Entropy-Based Quantification of Infiltration Model-Form Uncertainty

Infiltration is a quantitative expression of water loss in the urban hydrological cycle, but current hydrological models often use empirical or semi-empirical equations. The inherent uncertainties in these equations (often simplifying boundary conditions or water content expression) are not accurately conveyed to end users via hydrological models. As well, these empirical equations introduce model-form uncertainty that is often ignored before model calibration. This research focuses on analyzing the uncertainty in the infiltration process by constructing a quantitative framework based on uncertainty propagation from a true, physical model (Richards Equation) to conceptually simpler models (Green-Ampt and Horton’s model) that uses entropy to track the uncertainty’s magnitude change. Firstly, we conducted sensitivity analyses using various designed rainfalls (time series as well as IDF curve) in a watershed over varying spatial-temporal scales to isolate the uncertainty propagation in the infiltration equations arising from different spatial-temporal scales. This uncertainty propagation framework for infiltration answers the question of how changes in the structural assumptions of the infiltration equation affect peak flowrate errors or volume estimation errors. It adopts entropy as a quantitative index to describe the amount of information loss in the infiltration process, as well as how the uncertainty propagates over time and space. Furthermore, this entropy uncertainty framework can help in decision making related to when a more physically-based approach must be used, or when a simplified equation is still acceptable.