Germán Galarza

A discussion on validation of hydrogeological models

Abstract Groundwater flow and solute transport are often driven by heterogeneities that elude easy identification. It is also difficult to select and describe the physico-chemical processes controlling solute behavior. As a result, definition of a conceptual model involves numerous assumptions both on the selection of processes and on the representation of their spatial variability. Even if a unique conceptual model could be identified, estimation of its parameters may be highly uncertain. Using a calibrated model for making groundwater predictions involves three types of uncertainties: those associated with the correctness of the conceptual model, which may arise during model construction or during prediction; those related to the accuracy of model parameters; and those corresponding to uncertainties in future stresses. In this context, validating a numerical model by comparing its predictions with actual measurements may not be sufficient for evaluting whether or not it provides a good representation of ‘reality’. Predictions will be close to measurements, regardless of model validity, if these are taken from experiments that stress well-calibrated model modes. On the other hand, predictions will be far from measurements when model parameters are very uncertain, even if the model is indeed a very good representation of the real system. Hence, we contend that ‘classical’ validation of hydrogeological models is not possible. Rather, models should be viewed as theories about the real system. This can be proven wrong, but they cannot be proven right. In this sense, we propose to follow a rigorous modeling approach in which different sources of uncertainty are explicitly recognized. The application of one such approach is illustrated by modeling a laboratory uranium tracer test performed on fresh granite, which was used as Test Case 1b in INTRAVAL.

Computational techniques for optimization of problems involving non-linear transient simulations

Many optimization problems in engineering require coupling a mathematical programming process to a numerical simulation. When the latter is non-linear, the resulting computer time may become unaffordably large because three sequential procedures are nested: the outer loop is associated to the optimization process, the middle one corresponds to the time marching scheme and the innermost loop is required for solving iteratively the non-linear system of equations at each time step. We propose four techniques for reducing CPU time. First, derive the initial values of state variables at each time (innermost loop) from those computed at the previous optimization iteration (outermost loop). Second, select time increment on the basis of those used for the previous optimization iteration. Third, define convergence criteria for the simulation problem on the basis of the optimization process, so that they are only as stringent as really needed. Finally, computations associated to the optimization are shown to be greatly reduced by adopting Newton–Raphson, or a variant, for solving the simulation problem. The effectiveness of these techniques is illustrated through application to three examples involving automatic calibration of non-linear groundwater flow problems. The total number of iterations is reduced by a factor ranging between 1·7 and 4·6. Copyright

Interpretation of Field Tests in Low Permeability Fractured Media. Recent Experiences

We have been treating fractured media as the result of embedding conductive 2D fractures in a 3D continuum medium. Automatic calibration has normally succeeded in producing models capable of predicting independent data sets. However, in recent times, we have faced a set of tests performed in very low conductive, highly heterogeneous granite where using exclusively the standard procedure has not produced good results. Difficulties include the following: (1) complex fracture geometry; (2) spurious effects caused by ill-shaped tetrahedra; (3) weak responses to pumping; (4) superposition of natural head data (controlled by boundary conditions) with drawdowns caused by pumping; (5) coupling these two flow conditions to produce the flow field needed for the tracer test is extremely sensitive to small errors. Finally, these difficulties are aggravated by the large computer times required by a fully 3D medium. Suggestions for overcoming these problems are outlined.