Optimal Spatiotemporal Prediction of Karstwater Levels

Abstract

In many fields of applied statistics samples from several locations in an investigation area are taken repeatedly over time. Especially in environmental monitoring the chemical and physical conditions in water, air and soil are measured using fixed and possibly mobile monitoring stations. The monitoring studies are aimed to model the phenomenon of interest (e.g. ground-level ozone, rain fall acidity or groundwater levels in karststone) and to predict the phenomenon at unsampled locations as well as into the future. For this purposes the spatiotemporal dynamic linear model is proposed, which builds up the framework for recursive best linear predictions. On one hand the spatiotemporal recursive best linear predictor is strongly connected with the predictors arising from the Kalman filter. On the other hand, this spatiotemporal predictor includes the method of linear Bayesian kriging as a special case. Thus the proposed method for spatiotemporal prediction is related to frequently used geostatistical and time series analysis methods. The spatiotemporal modeling and prediction approach will be applied to hydrogeological data of yearly averaged karstwater levels from 50 wells monitoring a Triassic karstwater reservoir in a mining region of Hungary from 1970 to 1990.