Spatiotemporal forecast with local temporal drift applied to weather patterns in Patagonia

Abstract

Geostatistics was developed to generate maps or 3D models interpolating observed values in space. The so-called spatiotemporal geostatistic applies the same principles to estimate observed values that have both spatial and temporal distribution. Moreover, time series analysis can decompose and extrapolate its main trends and seasonality, preparing data for geostatistical assumptions. Using this principle, this study aims to decompose the time series of a spatiotemporal dataset as external drifts and estimate its residuals by spatiotemporal kriging. Since each observation point is a time series, it is possible to decompose its trend and seasonality locally and map its parameters, preferable, by traditional geostatistics. Aftermath, it is possible to extrapolate the trend and seasonality at each pixel. This procedure can achieve great long-term forecasting maps even in regions with poor sampling due to its time series analysis. As well as, the geostatistics guarantee that the spatio-temporal correlation is maintained. This method is especially good for prediction in regions that the time series pattern depends on its location, which is a common problem in large areas and the problem is worsened in poorly sampled regions. This study presents a 10 years map forecast (2008-2017) comparison by spatiotemporal geostatistics, the first with original data, with ARIMA Models Panels, then with global decomposition, finally, with the local decomposition approach. The target variable is temperature captured by the 18 active weather stations in Patagonia between 1973 and 2007. To validate the results, they are compared to Land Surface Temperature (LST), which is an image product MOD11C3 derived from the MODIS sensor onboard on Terra/Aqua satellites. The proposed method can make long-term forecasts with low error, low smoothing effect and similar spatiotemporal statistics (mean and variance) of the stations and the LST product. Finally, its results are comparable with the ARIMA Models Panels with the advantage that it can generate maps with spatiotemporal correlation and better than the often-used methods (stkriging and global decomposition) to forecast large areas maps.