ESTIMATING UNCERTAIN FLOW AND TRANSPORT PARAMETERS USING A SEQUENTIAL UNCERTAINTY FITTING PROCEDURE

Authors: ABBASPOUR, K - SWISS EAWAG, SWITZERLAND; JOHNSON, C - SWISS EAWAG, SWITZERLAND; Van Genuchten, Martinus

Submitted to: Vadose Zone Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/10/2004
Publication Date: 11/30/2004
Citation: Abbaspour, K.C., Johnson, C.A., Van Genuchten, M.T. 2004. Estimating uncertain flow and transport parameters using a sequential uncertainty fitting procedure. Vadose Zone Journal. 3:1340-1352.

Interpretive Summary: Soil and water pollution by industrial and agricultural contaminants is an ever increasing problem worldwide. Billions of dollars are being spend each year in efforts to limit future (or remediate past) contamination of the subsurface. Computer models can be very helpful in understanding and forecasting the future extent of site-specific pollution problems. Unfortunately, running such models requires many soil and chemical parameters that are inherently uncertain and difficult to measure because of the overwhelming heterogeneity of the subsurface, and such other factors as instrumental limitations. Inverse modeling has recently become very popular in the earth and environmental sciences to estimate parameters that are difficult or impossible to measure directly. One complicating factor is that parameters resulting from inverse analyses are generally very uncertain (poorly defined) because of uncertainty in the measured data and simplifications in the adopted hydrologic model. One task of this study was to quantify this uncertainty by determining the smallest range of the unknown parameters needed in the adopted flow/transport model. A state-of-the-art program, SUFI-2 (Sequential Uncertainty Fitting, Version 2) was developed for this purpose and applied to two municipal solid waste incinerator bottom ash landfills (monofills) in Switzerland: the Lostorf monofill situated in an unused gravel pit, and the Seckenberg monofill established on sandstone and dolomite formations on a hillside. Bottom ash contains high levels of toxic trace elements and other salts. The study was conducted from 2001 to 2003. Calibration of the two monofills was very successful as reflected by high correlation between measured and predicted flow and transport data of the monofills using both calibration and independent test data sets. The same methodology can be easily applied to other hydrologic problems. The great advantage of SUFI-2 is that it combines optimization and uncertainty analysis, and is easy to link to any hydrologic model. Despite the apparent advantages of inverse models, the detailed uncertainty analysis indicated the possible existence of other more acceptable solutions (given by alternative combinations of the 34 parameters needed to describe the monofill pollution problems). This apparent weakness is closely related to the main purpose of inverse modeling, i.e., to use more easily measured information to obtain parameters that are difficult or very costly to measure directly. In other words, the inverse optimization procedure is used to convert data of relatively low value to obtain data of higher value. Unfortunately, the notion to get more for less is inherently problematic since nature does not readily permit such easy transformations. For this reason one must accept the fact that the SUFI-2 procedure, or similar inverse methods, can only produce a certain range of solutions, rather than a specific single unique solution. Inverse methods hence will lead to many solutions. One way to limit multiple (non-unique) solutions is to constrain the solution as much as possible by using a combination of multi-criteria, multi-objective, and multi-compartment formulations. The inverse algorithm described in this paper should be of considerable interest to both theoretical and applied scientists and engineers concerned with the movement of water and a range of contaminants in soils and groundwater. The research showed that application of the SUFI-2 program should lead to more cost-effective and accurate predictions of subsurface contamination from both point and non-point pollution sources.

Technical Abstract: Inversely obtained hydrologic parameters are always uncertain (non-unique) because of errors associated with the measurements and the invoked conceptual model, among other factors. Quantification of this uncertainty in multidimensional parameter space is often difficult because of complexities in the structure of the objective function. In this study we describe parameter uncertainties using uniform distributions and fit these distributions iteratively within larger absolute intervals such that two criteria are met: (i) bracketing most of the measured data (>90%) within the 95% prediction uncertainty (95PPU) and (ii) obtaining a small ratio (<1) of the average difference between the upper and lower 95PPU and the standard deviation of the measured data. We define a model as calibrated if, upon reaching these two criteria, a significant R2 exists between the observed and simulated results. A program, SUFI-2, was developed and tested for the calibration of two bottom ash landfills. SUFI-2 performs a combined optimization and uncertainty analysis using a global search procedure and can deal with a large number of parameters through Latin hypercube sampling. We explain the above concepts using an example in which two municipal solid waste incinerator bottom ash monofills were successfully calibrated and tested for flow, and one monofill also for transport. Because of high levels of heavy metals in the leachate, monitoring and modeling of such landfills is critical from environmental points of view.