DOI: 10.5066/p17nxghv
title: Example Groundwater-Level Datasets and Benchmarking Results for the Automated Regional Correlation Analysis for Hydrologic Record Imputation (ARCHI) Software Package

description: This data release provides two example groundwater-level datasets used to benchmark the Automated Regional Correlation Analysis for Hydrologic Record Imputation (ARCHI) software package (Levy and others, 2024). The first dataset contains groundwater-level records and site metadata for wells located on Long Island, New York (NY) and some surrounding mainland sites in New York and Connecticut. The second dataset contains groundwater-level records and site metadata for wells located in the southeastern San Joaquin Valley of the Central Valley, California (CA). For ease of exposition these are referred to as NY and CA datasets, respectively. Both datasets are formatted with column headers that can be read by the ARCHI software package within the R computing environment. These datasets were used to benchmark the imputation accuracy of three ARCHI model settings (OLS, ridge, and MOVE.1) against the widely used imputation program missForest (Stekhoven and Bühlmann, 2012). The ARCHI program was used to process the NY and CA datasets on monthly and annual timesteps, respectively, filter out sites with insufficient data for imputation, and create 200 test datasets from each of the example datasets with 5 percent of observations removed at random (herein, referred to as "holdouts"). Imputation accuracy for test datasets was assessed using normalized root mean square error (NRMSE), which is the root mean square error divided by the standard deviation of the observed holdout values. ARCHI produces prediction intervals (PIs) using a non-parametric bootstrapping routine, which were assessed by computing a coverage rate (CR) defined as the proportion of holdout observations falling within the estimated PI. The multiple regression models included with the ARCHI package (OLS and ridge) were further tested on all test datasets at eleven different levels of the p_per_n input parameter, which limits the maximum ratio of regression model predictors (p) per observations (n) as a decimal fraction greater than zero and less than or equal to one.

This data release contains ten tables formatted as tab-delimited text files. The “CA_data.txt” and “NY_data.txt” tables contain 243,094 and 89,997 depth-to-groundwater measurement values (value, in feet below land surface) indexed by site identifier (site_no) and measurement date (date) for CA and NY datasets, respectively. The “CA_sites.txt” and “NY_sites.txt” tables contain site metadata for the 4,380 and 476 unique sites included in the CA and NY datasets, respectively. The “CA_NRMSE.txt” and “NY_NRMSE.txt” tables contain NRMSE values computed by imputing 200 test datasets with 5 percent random holdouts to assess imputation accuracy for three different ARCHI model settings and missForest using CA and NY datasets, respectively. The “CA_CR.txt” and “NY_CR.txt” tables contain CR values used to evaluate non-parametric PIs generated by bootstrapping regressions with three different ARCHI model settings using the CA and NY test datasets, respectively. The “CA_p_per_n.txt” and “NY_p_per_n.txt” tables contain mean NRMSE values computed for 200 test datasets with 5 percent random holdouts at 11 different levels of p_per_n for OLS and ridge models compared to training error for the same models on the entire CA and NY datasets, respectively.

References Cited

Levy, Z.F., Stagnitta, T.J., and Glas, R.L., 2024, ARCHI: Automated Regional Correlation Analysis for Hydrologic Record Imputation, v1.0.0: U.S. Geological Survey software release, https://doi.org/10.5066/P1VVHWKE.

Stekhoven, D.J., and Bühlmann, P., 2012, MissForest—non-parametric missing value imputation for mixed-type data: Bioinformatics 28(1), 112-118. https://doi.org/10.1093/bioinformatics/btr597.