Three‐Dimensional Distribution of Groundwater Residence Time Metrics in the Glaciated United States Using Metamodels Trained on General Numerical Simulation Models

Abstract

Residence time distribution (RTD) is a critically important characteristic of groundwater flow systems; however, it cannot be measured directly. RTD can be inferred from tracer data with analytical models (few parameters) or with numerical models (many parameters). The second approach permits more variation in system properties but is used less frequently than the first because large‐scale numerical models can be resource intensive. Using a novel automated approach, a set of 115 inexpensive general simulation models (GSMs) was used to create RTD metrics (fraction of young groundwater, defined as <65 years old; mean travel time of young fraction; median travel time of old fraction; and mean path length). GSMs captured the general trends in measured tritium concentrations in 431 wells. Boosted Regression Tree metamodels were trained to predict these RTD metrics using available wall‐to‐wall hydrogeographic digital sets as explanatory features. The metamodels produced a three‐dimensional distribution of predictions throughout the glacial system that generally matched with the numerical model RTD metrics. In addition to the expected importance of aquifer thickness and recharge rate in predicting RTD metrics, two new data sets, Multi‐Order Hydrologic Position (MOHP) and hydrogeologic terrane were important predictors. These variables by themselves produced metamodels with Nash‐Sutcliffe efficiency close to the full metamodel. Metamodel predictions showed that the volume of young groundwater stored in the glaciated United States is about 6,000 km3, or about 0.5% of globally stored young groundwater.

Machine Learning Predicted Redox Conditions in the Glacial Aquifer System, Northern Continental United States

“…For example, the most influential predictor variable for low DO, as well as being an influential predictor variable for high Fe, was the mean age of the young fraction of water (water <60 years old, YngWtrMeanAge). The mean age of young water is, itself, a modeled parameter, one of several produced by a comprehensive model of age metrics across the GLAC (Starn et al., 2021). As the mean age of young water increases, the likelihood of anoxic conditions increases (Figure 3).…”

“…In some terranes the water table is very near to land surface, while in other areas the depth to water is greater than 10 m. The saturated thickness of the aquifer (Figure 1c) also varies substantially across the GLAC. Detailed descriptions of the methods used to determine the depth to the water table and the aquifer saturated thickness are described in Starn et al (2021). In terranes with substantial topography (e.g., 1A, 1F, eastern 1G, Figure 1a) the saturated thickness of the aquifer can be very thin (<10 m).…”

“…Detailed descriptions of the methods used to determine the depth to the water table and the aquifer saturated thickness are described in Starn et al. (2021). In terranes with substantial topography (e.g., 1A, 1F, eastern 1G, Figure 1a) the saturated thickness of the aquifer can be very thin (<10 m).…”

“…Models were developed with predictive variables representing glacial sediment and aquifer conditions (glacial sediment texture and thickness, watershed location, fraction of young water, etc. ), which are themselves outputs of numerical and textural maps (Bayless et al., 2017; Belitz et al., 2019; Starn et al., 2021). We also incorporated surficial characteristics, soil chemistry, aquifer characteristics, and hydrologic setting to predict redox.…”

Modeling and interpreting hydrological responses of sustainable urban drainage systems with explainable machine learning methods

“…Post hoc explainability techniques aim to explain ML models that are not transparent. For instance, in hydrology, the integrated gradients method (Sundararajan et al, 2017) has been used in Kratzert et al (2019) to understand the contribution of meteorological input at different time steps to streamflow discharge prediction in neural networks, the permutation feature importance method has been used in Schmidt et al (2020) to assess the importance of the predictors for flood magnitude prediction in various ML models, and the SHAP (SHapley Additive exPlanations) method (Lundberg and Lee, 2017) has been used in Starn et al (2021) to identify the factors affecting groundwater residence time distribution predictions in XGBoost models (Chen and Guestrin, 2016).…”