Extending Kriging Methods to Large Datasets with Applications to California Groundwater Data
Brice Charles Randolph
Advisor: Frederick R Paik Schoenberg
Spatial interpolation is performed to predict data values of unseen locations based on the distribution of known samples. In the field of geostatistics, the technique of unbiased linear interpolation, known as kriging, is used to predict data at unsampled locations. When working with large data sets or a large domain of interest, standard kriging methods such as ordinary and universal kriging can become computationally slow or require the domain to be partitioned with different models fit to different partitions. In this paper, we review common kriging methods as well as an extension known as fixed rank kriging that circumvents these problems. We apply the method of fixed rank kriging to a dataset of 2016 California groundwater, evaluating prediction accuracy under various model setups. We also compare fixed rank kriging to ordinary and universal kriging based on prediction accuracy and time taken to build the model and make predictions.