Conditioning Stochastic Groundwater Flow Models on Head Data
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CONDITIONING STOCHASTIC GROUNDWATER FLOW MODELS ON HEAD DATA K ANDREW CLIFFE AND C PETER JACKSON AEA Technology, 424.4 Harwell, Oxon, OX1 1 ORA, UK.
ABSTRACT We present a new method for conditioning realizations of the logarithm Y of transmissivity on head data. Each realization is conditioned by subtracting a linear combination of certain basis functions, each corresponding to a measurement, obtained by a process based on co-kriging. The required cross covariance between head and Y can be numerically computed very efficiently using the adjoint method. The coefficients in the linear combination are chosen to try to minimise the differences between computed and measured heads. The most efficient methods for such non-linear optimisation problems are those that exploit information about the second derivatives of the function being minimised. We show how these second derivatives can be computed very efficiently using the adjoint method for certain classes of finite-element schemes. We illustrate our method by application to the WIPP-2 test case of the international INTRAVAL project. We show that the match between computed and measured heads is greatly improved. We compare our method with approaches that use pilot points. Our method is exact if the variability of the Y field and the deviations of the measured heads from the values computed for the mean of the Y field are both small, whereas pilot-point methods are only approximate. However, our method may be more expensive computationally. Finally, we discuss the extension of our method to conditioning on transient head data and to dealing with boundary conditions. INTRODUCTION In many countries the favoured option for disposal of radioactive waste is burial deep underground. The most likely pathway by which radionuclides from radioactive waste in an underground repository might return to the biosphere is the groundwater pathway: leaching from the repository, followed by transport by flowing groundwater. Analysis of this pathway forms
an important part of assessing the performance of a potential repository. One particular issue that may need to be addressed in the required groundwater flow and transport calculations is the heterogeneity of the rocks through which the groundwater is flowing. The heterogeneity means that the hydrogeological properties of the rocks cannot be precisely determined using a limited number of borehole measurements. This leads to uncertainty, which must be taken into account in a performance assessment. The treatment of heterogeneity is being studied in the Nirex Safety Assessment Research Programme. A Monte-Carlo approach is usually adopted for dealing with heterogeneity. Many numerical realizations of the transmissivity (or permeability in a three-dimensional case) are generated with the same statistical distribution as the transmissivity of the rocks. This distribution is inferred from the experimental data. Then for each realization the quantities of interest (such as groundwater velocity or travel time) are computed (using standard numeri
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