Learning Errors of Environmental Mathematical Models

Abstract

In solving civil engineering problems the use of various models for forecasting environmental variables (for example, water levels in a river during flooding) is a must. Mathematical models of environmental processes inevitably contain errors (even if models are calibrated on accurate data) which can be represented as realizations of a stochastic process. Parameters of this process vary in time and cannot be reliably estimated without making (unrealistic) assumptions. However the model errors depend on various factors characterizing environmental conditions (for example, for extreme events errors are typically higher), and such dependencies can be reconstructed based on data. We present a unifying approach allowing for building machine learning models (in particular ANN and Local weighted regression) able to predict such errors as well as the properties of their distributions. Examples in modelling hydrological processes are considered.