Using predictive uncertainty analysis to optimise tracer test design and data acquisition

Wallis, Ilka; Moore, Catherine; Post, Vincent; Wolf, Leif; Martens, Evelien; Prommer, Henning

doi:10.1016/j.jhydrol.2014.04.061

Cited by 16 publications

(21 citation statements)

References 30 publications

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“…Because Equation 1 only holds parameter sensitivities to modeled targets (observations and forecasts) and not absolute data values, it can be used to evaluate the value of existing or new data sets based on their ability to reduce the uncertainty of a given forecast of interest. This type of analysis has been documented previously in the literature (Dausman et al 2010;Fienen et al 2010;Brunner et al 2012;Wallis et al 2014;Wöhling et al 2016). Equation 1 can thereby be used to evaluate the value of existing and yet to be collected data sets.…”

Section: The Concept Of Dwmentioning

confidence: 95%

“…OD studies can also be subdivided into two main categories: those applying nonlinear Monte‐Carlo (MC) based methods to estimate predictive uncertainties (e.g., Nowak ; Leube et al ; Kikuchi et al ), and those applying linear approximations (Dausman et al ; Fienen et al ; Engelhardt et al ; Hill et al ; Wallis et al ; Wöhling et al ). Nonlinear MC methods may be necessary for problems including processes or parameter interactions that lead to highly nonlinear responses.…”

Section: Introductionmentioning

confidence: 99%

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Extending Data Worth Analyses to Select Multiple Observations Targeting Multiple Forecasts

Vilhelmsen

Ferré

2017

Groundwater

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Hydrological models are often set up to provide specific forecasts of interest. Owing to the inherent uncertainty in data used to derive model structure and used to constrain parameter variations, the model forecasts will be uncertain. Additional data collection is often performed to minimize this forecast uncertainty. Given our common financial restrictions, it is critical that we identify data with maximal information content with respect to forecast of interest. In practice, this often devolves to qualitative decisions based on expert opinion. However, there is no assurance that this will lead to optimal design, especially for complex hydrogeological problems. Specifically, these complexities include considerations of multiple forecasts, shared information among potential observations, information content of existing data, and the assumptions and simplifications underlying model construction. In the present study, we extend previous data worth analyses to include: simultaneous selection of multiple new measurements and consideration of multiple forecasts of interest. We show how the suggested approach can be used to optimize data collection. This can be used in a manner that suggests specific measurement sets or that produces probability maps indicating areas likely to be informative for specific forecasts. Moreover, we provide examples documenting that sequential measurement election approaches often lead to suboptimal designs and that estimates of data covariance should be included when selecting future measurement sets.

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Section: The Concept Of Dwmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Extending Data Worth Analyses to Select Multiple Observations Targeting Multiple Forecasts

Vilhelmsen

Ferré

2017

Groundwater

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“…The worth of such an addition (subsequently referred to as data worth [DW]) on reducing model prediction uncertainty is then evaluated. Wallis et al (2014) extended the DW-based OD for selecting multiple observations, and Wöhling et al (2016) extended it further by using a genetic algorithm (GA) to incorporate multiple new observations of head and/or hydraulic conductivity to decrease the predictive uncertainty. Wallis et al (2014) extended the DW-based OD for selecting multiple observations, and Wöhling et al (2016) extended it further by using a genetic algorithm (GA) to incorporate multiple new observations of head and/or hydraulic conductivity to decrease the predictive uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…Dausman et al (2010) applied the DW-based OD on the Henry problem to define the optimal locations of salinity concentration and temperature that would reduce the uncertainty of predicting the displacement of a salt/fresh water interface caused by a change in the inflow rate to the system. Wallis et al (2014) extended the DW-based OD for selecting multiple observations, and Wöhling et al (2016) extended it further by using a genetic algorithm (GA) to incorporate multiple new observations of head and/or hydraulic conductivity to decrease the predictive uncertainty. Vilhelmsen and Ferre (2017) carried out yet another extension to simultaneously select multiple new measurements targeting multiple forecasts of interest.…”

Section: Introductionmentioning

confidence: 99%

Data‐Worth Assessment for a Three‐Dimensional Optimal Design in Nonlinear Groundwater Systems

et al. 2018

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Groundwater model predictions are often uncertain due to inherent uncertainties in model input data. Monitored field data are commonly used to assess the performance of a model and reduce its prediction uncertainty. Given the high cost of data collection, it is imperative to identify the minimum number of required observation wells and to define the optimal locations of sampling points in space and depth. This study proposes a design methodology to optimize the number and location of additional observation wells that will effectively measure multiple hydrogeological parameters at different depths. For this purpose, we incorporated Bayesian model averaging and genetic algorithms into a linear data‐worth analysis in order to conduct a three‐dimensional location search for new sampling locations. We evaluated the methodology by applying it along a heterogeneous coastal aquifer with limited hydrogeological data that is experiencing salt water intrusion (SWI). The aim of the model was to identify the best locations for sampling head and salinity data, while reducing uncertainty when predicting multiple variables of SWI. The resulting optimal locations for new observation wells varied with the defined design constraints. The optimal design (OD) depended on the ratio of the start‐up cost of the monitoring program and the installation cost of the first observation well. The proposed methodology can contribute toward reducing the uncertainties associated with predicting multiple variables in a groundwater system.

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“…For example, groundwater managers are often limited to a prescribed financial budget; therefore, managers must develop a means to maximize the amount of information they can obtain, subject to the funds available. There exist a number of strategies developed to optimize data acquisition, known as either data‐worth (Baú & Mayer, ; Brunner et al, ; Dausman et al, ; Engelhardt et al, ; Wallis et al, ), or as experimental design strategies (Cleveland & Yeh, ; Geiges et al, ; McPhee & Yeh, ; Pham & Tsai, ; Sun & Yeh, ; Ushijima & Yeh, ; Wagner, ; Yeh, ). Both of these strategies aim for optimal data acquisition, and are often equivalent.…”

Section: Introductionmentioning

confidence: 99%

A Practical, Robust Methodology for Acquiring New Observation Data Using Computationally Expensive Groundwater Models

Siade

Hall

Karelse

2017

Water Resources Research

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Regional groundwater flow models play an important role in decision making regarding water resources; however, the uncertainty embedded in model parameters and model assumptions can significantly hinder the reliability of model predictions. One way to reduce this uncertainty is to collect new observation data from the field. However, determining where and when to obtain such data is not straightforward. There exist a number of data‐worth and experimental design strategies developed for this purpose. However, these studies often ignore issues related to real‐world groundwater models such as computational expense, existing observation data, high‐parameter dimension, etc. In this study, we propose a methodology, based on existing methods and software, to efficiently conduct such analyses for large‐scale, complex regional groundwater flow systems for which there is a wealth of available observation data. The method utilizes the well‐established d‐optimality criterion, and the minimax criterion for robust sampling strategies. The so‐called Null‐Space Monte Carlo method is used to reduce the computational burden associated with uncertainty quantification. And, a heuristic methodology, based on the concept of the greedy algorithm, is proposed for developing robust designs with subsets of the posterior parameter samples. The proposed methodology is tested on a synthetic regional groundwater model, and subsequently applied to an existing, complex, regional groundwater system in the Perth region of Western Australia. The results indicate that robust designs can be obtained efficiently, within reasonable computational resources, for making regional decisions regarding groundwater level sampling.

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Using predictive uncertainty analysis to optimise tracer test design and data acquisition

Cited by 16 publications

References 30 publications

Extending Data Worth Analyses to Select Multiple Observations Targeting Multiple Forecasts

Extending Data Worth Analyses to Select Multiple Observations Targeting Multiple Forecasts

Data‐Worth Assessment for a Three‐Dimensional Optimal Design in Nonlinear Groundwater Systems

A Practical, Robust Methodology for Acquiring New Observation Data Using Computationally Expensive Groundwater Models

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