Optimality and self-organization in subsurface flow processes

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Flow patterns in the subsurface are governed by a strong heterogeneity at all scales. This heterogeneity affects both the properties of the subsurface as a water storage and the transport of solutes. Despite the undoubted importance of this multi-scale heterogeneity, integrating it in numerical models of subsurface flow is still a major challenge. First, little is known about the spatial structure of the heterogeneity and its relationship to the geological conditions, and second the required range would result in an unreasonable numerical effort.In the last decades, deriving statistical properties of flow patterns from principles of optimality (here, minimum energy dissipation) has turned to be a successful approach atleast for two systems -- river networks at Earth's surface and the cardiovascular system.Recently a theoretical framework for deriving spatial patterns of porosity and hydraulic conductivity for flow in porous media from the principle of minimum energy dissipation was published by the applicant. However, the related research is still on the level of a theoretical concept mainly consisting of relations between porosity, conductivity and flux densitiy (Darcy velocity).Validating this concept, developing it further for application to realistic scenarios, and transferring it to lumped parameter models are the main goals of the proposed project. Validation will cover the statistical distribution of catchment sizes in relation to spring-size distributions found in nature and individual spring discharge curves. Extensions of the original generic model will contain horizontal and sloping unconfined aquifers in Boussinesq approximation and genuine 3D patterns. Lumped parameter models will be derived from all versions of the distributed models in order to make them numerically treatable.