Effiziente nichtlineare Modellreduktionsverfahren für verbesserte Unsicherheitsquantifizierung und Messnetzoptimierung in Grundwasser-Oberflächenwasser-Systemen.
Zusammenfassung der Projektergebnisse
In this project, three different model simplification methods were analyzed for their utility as surrogates for uncertainty estimation and experimental design with computationally expensive, complex surface-water groundwater models. The investigated simplification methods were (i) model upscaling (parameter simplification and grid coarsening), (ii) a data-driven method (artificial neural networks, ANNs), and (iii) a projection-based method (proper-orthogonal decomposition, POD). Corresponding surrogate models were built for a highly complex, regional surface water - groundwater interaction model and their performance was tested for different model predictions and for different modeling tasks. A paired simple-complex model methodology was adapted to estimate the model simplification error variance and bias. For the first time this method was applied to a real-world test case and extended to evaluate the error estimates for several prediction types with actual data. This provided insights into the intricate interplay between model, model simplification method, data, and prediction type. Model upscaling was implemented by a zoned, grid-coarsened version of the complex model. The simplification error was generally low for model predictions of similar type and location as contained in the calibration data set. But upscaling failed for other data types and locations, particularly for those relying on parameter detail, because the parameters in the upscaled model are composed of a diverse mixture of complex-model parameter detail. This suggests that the relation to complex-model parameters is lost by upscaling. It also poses a strong limitation for its use in uncertainty estimation and experimental design. The sensitivity of existing data to model predictions was largely retained in the upscaled model which shows some potential for the evaluation of existing monitoring networks. ANNs reproduced all model predictions very well and exhibited a small simplification error and bias. Since the method is data-driven, individual ANN models had to be setup for each data type and location in the data set. The effort to set up ANNs is therefore higher than for other ROM methods, where predictions of several data types and locations are made with a single model. Due to the prediction-specific setup, a high(er) accuracy of ANNs could be expected - at least for historic data. Data-driven methods can only be applied where measurements already exist and only within the bounds of historic observations. In such cases, ANNs are exceptionally powerful in reproducing complex-model outputs at minimal computational costs. However, data-driven methods can not be used for experimental design, because new observations can not be evaluated and there is no expression of complex-model parameters in the ANN. The POD method was superior to model upscaling and performed very well as a predictive surrogate in most of the investigated cases, particularly for data types and locations contained in the calibration data set. Due to the linearity of the POD method, it failed for a prediction affected by high non-linearity of the complex model. But model reduction through subspace projection means that the full model’s parameter set is retained in the POD model. This leads to a good reproduction of the complex model’s estimates of data worth, which makes POD a suitable surrogate method for uncertainty estimation, monitoring network evaluation and optimal network design. The results from the project demonstrated that model surrogacy comes at a cost and that there is no single method that suits all modeling purposes. Guidelines are given that help modelers chose the most promising ROM method for a given task. The newly developed eb-POD method alleviates the effects of model nonlinearities on POD by explicitly treating dynamic model boundaries. For the first time, this gives groundwater modelers using POD a fast and easy to implement method to purposefully eliminate boundary-related errors in the POD models. (eb-)POD is a promising surrogate method for computationally expensive surface-water groundwater models. Model-based monitoring network design on the basis of pragmatic data-worth analysis is computationally efficient, and POD has been further extended for random sampling of the null-space of the linearized model, i.e., the part that is not informed by data but may have an influence on the prediction. This extension for robust optimal design with POD was successfully applied to different predictions (groundwater heads, river-groundwater exchange flows, spring flows, and aquifer storage). The resulting monitoring designs compare favorably to their complex-model counterparts and can be derived by a fraction of the computational time.
Projektbezogene Publikationen (Auswahl)
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(2016). Model reduction in coupled groundwater-surface water systems - potentials and limitations of the applied proper orthogonal decomposition (POD) method, Geophysical Research Abstracts Vol. 18, EGU2016-6012, EGU General Assembly 2016
Gosses, M., Wöhling, T., Moore, C., Nowak, W.
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(2017). Comparing and improving proper orthogonal decomposition (POD) to reduce the complexity of groundwater models. Geophysical Research Abstracts Vol. 19, EGU2017-1270, EGU General Assembly 2017
Gosses, M., Nowak, W., Wöhling, T.
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(2018). Assessing the utility of reduced order models (ROMs) as surrogates for the Wairau Plain groundwater model. New Zealand Hydrological Society Annual Conference, 4-7 Dec 2018, Christchurch, New Zealand
Gosses, M., Wöhling, T.
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(2018). Effective predictive uncertainty analysis using reduced order models. Geophysical Research Abstracts Vol. 20, EGU2018-6933, EGU General Assembly 2018, Vienna, Austria
Gosses, M., Wöhling, T.
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(2018). Explicit treatment for Dirichlet, Neumann and Cauchy boundary conditions in POD-based reduction of groundwater models. Advances in Water Research, 115, 160-171
Gosses, M., Nowak, W., Wöhling, T.
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(2018). Prioritizing uncertainty sources in modelling surface water - groundwater interactions of gravel-bed rivers. Geophysical Research Abstracts Vol. 20, EGU2018-8708, EGU General Assembly 2018, 8-13 April 2018, Vienna, Austria
Wöhling, T., Gosses, M.
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(2018). Quantifying river-groundwater interactions of New Zealand's gravel-bed rivers: The Wairau Plain. Groundwater, 56(4), 647-666
Wöhling T., Gosses, M., Wilson, S., Davidson, P.
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(2019). Model-based data worth analysis in multi-purpose groundwater monitoring networks. Geophysical Research Abstracts, Vol. 21, EGU2019-3293, EGU General Assembly 2019, 7-14 April 2019, Vienna, Austria
Wöhling, T., Gosses, M.
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(2019). Simplication error analysis for groundwater predictions with reduced order models. Advances in Water Research, 125, 41-56
Gosses, M. and Wöhling, T.
