HR: 16:30h
AN: H14C-02    [Abstracts]
TI: Impact of Sampling Volume on the Probability Density Function of Steady-State Concentration
AU: * Schwede, R L
EM: ronnie.schwede@eawag.ch
AF: Swiss Federal Institute of Aquatic Science and Technology (Eawag), Überlandstr. 133, Dübendorf, 8600, Switzerland
AU: Nowak, W
EM: wolfgang.nowak@iws.uni-stuttgart.de
AF: University of Stuttgart, Institute for Hydraulic Engineering (LH2), Pfaffenwaldring 61, Stuttgart, 70569, Germany
AU: Cirpka, O A
EM: olaf.cirpka@eawag.ch
AF: Swiss Federal Institute of Aquatic Science and Technology (Eawag), Überlandstr. 133, Dübendorf, 8600, Switzerland
AB: In recent years, statistical theory has been used to compute the ensemble mean and variance of concentration in formations with second-order stationary log-conductivity fields. The merit of accurately estimating the mean and variance of concentration, however, remains unclear without knowing the shape of the probability density function (pdf). In a set-up where a conservative solute is continuously injected into a domain, the concentration can never exceed the range between zero and the concentration value in the injected solution. At small travel distances close to the fringe of the plume, an observation point may fall into the plume or outside, so that the statistical concentration distribution clusters at the two limiting values. Obviously, this results in non-Gaussian pdf's of concentration. With increasing travel distance, the lateral plume boundaries are smoothed, resulting in increased probability of intermediate concentrations. Likewise, averaging the concentration in a larger sampling volume, as typically done in field measurements, leads to intermediate concentrations. We present analytical results of concentration pdf's for point-like and spatially averaged measurements based on stochastic theory applied to stationary media. The approach is based on backtracking of the sampling volume to the injection plane. While effective dispersion describes the increase of the volume of influence with increasing time of backtracking, the difference between ensemble and effective dispersion quantifies the uncertainty of identifying the center of mass. We assume Gaussian pdf's for lateral displacements and the shape of the volume of influence. The resulting concentration pdf can be fitted by beta distributions. The results are compared to Monte Carlo simulations of flow and steady-state transport in 3-D heterogeneous domains. In both methods the shape of the pdf changes with distance to the contaminant source: Near the source, the distribution is bimodal, whereas it becomes an unimodal beta distribution far away from the contaminant source. The pdf of concentrations in the Monte Carlo simulations approaches a Gaussian-like shape with increasing distance to the contaminant source. Increasing the measurement volume decreases the distance over which the bimodal shape is a predominant feature of the concentration pdf. The analytical and empirical pdf's differ slightly, which we contribute to numerical artifacts in the Monte Carlo simulations but also to the hard assumptions made in the analytical approach. Our results imply that geostatistical techniques for interpolation and other statistical inferences based on Gaussian distributions, such as kriging and cokriging, maybe feasible only far away from the contaminant source. For calculations near the source, the beta-like distribution of concentration must not be neglected.
DE: 1832 Groundwater transport
DE: 1869 Stochastic hydrology
SC: Hydrology [H]
MN: 2007 Fall Meeting