Horus, a conceptual model for pollution simulation in sewer networks - structure and validation
Urban wet weather pollution represents at the present time one of the major causes of pollution of receiving waters. During a storm event, generation of pollution and erosion of the impervious area or the sewer itself are very complex processes, which respond to a large number of relevant factors. In this context, modelling is one way to study, characterize, understand and eventually anticipate this pollution. HORUS is an event-based conceptual research model. The objective of the HORUS model is, taking into account the characteristics of the catchment and the structure of the sewerage system, to reproduce the hydrographs and TSS, COD and BOD concentrations generated by any rainfall event. The desire to develop a model with a reduced number of parameters oriented our choice towards conceptual formulations, calibrated and validated on the maximum number of real sites. HORUS simulates the principal phenomena involved in the generation and transfer of pollution in urban drainage systems, with a homogeneous level of complexity for all steps in the calculations. The algorithms have been chosen for their robustness, their simple mathematical formulation, their reduced number and their suitability for calibration and validation. HORUS consists of five main connected modules: - a hydrological module consisting of a linear reservoir including runoff losses - a hydraulic module based on the solution of the Muskingum equations (including particularities such as weirs, basins, sluice gates, ...) - a module for producing and transporting solids in the catchment, which covers several phenomena. The build-up model of catchment deposits is one initially proposed by the SWMM. The washoff by rainfall is modelled by a modification of the SWMM formulation, adapted for a large range of rainfall events. The propagation of particles by runoff is modelled using a linear reservoir with a lag-time different from the runoff initially proposed by Brombach. COD and BOD are calculated through a potency factor governing the relations between these pollutants and TSS. This module includes an algorithm for gully pots; this algorithm has been programmed but is not yet activated. - a module for producing and transporting solids in the sewer system. Sediment transport in the sewer is modelled by the Velikanov theory, with the calculation of sedimentation and erosion of solids during dry or rainy weather. Pollutographs are propagated by convection. COD is calculated through a potency factor governing the relations between this pollutant and TSS. This module includes algorithms for bed load and wash load calculations; these algorithms have been programmed but are not presently active. - a module for numerical optimization using the Powell method and evaluation of hydraulic and pollution results for calibration and continuous simulations. We have used ten different sites (combined, mixed or separate systems, with or without deposits in collectors), where there were reliable quantitative and qualitative measurements during main rainfall events, for the phases of calibration, validation or transposition. The urban catchments present different characteristics: imperviousness coefficients between 22 and 78%; mean catchment slopes between 0.3 and 6.5%; collector slopes between 0 and 27.4 mm/m. The rainfall events used for model development cover a wide range: antecedent dry weather periods (ADP) between 2 hours and 21 days; rainfall heights up to 40 mm; rainfall peaks over five minutes (Imax5) between 2.2 and 60 mm/h; and rainfall durations between 20 minutes and 12 hours. During the calibration stage, the different parameters were adjusted through numerical optimization using the Powell method. This method allowed the choice of one group of parameters for all the catchments and rainfalls used in this stage. The validation phase was carried out in two stages. The first stage was completed with 47 other rainfall events (with different dry weather periods, rainfall heights, rainfall peaks,...) on the same sites that were used for the calibration. The second stage was carried out on three other sites (Aix-Zup, Budron and Mantes la Ville). In these two stages, the simulations were made without changes to the calibrated parameters. The single adjusted parameter was the initial mass of particles present in the catchment and in the sewer after the preceding rain. The qualitative validation showed satisfactory results for TSS, COD and BOD pollutographs expressed in concentrations, with respect to the shape of the pollutographs, their maximum, and the mass transported in the system. The quantitative validation step revealed that the most significant errors are for the TSS concentrations lower than 50 mg/l for the separate catchment and 100 mg/l for the mixed and combined sewers. Thus, for measurements higher than 50 mg/l for the separate catchment, the mean relatives errors and standard deviation are of 0.15% and 40% and for measurements higher than 100 mg/l for the mixed and combined sewer, the mean relative errors and standard deviation are of 13% and 60%. Moreover, for 75% of the simulated rainfalls the calculation of the transited mass of TSS ranged between -20 and +20%.