scholarly journals A framework for testing the use of electric and electromagnetic data to reduce the prediction error of groundwater models

2015 ◽  
Vol 12 (9) ◽  
pp. 9599-9653 ◽  
Author(s):  
N. K. Christensen ◽  
S. Christensen ◽  
T. P. A. Ferre
Keyword(s):  
Hydraulic Conductivity ◽  
Tikhonov Regularization ◽  
Prediction Error ◽  
Model Calibration ◽  
Groundwater Modeling ◽  
Hydrologic Model ◽  
Geophysical Data ◽  
Model Parameters ◽  
Calibration Data ◽  
And Inversion

Abstract. Despite geophysics is being used increasingly, it is still unclear how and when the integration of geophysical data improves the construction and predictive capability of groundwater models. Therefore, this paper presents a newly developed HYdrogeophysical TEst-Bench (HYTEB) which is a collection of geological, groundwater and geophysical modeling and inversion software wrapped to make a platform for generation and consideration of multi-modal data for objective hydrologic analysis. It is intentionally flexible to allow for simple or sophisticated treatments of geophysical responses, hydrologic processes, parameterization, and inversion approaches. It can also be used to discover potential errors that can be introduced through petrophysical models and approaches to correlating geophysical and hydrologic parameters. With HYTEB we study alternative uses of electromagnetic (EM) data for groundwater modeling in a hydrogeological environment consisting of various types of glacial deposits with typical hydraulic conductivities and electrical resistivities covering impermeable bedrock with low resistivity. It is investigated to what extent groundwater model calibration and, often more importantly, model predictions can be improved by including in the calibration process electrical resistivity estimates obtained from TEM data. In all calibration cases, the hydraulic conductivity field is highly parameterized and the estimation is stabilized by regularization. For purely hydrologic inversion (HI, only using hydrologic data) we used Tikhonov regularization combined with singular value decomposition. For joint hydrogeophysical inversion (JHI) and sequential hydrogeophysical inversion (SHI) the resistivity estimates from TEM are used together with a petrophysical relationship to formulate the regularization term. In all cases, the regularization stabilizes the inversion, but neither the HI nor the JHI objective function could be minimized uniquely. SHI or JHI with regularization based on the use of TEM data produced estimated hydraulic conductivity fields that bear more resemblance to the reference fields than when using HI with Tikhonov regularization. However, for the studied system the resistivities estimated by SHI or JHI must be used with caution as estimators of hydraulic conductivity or as regularization means for subsequent hydrological inversion. Much of the lack of value of the geophysical data arises from a mistaken faith in the power of the petrophysical model in combination with geophysical data of low sensitivity, thereby propagating geophysical estimation errors into the hydrologic model parameters. With respect to reducing model prediction error, it depends on the type of prediction whether it has value to include geophysical data in the model calibration. It is found that all calibrated models are good predictors of hydraulic head. When the stress situation is changed from that of the hydrologic calibration data, then all models make biased predictions of head change. All calibrated models turn out to be a very poor predictor of the pumping well's recharge area and groundwater age. The reason for this is that distributed recharge is parameterized as depending on estimated hydraulic conductivity of the upper model layer which tends to be underestimated. Another important insight from the HYTEB analysis is thus that either recharge should be parameterized and estimated in a different way, or other types of data should be added to better constrain the recharge estimates.

scholarly journals Testing alternative uses of electromagnetic data to reduce the prediction error of groundwater models

2016 ◽  
Vol 20 (5) ◽  
pp. 1925-1946 ◽  
Author(s):  
Nikolaj Kruse Christensen ◽  
Steen Christensen ◽  
Ty Paul A. Ferre
Keyword(s):  
Electrical Resistivity ◽  
Hydraulic Conductivity ◽  
Prediction Error ◽  
Model Calibration ◽  
Hydrologic Model ◽  
Geophysical Data ◽  
Model Parameters ◽  
Calibration Data ◽  
Groundwater Model ◽  
And Inversion

Abstract. In spite of geophysics being used increasingly, it is often unclear how and when the integration of geophysical data and models can best improve the construction and predictive capability of groundwater models. This paper uses a newly developed HYdrogeophysical TEst-Bench (HYTEB) that is a collection of geological, groundwater and geophysical modeling and inversion software to demonstrate alternative uses of electromagnetic (EM) data for groundwater modeling in a hydrogeological environment consisting of various types of glacial deposits with typical hydraulic conductivities and electrical resistivities covering impermeable bedrock with low resistivity (clay). The synthetic 3-D reference system is designed so that there is a perfect relationship between hydraulic conductivity and electrical resistivity. For this system it is investigated to what extent groundwater model calibration and, often more importantly, model predictions can be improved by including in the calibration process electrical resistivity estimates obtained from TEM data. In all calibration cases, the hydraulic conductivity field is highly parameterized and the estimation is stabilized by (in most cases) geophysics-based regularization. For the studied system and inversion approaches it is found that resistivities estimated by sequential hydrogeophysical inversion (SHI) or joint hydrogeophysical inversion (JHI) should be used with caution as estimators of hydraulic conductivity or as regularization means for subsequent hydrological inversion. The limited groundwater model improvement obtained by using the geophysical data probably mainly arises from the way these data are used here: the alternative inversion approaches propagate geophysical estimation errors into the hydrologic model parameters. It was expected that JHI would compensate for this, but the hydrologic data were apparently insufficient to secure such compensation. With respect to reducing model prediction error, it depends on the type of prediction whether it has value to include geophysics in a joint or sequential hydrogeophysical model calibration. It is found that all calibrated models are good predictors of hydraulic head. When the stress situation is changed from that of the hydrologic calibration data, then all models make biased predictions of head change. All calibrated models turn out to be very poor predictors of the pumping well's recharge area and groundwater age. The reason for this is that distributed recharge is parameterized as depending on estimated hydraulic conductivity of the upper model layer, which tends to be underestimated. Another important insight from our analysis is thus that either recharge should be parameterized and estimated in a different way, or other types of data should be added to better constrain the recharge estimates.

scholarly journals Assessment of The Uncertainties of a Conceptual Hydrologic Model By Using Artificially Generated Flows

2012 ◽  
Vol 20 (4) ◽  
pp. 35-43 ◽  
Author(s):  
Peter Valent ◽  
Ján Szolgay ◽  
Carlo Riverso
Keyword(s):  
Calibration Method ◽  
Calibration Procedure ◽  
Hydrologic Model ◽  
Point Of View ◽  
Model Parameters ◽  
Calibration Data ◽  
Artificial Flow ◽  
Calibration Techniques ◽  
Hbv Model ◽  
Further Development

ABSTRACTMost of the studies that assess the performance of various calibration techniques have todeal with a certain amount of uncertainty in the calibration data. In this study we testedHBV model calibration procedures in hypothetically ideal conditions under the assumptionof no errors in the measured data. This was achieved by creating an artificial time seriesof the flows created by the HBV model using the parameters obtained from calibrating themeasured flows. The artificial flows were then used to replace the original flows in thecalibration data, which was then used for testing how calibration procedures can reproduceknown model parameters. The results showed that in performing one hundred independentcalibration runs of the HBV model, we did not manage to obtain parameters that werealmost identical to those used to create the artificial flow data without a certain degree ofuncertainty. Although the calibration procedure of the model works properly froma practical point of view, it can be regarded as a demonstration of the equifinality principle,since several parameter sets were obtained which led to equally acceptable or behaviouralrepresentations of the observed flows. The study demonstrated that this concept forassessing how uncertain hydrological predictions can be applied in the further developmentof a model or the choice of calibration method using artificially generated data.

Multi-objective Optimization of Catchment Reforestation Robust to Uncertainty in Bayesian-Calibrated Watershed Model Parameters

2021 ◽  
Author(s):  
Jared Smith ◽  
Laurence Lin ◽  
Julianne Quinn ◽  
Lawrence Band
Keyword(s):  
Computational Cost ◽  
Bayesian Framework ◽  
Hydrologic Model ◽  
Low Flow ◽  
Critical Parameters ◽  
Model Parameters ◽  
Calibration Data ◽  
Baltimore County ◽  
True Parameter ◽  
Multi Objective

<p>Urban land expansion is expected for our changing world, which unmitigated will result in increased flooding and nutrient exports that already wreak havoc on the wellbeing of coupled human-natural systems worldwide. Reforestation of urbanized catchments is one green infrastructure strategy to reduce stormwater volumes and nutrient exports. Reforestation designs must balance the benefits of flood flow reduction against the costs of implementation and the chance to exacerbate droughts via reduction in recharge that supplies low flows. Optimal locations and numbers of trees depend on the spatial distribution of runoff and streamflow in a catchment; however, calibration data are often only available at the catchment outlet. Equifinal model parameterizations for the outlet can result in uncertainty in the locations and magnitudes of streamflows across the catchment, which can lead to different optimal reforestation designs for different parameterizations.</p><p>Multi-objective robust optimization (MORO) has been proposed to discover reforestation designs that are robust to such parametric model uncertainty. However, it has not been shown that this actually results in better decisions than optimizing to a single, most likely parameter set, which would be less computationally expensive. In this work, the utility of MORO is assessed by comparing reforestation designs optimized using these two approaches with reforestation designs optimized to a synthetic true set of hydrologic model parameters. The spatially-distributed RHESSys ecohydrological model is employed for this study of a suburban-forested catchment in Baltimore County, Maryland, USA. Calibration of the model’s critical parameters is completed using a Bayesian framework to estimate the joint posterior distribution of the parameters. The Bayesian framework estimates the probability that different parameterizations generated the synthetic streamflow data, allowing the MORO process to evaluate reforestation portfolios across a probability-weighted sample of parameter sets in search of solutions that are robust to this uncertainty.</p><p>Reforestation portfolios are designed to minimize flooding, low flow intensity, and construction costs (number of trees). Comparing the Pareto front obtained from using MORO with the Pareto fronts obtained from optimizing to the estimated maximum a posteriori (MAP) parameter set and the synthetic true parameter set, we find that MORO solutions are closer to the synthetic solutions than are MAP solutions. This illustrates the value of considering parametric uncertainty in designing robust water systems despite the additional computational cost.</p>

scholarly journals Applicability of a distributed watershed pollution model in a data-poor environment in Santa Catarina State, Brazil

2008 ◽  
Vol 32 (4) ◽  
pp. 1699-1712 ◽  
Author(s):  
Ivan Luiz Zilli Bacic ◽  
David G. Rossiter ◽  
Christiaan Mathias Mannaerts
Keyword(s):  
Sensitivity Analysis ◽  
Model Calibration ◽  
Management Practices ◽  
Expert Knowledge ◽  
Stream Water ◽  
Model Parameters ◽  
Calibration Data ◽  
Santa Catarina ◽  
Environmental Models ◽  
Santa Catarina State

Intensification of agricultural production without a sound management and regulations can lead to severe environmental problems, as in Western Santa Catarina State, Brazil, where intensive swine production has caused large accumulations of manure and consequently water pollution. Natural resource scientists are asked by decision-makers for advice on management and regulatory decisions. Distributed environmental models are useful tools, since they can be used to explore consequences of various management practices. However, in many areas of the world, quantitative data for model calibration and validation are lacking. The data-intensive distributed environmental model AgNPS was applied in a data-poor environment, the upper catchment (2,520 ha) of the Ariranhazinho River, near the city of Seara, in Santa Catarina State. Steps included data preparation, cell size selection, sensitivity analysis, model calibration and application to different management scenarios. The model was calibrated based on a best guess for model parameters and on a pragmatic sensitivity analysis. The parameters were adjusted to match model outputs (runoff volume, peak runoff rate and sediment concentration) closely with the sparse observed data. A modelling grid cell resolution of 150 m adduced appropriate and computer-fit results. The rainfall runoff response of the AgNPS model was calibrated using three separate rainfall ranges (< 25, 25-60, > 60 mm). Predicted sediment concentrations were consistently six to ten times higher than observed, probably due to sediment trapping along vegetated channel banks. Predicted N and P concentrations in stream water ranged from just below to well above regulatory norms. Expert knowledge of the area, in addition to experience reported in the literature, was able to compensate in part for limited calibration data. Several scenarios (actual, recommended and excessive manure applications, and point source pollution from swine operations) could be compared by the model, using a relative ranking rather than quantitative predictions.

Uncertainty analysis of calibrated parameter values of an urban storm water quality model using metropolis monte carlo algorithm

1997 ◽  
Vol 36 (5) ◽  
pp. 141-148 ◽  
Author(s):  
A. Mailhot ◽  
É. Gaume ◽  
J.-P. Villeneuve
Keyword(s):  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Model Calibration ◽  
Monte Carlo Algorithm ◽  
Storm Water ◽  
Model Parameters ◽  
Calibration Data ◽  
Parameter Uncertainties ◽  
Metropolis Monte Carlo ◽  
Parameter Values

The Storm Water Management Model's quality module is calibrated for a section of Québec City's sewer system using data collected during five rain events. It is shown that even for this simple model, calibration can fail: similarly a good fit between recorded data and simulation results can be obtained with quite different sets of model parameters, leading to great uncertainty on calibrated parameter values. In order to further investigate the lack of data and data uncertainty impacts on calibration, we used a new methodology based on the Metropolis Monte Carlo algorithm. This analysis shows that for a large amount of calibration data generated by the model itself, small data uncertainties are necessary to significantly decrease calibrated parameter uncertainties. This also confirms the usefulness of the Metropolis algorithm as a tool for uncertainty analysis in the context of model calibration.

scholarly journals The Applicability of SWOT’s Non-Uniform Space–Time Sampling in Hydrologic Model Calibration

2020 ◽  
Vol 12 (19) ◽  
pp. 3241
Author(s):  
Cassandra Nickles ◽  
Edward Beighley ◽  
Dongmei Feng
Keyword(s):  
Surface Water ◽  
Model Calibration ◽  
Optimal Parameter ◽  
Uniform Space ◽  
Hydrologic Model ◽  
Space Time ◽  
Added Value ◽  
Model Parameters ◽  
Time Sampling ◽  
Hydrologic Model Calibration

The Surface Water and Ocean Topography (SWOT) satellite mission, expected to launch in 2022, will enable near global river discharge estimation from surface water extents and elevations. However, SWOT’s orbit specifications provide non-uniform space–time sampling. Previous studies have demonstrated that SWOT’s unique spatiotemporal sampling has a minimal impact on derived discharge frequency distributions, baseflow magnitudes, and annual discharge characteristics. In this study, we aim to extend the analysis of SWOT’s added value in the context of hydrologic model calibration. We calibrate a hydrologic model using previously derived synthetic SWOT discharges across 39 gauges in the Ohio River Basin. Three discharge timeseries are used for calibration: daily observations, SWOT temporally sampled, and SWOT temporally sampled including estimated uncertainty. Using 10,000 model iterations to explore predefined parameter ranges, each discharge timeseries results in similar optimal model parameters. We find that the annual mean and peak flow values at each gauge location from the optimal parameter sets derived from each discharge timeseries differ by less than 10% percent on average. Our findings suggest that hydrologic models calibrated using discharges derived from SWOT’s non-uniform space–time sampling are likely to achieve results similar to those based on calibrating with in situ daily observations.

scholarly journals Attribution of hydrologic forecast uncertainty within scalable forecast windows

2013 ◽  
Vol 10 (9) ◽  
pp. 11795-11828 ◽  
Author(s):  
L. Yang ◽  
F. Tian ◽  
Y. Sun ◽  
X. Yuan ◽  
H. Hu
Keyword(s):  
Model Calibration ◽  
Transition Period ◽  
Hydrologic Model ◽  
Dry Season ◽  
Forecast Skill ◽  
Model Parameters ◽  
Combined Effects ◽  
Wet Season ◽  
Streamflow Forecast ◽  
Monthly Streamflow

Abstract. Hindcasts based on the Extended Streamflow Prediction (ESP) approach are carried out in a typical rainfall-dominated basin in China, aiming to examine the roles of initial condition (IC), future atmospheric forcing (FC) and hydrologic model uncertainty (MU) in the streamflow forecast skill. The combined effects of IC and FC are explored within the framework of a forecast window. By implementing virtual numerical simulations without the consideration of MU, it is found that the dominance of IC could last up to 90 days in dry season, while its impact gives way to FC for lead times exceeding 30 days in the wet season. The combined effects of IC and FC on the forecast skill are further investigated by proposing a dimensionless parameter (β) that represents the ratio of the total amount of initial water storage and the incoming rainfall. The forecast skill increases exponentially with β, and varies greatly in different forecast windows. Moreover, the influence of MU on forecast skill is examined by focusing on the uncertainty of model parameters. Two different hydrologic model calibration strategies are carried out. The results indicate that the uncertainty of model parameters exhibits a more significant influence on the forecast skill in the dry season than in the wet season. The ESP approach is more skillful in monthly streamflow forecast during the transition period from wet to dry than otherwise. For the transition period from dry to wet, the low skill of the forecasts could be attributed to the combined effects of IC and FC, but less to the biases in the hydrologic model parameters. For the forecasting in dry season, the usefulness of the ESP approach is heavily dependent on the strategy of the model calibration.

scholarly journals Attribution of hydrologic forecast uncertainty within scalable forecast windows

2014 ◽  
Vol 18 (2) ◽  
pp. 775-786 ◽  
Author(s):  
L. Yang ◽  
F. Tian ◽  
Y. Sun ◽  
X. Yuan ◽  
H. Hu
Keyword(s):  
Model Calibration ◽  
Transition Period ◽  
Hydrologic Model ◽  
Dry Season ◽  
Forecast Skill ◽  
Model Parameters ◽  
Combined Effects ◽  
Wet Season ◽  
Streamflow Forecast ◽  
Monthly Streamflow

Abstract. Hindcasts based on the extended streamflow prediction (ESP) approach are carried out in a typical rainfall-dominated basin in China, aiming to examine the roles of initial conditions (IC), future atmospheric forcing (FC) and hydrologic model uncertainty (MU) in streamflow forecast skill. The combined effects of IC and FC are explored within the framework of a forecast window. By implementing virtual numerical simulations without the consideration of MU, it is found that the dominance of IC can last up to 90 days in the dry season, while its impact gives way to FC for lead times exceeding 30 days in the wet season. The combined effects of IC and FC on the forecast skill are further investigated by proposing a dimensionless parameter (β) that represents the ratio of the total amount of initial water storage and the incoming rainfall. The forecast skill increases exponentially with β, and varies greatly in different forecast windows. Moreover, the influence of MU on forecast skill is examined by focusing on the uncertainty of model parameters. Two different hydrologic model calibration strategies are carried out. The results indicate that the uncertainty of model parameters exhibits a more significant influence on the forecast skill in the dry season than in the wet season. The ESP approach is more skillful in monthly streamflow forecast during the transition period from wet to dry than otherwise. For the transition period from dry to wet, the low skill of the forecasts could be attributed to the combined effects of IC and FC, but less to the biases in the hydrologic model parameters. For the forecasts in the dry season, the skill of the ESP approach is heavily dependent on the strategy of the model calibration.

scholarly journals Towards a more representative parametrisation of hydrologic models via synthesizing the strengths of Particle Swarm Optimisation and Robust Parameter Estimation

2012 ◽  
Vol 16 (2) ◽  
pp. 603-629 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann
Keyword(s):  
Parameter Estimation ◽  
Particle Swarm ◽  
Hydrologic Model ◽  
Data Depth ◽  
Particle Swarm Optimisation ◽  
Model Parameters ◽  
Calibration Data ◽  
Time Step ◽  
Robust Parameter ◽  
Robust Parameter Estimation

Abstract. The development of methods for estimating the parameters of hydrologic models considering uncertainties has been of high interest in hydrologic research over the last years. In particular methods which understand the estimation of hydrologic model parameters as a geometric search of a set of robust performing parameter vectors by application of the concept of data depth found growing research interest. Bárdossy and Singh (2008) presented a first Robust Parameter Estimation Method (ROPE) and applied it for the calibration of a conceptual rainfall-runoff model with daily time step. The basic idea of this algorithm is to identify a set of model parameter vectors with high model performance called good parameters and subsequently generate a set of parameter vectors with high data depth with respect to the first set. Both steps are repeated iteratively until a stopping criterion is met. The results estimated in this case study show the high potential of the principle of data depth to be used for the estimation of hydrologic model parameters. In this paper we present some further developments that address the most important shortcomings of the original ROPE approach. We developed a stratified depth based sampling approach that improves the sampling from non-elliptic and multi-modal distributions. It provides a higher efficiency for the sampling of deep points in parameter spaces with higher dimensionality. Another modification addresses the problem of a too strong shrinking of the estimated set of robust parameter vectors that might lead to overfitting for model calibration with a small amount of calibration data. This contradicts the principle of robustness. Therefore, we suggest to split the available calibration data into two sets and use one set to control the overfitting. All modifications were implemented into a further developed ROPE approach that is called Advanced Robust Parameter Estimation (AROPE). However, in this approach the estimation of the good parameters is still based on an ineffective Monte Carlo approach. Therefore we developed another approach called ROPE with Particle Swarm Optimisation (ROPE-PSO) that substitutes the Monte Carlo approach with a more effective and efficient approach based on Particle Swarm Optimisation. Two case studies demonstrate the improvements of the developed algorithms when compared with the first ROPE approach and two other classical optimisation approaches calibrating a process oriented hydrologic model with hourly time step. The focus of both case studies is on modelling flood events in a small catchment characterised by extreme process dynamics. The calibration problem was repeated with higher dimensionality considering the uncertainty in the soil hydraulic parameters and another conceptual parameter of the soil module. We discuss the estimated results and propose further possibilities in order to apply ROPE as a well-founded parameter estimation and uncertainty analysis tool.

scholarly journals A Bayesian sequential updating approach to predict phenology of silage maize

2021 ◽  
Author(s):  
Michelle Viswanathan ◽  
Tobias K. D. Weber ◽  
Sebastian Gayler ◽  
Juliane Mai ◽  
Thilo Streck
Keyword(s):  
Parameter Uncertainty ◽  
Prediction Error ◽  
Model Parameters ◽  
Observation Data ◽  
Calibration Data ◽  
Time Step ◽  
Validation Data ◽  
Automatic Data ◽  
Silage Maize ◽  
Sequential Updating

Abstract. Crop models are tools used for predicting year to year crop development on field to regional scales. However, robust predictions are hampered by factors such as uncertainty in crop model parameters and in the data used for calibration. Bayesian calibration allows for the estimation of model parameters and quantification of uncertainties, with the consideration of prior information. In this study, we used a Bayesian sequential updating (BSU) approach to progressively incorporate additional data at a yearly time-step to calibrate a phenology model (SPASS) while analysing changes in parameter uncertainty and prediction quality. We used field measurements of silage maize grown between 2010 and 2016 in the regions of Kraichgau and Swabian Alb in southwestern Germany. Parameter uncertainty and model prediction errors were expected to progressively reduce to a final, irreducible value. Parameter uncertainty reduced as expected with the sequential updates. For two sequences using synthetic data, one in which the model was able to accurately simulate the observations, and the other in which a single cultivar was grown under the same environmental conditions, prediction error mostly reduced. However, in the true sequences that followed the actual chronological order of cultivation by the farmers in the two regions, prediction error increased when the calibration data was not representative of the validation data. This could be explained by differences in ripening group and temperature conditions during vegetative growth. With implications for manual and automatic data streams and model updating, our study highlights that the success of Bayesian methods for predictions depends on a comprehensive understanding of inherent structure in the observation data and model limitations.

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