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Abstract. The frequency distributions of rainfall volume, rainfall duration, and interevent time are examined using the historical rainfall record of Toronto, Canada. Exponential probability density functions are found to fit well to the histograms of the rainfall event characteristics. The rainfall-runoff transformation on an event basis is described by an equation which incorporates the hydrologic processes commonly considered in numerical simulation models. On the basis of this equation and the exponential probability density functions of rainfall event characteristics, closed-form analytical expressions are derived for average annual runoff volume and runoff event volume return period. Deterministic continuous simulation of various urban catchments are conducted using the Toronto historical rainfall record as input. Close agreement between simulation model results and those from analytical expressions is obtained. The event-based probabilistic models for the determination of average annual runoff volumes and runoff event volumes with specified return periods from urban catchments are proposed as an alternative to continuous simulation models.

[1] Water quality samples for most streams are collected at variable frequencies within monitoring periods of different lengths. On the basis of discrete concentration data obtained from these monitoring studies, loads of various pollutants passing through a gaging station for selected periods may be calculated using various load estimation methods. In this paper, nitrate-N load estimates were compared with their ''true'' values, calculated using 6 years of daily nitrate-N concentration and average discharge data at an agricultural watershed in central Illinois. A Monte Carlo subsampling study was conducted to simulate different sampling scenarios for variable sampling frequencies and different monitoring durations. Load calculations were compared for each sampling scenario based on rating curve, ratio estimator, and flow-weighted average estimator. In addition, two bias correction techniques (minimum variance unbiased estimator (MVUE) and smearing estimator) were applied to the rating curve method. The monitoring durations were 1, 2, 3, and 6 years, and the sampling frequencies ranged from weekly to bimonthly. The results demonstrated that a desired accuracy of the estimates could be achieved either by sampling more frequently or by monitoring the site longer. Although the ratio and the flow-weighted average estimators had a small negative bias, in most cases rating curve estimators were positively biased when applied to the study site. Also, neither of the two bias correction techniques, MVUE and smearing estimator, decreased this positive bias. On the contrary, those techniques produced a higher bias, which resulted in increased root-mean-square error (RMSE). The rating curve uncorrected for bias, the simple ratio, and the flow-weighted estimator had a significantly smaller RMSE for all sampling frequencies and all periods of record than the bias-corrected rating curve methods.

Abstract. Flood control detention facilities have been traditionally designed using the design storm approach. Because of the deficiencies associated with the design storm approach, continuous simulation using long-term historical rainfall data has been recommended for the planning and design of these facilities in order to examine the performance of the system under a wide range of meteorological and hydrological conditions. An analytical probabilistic approach is presented as a computationally efficient alternative to continuous simulation. In this approach the probability distribution of the peak outflow rate from a detention facility servicing an urban catchment is derived from the probability distribution of the rainfall event characteristics that generate the runoff received by the detention facility. These derived mathematical expressions are used to determine analytically the storage-discharge relationship required for a detention facility to achieve the desired level of flood control. Comparison with long-term continuous simulation modeling demonstrates that the closed-form mathematical expressions of the analytical probabilistic approach provide reasonable approximation of the continuous simulation results. The analytical probabilistic approach overcomes some of the conceptual problems of the design storm approach and is therefore proposed for the planning and design of flood control detention facilities. IntroductionFlood control is usually the first and most important objective of urban storm water management. This is because flooding problems are widespread and are often accompanied by significant economic and environmental consequences. Next to protecting life and property, urban flood control also seeks to minimize the annoying and costly disruption caused by flooding in urban communities. Detention facilities are widely used for flood control purposes. They are designed to store temporarily storm water runoff at or near the point of origin, with a subsequent slow release to downstream channels or storm sewers, and therefore to minimize disruption and damage in downstream areas during both minor and major events. In addition to their primary surface water control function, detention facilities are often designed to provide, or be part of, sites for recreation purposes (e.g., incorporated into a park). Thus the storage areas of a detention facility are usually irregular in shape, and gravity-driven inflow to and outflow from the detention facility are usually most desirable.Some communities have storm water management regulations that specify that for a flood of specific return period the peak discharge rate after the development of a site shall not exceed the peak discharge rate from the site under existing conditions before the proposed development [Walesh, 1989]. Accordingly, some detention facilities are designed on the basis of a single return period criterion. That is, the design does not explicitly address performance under other more or less severe flood events. It is shown that for other t...

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