Urban Drainage Models Research Articles

Appraisal of data-driven and mechanistic emulators of nonlinear simulators: The case of hydrodynamic urban drainage models

System identification, sensitivity analysis, optimization and control, require a large number of model evaluations. Accurate simulators are too slow for these applications. Fast emulators provide a solution to this efficiency demand, sacrificing unneeded accuracy for speed. There are many strategies for developing emulators but selecting one remains subjective. Herein we compare the performance of two kinds of emulators: mechanistic emulators that use knowledge of the simulator's equations, and purely data-driven emulators using matrix factorization. We borrow simulators from urban water management, because more stringent performance criteria on water utilities have made emulation a crucial tool within this field. Results suggest that naive data-driven emulation outperforms mechanistic emulation. We discuss scenarios in which mechanistic emulation seems favorable for extrapolation in time and dealing with sparse and unevenly sampled data. We also point to advances in Machine Learning that have not permeated yet into the environmental science community.

Analysing changes in short-duration extreme rainfall events

Two approaches are presented for using the UKCP09 weather generator (WG) to assess changes in extreme short-duration rainfall. The first provides change factors for design storms of varying duration and frequency, building on established hydrological techniques and with uncertainty estimation. The second approach characterises and facilitates the selection of WG timeseries for use in impact models. The methods have been tested at ten case study sites around the UK. The results show an increase in the intensity of short-duration (1 h and 12 h) events in winter but a reduction in summer, although the latter is subject to high levels of uncertainty. The number of intense events increases slightly and more significantly for some locations, especially in winter. Generally, it is hard to establish any conclusions geographically, although increases in rainfall intensity and events in the Lake District site stand out. The methods provide practical techniques for utilising the UKCP09 WG to assess the impacts of climate change, in particular for urban drainage and sewer modelling.

Estimation of combined sewer overflow discharge: a software sensor approach based on local water level measurements.

Combined sewer overflow (CSO) structures are constructed to effectively discharge excess water during heavy rainfall, to protect the urban drainage system from hydraulic overload. Consequently, most CSO structures are not constructed according to basic hydraulic principles for ideal measurement weirs. It can, therefore, be a challenge to quantify the discharges from CSOs. Quantification of CSO discharges are important in relation to the increased environmental awareness of the receiving water bodies. Furthermore, CSO discharge quantification is essential for closing the rainfall-runoff mass-balance in combined sewer catchments. A closed mass-balance is an advantage for calibration of all urban drainage models based on mass-balance principles. This study presents three different software sensor concepts based on local water level sensors, which can be used to estimate CSO discharge volumes from hydraulic complex CSO structures. The three concepts were tested and verified under real practical conditions. All three concepts were accurate when compared to electromagnetic flow measurements.

Lost in calibration: why people still do not calibrate their models, and why they still should - a case study from urban drainage modelling.

From a scientific point of view, it is unquestioned that numerical models for technical systems need to be calibrated. However, in sufficiently calibrated models are still used in engineering practice. Case studies in the scientific literature that deal with urban water management are mostly large cities, while little attention is paid to the differing boundary conditions of smaller municipalities. Consequently, the aim of this paper is to discuss the calibration of a hydrodynamic model of a small municipality (15,000 inhabitants). To represent the spatial distribution of precipitation, three distributed rain gauges were used for model calibration. To show the uncertainties imminent to the calibration process, 17 scenarios, differing in assumptions for calibration, were distinguished. To compare the impact of the different calibration scenarios on actual design values, design rainfall events were applied. The comparison of the model results using the different typical design storm events from all the surrounding data points showed substantial differences for the assessment of the sewers regarding urban flooding, emphasizing the necessity of uncertainty analysis for hydrodynamic models. Furthermore, model calibration is of the utmost importance, because uncalibrated models tend to overestimate flooding volume and therefore result in larger diameters and retention volumes.

Designing and implementing a multi-core capable integrated urban drainage modelling Toolkit:Lessons from CityDrain3

Integrated urban drainage modelling combines different aspects of the urban water system into a common framework. With increasing pressures of a changing climate, urban growth and economic constraints, the need for wider spread integration is necessary in the interest of a sustainable future. Greater complexity results in greater computational burden but modelling packages will, likewise, need to be flexible enough to allow incorporation of new algorithms. With advancements in modern information technology, a parallel implementation of such a modelling toolkit is mandatory while still leaving its users the flexibility of extensions. The design and implementation of the integrated modelling framework CityDrain3 shows that it is possible to write research code that is high-performance and extensible by many research projects. Three use case scenarios are presented to showcase the application of CityDrain3. The performance advantage of parallelization (up to 40 times compared to its predecessor) and the scalability of the framework are also demonstrated.

Impacts of combined sewer overflows on a large urban river – Understanding the effect of different management strategies

To support decision makers in planning effective combined sewer overflow (CSO) management strategies an integrated modelling and impact assessment approach has been developed and applied for a large urban area in Berlin, Germany. It consists of an urban drainage model, a river water quality model and a tool for the quantification of adverse dissolved oxygen (DO) conditions in the river, one of the main stressors for urban lowland rivers. The coupled model was calibrated successfully with average Nash-Sutcliffe-efficiencies for DO in the river of 0.61 and 0.70 for two validation years. Moreover, the whole range of observed DO concentrations after CSO down to 0 mg L−1 is simulated by the model. A local sensitivity analysis revealed that in the absence of CSO dissolved oxygen principally depends on phytoplankton dynamics. Regarding CSO impacts, it was shown that 97% of the observed DO deficit can be explained by the three processes (i) mixing of river water with CSO spill water poor in DO, (ii) reduced phytoplankton activity due to CSO-induced turbidity and (iii) degradation of organic matter by heterotrophic bacteria. As expected, process (iii) turned out to be the most important one. However depending on the time lag after CSO the other processes can become dominant. Given the different involved processes, we found that different mitigation schemes tested in a scenario analysis can reduce the occurrence of critical DO deficits in the river by 30–70%. Overall, the study demonstrates that integrated sewer-river-models can be set up to represent CSO impacts under complex urban conditions. However, a significant effort in monitoring and modelling is a requisite for achieving reliable results.

Stochastic evaluation of the impact of sewer inlets’ hydraulic capacity on urban pluvial flooding

Sewer inlet structures are vital components of urban drainage systems and their operational conditions can largely affect the overall performance of the system. However, their hydraulic behaviour and the way in which it is affected by clogging is often overlooked in urban drainage models, thus leading to misrepresentation of system performance and, in particular, of flooding occurrence. In the present paper, a novel methodology is proposed to stochastically model stormwater urban drainage systems, taking the impact of sewer inlet operational conditions (e.g. clogging due to debris accumulation) on urban pluvial flooding into account. The proposed methodology comprises three main steps: (i) identification of sewer inlets most prone to clogging based upon a spatial analysis of their proximity to trees and evaluation of sewer inlet locations; (ii) Monte Carlo simulation of the capacity of inlets prone to clogging and subsequent simulation of flooding for each sewer inlet capacity scenario, and (iii) delineation of stochastic flood hazard maps. The proposed methodology was demonstrated using as case study design storms as well as two real storm events observed in the city of Coimbra (Portugal), which reportedly led to flooding in different areas of the catchment. The results show that sewer inlet capacity can indeed have a large impact on the occurrence of urban pluvial flooding and that it is essential to account for variations in sewer inlet capacity in urban drainage models. Overall, the stochastic methodology proposed in this study constitutes a useful tool for dealing with uncertainties in sewer inlet operational conditions and, as compared to more traditional deterministic approaches, it allows a more comprehensive assessment of urban pluvial flood hazard, which in turn enables better-informed flood risk assessment and management decisions.

Dynamic gauge adjustment of high-resolution X-band radar data for convective rain storms: Model-based evaluation against measured combined sewer overflow

Summary Numerous studies have shown that radar rainfall estimates need to be adjusted against rain gauge measurements in order to be useful for hydrological modelling. In the current study we investigate if adjustment can improve radar rainfall estimates to the point where they can be used for modelling overflows from urban drainage systems, and we furthermore investigate the importance of the aggregation period of the adjustment scheme. This is done by continuously adjusting X-band radar data based on the previous 5–30 min of rain data recorded by multiple rain gauges and propagating the rainfall estimates through a hydraulic urban drainage model. The model is built entirely from physical data, without any calibration, to avoid bias towards any specific type of rainfall estimate. The performance is assessed by comparing measured and modelled water levels at a weir downstream of a highly impermeable, well defined, 64 ha urban catchment, for nine overflow generating rain events. The dynamically adjusted radar data perform best when the aggregation period is as small as 10–20 min, in which case it performs much better than static adjusted radar data and data from rain gauges situated 2–3 km away.

Urban Stormwater Management Model and Tools for Designing Stormwater Management of Green Infrastructure Practices

Urbanization is growing rapidly in Malaysia. Rapid urbanization has known to have several negative impacts towards hydrological cycle due to decreasing of pervious area and deterioration of water quality in stormwater runoff. One of the negative impacts of urbanization is the congestion of the stormwater drainage system and this situation leading to flash flood problem and water quality degradation. There are many urban stormwater management softwares available in the market such as Storm Water Drainage System design and analysis program (DRAINS), Urban Drainage and Sewer Model (MOUSE), InfoWorks River Simulation (InfoWork RS), Hydrological Simulation Program-Fortran (HSPF), Distributed Routing Rainfall-Runoff Model (DR3M), Storm Water Management Model (SWMM), XP Storm Water Management Model (XPSWMM), MIKE-SWMM, Quality-Quantity Simulators (QQS), Storage, Treatment, Overflow, Runoff Model (STORM), and Hydrologic Engineering Centre-Hydrologic Modelling System (HEC-HMS). In this paper, we are going to discuss briefly about several softwares and their functionality, accessibility, characteristics and components in the quantity analysis of the hydrological design software and compare it with MSMA Design Aid and Database. Green Infrastructure (GI) is one of the main topics that has widely been discussed all over the world. Every development in the urban area is related to GI. GI can be defined as green area build in the develop area such as forest, park, wetland or floodway. The role of GI is to improve life standard such as water filtration or flood control. Among the twenty models that have been compared to MSMA SME, ten models were selected to conduct a comprehensive review for this study. These are known to be widely accepted by water resource researchers. These ten tools are further classified into three major categories as models that address the stormwater management ability of GI in terms of quantity and quality, models that have the capability of conducting the economic analysis of GI and models that can address both stormwater management and economic aspects together.

High-quality observation of surface imperviousness for urban runoff modelling using UAV imagery

Abstract. Modelling rainfall–runoff in urban areas is increasingly applied to support flood risk assessment, particularly against the background of a changing climate and an increasing urbanization. These models typically rely on high-quality data for rainfall and surface characteristics of the catchment area as model input. While recent research in urban drainage has been focusing on providing spatially detailed rainfall data, the technological advances in remote sensing that ease the acquisition of detailed land-use information are less prominently discussed within the community. The relevance of such methods increases as in many parts of the globe, accurate land-use information is generally lacking, because detailed image data are often unavailable. Modern unmanned aerial vehicles (UAVs) allow one to acquire high-resolution images on a local level at comparably lower cost, performing on-demand repetitive measurements and obtaining a degree of detail tailored for the purpose of the study. In this study, we investigate for the first time the possibility of deriving high-resolution imperviousness maps for urban areas from UAV imagery and of using this information as input for urban drainage models. To do so, an automatic processing pipeline with a modern classification method is proposed and evaluated in a state-of-the-art urban drainage modelling exercise. In a real-life case study (Lucerne, Switzerland), we compare imperviousness maps generated using a fixed-wing consumer micro-UAV and standard large-format aerial images acquired by the Swiss national mapping agency (swisstopo). After assessing their overall accuracy, we perform an end-to-end comparison, in which they are used as an input for an urban drainage model. Then, we evaluate the influence which different image data sources and their processing methods have on hydrological and hydraulic model performance. We analyse the surface runoff of the 307 individual subcatchments regarding relevant attributes, such as peak runoff and runoff volume. Finally, we evaluate the model's channel flow prediction performance through a cross-comparison with reference flow measured at the catchment outlet. We show that imperviousness maps generated from UAV images processed with modern classification methods achieve an accuracy comparable to standard, off-the-shelf aerial imagery. In the examined case study, we find that the different imperviousness maps only have a limited influence on predicted surface runoff and pipe flows, when traditional workflows are used. We expect that they will have a substantial influence when more detailed modelling approaches are employed to characterize land use and to predict surface runoff. We conclude that UAV imagery represents a valuable alternative data source for urban drainage model applications due to the possibility of flexibly acquiring up-to-date aerial images at a quality compared with off-the-shelf image products and a competitive price at the same time. We believe that in the future, urban drainage models representing a higher degree of spatial detail will fully benefit from the strengths of UAV imagery.

Singularity-sensitive gauge-based radar rainfall adjustment methods for urban hydrological applications

Abstract. Gauge-based radar rainfall adjustment techniques have been widely used to improve the applicability of radar rainfall estimates to large-scale hydrological modelling. However, their use for urban hydrological applications is limited as they were mostly developed based upon Gaussian approximations and therefore tend to smooth off so-called "singularities" (features of a non-Gaussian field) that can be observed in the fine-scale rainfall structure. Overlooking the singularities could be critical, given that their distribution is highly consistent with that of local extreme magnitudes. This deficiency may cause large errors in the subsequent urban hydrological modelling. To address this limitation and improve the applicability of adjustment techniques at urban scales, a method is proposed herein which incorporates a local singularity analysis into existing adjustment techniques and allows the preservation of the singularity structures throughout the adjustment process. In this paper the proposed singularity analysis is incorporated into the Bayesian merging technique and the performance of the resulting singularity-sensitive method is compared with that of the original Bayesian (non singularity-sensitive) technique and the commonly used mean field bias adjustment. This test is conducted using as case study four storm events observed in the Portobello catchment (53 km2) (Edinburgh, UK) during 2011 and for which radar estimates, dense rain gauge and sewer flow records, as well as a recently calibrated urban drainage model were available. The results suggest that, in general, the proposed singularity-sensitive method can effectively preserve the non-normality in local rainfall structure, while retaining the ability of the original adjustment techniques to generate nearly unbiased estimates. Moreover, the ability of the singularity-sensitive technique to preserve the non-normality in rainfall estimates often leads to better reproduction of the urban drainage system's dynamics, particularly of peak runoff flows.

Comparison of two stochastic techniques for reliable urban runoff prediction by modeling systematic errors

AbstractIn urban rainfall‐runoff, commonly applied statistical techniques for uncertainty quantification mostly ignore systematic output errors originating from simplified models and erroneous inputs. Consequently, the resulting predictive uncertainty is often unreliable. Our objective is to present two approaches which use stochastic processes to describe systematic deviations and to discuss their advantages and drawbacks for urban drainage modeling. The two methodologies are an external bias description (EBD) and an internal noise description (IND, also known as stochastic gray‐box modeling). They emerge from different fields and have not yet been compared in environmental modeling. To compare the two approaches, we develop a unifying terminology, evaluate them theoretically, and apply them to conceptual rainfall‐runoff modeling in the same drainage system. Our results show that both approaches can provide probabilistic predictions of wastewater discharge in a similarly reliable way, both for periods ranging from a few hours up to more than 1 week ahead of time. The EBD produces more accurate predictions on long horizons but relies on computationally heavy MCMC routines for parameter inferences. These properties make it more suitable for off‐line applications. The IND can help in diagnosing the causes of output errors and is computationally inexpensive. It produces best results on short forecast horizons that are typical for online applications.

Stochastic Urban Pluvial Flood Hazard Maps Based upon a Spatial-Temporal Rainfall Generator

It is a common practice to assign the return period of a given storm event to the urban pluvial flood event that such storm generates. However, this approach may be inappropriate as rainfall events with the same return period can produce different urban pluvial flooding events, i.e., with different associated flood extent, water levels and return periods. This depends on the characteristics of the rainfall events, such as spatial variability, and on other characteristics of the sewer system and the catchment. To address this, the paper presents an innovative contribution to produce stochastic urban pluvial flood hazard maps. A stochastic rainfall generator for urban-scale applications was employed to generate an ensemble of spatially—and temporally—variable design storms with similar return period. These were used as input to the urban drainage model of a pilot urban catchment (~9 km2) located in London, UK. Stochastic flood hazard maps were generated through a frequency analysis of the flooding generated by the various storm events. The stochastic flood hazard maps obtained show that rainfall spatial-temporal variability is an important factor in the estimation of flood likelihood in urban areas. Moreover, as compared to the flood hazard maps obtained by using a single spatially-uniform storm event, the stochastic maps generated in this study provide a more comprehensive assessment of flood hazard which enables better informed flood risk management decisions.

Quantifying radar-rainfall uncertainties in urban drainage flow modelling

This work presents the results of the implementation of a probabilistic system to model the uncertainty associated to radar rainfall (RR) estimates and the way this uncertainty propagates through the sewer system of an urban area located in the North of England. The spatial and temporal correlations of the RR errors as well as the error covariance matrix were computed to build a RR error model able to generate RR ensembles that reproduce the uncertainty associated with the measured rainfall. The results showed that the RR ensembles provide important information about the uncertainty in the rainfall measurement that can be propagated in the urban sewer system. The results showed that the measured flow peaks and flow volumes are often bounded within the uncertainty area produced by the RR ensembles. In 55% of the simulated events, the uncertainties in RR measurements can explain the uncertainties observed in the simulated flow volumes. However, there are also some events where the RR uncertainty cannot explain the whole uncertainty observed in the simulated flow volumes indicating that there are additional sources of uncertainty that must be considered such as the uncertainty in the urban drainage model structure, the uncertainty in the urban drainage model calibrated parameters, and the uncertainty in the measured sewer flows.

Enhancement of radar rainfall estimates for urban hydrology through optical flow temporal interpolation and Bayesian gauge-based adjustment

Summary Rainfall estimates of the highest possible accuracy and resolution are required for urban hydrological applications, given the small size and fast response which characterise urban catchments. While radar rainfall estimates have the advantage of well capturing the spatial structure of rainfall fields and its variation in time, the commonly available radar rainfall products (typically at ∼1 km/5–10 min resolution) may still fail to satisfy the accuracy and resolution – in particular temporal resolution – requirements of urban hydrology. A methodology is proposed in this paper, to produce higher temporal resolution, more accurate radar rainfall estimates, suitable for urban hydrological applications. The proposed methodology entails two main steps: (1) Temporal interpolation of radar images from the originally-available temporal resolutions (i.e. 5–10 min) to finer resolutions at which local rain gauge data are commonly available (i.e. 1–2 min). This is done using a novel interpolation technique, based upon the multi-scale variational optical flow technique, and which can well capture the small-scale rainfall structures relevant at urban scales. (2) Local and dynamic gauge-based adjustment of the higher temporal resolution radar rainfall estimates is performed afterwards, by means of the Bayesian data merging method. The proposed methodology is tested using as case study a total of 8 storm events observed in the Cranbrook (UK) and Herent (BE) urban catchments, for which radar rainfall estimates, local rain gauge and depth/flow records, as well as recently calibrated urban drainage models were available. The results suggest that the proposed methodology can provide significantly improved radar rainfall estimates and thereby generate more accurate runoff simulations at urban scales, over and above the benefits derived from the mere application of Bayesian merging at the original temporal resolution at which radar estimates are available. The benefits of the proposed temporal interpolation + merging methodology are particularly evident in storm events with strong and fast-changing (convective-like) rain cells.

The use of WorldView-2 satellite imagery to model urban drainage system with low impact development (LID) Techniques

Within a wide range of best management practices for stormwater management in urban areas, there has been an increasing interest in source control measures. Source controls such as low-impact development (LID) techniques are potentially attractive as retrofit options for older developed areas that lack available land to implement conventional measures such as stormwater management ponds. Hence, distributed urban drainage models requiring detailed representation of developed drainage areas should be developed to accurately estimate the benefits that LIDs may provide. This study (1) presents a two-stage classification process on a high-resolution WorldView-2 image, and (2) demonstrates how to use the extracted land cover information in the subsequent hydrologic modelling and assessment of different LIDs’ performance. The proposed two-stage classification method achieved an overall accuracy of 80.6%, whereas a traditional pixel-based achieved 68.4% in classifying the same urban area into six land cover classes. From the classification results, the hydrologic properties of micro-subcatchments were imported in the United States Environmental Protection Agency Storm Water Management Model to assess the performance of LIDs. A reduction of run-off volume 18.2% and 37.1% was found with the implementation of porous pavement and bioretention, respectively, in a typical low-rise residential area located in the city of San Clemente, California, US. The study demonstrates the use of high-resolution remote sensing image to aid in evaluating LID retrofit options, and thus benefits in situations where detailed drainage area information is not available.

Correcting for wind drift in high resolution radar rainfall products: a feasibility study

Summary Increasing demands from emergency responders for accurate flood prediction, particularly in cities, have motivated consistent increases in the resolution of urban drainage models. Such models are now primarily limited by the accuracy and resolution of the initialising rainfall field. Surface rainfall estimates from radar, traditionally derived at scales of order 1 km, are now requested at grid lengths of 100 m to drive improvements in the outputs of these models. Deriving radar precipitation products on grids at the sub-kilometre scale introduces new requirements for the processing of reflectivity measurements into surface rainfall rates. A major source of uncertainty is the physical distance between the radar measurement and the surface onto which precipitation falls. Whilst adjustments to account for inhomogeneity in the vertical reflectivity profile have been extensively investigated, the effects of horizontal displacement have not. This paper discusses the issue of wind drift, first by outlining the need for correction, and then by evaluating the corrections available for impact at the required scale. One correction is detailed and its sensitivity evaluated with respect to the assumptions necessary in its derivation. These sensitivities are verified by trials on the Met Office operational radar processing system, where errors on wind drift displacement estimates are shown to be of order 1 km or more. This is significantly greater than the grid length desired by hydrological users. The paper therefore concludes by suggesting further research necessary to ensure the accuracy of radar precipitation estimates at sub-kilometre resolution.

The Influence of Objective Function and Acceptability Threshold on Uncertainty Assessment of an Urban Drainage Hydraulic Model with Generalized Likelihood Uncertainty Estimation Methodology

Urban drainage model is an important computer-aided tool in stormwater management and drainage planning and designing. A popular urban drainage hydraulic model, stormwater management model (SWMM), was applied in a pump lifting combined sewer system for a high-intensity urban catchment located in Shanghai, China. Uncertainty of SWMM water quantity parameters was assessed with generalized likelihood uncertainty estimation (GLUE) methodology. The sensitivity of parameters was discussed and compared based on the results of uncertainty analysis. To discuss the influence of the acceptability threshold on model parameter sensitivity and the margin of uncertainty band, the GLUE approach was applied several times varying acceptability threshold. The results indicated that a higher acceptability threshold value is contributed to achieve a stricter verification with a high confidence level, and the uncertainty analysis significant level can be featured by the value of acceptability threshold. The selection of acceptability threshold value can be regarded as a tradeoff process. Both reducing the low efficient simulation and reducing computation cost should be considered for the selection of acceptability threshold. Moreover, the GLUE approach was applied several times varying different objective functions with corresponding acceptability thresholds. The results indicated that some parameters may be sensitive to a specific objective function, and other parameters may be sensitive to another objective function. Some parameters cannot easily identified when a single objective function was used within the GLUE approach, and a multiple-objective function combined different objective functions requirements, may be a alternative approach to reduce the model prediction uncertainty.

Application of the UKCP09 WG Outputs to Assess Performance of Combined Sewers System in a Changing Climate

In many parts of the world old sewer systems have been designed without consideration for change in climate, so probabilities and risks of sewer surcharge and flooding are elevated due to increase in extreme rainfall events as a consequence of global warming. The current paper is aiming to assess how the climate change on interannual to multidecadal timescale (2020s, 2050s, 2080s) will affect design standards of waste water networks due to the presumed increase in rainfall intensity and frequency in the Northwest of England area (selected site). Design storms have been analysed for future rainfall obtained from the UK Climate Projection version 2009 (UKCP09) weather generator, which was applied to the existing urban drainage system to check the level of service in winter and summer seasons. Two emission scenarios (SRES) have been adopted to simulate the greenhouse gas concentration; high scenario (A1FI) and low scenario (B1). Results indicate that the impact of increase in the deign storm of the system in winter lead to a potential of increase flood volume from manholes and intern basements at risk of flooding with the worst condition associated with 24 hours storm in 2080s. Moreover, when this design storm depth increased by only 15%, the corresponding flood volume increase by 40%, this indicates that the relation between the cause of flooding and its consequences is non-linear. Summer season has an opposite picture and flood volume is projected to decrease with the increase in the storm duration causing low risk. Considering climate change in this study caused most of urban drainage models runs to be very slow with some interruption in the simulation due to the inflation in some parameters, so cautious should be taken.

Modelling of green roof hydrological performance for urban drainage applications

Green roofs are being widely implemented for stormwater management and their impact on the urban hydrological cycle can be evaluated by incorporating them into urban drainage models. This paper presents a model of green roof long term and single event hydrological performance. The model includes surface and subsurface storage components representing the overall retention capacity of the green roof which is continuously re-established by evapotranspiration. The runoff from the model is described through a non-linear reservoir approach. The model was calibrated and validated using measurement data from 3 different extensive sedum roofs in Denmark. These data consist of high-resolution measurements of runoff, precipitation and atmospheric variables in the period 2010–2012. The hydrological response of green roofs was quantified based on statistical analysis of the results of a 22-year (1989–2010) continuous simulation with Danish climate data. The results show that during single events, the 10 min runoff intensities were reduced by 10–36% for 5–10 years return period and 40–78% for 0.1–1 year return period; the runoff volumes were reduced by 2–5% for 5–10 years return period and 18–28% for 0.1–1 year return period. Annual runoff volumes were estimated to be 43–68% of the total precipitation. The peak time delay was found to greatly vary from 0 to more than 40 min depending on the type of event, and a general decrease in the time delay was observed for increasing rainfall intensities. Furthermore, the model was used to evaluate the variation of the average annual runoff from green roofs as a function of the total available storage and vegetation type. The results show that even a few millimeters of storage can reduce the mean annual runoff by up to 20% when compared to a traditional roof and that the mean annual runoff is not linearly related to the storage. Green roofs have therefore the potential to be important parts of future urban stormwater management plans.