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E. Crobeddu & S. Bennis (2007). Washoff model of total suspended particles in an urban context. Rev. Sci. Eau 20 (1) : 45-57. [article in French]

Original title: Modèle de lessivage des matières en suspension en milieu urbain.

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Urban runoff pollution due to suspended particles is of great concern for sewer system managers. Indeed, particles are the main source of urban water pollution because a large amount of chemical elements and organic wastes are associated with particles. Modelling runoff pollution due to particles is essential for the evaluation of its impact on receiving waters and for the adequate design of treatment structures.

This paper presents a new conceptual model called RQSM (Runoff Quality Simulation Model) used to simulate the washoff (erosion and transport of particles) of total suspended particles (TSS) at the outlet of urban catchments. Conceptual models can accurately represent complex physical phenomena with a limited number of parameters and a simple mathematical formulation. Moreover, they can be easily calibrated and used at many sites.

The build-up of solid particles in the RQSM model is infinite for pervious and impervious areas. The erosion process is related to the rainfall kinetic energy. Two relationships involving two erosion parameters are used, one for the impervious areas and the other for the pervious areas. The transport of suspended particles is described using the linear system theory. A rectangular impulse response function with a duration equal to the time of concentration describes the catchment response to an instantaneous erosion rate. Thereafter, a convolution product between the erosion rate and the rectangular impulse response function is used to compute loads of TSS at the catchment outlet.

The mathematical formulation of the RQSM model has three advantages. Firstly, it describes the washoff of TSS by using only rainfall intensity. Secondly, it treats the washoff of pervious and impervious areas separately. Finally, it uses only two parameters to describe the washoff.

The RQSM model was validated with the help of 285 TSS data points monitored during 22 rainfall events. Four rainfall events were monitored in the subcatchment (1) of Verdun borough in Canada and 18 rainfall events were monitored on three subcatchments in Champaign city (USA). The catchment areas varied between 6.8 and 177 ha, the catchment slopes between 0.4% and 1%, and the ratio of directly drained impervious area between 0.19 and 0.58. Land use was residential in two catchments and commercial for the other ones.

The first step in the RQSM model validation was to calibrate the two erosion parameters. This step was realized using 11 measured TSS pollutographs. The erosion parameter for impervious areas was calibrated first for low intensity rainfall. The erosion parameter for pervious areas was then calibrated for high intensity rainfall.

The second validation step was to simulate the TSS load resulting from 11 other rainfalls. The simulated loads of the RQSM model were compared to the measured loads. They were also compared to the simulated loads obtained with the rating curve model and with the SWMM exponential washoff model. Comparisons were made using three performance criteria: the Nash criterion, the ratio of the simulated TSS mass divided by the measured TSS mass (RM), and the peak charge ratio (RP). Reasonable agreement was reached between loads computed with the RQSM model and measured loads. The mean RM was 1.08 and the standard deviation was 35%. Moreover, the Nash criterion was greater than 0.6 for 50% of simulated events. Unfortunately, the number of events was insufficient to detect statistically significant differences in accuracy, between the RQSM model, the rating curve and the exponential model. Nevertheless, a qualitative study based on the value of the three performance criteria showed that the results given by the RQSM model are equivalent to the results given by the SWMM exponential wash off model.

Finally, a sensitivity analysis was conducted on the RQSM model. In order to achieve the sensitivity analysis, reference values were attributed to the parameters of the RQSM model. The values of the RQSM parameters were then changed individually and the resulting change in the Nash criterion was noted. The change in the Nash value indicates that for rainfalls of high intensity and short duration, the RQSM method is particularly sensitive to the time of concentration. In the other cases, the erosion parameter of impervious areas was the most sensitive parameter.


Urban catchment, total suspended particles, buildup, washoff, comparative study.

Corresponding author

S. Bennis, École de technologie supérieure, Département de génie de la construction, 1100, Notre-Dame Ouest, Montréal (Québec), Canada H3C 1K3.

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Update: 2007-05-23
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