Model Assessment and Optimization Using a Flow Time Transformation

Hydrologic modeling is a particularly complex problem that is commonly confronted with complications due to multiple dominant streamflow states, temporal switching of streamflow generation mechanisms, and dynamic responses to model inputs based on antecedent conditions. These complexities can inhibit the development of model structures and their fitting to observed data. As a result of these complexities and the heterogeneity that can exist within a catchment, optimization techniques are typically employed to obtain reasonable estimates of model parameters. However, when calibrating a model, the cost function itself plays a large role in determining the "optimal" model parameters. In this study, we introduce a transformation that allows for the estimation of model parameters in the "flow time" domain. The flow time transformation dynamically weights streamflows in the time domain, effectively stretching time during high streamflows and compressing time during low streamflows. Given the impact of cost functions on model optimization, such transformations focus on the hydrologic fluxes themselves rather than on equal time weighting common to traditional approaches. The utility of such a transform is of particular note to applications concerned with total hydrologic flux (water resources management, nutrient loading, etc.). The flow time approach can improve the predictive consistency of total fluxes in hydrologic models and provide insights into model performance by highlighting model strengths and deficiencies in an alternate modeling domain. Flow time transformations can also better remove positive skew from the streamflow time series, resulting in improved model fits, satisfaction of the normality assumption of model residuals, and enhanced uncertainty quantification. We illustrate the value of this transformation for two distinct sets of catchment conditions (snow-dominated and subtropical).