Three-dimensional distribution of residence time metrics in the glaciated United States using boosted regression trees trained on numerical models

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 (more parameters). The second approach permits more variation in model input but is used less frequently than the first because large-scale numerical models can be expensive. Starn and Belitz (2018) demonstrated the feasibility of estimating RTDs using LASSO regression trained on 30 generalized small-scale (100 to 1,000 km²) three-dimensional numerical models. This approach was modified to estimate and map RTD metrics across the glaciated U.S. with a larger set of models (118) and Boosted Regression Trees (BRT) instead of LASSO. Training data was created by backtracking a cohort of particles from a random subsample (about 140,000) of numerical model cells. Parametric cell-based RTDs were created by fitting Weibull distributions to particle travel times. These distributions were convolved with atmospheric tritium data to produce predictions at 495 wells where tritium was measured. The Theil-Sen slope statistic between measured and predicted concentrations was 0.88. Many meaningful RTD metrics can be calculated from parametric distributions; we chose three: fraction of young groundwater (< 65 years old), mean age of young fraction, and median age of old fraction. Data were divided into training (80%) and hold-out (20%) data, and ten-fold cross-validation on training data was used to learn the relation between RTD metrics and predictor variables (recharge rate, aquifer geometry, hydrogeologic terrane, and hydrologic position). Nash-Sutcliffe efficiency on hold-out data for the three RTD metrics was 0.82, 0.80, and 0.34, respectively. Importance of individual models on predicted young-fraction was assessed by recursively removing one numerical model from the training data set. This showed some models contained more information with respect to RTD than others. In addition to the expected importance of aquifer thickness and recharge rate in predicting RTD, hydrologic position and hydrogeologic terrane were important predictors. These variables are available wall-to-wall in the glaciated U.S. and were used to map RTD metrics across the region.