Evaluating lateral flow in an experimental channel using the diffusive wave inverse problem. (May 2019)

• Record Type: Journal Article
• Authors: Moussa, Roger; Majdalani, Samer
• Is Part Of: Advances in water resources. Volume 127(2019)
• Page Start: 120
• Page End: 133
• Publication Date: 2019-05
• Subjects: Diffusive wave equation DWE -- Inverse problem -- Hayami equation -- Uniformly distributed lateral flow -- Experimental channel; Hydrology -- Periodicals; Hydrodynamics -- Periodicals; Hydraulic engineering -- Periodicals; 551.48
• DOI: 10.1016/j.advwatres.2019.03.009
• Languages: English
• ISSNs: 0309-1708

Abstract

Highlights: New experimental design representing inflow and lateral flow hydrographs (gains and losses) uniformly distributed along a channel. Evaluation of the lateral flow using the inverse problem of the Hayami diffusive wave equation (DWE). Validation of the solution of the inverse problem using a large variety of experimental hydrograph scenarios. Domain and limit of the DWE inverse problem. Abstract: Lateral flow L ( t ) is a major process during flood events, which can be either gains (positive) or losses (negative) to the channel. The inverse problem consists of evaluating L ( t ) knowing the inflow I ( t ) and the outflow O ( t ) on a channel. However L ( t ) is very difficult to measure on real channels, and we are always not sure to which extent the evaluated L ( t ) is close to the real one. This paper aims at evaluating L ( t ) in a channel using the analytical solution of the inverse problem of the Hayami diffusive wave equation (DWE) with L ( t ) uniformly distributed along the channel. We conceived and built a novel experimental channel where I ( t ), O ( t ) and L ( t ) are highly controlled at 1 s time step and we realize 62 experimental hydrograph scenarios corresponding to different shapes of I ( t ) and L ( t ) . We validate the hypotheses of both the DWE Hayami model and the corresponding inverse model (with very high criteria functions values for a large majority of scenarios) which reflects the ability of the DWE inverse model to reproduce complex lateral flow hydrograph dynamics. We discuss the limits of application of the DWE especially for short wave lengths. The coupled experimental-modelling approach proposed herein opens promising perspectives regarding the evaluation of lateral flow on real channels.