Bayesian Calibration Points to Misconceptions in Three‐Dimensional Hydrodynamic Reservoir Modeling. Issue 3 (2nd March 2023)

• Record Type: Journal Article
• Authors: Schwindt, Sebastian; Callau Medrano, Sergio; Mouris, Kilian; Beckers, Felix; Haun, Stefan; Nowak, Wolfgang; Wieprecht, Silke; Oladyshkin, Sergey
• Is Part Of: Water resources research. Volume 59:Issue 3(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-03-02
• Subjects: Gaussian process regression -- Bayesian optimization -- supervised machine learning -- Delft3D -- surrogate -- meta model; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2022WR033660
• Languages: English
• ISSNs: 0043-1397

Abstract

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. Plain Language Summary: Software tools for replicating a real‐world element, such as an artificial lake, need to account for many unknown parameters to create a physically sound conceptual computer model. Still, simplification assumptions are necessary to break down the complex reality into parameters that are easier to calculate. But the simplified parameters take on different values for each model and require specific adjustments. To perform these adjustments, a past event is typically reproduced with the conceptual model and different simplification parameter combinations. The simplification parameter combinations leading to the best possible replication of the past event are assumed to be valid to use the conceptual model for predictions of future events. Alas, many potentially false combinations can replicate a past event with very good results. Thus, a conceptual computer model can be overly adjusted regarding a particular phenomenon, such as heat transfer. Also, the number of possible adjustment tests is limited due to the long computing time of a conceptual model. For these reasons, we use a fast, simplified statistical model of a more complex conceptual model and machine learning for the adjustment process. We find that the statistic uncertainty increases with decreasing physical correctness of simplification parameter combinations. Key Points: Bayesian calibration efficiently and objectively fits constrained, case‐specific model parameters and identifies remaining uncertainties Post‐calibration uncertainty assessments help identify incorrect parameter combinations and constraints More constrained calibration leads to lower uncertainty, which is not detected by global statistics