Transport rate-based model for overland flow and solute transport: Parameter estimation and process simulation

Abstract

A one-dimensional mathematical model, termed a transport rate-based model, is developed for solute transport over infiltrating soil slopes under constant rainfall and declining sources. The model is comprised of (1) the kinematic-wave equation for overland flow, (2) a transport rate-based advection equation for overland solute transport, (3) a moment-based method for estimation of the parameters involved in the flow and solute transport equations, and (4) a semi-Lagrangian algorithm for numerical solution of the solute transport equation. Data from a single soil flume experiment under constant rainfall established the proof-of-concept for this new model. Sodium chloride was applied to the soil surface to simulate the presence of a declining diffuse pollutant. The parameters involved in the flow equation were found to take on the values that correspond to turbulent flow. With these turbulent flow parameters the simulated hydrograph displayed an initial rising limb, followed by a constant flow discharge. The profile of solute concentration exhibits a steep receding limb transitioning into an elongated tail. The solute transport rate follows a non-Gaussian distribution that does not appear to have been derived before. These theoretical hydrographs and pollutographs are in good agreement with those measured in laboratory, demonstrating the laboratory proofof-concept for the transport rate-based model on soil and pavement blocks. q

Modeling pollutant transport in overland flow over non-planar and non-homogenous infiltrating surfaces

“…Based on few observations, this study assumes that the solute in this surface active layer are uniformly distributed and the exchange rate of the solute between the active layer and overland flow are proportional to the difference between the concentrations in soil and water volume (Deng et al, 2005b). Generally, pollutant transport in overland flow can be described by the advection-dispersion equation (ADE) (Govindaraju, 1996).…”

“…(4) approaches zero. Decline of the solute transfer rate in the active surface layer caused by the transfer of solutes from soil to the overlying runoff can be assumed to follow an exponential law with a time constant μ as C s =C 0 exp(−μt) (Deng et al, 2005b). The initial condition of Eq.…”

“…To simulate the experiment, the developed model employed a mesh size of 22×22. The parameters used in the simulation, which were calibrated by Deng et al (2005b), are listed in Table 2. Fig.…”

“…Solute transfer from soil to overland flow and subsequent transport in surface flow were extensively studied both experimentally and numerically (Snyder and Woolhiser, 1985;Wallach et al, 1988;1989;2001;Payten and Sanders, 1990;Wallach and Van Genuchten, 1990;Wallach and Shabtai, 1993;Govindaraju, 1996;Garcia-Navarro and Playan, 2000;Yan and Kahawita, 2000;Walton et al, 2000;Abbasi et al, 2003;Deng et al, 2005a;2005b;He et al, 2009;Ouyang et al, 2012). Most of the previous studies carried out were generally 1D physical experiments in laboratories and 1D solute transport mathematical modeling (Govindaraju, 1996;Garcia-Navarro and Playan, 2000;Yan and Kahawita, 2000;Walton et al, Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering) ISSN 1673-565X (Print); ISSN 1862-1775 (Online) www.zju.edu.cn/jzus; www.springerlink.com E-mail: jzus@zju.edu.cn 2000; Wallach et al, 2001;Abbasi et al, 2003).…”

Hydraulic Characterization of Porous Materials Using a Rainfall Simulator to Model Flows in Natural and Artificial Non-Saturated Materials

“…Examples are hydrological and hydraulic calculations (e.g. Singh et al 2002), analysis of the transfer of soil solutes (Vogel et al 2006;Deng et al 2005), measurement of the impermeabity of ground covers, and optimisation of agricultural irrigation (Wöhling et al 2007). …”