Pesticide runoff from farms: upscaling from pesticide application in fields to concentrations in streams and rivers

The Great Barrier Reef off the coast of north eastern Australia is a natural wonder of the world, and recently there have been concerns about possible harm to the reef from pesticides flowing into the sea from streams and rivers. We present a theoretical basis for scaling data for pesticide application to the topsoil on a large number of farm fields up to watershed scale water quality. At the field scale the pesticide application is assumed to be a pulse input, with a distribution of application times over the season. For a large number of farms, the total mass in the topsoil at any time is represented by a convolution integral taking into account the distribution of inputs and applying first order decay. This enables the calculation of average mass, residual mass at the end of the season, and maximum mass of pesticide in the watershed. Runoff is assumed to occur after a threshold of 50 mm of rainfall or irrigation, and a simple transfer process of pesticide from topsoil to runoff is used. The convolution method together with 100 year climate records was used to model concentrations and annual pesticide losses from two agricultural watersheds draining to the Great Barrier Reef. Even with this highly simplified description of field and watershed hydrology, the convolution method gave predictions of the same order as measured pesticide values. The convolution method for predicting the amount of pesticide mass in the topsoil in a catchment can also be coupled to more sophisticated models of water runoff and mass transfer.