Mass balance

The mass balance equation is often used to calculate river quality downstream of a discharge using mean and percentiles of river and discharge flow and quality data. This approach cannot produce means and percentiles of downstream river quality nor the discharge quality required to achieve set mean or percentiles of downstream river quality. An analytical approach is described which enables such calculations to be done. The method is compared with simple mass balance, and with a computer based method, Monte Carlo simulation. Some numerical examples are presented which show the magnitude of the errors which can result from using the incorrect equations.