Bayesian inference to predict past and future nitrate concentrations

Area of Science:

• Environmental Science
• Hydrology
• Data Science

Background:

• Effective groundwater quality management necessitates accounting for the time delay between implementing management strategies and observing changes in nitrate nitrogen (NO₃N) levels.
• Traditional methods often struggle to accurately incorporate these temporal lags, potentially leading to suboptimal management decisions.

Purpose of the Study:

• To develop and validate a fast, data-driven Bayesian inference model for estimating historical and future NO₃N concentrations in groundwater.
• To assess the model's ability to detect NO₃N reductions more effectively and with a larger effect size compared to frequentist approaches, particularly in systems with minimal denitrification.

Main Methods:

• The study employed a Bayesian inference model integrating lumped parameter age models with measured NO₃N concentrations.
• Numerical experiments were conducted to evaluate the model's accuracy and performance against frequentist methods.

Main Results:

• The developed model demonstrated reasonable accuracy in numerical experiments.
• It significantly accelerated the detection of NO₃N reductions and increased the detected effect size, showing 20%-60% detection rates versus 5%-25% for frequentist methods (mean residence time > 10 years).
• Application to New Zealand's groundwater sites predicts a significant increase in NO₃N, with 20% of wells potentially exceeding drinking water standards at steady state.

Conclusions:

• The model provides a valuable tool for incorporating temporal lags into NO₃N management, enabling faster, more cost-effective investigations with reduced data requirements.
• Significant NO₃N reductions (≥20%) are necessary to maintain current water quality standards in New Zealand.
• The model supports hypothesis testing regarding historical land management and offers complementary evidence for informed decision-making.