Nitrate vulnerability projections from Bayesian inference of multiple groundwater age tracers

Abstract

s u m m a r yNitrate is a major source of contamination of groundwater in the United States and around the world. We tested the applicability of multiple groundwater age tracers ( 3 H, 3 He, 4 He, 14 C, 13 C, and 85 Kr) in projecting future trends of nitrate concentration in 9 long-screened, public drinking water wells in Turlock, California, where nitrate concentrations are increasing toward the regulatory limit. Very low 85 Kr concentrations and apparent 3 H/ 3 He ages point to a relatively old modern fraction (40-50 years), diluted with pre-modern groundwater, corroborated by the onset and slope of increasing nitrate concentrations. An inverse Gaussian-Dirac model was chosen to represent the age distribution of the sampled groundwater at each well. Model parameters were estimated using a Bayesian inference, resulting in the posterior probability distribution -including the associated uncertainty -of the parameters and projected nitrate concentrations. Three scenarios were considered, including combined historic nitrate and age tracer data, the sole use of nitrate and the sole use of age tracer data. Each scenario was evaluated based on the ability of the model to reproduce the data and the level of reliability of the nitrate projections. The tracer-only scenario closely reproduced tracer concentrations, but not observed trends in the nitrate concentration. Both cases that included nitrate data resulted in good agreement with historical nitrate trends. Use of combined tracers and nitrate data resulted in a narrower range of projections of future nitrate levels. However, use of combined tracer and nitrate resulted in a larger discrepancy between modeled and measured tracers for some of the tracers. Despite nitrate trend slopes between 0.56 and 1.73 mg/L/year in 7 of the 9 wells, the probability that concentrations will increase to levels above the MCL by 2040 are over 95% for only two of the wells, and below 15% in the other wells, due to a leveling off of reconstructed historical nitrate loadings to groundwater since about 1990.

A Bayesian approach to infer nitrogen loading rates from crop and land-use types surrounding private wells in the Central Valley, California

“…Each domestic well water sample represents a mix of water age (Horn and Harter, 2009;Alikhani et al, 2016;Eberts et al, 2012). Ransom et al (2017) showed that land-use and nitrogen leaching patterns from the 1970s are most closely associated with recent groundwater nitrate measurements.…”

Reaction Rate Constant Evaluation of Thermal Isomerization of α-Pinene

“…Following the method presented in [24], to show the level of uncertainty associated with the kinetic model of the thermal isomerization of α-pinene, a Monte As it is seen in Figure 4, the duplicate experimental points are used in the parameter estimation without taking their average to take into consideration the real measurement errors. In this way, the experimental data provide better information about the parameter values.…”

Application of Bayesian Approach in the Parameter Estimation of Continuous Lumping Kinetic Model of Hydrocracking Process

“…Albrecht [29] Parameter estimation and uncertainty analysis by using Bayesian approach are widely used in different fields of science. Alikhani et al [30] applied Bayesian inference to estimate the confidence interval of groundwater residence time distributions by using multiple groundwater age tracers as observed data points.…”

“…Nonetheless, the information about the parameter values in other studies can be used to construct the prior distributions; and Bayesian approach can extract the information in the observed data set to enhance our confidence about the parameter values [31]. To obtain the posterior distribution by using the Bayesian approach, the mechanistic model needs to be solved by using Markov Chain techniques in a random walk approach [30]. Metropolis-Hasting algorithm is applied in this study to sample parameter sets of λ from posterior distribution ( )…”