Modeling Techniques for Shallow Laminar Flow In Hydraulic Systems: An Experimental Series Analysis
Soil erosion; Vegetation cover; Hydraulic properties; GLM; GAMLSS; Reynolds number; Froude number; Darcy-Weisbach coefficient.
The combination of different types of vegetation cover significantly changes hydraulic properties, thereby controlling soil erosion. Generalized Linear Models (GLMs) form one of the most popular classes of statistical models and can provide accurate predictions by establishing a link function to linearize the deterministic relationship between the predictor and response variables. Furthermore, Generalized Additive Models for Location, Scale, and Shape (GAMLSS) are more refined distributional regression models that allow flexible regression and smoothing adjustments to data. In the present study, GLM modeling was performed using Gaussian and Gamma distributions, while GAMLSS modeling was conducted with Skew Exponential Power (SEP), Sinh-Arcsinh (SHASH), Johnson's Su (JSU), and Skew t (ST) distributions to determine the relationship between the Reynolds number (Re) and the Froude number (Fr) in the Darcy-Weisbach coefficient (f), which is frequently used to estimate hydraulic resistance to inter-rill erosion under different vegetation cover conditions. For GLM, in the univariate approach, the Froude number demonstrated superiority in explaining hydraulic resistance behavior in shallow surface flows. However, to improve the prediction model's accuracy, other variables were incorporated, such as water flow depth (h), unit discharge (q), and soil loss (SL). Diagnostic analyses were performed to evaluate the goodness-of-fit of the Gamma model with a logarithmic link function to the surface runoff database. In the GAMLSS analysis, the Froude number also demonstrated superiority in predicting hydraulic resistance, along with variables such as sediment concentration (C_s), rainfall intensity (I), infiltration rate (Inf.rate), runoff coefficient (C), mean flow velocity (V_m), h, inter-rill detachment rate (D_i), PS, and vegetation drag coefficient (CD), with an emphasis on the SEP type 4 distribution. The results demonstrated that the predictor variables were significant, and the Gamma modeling with a logarithmic link function (for GLM modeling) and SEP4 (for GAMLSS modeling) were satisfactory in accurately predicting the Darcy-Weisbach resistance coefficient (f) under different types of vegetation cover and bare soil conditions.