A statistical model has been developed to study the long-term behaviour of a stormwater detention unit. This unit stores a portion of the incoming runoff, corresponding to the empty space available in the unit, from which runoff is pumped to a treatment plant. The objective is to avoid, as much as possible, the discharge of untreated runoff to receiving bodies of water.

The model was developed by considering the arrival of independent runoff events at the urban catchment. The process variables of event depth, duration, and interevent time were treated as independent, identically distributed random variables. A storage equation was formulated from which the probability of detention unit overflow was obtained. With this distribution it was possible to define the trap efficiency of the unit in terms of the long-term fraction of the runoff volume trapped by the storage unit.

The trap efficiency expressions define storage/ treatment isoquants, which represent the combinations of storage capacity, treatment rate, and the sewer system runoff trapping capacity, which provide a fixed level of runoff control.

A pollutant load model was also formulated, based on a first-order washoff model. This model was used to define pollutant control isoquants.

Optimal values of the required storage capacity and treatment rate were obtained by treating the isoquants as production functions. Applying the results of production function theory, a cost minimization problem was solved for the value of the storage capacity and treatment rate, for prescribed runoff and pollutant trap efficiency levels.

The results obtained with the statistical model compared well with results obtained from major simulation models.

The statistical approach offers an advantage in that no simulation is required to obtain the isoquants, as the expressions are analytical, thus greatly simplifying the optimization process. Also, the evaluation of the storage unit pollutant trap efficiency can be easily evaluated for any type of pollutant whose washoff rate is known.