Modern space/time geostatistics using river distances: theory and applications for water quality mapping

The Clean Water Act requires that state and local agencies assess all river miles for potential impairments. However, due to the large number of river miles to be assessed, as well as budget and resource limitations, many states cannot feasibly meet this requirement. Therefore, there is a need for a framework that can accurately assess water quality at un-monitored locations, using limited data resources. Many researchers employ geostatistical techniques such as kriging and Bayesian Maximum Entropy (BME) to interpolate values in areas where no data exist. These techniques rely on the spatial and/or temporal autocorrelation between existing data points to estimate at un-monitored locations. This autocorrelation is traditionally a function of the Euclidean distance between those data points; however, a Euclidean distance does not take into account that many water quality variables may be spatially correlated due to the hydrogeography of the system. The focus of this work is the development of a space/time geostatistical framework for estimating and mapping water quality along river networks by using river distances instead of the traditional Euclidean distance. The Bayesian Maximum Entropy method of modern space/time geostatistics is modified and extended to incorporate the use of river distances to improve the estimation of basin-wide water quality. This new framework, termed river-BME, uses geostatistical models that integrate the use of permissible covariance functions with secondary information along with river distance. Factors, such as network complexity, are explored to determine the efficacy of using river-BME for water quality estimation. Additionally, simulation experiments and three real world case studies provide a broad application of this framework for a variety of basins and water quality parameters, including dissolved oxygen, Escherichia coli, and fish tissue mercury. Results show that the use of river-BME produces significantly more accurate estimates of water quality at un-monitored locations than traditional Euclidean based methods by more than 30%. Overall, this work provides a new tool for applying modern space/time geostatistics using river distances. It has the potential to aid not only future researchers but can ultimately provide environmental managers with the information necessary to better allocate resources and protect ecological and human health