Bayesian Calibration Points to Misconceptions in Three-Dimensional Hydrodynamic Reservoir Modeling

Abstract

Three-dimensional (3d) numerical models are state-of-the-art for investigating complex hydrodynamic flow patterns in reservoirs and lakes. Such full-complexity models are computationally demanding and their calibration is challenging regarding time, subjective decision-making, and measurement data availability. In addition, physically unrealistic model assumptions or combinations of calibration parameters may remain undetected and lead to overfitting. In this study, we investigate if and how so-called Bayesian calibration aids in characterizing faulty model setups driven by measurement data and calibration parameter combinations. Bayesian calibration builds on recent developments in machine learning and uses a Gaussian process emulator as a surrogate model, which runs considerably faster than a 3d numerical model. We Bayesian-calibrate a Delft3D-FLOW model of a pump-storage reservoir as a function of the background horizontal eddy viscosity and diffusivity, and initial water temperature profile. We consider three scenarios with varying degrees of faulty assumptions and different uses of flow velocity and water temperature measurements. One of the scenarios forces completely unrealistic, rapid lake stratification and still yields similarly good calibration accuracy as more correct scenarios regarding global statistics, such as the root-mean-square error. An uncertainty assessment resulting from the Bayesian calibration indicates that the completely unrealistic scenario forces fast lake stratification through highly uncertain mixing-related model parameters. Thus, Bayesian calibration describes the quality of calibration and correctness of model assumptions through geometric characteristics of posterior distributions. For instance, most likely calibration parameter values (posterior distribution maxima) at the calibration range limit or with widespread uncertainty characterize poor model assumptions and calibration.