EULERIAN-LAGRANGIAN ANALYSIS OF TRANSPORT CONDITIONED ON HYDRAULIC DATA .4. UNCERTAIN INITIAL PLUME STATE AND NON-GAUSSIAN VELOCITIES

In previous papers of this series we des crib ed an analytical-numeric al method to predict deterministically solute transport under uncertai nty based on a new Eulerian-Lagrangian theory. We examined the effect that conditioning on hydraulic data has on predicted velocities and co ncentrations due to instantaneous point and nonpoint sources and discu ssed the same effect on spatial plume moments, total mass flow rate ac ross a ''compliance surface,'' cumulative mass release across this sur face, and the corresponding travel time distribution. Our analysis to date assumed that the initial state of the plume (the source term or i nitial concentration) is known with certainty and that the groundwater velocity field is Gaussian. In reality, the initial state of the plum e is almost never known with certainty, especially when this state is inferred by sampling a plume at some arbitrary time t(0) following int roduction of the solute into the subsurface (as is the case at many co ntaminated sites). Likewise, Monte Carlo simulations have shown that i n Gaussian log hydraulic conductivity or log transmissivity fields, of the kind often indicated by in situ hydraulic test data, the longitud inal velocity becomes rapidly lognormal as the variance of the heterog eneities increases. In this paper we show how to handle both of these complications by means of our analytical-numerical method of computati on. By revisiting our previous examples, we explore the effects that u ncertainty in plume initial state and non-Gaussian velocities may have on predicted plume concentrations and uncertainty due to instantaneou s point and nonpoint sources with and without conditioning on measurem ents of log transmissivity or hydraulic head in two dimensions. One of our findings is that the more common Gaussian models are nonconservat ive (in a regulatory sense) when applied during early dimensionless ti mes to plumes that are initially short in the direction of mean flow.