Encapsulation of parametric uncertainty statistics by various predictive machine learning models: MLUE method

Monte Carlo simulation-based uncertainty analysis techniques have been applied successfully in hydrology for quantification of the model output uncertainty. They are flexible, conceptually simple and straightforward, but provide only average measures of uncertainty based on past data. However, if one needs to estimate uncertainty of a model in a particular hydro-meteorological situation in real time application of complex models, Monte Carlo simulation becomes impractical because of the large number of model runs required. This paper presents a novel approach to encapsulating and predicting parameter uncertainty of hydrological models using machine learning techniques. Generalised likelihood uncertainty estimation method (a version of the Monte Carlo method) is first used to assess the parameter uncertainty of a hydrological model, and then the generated data are used to train three machine learning models. Inputs to these models are specially identified representative variables. The trained models are then employed to predict the model output uncertainty which is specific for the new input data. This method has been applied to two contrasting catchments. The experimental results demonstrate that the machine learning models are quite accurate. An important advantage of the proposed method is its efficiency allowing for assessing uncertainty of complex models in real time.