Toward improving the reliability of hydrologic prediction: Model structure uncertainty and its quantification using ensemble‐based genetic programming framework

Abstract

Uncertainty analysis is starting to be widely acknowledged as an integral part of hydrological modeling. The conventional treatment of uncertainty analysis in hydrologic modeling is to assume a deterministic model structure, and treat its associated parameters as imperfectly known, thereby neglecting the uncertainty associated with the model structure. In this paper, a modeling framework that can explicitly account for the effect of model structure uncertainty has been proposed. The modeling framework is based on initially generating different realizations of the original data set using a non‐parametric bootstrap method, and then exploiting the ability of the self‐organizing algorithms, namely genetic programming, to evolve their own model structure for each of the resampled data sets. The resulting ensemble of models is then used to quantify the uncertainty associated with the model structure. The performance of the proposed modeling framework is analyzed with regards to its ability in characterizing the evapotranspiration process at the Southwest Sand Storage facility, located near Ft. McMurray, Alberta. Eddy‐covariance‐measured actual evapotranspiration is modeled as a function of net radiation, air temperature, ground temperature, relative humidity, and wind speed. Investigating the relation between model complexity, prediction accuracy, and uncertainty, two sets of experiments were carried out by varying the level of mathematical operators that can be used to define the predictand‐predictor relationship. While the first set uses just the additive operators, the second set uses both the additive and the multiplicative operators to define the predictand‐predictor relationship. The results suggest that increasing the model complexity may lead to better prediction accuracy but at an expense of increasing uncertainty. Compared to the model parameter uncertainty, the relative contribution of model structure uncertainty to the predictive uncertainty of a model is shown to be more important. Furthermore, the study advocates that the search to find the optimal model could be replaced by the quest to unearth possible models for characterizing hydrological processes.