The use of deconvolution techniques to identify the fundamental mixing characteristics of urban drainage structures

Mixing and dispersion processes affect the timing and concentration of contaminants transported within urban drainage systems. Hence, methods of characterising the mixing effects of specific hydraulic structures are of interest to drainage network modellers. Previous research, focusing on surcharged manholes, utilised the first-order Advection-Dispersion Equation (ADE) and Aggregated Dead Zone (ADZ) models to characterise dispersion. However, although systematic variations in travel time as a function of discharge and surcharge depth have been identified, the first order ADE and ADZ models do not provide particularly good fits to observed manhole data, which means that the derived parameter values are not independent of the upstream temporal concentration profile. An alternative, more robust, approach utilises the system's Cumulative Residence Time Distribution (CRTD), and the solute transport characteristics of a surcharged manhole have been shown to be characterised by just two dimensionless CRTDs, one for pre- and the other for post-threshold surcharge depths. Although CRTDs corresponding to instantaneous upstream injections can easily be generated using Computational Fluid Dynamics (CFD) models, the identification of CRTD characteristics from non-instantaneous and noisy laboratory data sets has been hampered by practical difficulties. This paper shows how a deconvolution approach derived from systems theory may be applied to identify the CRTDs associated with urban drainage structures.