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Stochastic analysis of nonstationary subsurface solute transport: 2. Conditional moments
Author(s) -
Graham Wendy,
McLaughlin Dennis
Publication year - 1989
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr025i011p02331
Subject(s) - plume , advection , sampling (signal processing) , statistical physics , stochastic process , statistics , mathematics , environmental science , filter (signal processing) , meteorology , physics , thermodynamics , computer science , computer vision
Stochastic analyses of subsurface transport indicate that the concentration distributions of individual solute plumes may deviate significantly from those predicted by unconditional ensemble statistics, particularly in near‐source regions. This paper presents a method for developing improved concentration predictions which are tailored to site‐specific conditions. The improved predictions are obtained by conditioning ensemble moments on field observations of log hydraulic conductivity, head, and solute concentration. The conditional moments are obtained from a distributed parameter Kaiman filter which is recursively linearized about the most recent estimates of solute concentration and velocity. The conditioning procedure is illustrated for two synthetic random solute plumes. Reasonably good estimates of the solute concentration distributions are obtained by conditioning the ensemble moments on a small number of measurements located in regions of high concentration uncertainty. The sampling networks adapt to the unique characteristics of each plume as they evolve over time. The example indicates that it is important to capture the dominant trends of the velocity field at as early a time as possible. As more measurements become available, advection accounts for a greater portion of small‐scale velocity variability, and the magnitude of the macrodispersion term diminishes. This is reflected in the behavior of the conditional ensemble moments.