Establishing performance criteria for evaluating watershed-scale sediment and nutrient models at fine temporal scales

Watershed water quality models are mathematical tools used to simulate processes related to water, sediment, and nutrients. These models provide a framework that can be used to inform decision-making and the allocation of resources for watershed management. Therefore, it is critical to answer the question "when is a model good enough?" Established performance evaluation criteria, or thresholds for what is considered a 'good' model, provide common benchmarks against which model performance can be compared. Since the publication of prior meta-analyses on this topic, developments in the last decade necessitate further investigation, such as the advancement in high performance computing, the proliferation of aquatic sensors, and the development of machine learning algorithms. We surveyed the literature for quantitative model performance measures, including the Nash-Sutcliffe efficiency (NSE), with a particular focus on process-based models operating at fine temporal scales as their performance evaluation criteria are presently underdeveloped. The synthesis dataset was used to assess the influence of temporal resolution (sub-daily, daily, and monthly), calibration duration (< 3 years, 3 to 8 years, and > 8 years), and constituent target units (concentration, load, and yield) on model performance. The synthesis dataset includes 229 model applications, from which we use bootstrapping and personal modeling experience to establish sub-daily and daily performance evaluation criteria for flow, sediment, total nutrient, and dissolved nutrient models. For daily model evaluation, the NSE for sediment, total nutrient, and dissolved nutrient models should exceed 0.45, 0.30, and 0.35, respectively, for 'satisfactory' performance. Model performance generally improved when transitioning from short (< 3 years) to medium (3 to 8 years) calibration durations, but no additional gain was observed with longer (> 8 years) calibration. Dissolved nutrient models calibrated to load (e.g., kg/s) out-performed those calibrated to concentration (e.g., mg/L), whereas selection of target units was not significant for sediment and total nutrient models. We recommend the use of concentration rather than load as a water quality modeling target, as load may be biased by strong flow model performance whereas concentration provides a flow-independent measure of performance. Although the performance criteria developed herein are based on process-based models, they may be useful in assessing machine learning model performance. We demonstrate one such assessment on a recent deep learning model of daily nitrate prediction across the United States. The guidance presented here is intended to be used alongside, rather than to replace, the experience and modeling judgement of engineers and scientist who work to maintain our collective water resources.

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