A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow

Abstract

Abstract. This paper describes the first major attempt to compare seven different inverse approaches for identifying aquifer transmissivity. The ultimate objective was to determine which of several geostatistical inverse techniques is better suited for making probabilistic forecasts of the potential transport of solutes in an aquifer where spatial variability and uncertainty in hydrogeologic properties are significant. Seven geostatistical methods (fast Fourier transform (FF), fractal simulation (FS), linearized cokriging (LC), linearized semianalytical (LS), maximum likelihood (ML), pilot point (PP), and sequential self-calibration (SS)) were compared on four synthetic data sets. Each data set had specific features meeting (or not) classical assumptions about stationarity, amenability to a geostatistical description, etc. The comparison of the outcome of the methods is based on the prediction of travel times and travel paths taken by conservative solutes migrating in the aquifer for a distance of 5 km. Four of the methods, LS, ML, PP, and SS, were identified as being approximately equivalent for the specific problems considered. The magnitude of the variance of the transmissivity fields, which went as high as 10 times the generally accepted range for linearized approaches, was not a problem for the linearized methods when applied to stationary fields; that is, their inverse solutions and travel time predictions were as accurate as those of the nonlinear methods. Nonstationarity of the "true" transmissivity field, or the presence of "anomalies" such as high-permeability fracture zones was, however, more of a problem for the linearized methods. The importance of the proper selection of the semivariogram of the 1og•0 (T) field (or the ability of the method to optimize this variogram iteratively) was found to have a significant impact on the accuracy and precision of the travel time predictions. Use of additional transient information from pumping tests did not result in major changes in the outcome. While the methods differ in their underlying theory, and the codes developed to implement the theories were limited to varying degrees, the most important factor for achieving a successful solution was the time and experience devoted by the user of the method. •2Stanford University, Stanford, California.•3Duke Engineering and Services, Inc., Austin, Texas.•4University of Arizona, Tucson.•Slnstitut Franqais du Pftrole, Rueil-Malmaison, France.•6University of California, Berkeley.Copyright 1998 by the American Geophysical Union. Paper number 98WR00003.0043-1397/98/98WR-00003509.00 tion, or performance assessment of planned waste disposal projects, it is no longer enough to determine the "best estimate" of the distribution in space of the aquifer parameters. A measure of the uncertainty associated with this estimation is also needed. Geostatistical techniques are ideally suited to filling this role. Basically, geostatistics fits a "structural model" to the data, reflecting their spatial variability. Then, both "best estim...

A multiscale approach for estimating solute travel time distributions

“…Each realization derived in this way requires O d 2 N f computations. This can be considerably more e cient than alternative conditional simulation methods (such as those described in [19]), even when the log conductivity ®eld is Gauss±Markov and d is O N 0X5 f . The travel time example discussed in the next section illustrates both the estimation and conditional simulation aspects of the multiscale approach.…”

“…The travel times of wastes released from underground storage facilities to the accessible environment provide valuable information for assessing possible exposure risks. Travel time is particularly important in radioactive waste disposal applications, since the exposure level for any given constituent depends on the ratio of travel time to halflife [19]. When the factors controlling solute transport are highly variable and uncertain it is best to use probabilistic approaches to characterize travel times and related risks.…”

“…As an example, we describe a multiscale algorithm which estimates groundwater travel times and generates travel time probability distributions. Our example is a simpli®ed version of the waste isolation performance assessment problem considered in a recent comparison of popular groundwater inverse procedures [19]. In the remaining sections of this paper we review relevant multiscale estimation concepts, describe the travel time estimation problem, and present some typical results.…”

Agricultural Impacts on Groundwater: Processes, Modelling and Decision Support

“…The procedures commonly used range from ad hoc trial-and-error methods to sophisticated mathematical/statistical inverse algorithms. In a recent and exhaustive study comparing seven inverse approaches to estimate parameters for flow and solute transport models (Zimmerman et al, 1998), the authors concluded that "…the most important factor for achieving a successful solution was the time and experience devoted by the user of the method". This underlines an important point that applies not only to inverse methods, but more importantly to groundwater models themselves: Comprehensive physically-based numerical models are powerful tools, and are increasingly being equipped with user-friendly graphical interfaces and instant post-processing utilities (plots, maps, summary reports, etc), but their proper use for analysis and decision support will continue to require on the part of the user some knowledge of the underlying processes and their interactions, of the mathematical representation of these processes via equations and parameters, and of the particular features of the computer implementation -these are elements that can make the difference between a successful simulation and a meaningless one.…”

Data fusion modeling for groundwater systems

“…Numerous methods are able to work with a variety of data and model types in hydrology, meteorology, and oceanography such as those in Kitanidis and Vomvoris 1983, Hoeksema and Kitinidis 1984, Dagan 1985, Gelhar 1986 Neuman 1986a;b;c , Ghil 1989, Carrera and Glorioso 1991 , Yangxiao et al 1991, Bennett 1992, Sun and Yeh 1992, Courtier et al 1993 Daniel andWillsky 1997 andZimmerman et al 1998 . Many of the crucial issues in moving from theory to practice are well understood.…”