Stochastic modelling of water and nitrogen fluxes in stormwater biofiltration systems

Biofiltration systems represent an increasingly popular technology for the management of urban stormwater runoff. The performance of these systems, largely dependent on their physical characteristics, is also strongly affected by the natural variability of runoff occurrence and volumes. We present here a model to quantify the statistics of the main variables involved in the water balance of biofiltration systems, given its main physical features (filter media and vegetation types) and accounting for the natural variability of the inflow rates in terms of occurrence and water volumes. The model allows us to derive analytically the long-term (e.g., a year) probability density function of the soil water content in the filter media and thus to estimate the main statistics of outflow, evapotranspiration, and overflow. By relating the soil water content in the filter media before inflow events to the total nitrogen concentrations of the outflow, the model also gives estimates of the statistics of nitrogen removal performance as a function of inflow variability. An application of the model to a biofltration system in Melbourne is presented and discussed.