ASTERIX: Module for modelling the water flow on vegetated hillslopes

TL;DR

The paper introduces ASTERIX, an open-source C module that extends the Saint-Venant equations with spatially varying porosity to model vegetation-influenced water flow on vegetated hillslopes. It describes a first-order finite-volume scheme on a hexagonal grid and a data-porting workflow that enables lab-to-basin-scale simulations, including boundary-condition handling and visualization. The authors validate the approach through theoretical tests (radial symmetry, Thacker’s problem, vegetated Riemann problem), apply it to real terrain data (Şuşiţa Basin) and a slope-flow experiment, and perform a sensitivity analysis and inverse parameter estimation for friction coefficients. The work offers a practical, scalable tool for studying plant–soil–water interactions in catchments and provides a foundation for future extensions to infiltration and erosion processes. Overall, ASTERIX demonstrates accurate, efficient modeling of vegetated overland flow with accessible open-source software and GIS compatibility for environmental applications.

Abstract

The paper presents an open source software for numerical integration of an extended Saint-Venant model used as a mathematical tool to simulate the water flow from laboratory up to large-scale spatial domains applying physically-based principles of fluid mechanics. Many in-situ observations have shown that vegetation plays a key role in controlling the hydrological flux at catchment scale. In case of heavy rains, the infiltration and interception processes cease quickly, the remaining rainfall gives rise to the Hortonian overland flow and the flash flood is thus initiated. In this context, we also address the following problem: how do the gradient of soil surface and the vegetation influence the water dynamics in the Hortonian flow? The mathematical model and ASTERIX were kept as simple as possible in order to be accessible to a wide range of stakeholders interested in understanding the complex processes behind the water flow on hillslopes covered by plants.

Figures (18)

• Figure 1: Number of water-related and non-water-related disasters in OECD countries. Source: EM-DAT; The OFDA/CRED International Disaster Database, - Université catholique de Louvain (UCL) - CRED, Debarati Guha-Sapir - www.emdat.be, Brussels, Belgium.
• Figure 2: Watershed process
• Figure 3: Diagram (sketch) of the ASTERIX software
• Figure 4: The stationary solution of the water flow on two radial symmetric surfaces: crater type (first column) and hillock type (second column). Boundary conditions: $h=0.05$ m and $v=1$ m/s at the top of the surface and free drainage at the bottom.
• Figure 5: 2D Thacker's Problem: dynamics of the numerical free water surface. These snapshots are obtained using Gnuplot on the data calculated with ASTERIX at four different moments of time: $t=10,\, 30,\, 70,\, 330\, {\rm s}$. The error $err$ between the numerical and exact values of the free water surface at each of the four moments of time is calculated with $err=||((h+z)^{app}-(h+z)^{ex})/(h+z)^{ex}||_{\infty}$.

Theorems & Definitions (2)

• Remark 1
• Remark 2