Modelling decentralised systems for urban drainage and flood mitigation

Adapting to the impacts of climate change and urban growth in urban flood management requires approaches, which mitigate the flood risk and provide sustainable solutions. A combination of local drainage systems and water retention in public spaces may provide an appropriate strategy to cope with present and future pressures on the urban drainage infrastructure. To implement these small-scale hydrological systems in catchment models, novel hydrological modelling approaches are required that can handle a large number of spatially distributed measures. This paper presents the enhancement of a model system and the application for an urban catchment in Hamburg, Germany. The efficiency study of decentralised systems was conducted on the basis of climate change and urban growth scenarios. The results demonstrate the potential of sustainable drainage systems and multipurpose retention spaces for flood peak mitigation.


Introduction
Drainage infrastructures in urban areas prevent frequent flooding and protect water courses from combined sewage and stormwater runoff, but to manage uncertainties of the future development mainly shaped by climate change or increasing urbanisation (IPCC 2014), adaptive and more flexible strategies are required. Here, decentralised strategies (referred to as sustainable drainage systems (SUDS)) gain a growing importance in recent years, due to its positive effects on water quality and quantity and additionally their adaptive or multifunctional nature. These approaches accentuate the implementation of a combination of 'natural' systems with 'engineering' systems to collect, drain, treat, attenuate and reduce stormwater runoff (Cettner et al. 2013). On the local scale, it consists of (mostly vegetated) source-control structures such as swales or green roofs, with a limited capacity and a specific design threshold. In the case of storm events that surpass the capacity of SUDS, the control of exceedance flow is of particular concern. If the design value of an element (e.g. green roof) is exceeded, the 'overflow' can be conveyed by roads or streets to a multipurpose area (e.g. a park or open green space). A combination of strategies shall be stipulated, so that the flow can reach a destination (Digman et al. 2012).The recent progress in sustainable drainage and exceedance flow control is dealt with in literature across different disciplinary fields (e.g. DEFRA 2010; Digman et al. 2012;Stovin et al. 2013;Wong et al. 2013;Zhou 2014). *Corresponding author. Email: s.hellmers@tuhh.de However, a research need is seen in quantifying the hydrologic performance of those cascades of decentral hydrological systems and their performance on site scale as well as on catchment scale. A range of available modelling tools allow the simulation of SUDS (e.g. MIKE-SWMM, QQS, STORM, SWMM, MUSIC, KalypsoHydrology) for different purposes and applications (Elliott & Trowsdale 2007).
Selecting the appropriate model for the different purposes is one of the most important elements in stormwater modelling (Urbonas 2007). Some models are better for urban areas dealing with small sub-catchments (e.g. QQS, SWMM) and others (e.g. LARSIM) are better for large catchments (Urbonas 2007). Another aspect is the availability and usability of the model. Commercial models support (more or less) the usability, but their costs are often high and the availability is limited. In contrast, open-source models require only nominal costs, but the user may need more technical knowledge to apply the model (Zoppou 2001).
In this paper, the development of a theoretical approach to integrate decentral hydrological systems in catchment models as well as its implementation in an open-source semi-distributed hydrologic model (SDHM) KalypsoHydrology is presented. The model system has been applied to assess the efficiency of SUDS and retention spaces to mitigate the flood peak discharge and inundated areas in the Wandse catchment, a river in the urban area of Hamburg, Germany.

Methodology
The design and implementation of SUDS and multipurpose spaces in urban areas depend on local features of the land use. The distribution of green roofs depends on the availability of building shapes, whereas the distribution of retention spaces and infiltration measures depends on the availability of free spaces. This demands for a modelling approach which can handle a large number of spatially distributed measures, and a sufficiently detailed land-use map matching the spatial detail of the SUDS distribution in the model area is now required.
Further on, SUDS such as green roofs and swales can be regarded as little reservoirs where storage effects (retention) dominate over water movement (translation). Thus, hydrological models which are based on the linear reservoir theory and the lumped model approach are considered as appropriate to model the hydrological impact of SUDS on a catchment level.
SDHMs allow the simulation of the entire land-based part of the water balance on the basis of given precipitation time series. The catchment is divided into smaller hydrological systems: in the first order: sub-catchments and in the second order: hydrotops (a.k.a. hydrologic response units), that is, units with distinguished land use, drainage and soil characteristics, for which the water balance is computed. Depending on the level of details, the defined land-use units are composed of heterogeneous elements. For example, the land-use class 'detached buildings' contains both, a building and a green space. In the case that different SUDS elements are to be applied, this differentiation has to be made as green roofs and swales can be applied only on buildings or green spaces, respectively.

Theoretical approach -integration of SUDS into hydrologic modelling
In order to take into account the effects of SUDS, the existing data model of hydrotops in a SDHM should be redefined by integrating a differentiated description of the SUDS elements. Firstly, those SUDS elements should be spatially distributed to be in accordance with the given land-use data, as shown in Figure 1. The green roofs are, for instance, allocated on the existing or planned buildings, whereby the distribution of retention spaces is dependent on the availability of free space. The additional information of SUDS and retention areas is represented in the form of 'overlays'. The new, redefined, hydrotops are finally created by geometrically intersecting the land use, soil type, watershed and overlays. The main parameters are outlined in Figure 1.
Secondly, for modelling the physical processes in the individual SUDS elements, they are subdivided into a sequence of vertical layers which are defined based on their characteristics and functionality as shown in Figure 2.
For example, green roofs are subdivided into three layers: the upper layer with vegetation, the substrate layer and the drainage layer. In the substrate layer, vegetation is planted according to an extensive or intensive green roof definition. On the plane roof, a filter layer is provided above a root protection and insulating layer to drain the water to the rain water downpipe. At each layer, the hydrological processes are balanced on the basis of the following continuity equation (Equation (1)): (1) Figure 1. Spatial intersection and aggregation to define equal hydrological response units (hydrotops). The new hydrotops contain the SUDS information in the overlay layer. The soil water content (sw [l/m 2 ]) within the layers of the SUDS element changes according to the infiltration rate (inf [l/m 2 ]), the percolation rate (perc [l/m 2 ]) into the layer below, the evapotranspiration rate (Et a [l/m 2 ]) and the drainage through the downpipe (Q Drain [l]) per time (t) and area (A [m 2 ]). In the first layer, the inflow of the green roof is the effective precipitation, which includes loss through interception by the vegetation of the roof. Additionally to the drainage in the downpipe, the water balance is effected by an overflow (Q overflow [l]). It prevents the overloading of the green roof. The effective flow through the overflow pipe is the minimal discharge calculated with the Poleni approach (with the water level (h ov [m]), the diameter of the overflow pipe (d pipe [m]), the overflow coefficient [μ] and the maximal capacity of the pipe with the flow resistance [λ]): (2) In the last layer, the drainage layer, the percolation (perc [t]) is set to 0 for a green roof because of a sealing above the roof construction. The drainage through the downpipe begins when the water content in the drainage layer is above field capacity. Due to backwater effects at the downpipe, the free water will store in the drainage layer to the water height h w [m]. The effective flow through the downpipe is the minimal discharge calculated according to the Poleni approach (Equation (2), by taking into account the porosity in the drainage layer) and the maximum capacity of the pipe. The described hydrological processes and mathematical description exemplified on a green roof element correspond to the characteristics of the layers in swales and swale-filter-drain systems.
A cistern is represented in the model as one-layer element with a specific storage volume. The inflow of water into the cistern depends on the amount of rainfall falling within a specific storm event on the drained area (e.g. one or several roof areas). Within the cistern, the water is calmed down, meaning that no currents are induced within the cistern by the inflow. Water is stored in the cistern up to a maximum water level (h ov [m]). Above this water level, the exceedance flow is drained to another SUDS element or the stormwater drainage system. The stored water can be used for rainwater harvesting. For different cistern types, daily rainwater harvesting information can be defined according to a study finished in 2015 (Sverdlova 2015).
The parameters of the vertical layers of different SUDS are assigned to the corresponding units (i.e. green roofs, swales or cisterns) in the redefined hydrotops and input into the model. A detailed description of the modelling procedure and parameters of the individual measures is given in a previous work (Hellmers 2010).

Implementation -KalypsoHydrology and the method of overlays
KalypsoHydrology, an open-source SDHM for the simulation of the land-based water balances in river catchments (Pasche 2003), has been enhanced to include the differentiated description of SUDS and retention areas in the form of overlays. The hydrological model supports the simulation of snow, evapotranspiration, evaporation from water surfaces in retention ponds, soil moisture, interflow, baseflow and groundwater flow processes. The calculation core written in FORTRAN has been reworked mainly to support the new functionalities. The network in the hydrologic model used to describe the runoff concentration from upstream to downstream sections in a river system consists of sub-catchments, drainage strands and drainage nodes (cp. Figure 3). The enhanced methodology allows the conveyance of exceedance flow in a chain of smallscale SUDS measures and larger-scale retention spaces. For this purpose, the new model accounts for the possibility that a single SUDS measure or designated area may both receive and distribute water. For that purpose, the model network has been enhanced with additional linkages to redistribute water from drainage nodes to areas. The areas with the functionality to drain and receive water are defined in the model as overlays (see Figure 3 'system plan with overlays').
During the computation, these areas are transformed into additional hydrological systems, and an algorithm has been implemented in the model KalypsoHydrology to cross link these hydrological systems in the overall drainage net with drainage strands and drainage nodes. The partial or entire distribution of the water in the model network plan is attributed to drainage nodes. The exceedance flow is distributed to retention areas in the larger system (e.g. multipurpose spaces, such as a sports field) or to the drainage network, when the design capacity of the elements on properties (e.g. green roofs, swales) is reached by a storm event (P) (see Figure 4).

Integration in an urban drainage and flood management tool
The enhanced hydrological model, KalypsoHydrology, is part of the open-source modelling platform Kalypso (http://sourceforge.net/projects/kalypso/). This software tool connects hydrologic and hydrodynamic and risk simulation models for use in flood risk management planning. It comprises a set of applications and client-specific developments. The General User Interface (GUI) provides a work flow helping the user to build up and maintain a model. In KalypsoHydrology, the user interface has been completely reworked recently in 2013 using the programming language JAVA and now supports an ergonomic workflow that guides the user through all modelling tasks   of the model, such as data handling, model setup, calibration and result analysis. The data processing in the Kalypso modelling framework is presented in Figure 5. Scenario simulations of future urban development projections can be derived from a calibrated basic model using overlay areas representing adaptation strategies such as SUDS or retention areas. Before the computation, the original model network plan is updated with the overlay areas and their interconnections. Climate change projections are imported as continuous time series for long-term water balance and short-term flood peak simulations. In the process chain of Kalypso, steady-state non-uniform rivers hydraulics are computed with a one-dimensional water surface profile model (KalypsoWSPM). The computation module supports the methods and approaches which have been standardised in Germany for carrying out hydraulic computations for near-natural creaks and rivers, summarised in the Technical Bulletins 1/1999 of BWK (1999) and 220/1991 of DVWK (1991). Additionally, an unsteady and 1D/2D coupled surface flow can be calculated with the module Kalypso1D/2D. This module enables the connection of one-dimensionally modelled river sections with another section which has been modelled using a 2D model. The computation module supports the revised calculation core of the Institute of River and Coastal Engineering, which is based on RMA 10s by Dr Ian King. In the post-processing phase, the inundated areas and water level can be computed based on digital terrain data using the module KalypsoFlood. Further information about the implementation and software tools are published in Hellmers et al. (2015).

Application
The enhanced hydrological model has been applied to quantify the impacts of land use and climate-change projections for 2050 in the Wandse catchment in Hamburg, assuming adaptation strategies with small-scale SUDS measures and larger-scale retention areas. The river Wandse stretches over 21.5 km and drains a total catchment area of 88 km 2 . It is a typical small urban catchment with its spring located in rather undeveloped or rural areas. The main part of the area is covered by urbanised areas with high sealing rates and heavily modified water bodies. Results of the flood impacts in the study area of the Wandse catchment are illustrated for an 'urban', 'urbansuburban' and a 'suburban' neighbourhood. Partly, the application study and related results have been published before in Hellmers et al. (2015).

Climate change impacts
Based on two regional climate model runs of REMO for the scenario A1B (Jacob and Mahrenholz 2006;Jacob et al. 2009), long-term water balance and flood peak events are calculated for a climate period from 2036 to 2065. The used climate data series comprise daily average temperature, sun duration, air humidity and wind speed data in a spatial resolution of 10 km 2 . Of particular concern is the spatial and temporal distribution of precipitation for urban flood modelling. The regional climate model computes vertically falling daily and hourly precipitation time series for both A1B model runs. Additionally, these data have been post-processed with the information of wind drifted precipitation and the data have been bias-corrected. These three precipitation data sets span a range of six possible future projections. The deviation between the results is illustrated in Figure 6. For events with return periods of 2 or 5 years, an increase in the peak river discharge of up to 27% and 20%, respectively, has been calculated. For events with return periods of 10 or 30 years, there is no clear evidence of an increase or decrease in flood peak discharge. The largest variance has been found for events with return periods of up to 100 years. Here, an increase in the flood peak discharge of up to 20% has been computed. But several calculation runs showed as well a possible decrease in flood peak discharge of 30%. In order to assess the performance of SUDS, a high increase in flood peak discharge  ( + 20%) has been selected as basis for subsequent impact studies. In this way, the most negative consequences of the computed climate change impacts are taken into account for the application study.

Urban growth and adaptation strategies
In the KLIMZUG-Nord project, socio-economic scenarios for 2050 have been defined with a group of stakeholders in the Wandse catchment (i.e. authorities, spatial planners, ecologists, academia, NGOs) (Rottgardt et al. 2014). The first scenario (S1) assumes a decrease in population in the inner city, which means the people are moving into the suburbs. Because of less financial support, the buildings and infrastructure in the inner city remain more or less the same. In this scenario, no adaptation strategy is applied. The second scenario (S2) assumes an increase in the population in the city of Hamburg. New buildings are constructed and the infrastructure is enlarged. In this scenario, the impervious areas in the city increase, which raises the need for alternative urban drainage systems. In this scenario, a moderate implementation of SUDS measures is assumed to be financially supported. In the third scenario (S3), an increase in inhabitants is assumed, too. But here the demand for new living space is assumed to be met by increasing the height of buildings. Impervious areas increase to a lesser extent than in the second scenario. In this scenario, the government heavily subsidises the implementation of adaptation strategies such as SUDS (green roofs, swales, swale-filter-drain systems) and larger water retention facilities in the city.

Results
The software module KalypsoHydrology has been applied to develop scenario models on the basis of climate year flood event on the basis of the 3 land-use scenarios S1 (top), S2 (middle) and S3 (bottom) and a climate change impact of 20% increase in flood peak discharge. The results are illustrated for a highly urbanised (left), an urban-suburban (middle) and a suburban area (right) (Hellmers et al. 2015). change impact assumptions ( + 20% change in flood peak discharge) and three urban growth assumptions (S1, S2, S3), including adaptation strategies for 2050. Small-scale SUDS and larger-scale retention areas have been defined in the model as overlay areas. The detailed spatial distribution of these areas is illustrated for the socio-economic scenarios in Figure 7. Based on peak discharges resulting from KalypsoHydrology, the river hydraulics were computed with the one-dimensional water surface profile model KalypsoWSPM. The inundated areas and water level were calculated on the basis of digital terrain data with the module KalypsoFlood. The computed inundated areas and water level are illustrated in Figure 8 for an urban area, an urban-suburban area and a suburban area. For this catchment, a maximum increase of 20% in flood peak discharge due to climate change is projected for 2050 (Hellmers & Hüffmeyer 2014). For the selected urban and urban-suburban areas, minor impacts on the inundated areas of a 100-year flood were calculated for the climate change and urban growth scenarios. This can be explained by the high river banks which prevent flooding of adjacent properties. On the contrary, in the upstream river section, that is, the suburban area, the river topography is shallow. Here, the increased peak discharges due to climate change and urban growth enlarges the inundated areas. In particular, the northern side of the river is affected. The result in scenario S1 shows the increase in the inundation area by the impacts of climate change and urban growth without measures. By implementing measures in scenario S2 and scenario S3, the impacts of climate change and urban growth on the inundation areas can be mitigated.

Conclusion
The presented enhanced model system enables the integration of decentral small-scale hydrological systems in catchment models and a water redistribution functionality to combine strategies for exceedance flow control. The module is part of the well-established software product Kalypso for flood risk management planning. The application in the urban area of Hamburg offers a better understanding of the mitigation efficiency that can be reached using decentral hydrological systems (e.g. SUDS, retention spaces) within urban catchments. However, ongoing research is required to analyse the uncertainties in nature and magnitude of climate change projections, urban growth scenarios as well as of impact modelling to support future flood risk management planning in urban catchments.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
The work described in this paper was made possible through support by a grant from the German Ministry for Education and Research (Bundesministerium für Bildung und Forschung) as part of its KLIMZUG initiative and the Agency of Roads, Bridges and Waters (LSBG), Germany. The authors gratefully thank for this support.  (2010). Her area of expertise in research and teaching is in hydrological modelling. Her ongoing research aims to integrate local hydrological systems in catchment models and is exemplified on local stormwater management systems for forecast application.

Notes on contributors
Dr Natasa Manojlovic is a senior researcher at the Institute of River & Coastal Engineering (TUHH) and is a visiting researcher at the UNESCO-IHE in Delft, NL. She achieved academic qualifications at the Hamburg University of Technology-TUHH (M.Sc. (2003) andPh.D. (2015)) and at the Faculty of Civil Engineering, University of Belgrade (B.SC. (2000)). Her research and teaching are focused on the holistic flood risk management and urban hydrology. She is currently involved in a number of national and international projects the main one being the development of the models and tools for the holistic risk governance in coastal areas within the FP7 Project PEARL. She authored more than 30 scientific publications in conferences, books and international journals.
Giovanni Palmaricciotti is a civil and environmental engineer working since 2009 as a research assistant at the Institute for River & Coastal Engineering of the Hamburg University of Technology, Germany. His research focuses on rainwater management and flood protection, in particular physical modelling of rain water and drainage systems and laboratory tests at flood protection systems.
Prof. Peter Fröhle is head of the Institute of River and Coastal Engineering of the Hamburg University of Technology since 2012. He studied civil engineering with a focus on hydraulic and coastal engineering at the universities in Bochum and Hannover. He has over 20 years' experience in the field of river and coastal engineering with particular focus on the design and planning of coastal structures, impacts of climate change to coastal and estuarine systems as well as design and modelling of ports.