Modeling Techniques for Shallow Laminar Flow In Hydraulic Systems: An Experimental Series Analysis
Soil erosion; Vegetation cover; Hydraulic properties; Generalized Linear Models; Reynolds number; Froude number; Darcy-Weisbach coefficient
The combined cover of different vegetation types significantly changes hydraulic properties, thereby controlling soil erosion. Furthermore, Generalized Linear Models (GLMs) form one of the most popular classes of statistical models, and they can provide accurate predictions by establishing a link function to linearize the deterministic relationship between the predictor and response variables. In the present work, up to this moment, Gaussian and Gamma models have been applied to determine the relationship between Reynolds (𝑅𝑒) and Froude (𝐹𝑟) numbers in the Darcy-Weisbach coefficient (𝑓), often used to determine hydraulic resistance to inter-rill erosion, under different vegetation-covered conditions. In the univariate approach, the Froude number demonstrated superiority in explaining the hydraulic resistance behavior in shallow overland flows. However, to increase the prediction model accuracy, other variables were incorporated, such as water flow depth (ℎ), water discharge (𝑞), and soil loss (𝑆𝐿). Diagnostic analyses were performed to assess the goodness-of-fit of the Gamma model with a logarithmic link function to the overland flow database. The results demonstrated that the predictor variables were significant, and the Gamma modeling with a logarithmic link function was satisfactory for accurately predicting the Darcy-Weisbach resistance coefficient (𝑓) under different types of vegetation cover and bare soil. The next steps will involve comparing the performance of classical modeling with more refined statistical techniques.