Mustafa El-Rawy

Hydrology and ecology: how Natura 2000 and Military use can match

The military domain of Houthalen is a shooting area and also a protected Natura 2000 site, with an alternation of dunes, fens and heathlands. Already years ago, it was determined that the groundwater table is lowered by digging deep canals. Intensive consultation and study work (ecohydrological modeling) has shown that recovery is possible, taking into account the military use. Specific attention was paid to the accessibility through the fire roads and the water level in the fens. Recovery is started up, as well as a monitoring programme.

Zone-Integrated Double-Constraint Methodology for Calibration of Hydraulic Conductivities in Grid Cell Clusters of Groundwater Flow Models

Abstract This paper deals with the double-constraint methodology for calibration of steady-state groundwater flow models. The methodology is based on updating the hydraulic conductivity of the model domain by comparing the results of two forward groundwater flow models: a model in which known fluxes are specified as boundary conditions and a model in which known heads are specified as boundary conditions. A new zone-integrated double-constraint approach is presented by partitioning the model domain in zones with presumed constant hydraulic conductivity (soft data), and the double-constraint methodology is reformulated accordingly. The feasibility of the method is illustrated by a practical case study involving a numerical steady-state groundwater flow model with about 3 million grid blocks, subdivided into four zones corresponding to the major hydrogeological formations. The results of the zone-integrated double-constraint method for estimating the horizontal and vertical hydraulic conductivities of the zones compare favourably with a classical model calibration based on minimisation of the differences between calculated and measured heads, while the double-constraint method proves to be more robust and computationally less cumbersome.

Introduction: Setting the Scene

This chapter introduces the subject matter: parameter estimation for groundwater flow models by the double constraint methodology (DCM). After a brief introduction of forward and inverse modeling, the difference between imaging and calibration is mentioned. Some relevant literature is reviewed, and the contents of the chapters of this book are presented.

Foundations of Forward and Inverse Groundwater Flow Models

This chapter deals with the basic equation governing groundwater flow. In Sect. 2.1, the equations are presented in their full four-dimensional form (three spatial dimensions + time) with emphasis on the parameters. Section 2.2 introduces Calderon’s approach to determination of the spatially heterogeneous hydraulic conductivity field. To avoid negative hydraulic conductivities in the double constraint methodology (DCM), this approach is based on the square root of the hydraulic conductivity (sqrt-conductivity α). Section 2.3 introduces Stefanescu’s α-center method for parameter estimation, while Sect. 2.4 analyzes Calderon’s approach in more depth using inspiration from Stefanesco’s method. Although this chapter sets the scene for the real subject matter of this book—the double constraint methodology (DCM)—its reading may be skipped by readers who want to go directly to the DCM treated in Chap. 3.

The Pointwise Double Constraint Methodology

This chapter deals with the basic elements of the double constraint methodology (DCM). Since the DCM is an imaging method, while most parameter estimation methods are calibration methods, the difference is introduced in Sect. 3.1 and worked out in much greater depths in Sect. 3.9. Section 3.2 introduces the DCM in its most simple, intuitive form. To avoid presentation of three times the same equation for the three conductivity components in anisotropic media, we introduce the “voxel notation” in Sect. 3.3. Sections 3.4 and 3.5 present the theoretical justifications for the “intuitive DCM” presented in Sect. 3.2, while Sect. 3.6 discusses convergence and termination of the iterations. Section 3.7 presents some different approaches to handling anisotropy. Since the DCM is based on two models—the flux model and the head model—the rules for posing the correct boundary conditions for the two models are dealt with in Sect. 3.8.

The Zone-Integrated Double Constraint Method

This chapter deals with an extension of the double constraint methodology to handle clusters of grid volumes, or zones. In each zone, the conductivities in the grid volume are correlated. The equations presented in this chapter exemplify this “zone interaction” for clusters with the same grid block conductivities. The results of a case study with a limited number of zones are summarized.

Case Study Kleine Nete: Observation Error and Uncertainty

This chapter deals with a realistic case study in which a time series of conductivity observations by the double constraint methodology (DCM) is combined with the Kalman filter to determine the observation uncertainty from the spread of the observation noise.