The return periods of detrimental effects are often used as design criteria in urban storm water management. Considerable uncertainty is associated with the models used. This is either ignored or pooled with the inherent event to event variation such as rainfall depth. It is here argued that uncertainty and inherent event to event variation should be treated separately, in providing engineers and managers with the distributions of return periods. It is then possible to base management decisions on knowledge of both the expected return periods and their corresponding confidence limits. It is further argued that the traditional pooling of inherent variation and uncertainty leads to meaningless return period curves with little engineering value.
All quantities which are described by a probability distribution are placed in either of the two layers: an inner layer consisting of quantities varying from event to event and an outer layer consisting of uncertain but constant quantities. For each set of random realisation of the values in the outer uncertainty layer a full set of Monte Carlo simulations for the inner inherent variations layer is performed resulting in a return period curve. The many samplings in the outer layer results in a band of return period curves representing the distribution of return periods for which confidence limits may be calculated. The general methodology is here described as Embedded Error Propagation and its current implementation as Embedded Monte Carlo Simulations.
The approach is demonstrated in an integrated setting involving models for rainfall characteristics, combined sewer overflow (CSO) loads and impacts on the surface water dissolved oxygen (DO). CSO loads are modelled using event lumped non-linear regression models with rainfall as input and with overflow volume, duration and relevant event mean concentrations as output. Oxygen depletion in the surface water is described using a dynamic model including oxidation of dissolved chemical oxygen demand (COD) and nitrification. Conversion models had to be developed to integrate the output variables of the CSO model with the input variables of the surface water model. The parameters of all the models were estimated from observed data on rainfall, CSO load and surface water impacts. The background conditions of the surface water were modified creating a hypothetical, but more general and relevant case to present the methodology. Focus is in this paper on chemical effects of CSO on a surface water. The proposed distinction between event to event variation and uncertainty and the associated methodology are equally valid to the return period analysis of flooding.