The loss of pesticides from land to waterways is a well-studied problem at the plot or paddock scale and also within waterways. However, no coherent theory exists to scale the data from the plot and paddock scales to that of catchment scale for water quality. Here we develop a theoretical basis for that scaling. This is a complex problem as pesticides will usually be applied to different paddocks at different times, and there can be numerous paddocks in a catchment. The mass of pesticide in the topsoil for a periodical applied pesticide was described at the paddock scale as a pulse input with first-order kinetic decay. At the catchment scale, a summation of pulse inputs during an application window is shown to converge to a convolution integral. From the convolution solution, the residual mass, mean mass and maximum mass of pesticide can be determined. Results show that (1) maximum mass is reduced at the catchment scale compared to the paddock scale, (2) the mean mass is the same for all application functions with the same total mass per period, and (3) the residual mass is dependent on the half-life of the pesticide and the periodicity of its application.As an example the convolution method was applied to two agricultural catchments draining into the Great Barrier Reef, Australia, to predict the concentrations and annual masses of pesticide lost compared with measured losses. In these examples, runoff was assumed to occur after a threshold of 50. mm of rainfall/irrigation was received, based on 100 year climate records for the catchments. A simple transfer of mass from the topsoil to runoff was used with the amount of mass transferred being a ratio of that in the topsoil. Even with the highly simplified description of paddock and catchment hydrology, the convolution method gave concentrations in the same order of magnitude as measured values. The method developed here using convolution integrals has applications in explaining the results of pesticide measurements made at paddock and catchment scale, and can be linked to more complex models of catchment hydrology. It may also be applicable to other solutes and upscaling processes that occur in catchments. © 2011.
Knight, J., Silburn, D., Kookana, R., & Thorburn, P. (2013). Upscaling from paddocks to catchments of pesticide mass and concentration in runoff. Agriculture, Ecosystems and Environment, 180(10), 136-147. https://doi.org/10.1016/j.agee.2011.08.009