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Publication Type: Proceedings Publication Acceptance Date: 5/2/2007 Publication Date: 7/1/2007 Citation: Pachepsky, Y.A. 2007. Scale-dependent complexity in soil and hydrologic systems and models. Proceedings of the Workshop on Scale Dependences In Soil and Hydrological Systems, July 3-6, 2007, El Barco de Avila, Spain. p.8. Interpretive Summary: Technical Abstract: Complexity of soil and hydrologic systems is easy to perceive but is very difficult to represent in mathematical terms. This causes the structural uncertainty of models which introduces uncontrollable uncertainty in forecast results. Various measures of system complexity have been proposed. The objective of this work is to review the complexity measures suitable for natural hydrologic systems and hydrologic models and compare their application in a case study. Because of interrelation between soil/landscape structure and soil/landscape hydrologic function., both complexity of structural arrangement and complexity of flow have to be considered in parallel. The soil-water system complexity arises from the complexity of arrangement of structural units and from the complexity of flow within and among the structural units. Introducing complexity measures is based on the premise that complexity is a property rather than a quality. Measuring complexity is closely related to the practical questions of the best modeling practices that are “What complexity do we have?” and “What complexity do we need?” We consider (a) complexity measures based on the relative differences between probabilities of the system states and (b) complexity measures based on relative differences between probabilities of transitions from one state to another, and (c) complexity measures directly based on scale change. We use the metric entropy and the mean information gain as information content measures, and the effective complexity and fluctuation complexity as complexity measures. Fractal dimensions are used as the complexity measures directly based on scale change. Having a complexity measure allows one address the effect of scale on complexity and to determine whether the complexity of hydrologic systems increases with the change in scale and whether the change in complexity of model parallels the change in complexity of soil hydrologic systems. We demonstrate the effect of the scale with runoff/ precipitation data from four USDA ARS research watersheds. The runoff hydrologic regimes are more complex than precipitation regimes. The scale effect on complexity depends on whether the scale change is reflected either in aggregation or in the change of parametric characterization. The complexity measures can be used as useful indicators to define best modeling practices in soil and landscape hydrology. |
