On the computation of the Basal Envelope Surface of Talwegs using the Analytic Element Method

Abstract

The stream network is a major feature of a landscape, conveying water, sediment, and solute from hillslopes to the ocean. Noticeably, from a large-scale point of view, the elevation of the talwegs of perennial streams is an important head boundary condition for both surface and groundwater flow originating from hillslopes. Assuming a wireframe (1D) representation of talweg lines, the problem of interpolating elevation between talwegs has received attention for applications such as flood mapping using Height Above Nearest Drainage (HAND, [Nobre et al., 2011]), or groundwater level interpolation in low-conductivity aquifer systems. In this study we propose an alternate definition of this large-scale base level concept introduced by [Wyns et al., 2004], namely the Basal Envelope Surface of Talwegs (BEST) and the associated Height Above the Basal Envelope Surface of Talwegs (HABEST), along with a procedure to compute it using the Analytic Element Method (AEM). It can be defined as the head distribution satisfying Laplace equation (Darcy flow with vanishing divergence), with stream segments set as Dirichlet boundary conditions. The BEST is thus the real part of a complex analytic (holomorphic) function which can be modeled using analytic slit elements, with very low computational requirements and without the need for kriging, as it is often seen in the literature. This analytic model is extended to the case of a non-zero, uniform divergence flow (head distribution satisfying a Poisson equation) which can be useful to analyse groundwater levels at catchment scale.

Keywords

• Analytic Element Method
• Envelope Surface
• Talwegs
• Geomorphology
• Groundwater
• Hillslope
• Diffusive processes