Cluster-based ordinary kriging of piezometric head in West Texas/New Mexico – Testing of hypothesis

Most applications of geostatistical estimation and simulation techniques are concerned with casting the kriging system for the entire data set. Although there have been many successful applications of geostatistical analysis to capture the nonlinear relationships inherent in hydrological processes, there are numerous instances where more data does not necessarily imply better performance. In this research, it is hypothesized that when the data are clustered in some way and/or are anisotropic in nature, casting the kriging system based on the entire data set does not necessarily result in better performance statistics. For this purpose, a set of numerical experiments were conducted whereby the accelerated exact k-mean method was used to cluster data into similar patterns using both spatial coordinates and associated attribute values. For the data set under consideration, it was shown that classifying data into six clusters minimizes the mean squared distance from each data point to its nearest cluster center. Then, the ordinary kriging system with moving neighborhood was developed by limiting data to each cluster when trying to conduct a cross-validation procedure. Assessment of numerical results showed that the cluster-based ordinary kriging technique was more effective compared to its counterparts (i.e., ordinary kriging with one cluster) in capturing the dynamics of piezometric head in West Texas/New Mexico. The current study highlights the importance of data clustering on the performance of ordinary kriging estimator and initiates the need for further research to identify patterns and clusters in hydrologic data in similar studies.