Development of analytical probabilistic urban stormwater models

grantor: University of TorontoAnalytical probabilistic urban stormwater models are closed-form mathematical equations relating statistical urban drainage system performance measures directly to meteorological parameters, system properties and design variables. These equations are formulated using derived probability distribution theory with simplified representations of the hydrologic and hydraulic processes taking place on urban catchments. The purpose of this thesis is to improve the representation of the hydrologic and hydraulic processes by existing analytical probabilistic models and to extend their use to flood control analyses. In developing the new set of analytical probabilistic models, the rainfall-runoff transformation on an event basis is described by equations which incorporate the hydrologic processes commonly considered in numerical simulation models. The peak discharge rate of a runoff event is estimated from the runoff event volume, the duration of the causal rainfall event and the catchment time of concentration. The average catchment time of concentration is used for all runoff events and is treated as a physical characteristic of the urban catchment, independent of input rainfall characteristics. Incorporating the exponential probability density functions of rainfall event characteristics, closed-form analytical expressions are derived for the return periods of runoff event volume and peak discharge rate of urban catchments. Furthermore, the water quality control performance of urban stormwater detention ponds are analyzed. Analytical expressions are derived for estimating the flow capture efficiency and average detention time provided by a stormwater quality control detention pond servicing an urban catchment. Taking into account the variable inflow and outflow rates, the detention ponds considered are those where outflow is controlled by an orifice-type structure. The flow capture efficiency is determined with the estimation of the total spill volume. The total spill volume is calculated as the combination of the event spill volume and the carryover spill volume. Thus, the carryover effect of consecutive runoff events is quantified. The analytical probabilistic approach is further extended to flood control analyses with the derivation of the probability distribution of the peak outflow rate from a flood control detention facility servicing an urban catchment. The derived mathematical expressions are used to analytically determine the storage-discharge relationship required for a detention facility to achieve the desired level of flood control. Continuous simulation of various urban catchments and detention pond configurations are conducted using Toronto historical rainfall records. Close agreement is obtained between simulation model results and those from the analytical probabilistic models developed in this thesis. Thus, the analytical probabilistic models can be used as an alternative to, or together with, continuous simulation models for the planning and design of urban stormwater management facilities.Ph.D