Hydrologic and Water Quality Models: Performance Measures and Evaluation Criteria

Abstract

Performance measures (PMs) and corresponding performance evaluation criteria (PEC) are important aspects of calibrating and validating hydrologic and water quality models and should be updated with advances in modeling science. We synthesized PMs and PEC from a previous special collection, performed a meta-analysis of performance data reported in recent peer-reviewed literature for three widely published watershed-scale models (SWAT, HSPF, WARMF), and one field-scale model (ADAPT), and provided guidelines for model performance evaluation. Based on the synthesis, meta-analysis, and personal modeling experiences, we recommend coefficient of determination (R2; in conjunction with gradient and intercept of the corresponding regression line), Nash Sutcliffe efficiency (NSE), index of agreement (d), root mean square error (RMSE; alongside the ratio of RMSE and standard deviation of measured data, RSR), percent bias (PBIAS), and several graphical PMs to evaluate model performance. We recommend that model performance can be judged satisfactory for flow simulations if monthly R2 0.70 and d 0.75 for field-scale models, and daily, monthly, or annual R2 0.60, NSE 0.50, and PBIAS ≤ ±15% for watershed-scale models. Model performance at the watershed scale can be evaluated as satisfactory if monthly R2 0.40 and NSE 0.45 and daily, monthly, or annual PBIAS ≤ ±20% for sediment; monthly R20.40 and NSE 0.35 and daily, monthly, or annual PBIAS ≤ ±30% for phosphorus (P); and monthly R2 0.30 and NSE 0.35 and daily, monthly, or annual PBIAS ≤ ±30% for nitrogen (N). For RSR, we recommend that previously published PEC be used as detailed in this article. We also recommend that these PEC be used primarily for the four models for which there were adequate data, and used only with caution for other models. These PEC can be adjusted within acceptable bounds based on additional considerations, such as quality and quantity of available measured data, spatial and temporal scales, and project scope and magnitude, and updated based on the framework presented herein. This initial meta-analysis sets the stage for more comprehensive meta-analysis to revise PEC as new PMs and more data become available.