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Schoniger A.,University of Tubingen | Illman W.A.,University of Waterloo | Wohling T.,University of Tubingen | Wohling T.,Lincoln Agritech Ltd. | Nowak W.,University of Stuttgart
Journal of Hydrology | Year: 2015

Groundwater modelers face the challenge of how to assign representative parameter values to the studied aquifer. Several approaches are available to parameterize spatial heterogeneity in aquifer parameters. They differ in their conceptualization and complexity, ranging from homogeneous models to heterogeneous random fields. While it is common practice to invest more effort into data collection for models with a finer resolution of heterogeneities, there is a lack of advice which amount of data is required to justify a certain level of model complexity. In this study, we propose to use concepts related to Bayesian model selection to identify this balance. We demonstrate our approach on the characterization of a heterogeneous aquifer via hydraulic tomography in a sandbox experiment (Illman et al., 2010). We consider four increasingly complex parameterizations of hydraulic conductivity: (1) Effective homogeneous medium, (2) geology-based zonation, (3) interpolation by pilot points, and (4) geostatistical random fields. First, we investigate the shift in justified complexity with increasing amount of available data by constructing a model confusion matrix. This matrix indicates the maximum level of complexity that can be justified given a specific experimental setup. Second, we determine which parameterization is most adequate given the observed drawdown data. Third, we test how the different parameterizations perform in a validation setup. The results of our test case indicate that aquifer characterization via hydraulic tomography does not necessarily require (or justify) a geostatistical description. Instead, a zonation-based model might be a more robust choice, but only if the zonation is geologically adequate. © 2015 Elsevier B.V. Source

Roten R.L.,Lincoln Agritech Ltd. | Ferguson J.C.,Lincoln University at Christchurch | Hewitt A.J.,University of Queensland
New Zealand Plant Protection | Year: 2014

A field study was conducted in November 2013 to assess the drift reduction potential of a three headed spray-hood unit with either DG95-02 or DG95-015 low-drift nozzles used with the hoods either on or off (DG nozzles calibrated at 0.6 litres/min). A standard treatment of 110-03 nozzles calibrated at 1.25 litres/min without hoods was the control. One tank mix of 0.4 g/litre PTSA (1,3,6,8-pyrenetetrasulfonic acid tetrasodium salt) fluorescent dye was used for all treatments. Petri dishes and aluminium plate collectors were placed at 0.25, 0.5, 1, 2, 5, 10, 25, 50 and 100 m downwind in three lines spaced at 10 m. Collectors were placed in plastic bags under cool, dark storage until analysis. Results showed that total drift was reduced up to 99%, compared to the control, when the spray hoods where used. © 2014 New Zealand Plant Protection Society (Inc.). Source

Wohling T.,University of Tubingen | Wohling T.,Lincoln Agritech Ltd. | Schoniger A.,University of Tubingen | Gayler S.,University of Tubingen | Nowak W.,University of Stuttgart
Water Resources Research | Year: 2015

A Bayesian model averaging (BMA) framework is presented to evaluate the worth of different observation types and experimental design options for (1) more confidence in model selection and (2) for increased predictive reliability. These two modeling tasks are handled separately because model selection aims at identifying the most appropriate model with respect to a given calibration data set, while predictive reliability aims at reducing uncertainty in model predictions through constraining the plausible range of both models and model parameters. For that purpose, we pursue an optimal design of measurement framework that is based on BMA and that considers uncertainty in parameters, measurements, and model structures. We apply this framework to select between four crop models (the vegetation components of CERES, SUCROS, GECROS, and SPASS), which are coupled to identical routines for simulating soil carbon and nitrogen turnover, soil heat and nitrogen transport, and soil water movement. An ensemble of parameter realizations was generated for each model using Monte-Carlo simulation. We assess each model's plausibility by determining its posterior weight, which signifies the probability to have generated a given experimental data set. Several BMA analyses were conducted for different data packages with measurements of soil moisture, evapotranspiration (ETa), and leaf area index (LAI). The posterior weights resulting from the different BMA runs were compared to the weight distribution of a reference run with all data types to investigate the utility of different data packages and monitoring design options in identifying the most appropriate model in the ensemble. We found that different (combinations of) data types support different models and none of the four crop models outperforms all others under all data scenarios. The best model discrimination was observed for those data where the competing models disagree the most. The data worth for reducing prediction uncertainty depends on the prediction to be made. LAI data have the highest utility for predicting ETa, while soil moisture data are better for predicting soil water drainage. Our study illustrates, that BMA provides an objective framework for data worth analysis with respect to both model discrimination and model calibration for a wide range of applications. Key Points: BMA provides a data worth analysis framework for model selection and calibration BMA does not converge to the "true" model Different data types support different models and none outperforms all others © 2015. American Geophysical Union. All Rights Reserved. Source

SchoNiger A.,University of Tubingen | Wohling T.,University of Tubingen | Wohling T.,Lincoln Agritech Ltd. | Nowak W.,University of Stuttgart
Water Resources Research | Year: 2015

Bayesian model averaging (BMA) ranks the plausibility of alternative conceptual models according to Bayes' theorem. A prior belief about each model's adequacy is updated to a posterior model probability based on the skill to reproduce observed data and on the principle of parsimony. The posterior model probabilities are then used as model weights for model ranking, selection, or averaging. Despite the statistically rigorous BMA procedure, model weights can become uncertain quantities due to measurement noise in the calibration data set or due to uncertainty in model input. Uncertain weights may in turn compromise the reliability of BMA results. We present a new statistical concept to investigate this weighting uncertainty, and thus, to assess the significance of model weights and the confidence in model ranking. Our concept is to resample the uncertain input or output data and then to analyze the induced variability in model weights. In the special case of weighting uncertainty due to measurement noise in the calibration data set, we interpret statistics of Bayesian model evidence to assess the distance of a model's performance from the theoretical upper limit. To illustrate our suggested approach, we investigate the reliability of soil-plant model selection following up on a study by Wöhling et al. (2015). Results show that the BMA routine should be equipped with our suggested upgrade to (1) reveal the significant but otherwise undetected impact of measurement noise on model ranking results and (2) to decide whether the considered set of models should be extended with better performing alternatives. © 2015. American Geophysical Union. All Rights Reserved. Source

Wohling T.,University of Tubingen | Wohling T.,Lincoln Agritech Ltd. | Gayler S.,University of Tubingen | Priesack E.,Helmholtz Center for Environmental Research | And 10 more authors.
Water Resources Research | Year: 2013

Six models with differing representation of the physical process in the coupled soil-plant system are tested to simultaneously reproduce the dynamics of soil water contents, evapotranspiration, and leaf area index during a growing season of winter wheat at two contrasting field plots in the Kraichgau and the Swabian Alb regions in South-West Germany. The main aim of the study is the assessment of the performance and the identification of structural deficits of the models LEACHN, SUCROS, CERES, GECROS, and SPASS as well as the land-surface model CLM3.5. The calibration of each model is posed in a multiobjective framework with three different objective functions that summarize the fit between model simulations and the three observation types. The AMALGAM evolutionary search algorithm is utilized to simultaneously estimate the most important soil hydraulic and plant parameters. The six models exhibit a wide variability in the trade-offs between the fitting to the data types. Mechanistic process description, particularly of the root system, reduces the trade-off considerably for the SPASS and GECROS models. These models adequately simulate the reduction of root water uptake and transpiration during senescence under nonlimited soil water supply. The SPASS model in particular shows an overall better performance as compared to the more simpler models which is related to an adequate level of structural complexity in the interplay of all model compartments combined with a relatively low parameter sensitivity to the weighting scheme in the multiobjective optimization. The dynamic consideration of the root system formation is particularly important, which is simulated quite detailed in the SPASS model as a function of nitrogen (N) and water availability in the different soil horizons. The proposed multiobjective calibration procedure proved to be very useful to identify processes that are important to adequately simulate the coupled soil-plant system. The consideration of these processes and our insights about the value of different data types for model calibration is expected to lead to more accurate, predictive land-surface models. © 2013. American Geophysical Union. All Rights Reserved. Source

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