Field validation of a physically-based model for bioretention systems
Graphical abstract
Introduction
To mitigate the impacts of urbanization on the flow regimes and water quality of water bodies (Walsh et al., 2012), bioretention basins are increasingly used as part of a suite of stormwater control measures (SCMs). Bioretention basins are landscaped depressions filled with sand and gravel, often vegetated, that are designed to receive urban runoff (from roofs, roads, etc.). They provide storage and allow urban runoff to be released to the atmosphere by evapotranspiration and infiltrated in native soils rather than discharged in piped networks to urban streams or other receiving waters. As such, bioretention basins are extremely efficient at reducing urban runoff peak flows, stormwater volumes and pollutants loads (Liu et al., 2014; Roy-Poirier et al., 2010). Their application aims to restore lost fluxes of the water balance (evapotranspiration, infiltration) and to reduce stormwater runoff caused by creation of impervious areas and hydraulically-efficient drainage systems (Burns et al., 2012). Modelling the performance of bioretention basins is, however, a challenge, as physical mechanisms involved in these systems are complex. These requirements can often preclude their use by decision-makers, designers and practitioners, meaning that there is a need for models which can be simply but reliably calibrated using relatively easy-to-collect monitoring data. A model which is physically-based, yet easy to calibrate, could be attractive for urban water management practitioners in current and future cities.
A wide range of tools exist to model Low Impact Development (LID) structures (Elliott and Trowsdale, 2007). The popular SWMM model includes a very flexible landscape-scale infiltration module, offering a choice of Hortonian, Green-Ampt or Curve-Number infiltration (Rossman, 2010a, Rossman, 2010b). The LID module in SWMM is based on the Green-Ampt infiltration from the surface into the filter media, followed by Darcy's flow through the porous media below, with subsequent infiltration to groundwater assumed to be constant. To model retention in green roofs, Kasmin et al. (2010) present a conceptual process-based model, where the soil is described as a store with different soil moisture thresholds that drive hydrological processes (e.g. runoff produced when soil moisture is higher than field capacity). DRAINMOD is used extensively to model bioretention systems: infiltration is modeled with the Green-Ampt equation (Skaggs, 1980, 1985) and requires the user to specify the soil-water characteristic curve and saturated hydraulic conductivity (Brown et al., 2013). DRAINMOD was recently adapted to the urban case (Lisenbee et al., 2020). Drainage is modeled with the Hooghoudt's equation, taking into account lateral hydraulic conductivity and properties of the underdrain (particularly spacing and radius). In Australia, MUSIC is the industry standard to model bioretention basins and other Stormwater Control Measures (eWater, 2014, 2020). Infiltration within bioretention basins is described in MUSIC by Darcy's equation, accounting for impacts of soil texture and moisture, with infiltration calculated from both the base and sides, while underdrain flow is calculated from Darcy's flow through the porous media, again accounting for texture and degree of saturation. Richards' equation, that combines mass conservation and Darcy's equation (Richards, 1931; van Genuchten, 1980), was used to model flow in bioretention cells to predict peak flow and volume reduction by He and Davis (2011). Other models used the Green-Ampt equations, e.g. Gülbaz and Kazezyılmaz-Alhan (2017).
In general terms, bioretention models may be separated in two groups. The first group is made up of models that have no extensive physical basis and are mostly designed statistically for a given experimental site, thus requiring a low number of parameters to implement. However, these models are often case-specific, being difficult to extrapolate to other sites and having limited predictive capabilities. Conversely, the second group is composed of more complex models, that are based on the modelling of physical processes, and usually require significant effort for calibration (Alamdari and Sample, 2019) or access to specific soil parameters which are complicated to estimate (such as the soil water retention curve or the unsaturated hydraulic conductivity). There is thus a need for a third option: models that are simple to calibrate while offering a satisfying level of consistency with regards to the physics of water infiltration in the bioretention systems, the use of more sophisticated models not systematically improving modelling results, since more parameters are needed, and calibration becomes more difficult (Mourad et al., 2005) and thus less likely to be undertaken by decision-makers and system designers.
The aim of this study was therefore to develop and test a simplified, physically-based model requiring low effort for calibration and capturing the hydraulic dynamic of bioretention systems. We report the development and testing of a physically-based hydrologic model against data obtained from a monitored bioretention basin (Wicks Reserve Bioretention system). The modelling approach describes the whole bioretention system as a series of reservoirs storing water and exchanging fluxes. The approach includes consideration of mass conservation (continuity equation), Darcy's equation for the implementation of infiltration fluxes into the system and the soil below, orifice equation for the underdrain, with the computation of evapotranspiration, allowing the prediction of exchanges between the reservoirs, and thus the water level in the filter (body of the bioretention system) and the outflow rates. Therefore, we present a new model that explicitly accounts for physical processes (soil water storage, vertical gravity-driven infiltration, exfiltration, respect of mass balance) under unsteady flow conditions, to predict the outflow performance of bioretention systems. A key objective was to provide explicit and simplified formulation of existing modelling approaches and equations in order to create a physically-based model.
Section snippets
Model development
The model is a physically-based representation of bioretention basins, based on reservoirs or storages in series, accounting for the water balance in storages and water fluxes exchanges between storages (Fig. 1). All equations presented below were discretised using a first order, explicit numerical scheme, considering a fixed 6 min timestep, to fit with observed data. The complete algorithm and computation code (R scripts) are available as Supplementary material and the dataset used is publicly
Validation over 20 rainfall events
The performance of the model tested over 20 rainfall events (excluding the two events used for calibration) was satisfying (Fig. 4, Fig. 5), with a mean NSE of 0.53, a median NSE of 0.75 and a median RMSE of 0.48 l/s. The model tended to underestimate fluxes, with a median PBIAS of - 22% (Fig. 5). Overall, the proposed model was able to well replicate outflows from the basin for most rainfall events (Moriasi et al., 2015). However, the model was not able to replicate water level dynamics in the
Conclusions
A hydrologic model of a bioretention basin was built, based on equations representing all the components of the hydrological balance (water infiltration, evapotranspiration, underdrain outflow, overflow, exfiltration) in the different components of the studied basin (surface basin, filter). The main conclusions and observations, after a thorough field validation of the model, are as follows:
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It is possible to replicate outflows of a bioretention basin with a relatively simple modelprovided it is
CRediT authorship contribution statement
Jérémie Bonneau: Methodology, Software, Formal analysis, Data curation, Writing – original draft, Writing – review & editing. Gislain Lipeme Kouyi: Methodology, Software, Validation, Funding acquisition, Supervision, Writing – original draft, Writing – review & editing, Project administration. Laurent Lassabatere: Methodology, Validation, Funding acquisition, Supervision, Writing – review & editing, Project administration. Tim D. Fletcher: Methodology, Validation, Funding acquisition,
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was carried out in the framework of a visiting fellowship (CRCT – CNU section 60) from INSA Lyon to the University of Melbourne. The authors thank Peter Poelsma, Robert James from the University of Melbourne, along with Hervé Négro & Nicolas Invernon (Alison), Bernard Chocat for his important work in the early stages of the development of the model, Quentin Bichet, Matthieu Marin Dit Bertoud (INSA Lyon) for their help and support. The authors also benefited from ANR INFILTRON
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