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Nonlinear Aspects of Hillslope Subsurface Flow: A Study Based on the Kardar-Parisi-Zhang Equation (KPZ)

Author(s): Nuele Cordano

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Keywords: Infiltration; Subsurface flow; Richards’ Equation

Abstract: Severe rainfall events cause rapid variation of pressure head which propagates downward in soils. These” waves” can affect slope stabity and subsurface hydrogical response and are often controlled by the nonlinear aspects of Richards’ Equation (RE). In order to capture the main features of this phenomenology, in a less computationally expensive model, a simplification of Richards’ Equation (RE) which gives the Kardar-Parisi-Zhang equation (KPZ) is proposed. A semi-analytical solution of KPZ in term of convolution integrals, which can be implemented with efficient numerical methods and which strongly reduce the computational time required, is proposed. To discuss and validate the KPZ properties, a case study based on storm data of a small watershed close to Genoa, Italy, has been analyzed and the results of simulation with KPZ compared with the numerical solutions of RE. The KPZ proves to be able to capture the timing of the highest pressure peaks, and the comparison between KPZ and RE provided indications and suggestions about further feasible development of the presented approach.


Year: 2007

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