AN ANALYTICAL SOLUTION FOR THE LATERAL TRANSPORT OF DISSOLVED CHEMICALS IN OVERLAND FLOW-VARYING SOIL SURFACE CONCENTRATION

The role of overland flow dynamics on the lateral transport of soil-di ssolved chemicals toward an outlet is studied herein using the solutio ns of the mass conservation equations for overland flow and transport. The transfer of soil chemicals to the overland flow is a rate-limited process proportional to the chemical concentration at the soil surfac e which is time dependent. Some simplifying conditions are considered, to develop an analytical solution for both equations. The rainfall ra te f, the infiltration rate i, and the mass transfer coefficient k are assumed constant. The analytical solution is based on the characteris tic method for the two main stages of overland flow, namely, the risin g and falling stages. The first stage occurs from pending time to the time when rainfall ceases, at which point the second stage begins. Dur ing the second stage, the slope drains and overland flow depth gradual ly becomes zero. Although the initial water depth for the kinematic wa ve equation, h(0), could be chosen arbitrarily, its combination with t he solute equation requires that h(0) should be greater than zero, sin ce a singularity is obtained for h(0) = 0. Therefore, the solution for overland flow is developed for a general constant initial water depth , but in order to meet real initial conditions, h(0) is chosen to be v ery small, almost negligible. Use of the characteristic method imposes different solutions for each sub-zone that composes the domain. In on e sub-zone that belongs to the falling stage, the characteristic curve is solved by Euler's method. During the rising stage of overland flow the concentration hydrograph decreases rapidly followed by a moderate decrease thereafter. During the falling stage of overland flow, the c oncentration hydrograph increases gradually. Since here the soil surfa ce concentration is a function of time, the relative influence of the different rate-limited processes determining the shape of the concentr ation distribution at the slope outlet can be identified and analyzed. At time of pending and during the final period of overland flow reces sion, the assumption of constant k is not valid and, although mathemat ically correct, physically erroneous results are obtained. As an examp le, the analytical solution for c(s)(t), as obtained by Wallach and va n Genuchten (1990), is introduced into the solution and the overland f low concentration distributions at the slope outlet were compared and successfully agreed with measured data. (C) 1997 Elsevier Science B.V.