate over the study area. We identified some very depleted isotope values in June 2007, which were probably due to large precipitation events at that time. Some areas, for example, south of Sydney, were well documented giving good interpolation results. Others would benefit from more data collection. 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.