02 Fakultät Bau- und Umweltingenieurwissenschaften
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/3
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Item Open Access Diagnosing similarities in probabilistic multi-model ensembles : an application to soil-plant-growth-modeling(2022) Schäfer Rodrigues Silva, Aline; Weber, Tobias K. D.; Gayler, Sebastian; Guthke, Anneli; Höge, Marvin; Nowak, Wolfgang; Streck, ThiloThere has been an increasing interest in using multi-model ensembles over the past decade. While it has been shown that ensembles often outperform individual models, there is still a lack of methods that guide the choice of the ensemble members. Previous studies found that model similarity is crucial for this choice. Therefore, we introduce a method that quantifies similarities between models based on so-called energy statistics. This method can also be used to assess the goodness-of-fit to noisy or deterministic measurements. To guide the interpretation of the results, we combine different visualization techniques, which reveal different insights and thereby support the model development. We demonstrate the proposed workflow on a case study of soil–plant-growth modeling, comparing three models from the Expert-N library. Results show that model similarity and goodness-of-fit vary depending on the quantity of interest. This confirms previous studies that found that “there is no single best model” and hence, combining several models into an ensemble can yield more robust results.Item Open Access Strategies for simplifying reactive transport models : a Bayesian model comparison(2020) Schäfer Rodrigues Silva, Aline; Guthke, Anneli; Höge, Marvin; Cirpka, Olaf A.; Nowak, WolfgangFor simulating reactive transport on aquifer scale, various modeling approaches have been proposed. They vary considerably in their computational demands and in the amount of data needed for their calibration. Typically, the more complex a model is, the more data are required to sufficiently constrain its parameters. In this study, we assess a set of five models that simulate aerobic respiration and denitrification in a heterogeneous aquifer at quasi steady state. In a probabilistic framework, we test whether simplified approaches can be used as alternatives to the most detailed model. The simplifications are achieved by neglecting processes such as dispersion or biomass dynamics, or by replacing spatial discretization with travel‐time‐based coordinates. We use the model justifiability analysis proposed by Schöniger, Illman, et al. (2015, https://doi.org/10.1016/j.jhydrol.2015.07.047) to determine how similar the simplified models are to the reference model. This analysis rests on the principles of Bayesian model selection and performs a tradeoff between goodness‐of‐fit to reference data and model complexity, which is important for the reliability of predictions. Results show that, in principle, the simplified models are able to reproduce the predictions of the reference model in the considered scenario. Yet, it became evident that it can be challenging to define appropriate ranges for effective parameters of simplified models. This issue can lead to overly wide predictive distributions, which counteract the apparent simplicity of the models. We found that performing the justifiability analysis on the case of model simplification is an objective and comprehensive approach to assess the suitability of candidate models with different levels of detail.Item Open Access Combining crop modeling with remote sensing data using a particle filtering technique to produce real-time forecasts of winter wheat yields under uncertain boundary conditions(2022) Zare, Hossein; Weber, Tobias K. D.; Ingwersen, Joachim; Nowak, Wolfgang; Gayler, Sebastian; Streck, ThiloWithin-season crop yield forecasting at national and regional levels is crucial to ensure food security. Yet, forecasting is a challenge because of incomplete knowledge about the heterogeneity of factors determining crop growth, above all management and cultivars. This motivates us to propose a method for early forecasting of winter wheat yields in low-information systems regarding crop management and cultivars, and uncertain weather condition. The study was performed in two contrasting regions in southwest Germany, Kraichgau and Swabian Jura. We used in-season green leaf area index (LAI) as a proxy for end-of-season grain yield. We applied PILOTE, a simple and computationally inexpensive semi-empirical radiative transfer model to produce yield forecasts and assimilated LAI data measured in-situ and sensed by satellites (Landsat and Sentinel-2). To assimilate the LAI data into the PILOTE model, we used the particle filtering method. Both weather and sowing data were treated as random variables, acknowledging principal sources of uncertainties to yield forecasting. As such, we used the stochastic weather generator MarkSim® GCM to produce an ensemble of uncertain meteorological boundary conditions until the end of the season. Sowing dates were assumed normally distributed. To evaluate the performance of the data assimilation scheme, we set up the PILOTE model without data assimilation, treating weather data and sowing dates as random variables (baseline Monte Carlo simulation). Data assimilation increased the accuracy and precision of LAI simulation. Increasing the number of assimilation times decreased the mean absolute error (MAE) of LAI prediction from satellite data by ~1 to 0.2 m2/m2. Yield prediction was improved by data assimilation as compared to the baseline Monte Carlo simulation in both regions. Yield prediction by assimilating satellite-derived LAI showed similar statistics as assimilating the LAI data measured in-situ. The error in yield prediction by assimilating satellite-derived LAI was 7% in Kraichgau and 4% in Swabian Jura, whereas the yield prediction error by Monte Carlo simulation was 10 percent in both regions. Overall, we conclude that assimilating even noisy LAI data before anthesis substantially improves forecasting of winter wheat grain yield by reducing prediction errors caused by uncertainties in weather data, incomplete knowledge about management, and model calibration uncertainty.Item Open Access Bayesian calibration and validation of a large‐scale and time‐demanding sediment transport model(2020) Beckers, Felix; Heredia, Andrés; Noack, Markus; Nowak, Wolfgang; Wieprecht, Silke; Oladyshkin, SergeyThis study suggests a stochastic Bayesian approach for calibrating and validating morphodynamic sediment transport models and for quantifying parametric uncertainties in order to alleviate limitations of conventional (manual, deterministic) calibration procedures. The applicability of our method is shown for a large‐scale (11.0 km) and time‐demanding (9.14 hr for the period 2002-2013) 2‐D morphodynamic sediment transport model of the Lower River Salzach and for three most sensitive input parameters (critical Shields parameter, grain roughness, and grain size distribution). Since Bayesian methods require a significant number of simulation runs, this work proposes to construct a surrogate model, here with the arbitrary polynomial chaos technique. The surrogate model is constructed from a limited set of runs (n=20) of the full complex sediment transport model. Then, Monte Carlo‐based techniques for Bayesian calibration are used with the surrogate model (105 realizations in 4 hr). The results demonstrate that following Bayesian principles and iterative Bayesian updating of the surrogate model (10 iterations) enables to identify the most probable ranges of the three calibration parameters. Model verification based on the maximum a posteriori parameter combination indicates that the surrogate model accurately replicates the morphodynamic behavior of the sediment transport model for both calibration (RMSE = 0.31 m) and validation (RMSE = 0.42 m). Furthermore, it is shown that the surrogate model is highly effective in lowering the total computational time for Bayesian calibration, validation, and uncertainty analysis. As a whole, this provides more realistic calibration and validation of morphodynamic sediment transport models with quantified uncertainty in less time compared to conventional calibration procedures.Item Open Access Characterization of export regimes in concentration-discharge plots via an advanced time-series model and event-based sampling strategies(2021) González-Nicolás, Ana; Schwientek, Marc; Sinsbeck, Michael; Nowak, WolfgangCurrently, the export regime of a catchment is often characterized by the relationship between compound concentration and discharge in the catchment outlet or, more specifically, by the re-gression slope in log-concentrations versus log-discharge plots. However, the scattered points in these plots usually do not follow a plain linear regression representation because of different processes (e.g., hysteresis effects). This work proposes a simple stochastic time-series model for simulating compound concentrations in a river based on river discharge. Our model has an ex-plicit transition parameter that can morph the model between chemostatic behavior and che-modynamic behavior. As opposed to the typically used linear regression approach, our model has an additional parameter to account for hysteresis by including correlation over time. We demonstrate the advantages of our model using a high-frequency data series of nitrate concen-trations collected with in situ analyzers in a catchment in Germany. Furthermore, we identify event-based optimal scheduling rules for sampling strategies. Overall, our results show that (i) our model is much more robust for estimating the export regime than the usually used regres-sion approach, and (ii) sampling strategies based on extreme events (including both high and low discharge rates) are key to reducing the prediction uncertainty of the catchment behavior. Thus, the results of this study can help characterize the export regime of a catchment and manage water pollution in rivers at lower monitoring costs.Item Open Access Towards a community-wide effort for benchmarking in subsurface hydrological inversion : benchmarking cases, high-fidelity reference solutions, procedure, and first comparison(2024) Xu, Teng; Xiao, Sinan; Reuschen, Sebastian; Wildt, Nils; Hendricks Franssen, Harrie-Jan; Nowak, WolfgangInversion in subsurface hydrology refers to estimating spatial distributions of (typically hydraulic) properties often associated with quantified uncertainty. Many methods are available, each characterized by a set of assumptions, approximations, and numerical implementations. Only a few intercomparison studies have been performed (in the remote past) amongst different approaches (e.g., Zimmerman et al., 1998; Hendricks Franssen et al., 2009). These intercomparisons guarantee broad participation to push forward research efforts of the entire subsurface hydrological inversion community. However, from past studies until now, comparisons have been made among approximate methods without firm reference solutions. Note that the reference solutions are the best possible solutions with the best estimate and posterior standard deviation and so forth. Without reference solutions, one can only compare competing best estimates and their associated uncertainties in an intercomparison sense, and absolute statements on accuracy are unreachable. Our current initiative defines benchmarking scenarios for groundwater model inversion. These are targeted for community-wide use as test cases in intercomparison scenarios. Here, we develop five synthetic, open-source benchmarking scenarios for the inversion of hydraulic conductivity from pressure data. We also provide highly accurate reference solutions produced with massive high-performance computing efforts and with a high-fidelity Markov chain Monte Carlo (MCMC)-type solution algorithm. Our high-end reference solutions are publicly available along with the benchmarking scenarios, the reference algorithm, and the suggested benchmarking metrics. Thus, in comparison studies, one can test against high-fidelity reference solutions rather than discussing different approximations. To demonstrate how to use these benchmarking scenarios, reference solutions, and suggested metrics, we provide a blueprint comparison of a specific ensemble Kalman filter (EnKF) version. We invite the community to use our benchmarking scenarios and reference solutions now and into the far future in a community-wide effort towards clean and conclusive benchmarking. For now, we aim at an article collection in an appropriate journal, where such clean comparison studies can be submitted together with an editorial summary that provides an overview.Item Open Access Surrogate-based Bayesian comparison of computationally expensive models : application to microbially induced calcite precipitation(2021) Scheurer, Stefania; Schäfer Rodrigues Silva, Aline; Mohammadi, Farid; Hommel, Johannes; Oladyshkin, Sergey; Flemisch, Bernd; Nowak, WolfgangGeochemical processes in subsurface reservoirs affected by microbial activity change the material properties of porous media. This is a complex biogeochemical process in subsurface reservoirs that currently contains strong conceptual uncertainty. This means, several modeling approaches describing the biogeochemical process are plausible and modelers face the uncertainty of choosing the most appropriate one. The considered models differ in the underlying hypotheses about the process structure. Once observation data become available, a rigorous Bayesian model selection accompanied by a Bayesian model justifiability analysis could be employed to choose the most appropriate model, i.e. the one that describes the underlying physical processes best in the light of the available data. However, biogeochemical modeling is computationally very demanding because it conceptualizes different phases, biomass dynamics, geochemistry, precipitation and dissolution in porous media. Therefore, the Bayesian framework cannot be based directly on the full computational models as this would require too many expensive model evaluations. To circumvent this problem, we suggest to perform both Bayesian model selection and justifiability analysis after constructing surrogates for the competing biogeochemical models. Here, we will use the arbitrary polynomial chaos expansion. Considering that surrogate representations are only approximations of the analyzed original models, we account for the approximation error in the Bayesian analysis by introducing novel correction factors for the resulting model weights. Thereby, we extend the Bayesian model justifiability analysis and assess model similarities for computationally expensive models. We demonstrate the method on a representative scenario for microbially induced calcite precipitation in a porous medium. Our extension of the justifiability analysis provides a suitable approach for the comparison of computationally demanding models and gives an insight on the necessary amount of data for a reliable model performance.Item Open Access The method of forced probabilities : a computation trick for Bayesian model evidence(2022) Banerjee, Ishani; Walter, Peter; Guthke, Anneli; Mumford, Kevin G.; Nowak, WolfgangBayesian model selection objectively ranks competing models by computing Bayesian Model Evidence (BME) against test data. BME is the likelihood of data to occur under each model, averaged over uncertain parameters. Computing BME can be problematic: exact analytical solutions require strong assumptions; mathematical approximations (information criteria) are often strongly biased; assumption-free numerical methods (like Monte Carlo) are computationally impossible if the data set is large, for example like high-resolution snapshots from experimental movies. To use BME as ranking criterion in such cases, we develop the “Method of Forced Probabilities (MFP)”. MFP swaps the direction of evaluation: instead of comparing thousands of model runs on random model realizations with the observed movie snapshots, we force models to reproduce the data in each time step and record the individual probabilities of the model following these exact transitions. MFP is fast and accurate for models that fulfil the Markov property in time, paired with high-quality data sets that resolve all individual events. We demonstrate our approach on stochastic macro-invasion percolation models that simulate gas migration in porous media, and list additional examples of probable applications. The corresponding experimental movie was obtained from slow gas injection into water-saturated, homogeneous sand in a 25 x 25 x 1 cm acrylic glass tank. Despite the movie not always satisfying the high demands (resolving all individual events), we can apply MFP by suggesting a few workarounds. Results confirm that the proposed method can compute BME in previously unfeasible scenarios, facilitating a ranking among competing model versions for future model improvement.