Measurement Network Design for Minimizing the ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Measurement Network Design for Minimizing the Uncertainty in Breakthrough Predictions
Author:Gijs Janssen <> (Wageningen University, Department of Soil Quality)
Johan Valstar <> (Netherlands Institute for Applied Geoscience TNO-National Geological Survey)
Sjoerd van der Zee <> (Wageningen University, Department of Ecohydrology)
Presenter:Gijs Janssen <> (Wageningen University, Department of Soil Quality)
Date: 2006-06-18     Track: Special Sessions     Session: Data assimilation in water resources modelling

We are developing a first-order measurement network optimization algorithm that can find the optimal combination and configuration of hydraulic conductivity, head and travel time measurements. The method is based on a representer-based inverse method for groundwater flow and transport applications (Valstar et al., Water Resources Research 2004). In the representer approach, unknown variables are linearly expanded in finite series which depend on unknown functions called representers. Each representer quantifies the influence of a given measurement on the estimate of a particular (state or static) variable. This procedure replaces the original inverse problem by an equivalent problem where the number of independent unknowns is reduced to the number of measurements. The representers can be shown to be equivalent to the linearized cross-covariance between the measurement and the (state or static) variable for which the representer is defined. As such, the representers can be used to estimate the prior covariances of certain goal variables, if a (pseudo) measurement for this variable is defined. Also, the representers can be used for a first-order approximation of the posterior covariances of the goal variables if a certain measurement set is assumed (because these covariances are functions of the prior variances and the cross-covariances between all measurements and the cross- covariances between the measurements and the goal variables). In our study, we are interested in minimizing the uncertainty in the prediction of contaminant breakthrough through confining layers. The uncertainty in breakthrough is a convolution between the contaminant arrival time and contaminant arrival location probability at the bottom of the confining layer. So the contaminant arrival time and the contaminant arrival location are our goal variables, and we derived representer definitions for advectively transported particles accordingly. The posterior covariance of the goal variables obtained by the representer method are based on a normal distribution. Using Monte Carlo calculation it turned out that arrival times are nearly log-normally distributed. Therefore we choose the logarithm of the arrival time rather than the arrival time itself as the goal variable. The derivation of the travel time representers now requires an additional linearization. However, the uncertainty estimates (both prior and posterior) of the arrival times as given by the thus derived travel time representers turned out to approximate Monte Carlo results very well , even for large variances of the hydraulic conductivity field. Once all representers that describe the relationships between a chosen set of potential measurements (with their locations) and the goal variables are known, the posterior covariances of the goal variables and therefore also the posterior breakthrough prediction uncertainty can in principle be calculated for every possible measurement set. Because the number of possible measurement combinations is usually excessively large, we use a Genetic Algorithm for an efficient search for a (close to) optimal measurement network within the available configuration space. The novelty of this work lies primarily in the incorporation of travel time measurements (for example Tritium/3He measurements) into a measurement network optimization algorithm, which to our knowledge has never been reported before. It requires an additional linearization in the derivation of the travel time representers, which is also new. Furthermore, our approach of evaluating the performance of a measurement network to the convolution of arrival time and arrival location probability is a new approach. Within the applied inverse method this requires the derivation of particle position representers, which has not been published before.