Bayesian inference to predict past and future nitrate concentrations

Abstract

Rigorously incorporating the lag between management actions and changes in water quality is essential to better manage NO₃-N (nitrate nitrogen) in groundwater. We present a fast data driven Bayesian inference model. It combines lumped parameter age models with measured NO₃-N concentrations to estimate historical and future NO₃-N concentrations for systems with negligible denitrification. Numerical experiments showed the model to be reasonably accurate. It can accelerate the detection of, and increase the detected effect size of, NO₃-N reductions relative to frequentist approaches. For instance, the model detects 20%-60% of the true effect as compared to 5%-25% for frequentist approaches when the mean residence time is greater than 10 years. Using the model for all groundwater sites with age data in New Zealand, we predict NO₃-N concentrations in New Zealand will increase significantly, with 20% of monitored wells exceeding the drinking water standard at steady state. NO₃-N reductions of 20% or more are required to maintain the current 15% of wells over the standard. The model allows much faster, lower cost, investigations with fewer data requirements than traditional approaches. We find that the model is a useful tool for incorporating lag into NO₃-N management decisions, testing hypotheses about historical land management, and providing parallel lines of evidence to support decision-making.