338, 1803–1811. Analysis of multi-step experiment

analyze data from non-standard, specially designed experi- ments. These experiments can be optimized to produce data that contain significantly more information about the system to be modeled. We have shown that the radial flow experi- ment provides sensitive data for the simultaneous determi- nation of absolute permeability and the parameters of the relative permeability and capillary pressure functions. Installation of the tensiometer near the outer wall of the flow cell is a slightly sub-optimal, but robust configuration. ColIecting transient flow data from a multi-step experiment provides the information needed to constrain the effective permeability governing unsaturated flow. In many cases, applying conventional curve fitting pro- cedures to capillary pressure data collected under equi- librium conditions does not allow one to distinguish between alternative conceptual models such as the Brooks–Corey–Burdine or van Genuchten–Mualem model. As a consequence, predictions made with the result- ing parameter set may be erroneous if the wrong model is chosen, and if absolute permeability and unsaturated hydraulic properties are determined independently. It is therefore important to numerically simulate a transient experiment, capturing the relevant processes governing unsaturated flow, as opposed to inferring effective permeability from geometric pore size distribution models. We have used three criteria to evaluate inversions that use different conceptual models and have different numbers of adjustable parameters. We have demonstrated that the good- ness-of-fit criterion is insufficient and misleading. It has to be complemented by an aggregate measure for estimation uncertainty, and a penalty term to guard against over- parameterization. We have pointed out in this paper that the estimated parameters are not intrinsic properties of the porous med- ium; they are related to the functional model being used as illustrated by the dependence of the absolute permeability estimate on the hydraulic model. If an independent measure- ment of absolute permeability or any value of effective permeability were made, the inverse solution can be further constrained, making it possible to select the model that is more likely to be true. On the other hand, if no such mea- surement is available, the parameter value concurrently esti- mated by inverse modeling partly compensates for the error in the model, making the subsequent predictions more accurate. The proposed experimental design and analysis proce- dure will be used in the future to investigate additional effects caused by temperature changes, entrapped air, ani- sotropy, and hysteresis. 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