Use of a Relevance Vector Machine for Groundwater Quality Monitoring Network Design Under Uncertainty
Environmental Modelling & Software
This paper presents a methodology for groundwater quality monitoring network design. This design takes into account uncertainties in aquifer properties, pollution transport processes, and climate. The methodology utilizes a statistical learning algorithm called relevance vector machines (RVM), which is a sparse Bayesian framework that can be used for obtaining solutions to regression and classification tasks. Application of the methodology is illustrated using the Eocene Aquifer in the northern part of the West Bank, Palestine. The procedure presented in this paper utilizes a Monte Carlo (MC) simulation process to capture the uncertainties in recharge, hydraulic conductivity, and nitrate reaction processes through the application of a groundwater flow model and a nitrate fate and transport model. This MC modeling approach provides several thousand realizations of nitrate distribution in the aquifer. Subsets of these realizations are then used to design the monitoring network. This is done by building a best-fit model of nitrate concentration distribution everywhere in the aquifer for each Monte Carlo subset using RVM. The outputs from the RVM model are the distribution of nitrate concentration everywhere in the aquifer, the uncertainty in the characterization of those concentrations, and the number and locations of “relevance vectors” (RVs). The RVs form the basis of the optimal characterization of nitrate throughout the aquifer and represent the optimal locations of monitoring wells. In this paper, the number of monitoring wells and their locations where chosen based on the performance of the RVM model runs. The results from 100 model runs show the consistency of the model in selecting the number and locations of RV‘s. After implementing the design, the data collected from the monitoring sites can be used to estimate nitrate concentration distribution throughout the entire aquifer and to quantify the uncertainty in those estimates.
Khader, A. I., and M. McKee. 2014. Use of a Relevance Vector Machine for Groundwater Quality Monitoring Network Design Under Uncertainty. Environmental Modelling and Software, 57(2014):115-126 (http://dx.doi.org/10.1016/j.envsoft.2014.02.015).