A new concept to calibrate and evaluate hydrological model based on functional data analysis

The performance of a hydrological model depends on different factors including the calibration procedure, the objective function, and the quality and quantity of data, etc… It has been reported that it is very difficult to construct an objective function that describes the ability of a hydrological model to simulate the watershed response. One must sacrifice certain aspects (e.g. high flows vs low flows) at the expense of the other. This is mainly because the majority of the objective functions reflect the adequacy of simulations in one value as a sum of residuals between daily or hourly series of simulated and observed streamflow. Meanwhile, it is more adequate to conserve temporal flow variability and evaluate the model on its adequacy to simulate the same variability. For this reason, the proposed calibration concept is based on functional data analysis. It is a mathematical tool that allows analyzing a set of data observed within a spatial or temporal framework as a single entity represented by a continuous function. In our case, this tool is used to analyze the annual hydrographs as curves instead of 365 daily observations. Thus, the model is evaluated on its ability to reproduce the same shape and variability of the observed hydrographs. The functional statistics, defined for each time step, are used to construct the objective function for model calibration as well as further model evaluation. Regarding the calibration procedure, an approach combining a Monte Carlo simulation with the Tabu search algorithm is used. The proposed concept can be used with any model and calibration scheme.