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Journal of Hydrology X
journal homepage:www.journals.elsevier.com/journal-of-hydrology-x
Research papers
A parameter parsimonious approach for catchment scale urban hydrology – Which processes are important?
Thomas Skaugen
⁎, Deborah Lawrence, Rengifo Zenon Ortega
Norwegian Water Resources and Energy Directorate, P.O Box 5091 Maj, 0301 Oslo, Norway
A R T I C L E I N F O
Keywords:
Parsimonious urban rainfall-runoffmodels Saturation excess overlandflow Subsurfaceflow in urban environments Low impact development-raingardens
A B S T R A C T
Increased urbanization and increased observed precipitation intensity and -frequency due to climate change call for urban hydrological models capable of describing urbanflow dynamics in data-scarce areas. A parameter parsimonious rainfall-runoffmodel, DDDUrban, forced by precipitation and temperature in which most model parameters are estimated from a detailed digital elevation model using GIS or taken from the literature is presented. Snowmelt and evapotranspiration are calculated using an energy balance approach, with proxy models for the energy balance elements driven by temperature and precipitation. The model focusses on sub- surface and surfaceflow processes using an analysis of travel time distributions which indicates that the shape of the urban hydrograph is largely independent of the comparatively very rapid process of water transport in conduits. The model uses an estimate of the distribution of subsurface velocities as a function of saturation. The study shows that the calibrated mean of this distribution agrees with the saturated hydraulic conductivity es- timated from infiltration measurements. The model has been calibrated and validated on observed runoffdata at a 10 min temporal resolution for two Norwegian catchments in Oslo and Trondheim with acceptable validation results measured by the Kling-Gupta Efficiency criterion (KGE = 0.56–0.69). Simulations show that precipita- tion infiltrated on permeable areas contributes, on average, to the totalflow at a fraction corresponding to the areal fraction of permeable areas. In addition, simulations show that for saturated conditions, a significant part (~30–60%) of theflood peak is derived from saturation excess overlandflow. Simulation of snowmelt indicates that a more detailed model for the spatial distribution of snow accounting for snow removal, is needed. The catchment-scale effects of Low Impact Developments in the form of 10 m2raingardens are simulated. In a residential area with 500 houses, 60 raingardens can reduce theflood peaks about 10%. A higher number of raingardens further reduce theflood peaks, but raingardens of too low capacity may increase secondaryflood peaks for episodes of multiple heavy precipitation events.
1. Introduction
Understanding the hydrological response to intense rainfall in urban areas is of paramount importance, as both increased levels of urbani- sation (Fletcher et al., 2013; Salvadore et al., 2015) and higher ob- served short-term rainfall intensities in recent years (Hanssen-Bauer et al., 2017) exert increased pressure on urban runoffsystems. Quan- tifying urban hydrological response is a significant challenge, however, due to the highly dynamic nature of the urban infrastructure and to a relative lack of long-term monitoring of runoffprocesses in built-up areas. The locations of roads and buildings and the drainage networks serving them can change rapidly in time, leading to non-stationarity in data series used for quantifying the hydrological response (Bayazit, 2015). In addition, in many urban areas, the only available runoffdata
are discharge series from combined (CSS) sewer systems in which both wastewater and stormwaterflows are combined, leading to a high de- gree of uncertainty when these data are used for hydrological analyses.
Simultaneously, many green solutions for coping with increased stormflow by implementing Low Impact Developments (LIDs), such as green roofs and rain gardens, represent strategies that are of an ex- plicitly hydrological character. Their effectiveness and cost benefit can only be assessed to a reasonable degree of certainty if their potential role in mitigating the urban response to intense rainfall can be reliably quantified. There is, therefore, a clear need for robust tools for mod- elling the urban hydrological regime that can be applied under condi- tions of limited data availability.
Current approaches used in practise for urban hydrological analyses include a spectrum of strategies ranging from simple methods that
https://doi.org/10.1016/j.hydroa.2020.100060
Received 19 June 2020; Received in revised form 17 July 2020; Accepted 23 July 2020
⁎Corresponding author.
E-mail address:[email protected](T. Skaugen).
Available online 28 July 2020
2589-9155/ © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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transform a rainfall intensity or hyetograph into a stormflow response, such as a peakflow rate, to complex urban hydrological models that invoke more physically-based processes and storages with the goal of creating a simulated runofftimeseries. An example of thefirst of these two approaches is the Rational Method (Grimaldi and Petroselli, 2014), while both SWMM (Rossmann and Huber, 2016), and MOUSE (DHI, 2017; MIKE, 2020) are examples of urban hydrological models.
Whereas the simple methods have the clear advantage of having minimal data requirements, important processes linked to subsurface flow are not physically represented nor is the overall water balance before and after events fully characterised in the analysis. The con- tribution of subsurfaceflow to urban runoffhas been debated in the literature and is an important knowledge gap (Elliott and Trowsdale, 2007; Fletcher et al., 2013; Salvadore et al., 2015). Several authors, however, have reported significant contributions from subsurfaceflow to both runoffvolumes and dynamics (Belhadj et al., 1995;Berthier et al., 2004; Hailegeorgis and Alfredsen, 2018; Broekhuizen et al., 2019). In addition to subsurfaceflow, evapotranspiration in urban areas is considered important for mitigating the effect of anthropogenic heat, and knowledge regarding its efficacy is imperative for closing the urban water balance (Fletcher et al., 2013). In order to simulate a realistic partitioning of overland- and subsurface flow, losses due to evapo- transpiration between rainfall events are also required. Therefore, for assessing the potential benefits of many LID strategies in attenuating or reducing urban stormflow, models that account for subsurface flows and evapotranspiration, including their overall role in the water bal- ance, are needed.
Urban hydrological models, such as MOUSE and SWMM, usually include schemes for characterising subsurface processes and losses due to evapotranspiration. Simultaneously, the models have a large number of parameters in the equations characterising these processes, and these parameters must be either calibrated orfixed using, for example, pre- viously reported values found in the literature. In MOUSE applications, for example, a classic conceptual model, NAM (Gustafsson, 1992) is used for runoffgeneration and routing from permeable areas in urban catchments. NAM is a hydrological model with linear reservoirs de- scribing both rapid and delayed runoffprocesses, as well as a scheme for accounting for evapotranspiration. The NAM model has, however, 15 parameters in the equations describing these processes. These parameters are of a conceptual nature and are difficult to associate with measurable physical properties and, therefore, must be determined via model calibration. In SWMM subsurface processes are modelled using a two-zone (saturated–and unsaturated zones) groundwater model and 13 parameters must be determined to implement the groundwater model. In addition, several different infiltration schemes are available within SWMM, each of which introduces a set of parameters. Similarly, the urban hydrological model presented byHailegeorgis and Alfredsen (2018)requires values for 43 parameters, most of which must be de- termined from calibration against observed runoff. Although the need for model parameter calibration is not unique to urban hydrological modelling, the relative paucity of reliable long-term series for urban catchments leads to a high degree of uncertainty in the calibrated models. In addition, a problem that can plague all models with a large number of conceptual parameters is the issue of equifinality, in that a range of possible combinations of parameters can produce the same runoffresults (Beven and Binley, 1992;Kirchner, 2006). Model over- parameterization can make it difficult to identify the dominant physical processes controlling the runoffresponse and to diagnose model errors and is especially problematic when data for model calibration are scarce (Kirchner, 2006).
Over the years, various approaches and strategies for modelling hydrological processes in data-sparse catchments have been developed, primarily for natural, non-urban catchments e.g. (Blöschl et al., 2013).
A principal goal of such approaches is to reduce the number of para- meters that require calibration, by simplifying or refining process de- scriptions and by incorporating other data sources that can be used to
either set or eliminate model parameters. One can reduce model com- plexity and associated data requirements byfirst identifying processes and pathways that dominate the runoff response for the problem of interest, e.g. in this case, the urban hydrological response to intense rainfall, based on characteristic length- and timescales for a relevant model application (seeSalvadore et al., 2015and references therein).
Processes that vary over much shorter or longer length- or timescales, relative to those that dominate the problem of interest, can often be either entirely neglected or set tofixed values using other data. The Distance Distribution Dynamics model (DDD,Skaugen and Onof, 2014;
Skaugen and Mengistu, 2016) is an example of a parameter parsimo- nious rainfall-runoffmodel developed for natural catchments, that has also been previously extended to ungauged, natural catchments (Skaugen et al, 2015), including at high temporal (1-hour) resolution (Tsegaw et al., 2019). The DDD model has been developed following the principle of replacing process descriptions requiring long timeseries for calibration with alternative descriptions with parameters that can be estimated from other types of data. In the ungauged applications mentioned above, the model has 7 process parameters that are re- gionalised based on catchment properties. In the current version of the model, 5 of these process parameters have been replaced by process descriptions without parameters in need of calibration. Given the suc- cessful application of the DDD model to predicting runoff at high- temporal resolution, its further extension to runoff in urban areas, which requires an even higher temporal resolution (e.g. 10-min.) is potentially feasible.
Given the need for reliable models for both assessing urban storm- flow response and evaluating hydrologically-based mitigation strate- gies, the main objectives of this study are 1) to investigate if the phy- sically-based, parameter parsimonious DDD model can be further developed for urban hydrological applications; 2) to assess the relative importance of the subsurface processes and evapotranspiration in the urban landscape using the developed model; 3) to apply the model to evaluate the catchment scale mitigating effects of distributed rain gardens (e.g.Elliott and Trowsdale, 2007;Eckart et al., 2017) in re- ducing peakflows.
2. Study area and data
In order to demonstrate and validate the water balance approach used in this study we use urban catchments where high temporal re- solution measurements of water in and water out of the catchment are available, thereby giving a reasonable level of control on the water balance. In addition, detailed digital elevation models (DEM) and in- formation of land use are needed. Two catchments in Norway were accordingly chosen for this study (Fig. 1): A catchment in Trondheim at Risvollan (RIS) and a catchment in Oslo at Grefsen-Kjelsås (GK). All simulations are carried out at a 10 min temporal resolution.
The RIS catchment is situated 4 km southeast of the city centre of Trondheim and is a research catchment of the Norwegian University of Science and Technology (NTNU). The catchment has a separate system for stormwater and sewage and the catchment size is 0.18 km2, with an elevation range of 82–129 masl. The area is mostly residential and fractions of impermeable (roads and roofs) and permeable areas are 0.49 and 0.51, respectively. The fractional area of roofs is 0.13, and 1500 residents are registered in this catchment (Matheussen, 2004).
The catchment has been the subject of many research projects in urban hydrology (seeDalen et al. (2016)and references therein), and Haile- georgis and Alfredsen (H&A) (2018) used this catchment for assessing their urban hydrological model. The results from H&A (2018) will herein be compared with results from our work.
The Grefsen-Kjelsås (GK) catchment is situated about 5 km north- east of the city centre of Oslo. The catchment has a combined storm- water-sewage system, a catchment size of 0.3 km2 and an elevation range of 170–188 masl. The area is mostly residential, with imperme- able/permeable fractions of 0.27 and 0.73, respectively. About 500
houses and 1080 residents are registered in this catchment (pers. com.
Bjørn Christoffersen, Oslo Municipality). According toSivertsen and Bomo (2016), freshwater consumption in Norway per person is, on average, 140 l/day. In addition, we include a 30% leakage from the water supply (SSB, 2017). Total wastewater per person, including
leakage, is hence 182 l/day. Note, however, that these numbers re- present national averages and may not be representative for this spe- cific catchment.
Runoff (i.e. stormflow in RIS and CSSflux in GK) from the two catchments are measured by the Norwegian Water Resources and Fig. 1.Study catchments. Yellow and green colours represent impermeable (IP) and permeable areas (P), respectively. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)
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Energy Directorate (NVE) (RIS) and by Oslo municipality (GK). The records lengths vary significantly. NVE has measuredflow at RIS since 1986 (though not continuously), and the installation of the station was motivated by a need for continuous measurements of urban runoff, including winter periods. We use four time series from RIS: RIS1 (1993–1-1 00:00 – 1994–10-4 15:20), RIS2 (1994–10-12 15:50 – 1997–7-25 18:50), RIS3 (1997–7-28 11:00 – 1997–9-23 07:20) and RIS4 (1997–11-18 16:00–1998–8-31 23:20). RIS3 is used for model calibration and the other time series for validation. Measurements at GK were carried out as a campaign over a short period, and only data for June–November 2010 are available. This time series is split into two: GK1 (2010–9-1 00:00 – 2010–8-31 23:50) and GK2 (2010–9-1 00:00 –2010–11-15 12:20). GK2 is used for calibration and GK1 for validation.
At RIS, runoff, precipitation and temperature are measured at the runoff gauging station. Precipitation data for GK, measured about 100 m from the outlet, are provided by measurements from Oslo mu- nicipality and temperature data are from The Norwegian Meteorological Institute located about 3 km north-west, at an elevation of 94 masl. (i.e. somewhat lower than the GK catchment) and at lower temporal resolution (1 hr) than the runoffand precipitation data.
In this study, we use two datasets from the national common da- tabase (FKB) with roads and buildings and the national areal resources database (AR5) landcover dataset from NIBIO (NIBIO, 2019). For GK we use a hybrid DEM with 0.5-m resolution containing buildings and roads, provided by the municipality of Oslo (Blom, 2014; PBE, 2014).
For RIS we use a DEM with 2 m resolution, downloaded from the Norwegian DEM data repository (https://www.kartverket.no/data/
hoydedata-og-terrengmodeller/). The 2 m resolution DEM required pre-processing to remove spurious data. We use the FKB datasets to generate a data layer representing the impermeable surfaces and AR5- class landcover data to generate the data layer representing the permeable surfaces. Using a toolkit for drainage networks available in GRASS GIS (Jasiewicz and Metz, 2011), we generate GIS layers con- tainingflow direction andflow accumulation, distance to outlet and the urban catchment boundaries. Based on the analysis of the upslope contributing area suggested bydi Leo and di Stefano (2013), we esti- mate the optimal contributing area (CA) for the extraction of the river networks.
3. Methods
3.1. Distance distributions in the urban landscape
In this study, we consider two possible urban landscape classes:
permeable (P) and impermeable (IP) surfaces (seeFig. 1). Impermeable areas (IP) are areas classified as roofs and roads, and all other areas are classified as permeable (P). Using GIS analysis, we derive the dis- tribution of distances (DDs) between points in the landscape and the closest reach of the“river”network: This DD is derived for each land- scape class (i.e. permeable and impermeable).Fig. 2illustrates how the DD’s are computed.
The DDs hence describes the configurations of the landscape classes with respect to the river network. The DD is an important model component as it partitions travel times between the slower rates offlow in the landscape and the relatively rapidflow rates in the river network.
In the absence of a natural river network in the urban landscape, the network of conduits for stormwater and sewage, which are sometimes combined (CSS), represent the river, i.e. rapid flow, network. In the case of insufficient information as to the structure of this network, we apply a GIS tool such as the multipleflow algorithm to create a sur- rogateflow network (Holmgren, 1994; Ehlschlaeger, 1989). We here- after refer to the network of conduits or the river network as the“river network”. From previous work (Skaugen and Onof, 2014), the shape of the different DDs has been shown to be exponential for distances be- tween points in the catchment and the river network and normal for
distances measured in the river network to the downstream outlet. The GIS analysis provides parameters (a mean distance for exponential distributions, and the mean and standard deviation for normal dis- tributions) of the DDs. The DD of a generic raingarden (area = 10 m2, 2.2 × 4.4 m) is approximated by a normal distribution, and is, similarly to the DDs for the landscape classes, the distribution of distances from points in the raingarden to the river network.Fig. 3shows boxplots of the DDs for the landscape classes, river network and raingarden for the two catchments.
3.2. Water velocities in the urban landscape
For natural catchments, velocities of subsurface- and overlandflow can be determined from a recession analysis (see Skaugen and Mengistu, 2016) in which high and low runoffare assumed to reflect high and low subsurface saturation states and velocities, respectively.
However, experience indicates that observed runofffrom CSSs is not suitable for such analysis since, amongst other issues, the presence of wastewater disturbs the recession signal. As an alternative, we have a) used overlandflow velocities for P and IP from the literature, b) used observed velocities from conduits, and c) calibrated the subsurface velocities. Observed saturated hydraulic conductivities from infiltration measurements bySolheim (2017)at GK andMuthanna et al (2018)at RIS serve as a validation for the calibrated subsurface velocities. The distribution of subsurface velocities corresponding to different levels of subsurface saturation is assumed to follow a two-parameter gamma distribution, followingSkaugen and Mengistu (2016). They define a recession characteristicΛ, from observed runoffseries, i.e.
Fig. 2.Extraction of the distance distribution from the GK catchment. Note the exponential shape of the histogram of distances.
= Q t − Q t+ t
Λ log( ( )) log( ( Δ )), (1)
where Q is the observed runoffandΔtis the temporal resolution of the observed series. A gamma distribution is then fitted to the empirical distribution ofΛ. The recession characteristic is related to the velocity v, by (Skaugen and Onof, 2014):
=
−
v d
t Λ
Δ (2)
where,
−
d is the mean of the DD. Input to DDDUrban is the shape (Gsh) and scale (Gsc) parameter of the gamma distributed recession char- acteristic Λ (Eq.1). Subsurface velocities are estimated from these parameters according to a procedure described inSkaugen and Onof (2014).
Table 1lists the various velocities and the characteristic distance- and time scales associated with the different flows for the study catchments GK and RIS.
We observe that the transport of water in the conduits is not re- solved using a 10 min temporal resolution and that the temporal re- solution of infiltration is highly uncertain. The velocity of infiltration is low, but the distances are short, whereas the velocity offlow through conduits is high, but the transport distance is long. InFig. 4we have illustrated this point by plotting travel time distributions for the pro- cesses that have a distribution of distances we can measure (infiltration is not such a process and its inclusion inTable 1above is for illustrative purposes). The travel time distributions are derived from randomly drawn distances (from their respective distance distributions) divided
by the characteristic velocity of the process. Certainly, the processes also have a temporal distribution of velocities, but in thefigure (as in the proposed model) velocity is a constant for each process.Fig. 4il- lustrates the temporal scale of the processes compared to that of the model resolution, and we see that travel times in the river network are resolved within one timestep, whereas the other processes are resolved in many timesteps.
3.3. DDDUrban, the model structure
DDDUrban models runoffdynamics, snow and evapotranspiration separately for the landscape classes P and IP (seeFig. 1). The simulated runoffgeneration of the landscape classes is coupled together with the river network through the DDs. The DDs form the basis for the runoff dynamics and, with estimated water velocities, provide the shape and scale of the unit hydrographs (UHs) used to distribute the water in time to the river network. The subsurface and overlandflows in DDDUrban usefive UHs in parallel. They all have the same shape, derived from the same DD, but have different temporal scales that are determined by differences in water velocity as a function of subsurface saturation. The five UHs (one for overlandflow and four for the subsurface) constitute the subsurface saturation layers with a given specific capacity and ve- locity. The specific capacity is derived according to Skaugen and Mengistu (2016)and considers the capacity of subsurface storage at steady-state conditions. The routing of water in the river network itself is carried out in the same manner as above; i.e. the DD of distances Fig. 3.Box plots of Distance Distributions (DDs) for a) different landscape classes, b) river networks and c) raingarden. Note that the empirical distributions for the landscape classes and the river network and raingarden are approximated by exponential and normal distributions, respectively.
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between points in the river network to the outlet together with the water velocity in the conduits constitute a UH that distributes the water entering the river network to the outlet as a function of time. The main difference between DDDUrban and the original DDD model is that in- filtration capacity is explicitly modelled for the different landscape classes. For P areas the infiltration capacity is equal to the mean sub- surface water velocity; 5.3*10−5m/s corresponds to 3.2 mm/minute, which is an extremely high precipitation intensity and close to the IDF estimate for the 50 year return period at Oslo (https://
klimaservicesenter.no/faces/desktop/idf.xhtml). Overlandflow occurs for these landscape classes if the capacity of the subsurface is exceeded, i.e. “saturation overland flow” (Dunne and Black, 1970), and, pre- sumably more seldom, if the infiltration capacity is exceeded. For IP, on the other hand, the infiltration capacity is set very low, although it is not set to zero, as streets covered with asphalt may have some
infiltration, (Ramier, et al., 2011; Fletcher et al., 2013). The subsurface contribution toflow from IP areas is nevertheless negligible and runoff from IP areas consists mainly of overlandflow.
When water infiltrates (i.e. the rainfall intensity is less than the infiltration capacity), the subsurface isfilled up from the base layer upward so that the slower (i.e. lower) layers of the subsurface are the first to get saturated. The velocity of the subsurfaceflow and level of saturation is, therefore, a monotonically increasing function. The function is, however, non-linear, due to the superposition of the UHs having different time scales.
Skaugen and Mengistu (2016) introduced a procedure for esti- mating the capacity of the subsurface. Based on the mean annual runoff (MAD) and a UH derived from the DD and the estimated mean velocity, an estimate of the mean subsurface storage can be obtained. The ca- pacity of the subsurface is estimated as the 99% quantile of the Table 1
Characteristic velocities, time and length scales for GK and RIS.
Flow Velocity [m/s] Mean distance of
systems [m]
Mean time scale [hrs] Time steps at 10 min temporal resolution
Source of velocity estimate
GK RIS GK RIS GK RIS GK RIS
Surface processes
Overlandflow, P-areas 0.007 0.007 47 31 1.9 1.23 11 7 Holden et al. (2008)
Overlandflow, IP-areas 0.01 0.01 45 69 1.25 1.9 8 12 Sedyowati et al. (2017)
Subsurface processes Infiltration (high values) and
saturated hydraulic conductivity (low values)
5.3*10−3− 5.3*10−5
5.3*10−3− 2.7*10−6
0.1–2 0.1–2 0.005–10 0.005–206 0.03–60 0.03–1236 Solheim (2017)(GK) and Muthanna et al. (2018)(RIS)
Subsurface Layer 1 0.00015 0.00012 47 31 87 71 522 430 Estimated subsurface velocity
profile according toSkaugen and Mengistu (2016). The horizontal velocity decreases with depth.
Subsurface Layer 2 7.9*10−5 6.3*10−5 47 31 165 137 991 820
Subsurface Layer 3 4.1*10−5 3.5*10−5 47 31 318 246 1910 1476
Subsurface Layer 4 1.4*10−5 1.3*10−5 47 31 932 662 5595 3974
Infrastructure and LID
Conduits 1.45 1.55 632 142 0.12 0.03 0.7 0.15 Mean velocity in conduits observed
by Oslo municipality (GK) and NVE (RIS)
Raingarden 3*10−5 3*10−5 2.6 2.6 24 24 144 144 Paus and Braskerud (2013)
Fig. 4.Example of travel time distributions for urban hydrological processes (GK) compared to the model re- solution. Note the difference in the scale of the x-axis.
Non-realistic negative travel times are caused by a den- sity function beingfitted to the distances drawn from the exponential and normal distributions. InFig. 4a) RN is the river network, OF_P and OF_IP are overlandflow for permeable and impermeable surfaces, respectively. In Fig. 4b) RG denotes raingarden, SS1-4 denote subsurface layers with decreasing velocity.
temporal distribution of the subsurface storage. In addition, one can estimate the capacity of the different subsurface layers through the temporal distribution of saturation (seeSkaugen and Mengistu (2016) for a more detailed description).
Table 2provides an overview of the DDDUrban model parameters, their description and method of estimation. Although there are many model parameters, most of them can be determined independently of model calibration. Calibrated parameters are shown in bold face in Table 2.
3.4. Raingardens
Low Impact Developments (LIDs) such as raingardens for storm- water retention represent important strategies for urbanflood mitiga- tion. The city of Oslo, as well as other Norwegian cities, have adopted the so- called Stormwater-3-Step-Approach (S3SA) (Lindholm et al.
2008) as the main instrument for developing sustainable urban drai- nage systems that incorporate LIDs. The three steps in this approach are 1) to handle low intensity precipitation locally at site through infiltra- tion (Becker et al., 2016; Solheim, 2017); 2) to delay rainfall with higher intensities as long as possible through infiltration and attenua- tion using, for example raingardens, wet or dry ponds, or constructed wetlands; and 3) to transport overflow and excess surface runoffafter heavy rainfall using dedicated, secureflow pathways.
An algorithm for a generic raingarden has been developed for the DDDUrban so that the potential effect and benefit of this type of LID can
be evaluated. The design of the raingarden is derived from the studies of raingardens in Norway undertaken byPaus and Braskerud (2013) and Dalen et al. (2012). The geometric shape of the raingarden is a rectangle with the length being twice the width (i.e. 2.2 × 4.4 m). The filter medium’s depth is 1 m, its porosity is 50% and its saturated hy- draulic conductivity is 3 * 10−5m/s (seeTable 1) (Paus and Braskerud, 2013; Dalen et al., 2012). From experience and empirical formulations, Paus and Braskerud (2013)recommend a ratio between the size of a raingarden and the IP-area to be 0.07 (7%), which implies that given the size of the raingarden proposed above (10 m2), every 140 m2of IP- area needs a raingarden if this measure is to be effective. Hence, if we specify the fraction of the total IP-area to be managed by a raingarden, we obtain the number of raingardens with specifications as above. The raingarden is located on P-areas, which is reduced accordingly, and flow generated from the specified fraction of IP areas is routed to the raingardens. The raingarden is drained at a bottom corner and the drained water is further transported by the river network. The DD for such a raingarden is estimated simply by calculating the possible dis- tance from a grid over the raingarden to the corner (seeFig. 3for the DD of a raingarden the size of 10 m2). We see fromFig. 4that the raingarden has a significant distribution of the input in time and has hence the capacity to delay water compared to runofffrom imperme- able surfaces.
Table 2
Parameters of DDDUrban for the GK catchment.
Parameter Value (GK) Description Method of estimation
Catchment characteristics
Hypsographic curve 170,177,179,180, 181, 182, 182, 183, 185, 188, 208
Elevation at the quantiles: 0,10,20,30,40,50,60,70,80,90,100. From GIS.
Latitude Longitude 59.95487, 10.78591 Location From digitized maps
MAD [m3/s] 0.00664 Mean annual runoff Determined from observations
Area [m2] 301,626 Catchment area. From GIS
Hydrological process parameters
θPc[–] 1.0 Correction factor for precipitation. Fixed
θSc[–] 1.0 Correction factor for precipitation as snow. Fixed.
θu[m/s] 1.5 Average annual wind speed Fixed
θWs[%] 0.05 Max liquid water content in snow. Fixed
θTX[°C] 0.5 Threshold temperature rain/snow. Fixed.
α0[–], D [–] 42.36, 413 Scale parameter of unit precipitation, and decorrelation length of spatial precipitation. Used to estimate the spatial distribution of snow. (same values for P and IP)
Estimated from observed spatial variability of precipitation (Fixed, according toSkaugen and Weltzien, 2016).
NOL[–] 5 Number of subsurface storage levels. Fixed, seeSkaugen and Onof, (2014).
R[–] 0.3 Parameter definingfield capacity, Fixed, seeSkaugen and Onof, (2014).
Distance distribution parameters
Pfrac, IPfrac [–] 0.73, 0.21 Areal fraction for landscape classes. From GIS
Pmax, IPmax [m] 240, 235 Max observed distance for landscape classes. From GIS
Pmid, IPmid [m] 47, 45 Mean of distance distribution for landscape classes. From GIS
Pz, IPz [–] 0.01, 0.0 Areal fraction of zero distance to the river network for landscape classes. From GIS RNmid, RNstd,
RNmax [m]
632, 332,1232 Mean, standard deviation and maximum of the distance distribution of the river network.
From GIS Velocity parameters
OF_P,OF_IP [m/s] 0.007, 0.1 Overlandflow velocity for landscape classes. From literature (seeTable 1above), Gsh,Gsh[–] 2.23, 0.000285 Shape and scale parameter of gamma distributed recession
characteristic. For determining subsurface velocity
Calibrated
θvr[m/s] 1.45 Mean velocity in river network. From observed runoff
Wastewater parameter
Number of residents 3200 Contribution of wastewater in combined sewers from residents (182 l/day, per person)
From municipality records Parameters for Raingardens
IPLIDfrac [–] 0.1 Areal fraction impermeable area managed by a raingarden Measured or specified
LIDIPfrac [–] 0.07 Areal fraction of raingarden compared to IP area, i.e. a raingarden area is 7% of the roof area.
Paus and Braskerud (2013) LIDvelocity [m/s] 3*10−5 Saturated hydraulic conductivity offilter material in raingarden. Paus and Braskerud (2013) LIDporosity [–] 0.5 Porosity of raingarden, determines the water holding capacity of the
raingarden.
Dalen et al. (2012)
LIDdepth [m] 1 Depth of raingardenfilter medium Paus and Braskerud (2013)
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3.5. Snow, snowmelt and evapotranspiration
DDDUrban uses procedures for the spatial distribution of snow and for snowmelt fromSkaugen and Weltzien (2016) and Skaugen et al.
(2018), respectively. The model for snow accumulation and melt is an energy balance approach and is forced by precipitation and tempera- ture. Proxy modelling simulates the different energy balance elements.
A new model development in this study is to use the simulated energy balance elements to simulate potential evapotranspiration using the Priestly-Taylor relation (Priestly and Taylor, 1972;Weiβand Mentzel, 2008):
⎜ ⎟
= ⎛
⎝ +
⎞
⎠
E α
γ R λ ρ
mm t Δ
Δ ( )1000
[Δ ]
p n
V W (3)
whereΔis the gradient of saturated vapour pressure:
⎜ ⎟
= +
⎛
⎝
∗ +
⎞ T ⎠
T Δ 2508.3 T
( 237.3) exp 17.3 237.3 ,
a
a 2 a
andγthe psychrometric constant:
c P 0.622λ
a a V
andλVis the latent heat pf vaporization andRnis the net radiation and calculated as:
= + −
Rn SWnet LA LT
whereSWnetis the net shortwave radiation andLAandLT are the at- mospheric and terrestrial longwave radiation, respectively. The para- meterαis a lumped representation of the turbulentfluxes and is equal toα=1.26for humid areas (Weiβand Mentzel, 2008).
Actual evapotranspiration,Ea,is the evaporation potential, scaled non-linearly by the amount of water in the subsurface:
⎜ ⎟
= ⎛
⎝
− ⎛
⎝− ∗ − + + ⎞
⎠
⎞
⎠
E E E M D Z G
min( , 1 exp 4 M )
a p p
(4) where M is the capacity of the subsurface, D is the deficit, Z is the soil moisture and G is the precipitation/snowmelt. The non-linearity of actual evapotranspiration as a function of the degree of soil saturation has previously been proposed by Chanzy and Bruckler (1993) and Arnell (2002. p50).
4. Results
DDDUrban was calibrated using the timeseries GK2 and RIS3 and validated on the remaining time series. Only two parameters,Gshand Gscwere calibrated, and all other model parameters were either de- termined from GIS or the literature (seeTable 2). DDDurban is coded in Julia (https://julialang.org/) and the Kling Gupta efficiency criterion (KGE; Gupta et al, 2009; Kling et al., 2012) was optimized using the global optimization package BlackBoxoptim (https://github.com/
jbrea/BlackBoxOptim.jl). The KGE ranges from 1 for a perfect simula- tion to minus infinity and assesses the errors in the mean bias and the bias in the variance, in addition to the correlation between observed and simulated values. The widely-used Nash-Sutcliffe efficiency cri- terion (Nash and Sutcliffe, 1970) only assesses the correlation, and other factors, such as the bias must be assessed using separate criteria during the calibration. In addition, due to the differing definitions of these two criteria, their scores are not directly comparable (Knoben et al., 2019).
Fig. 5shows examples of simulated and observed time series for GK (a) and RIS (b). To achieve a suitable calibration at GK, we had to in- crease the wastewater contribution significantly since the reported number of residents (1080) and their estimated daily water use of 180 l/day only gives a total wastewater runoff of 0.002 m3/s. This amount does not correspond to the dry-weather runoff, which is
measured to be about 0.006 m3/s. This discrepancy of 0.004 m3/s has also been observed by Oslo Municipality, and cannot be explained by the estimated water use or by the local hydrology. The reason for this discrepancy may be a significant water leakage into the system, un- known industrial discharge or simply measurement errors. We observe that the simulated runoffis in good agreement with the observed runoff for both catchments. Runofffrom both P areas and IP areas contribute to a good agreement in the timing and the level of the peakflows be- tween simulated and observed runoff, although the runoff volume during peakflow appears to come mostly from IP areas.
Table 3shows the KGE skill scores for calibration (RIS3 and GK2) and validation. High values of KGE were obtained for RIS3 and GK2 and lower values for the validation periods. We note that flow from permeable areas makes a steady contribution to the totalflow corre- sponding, on average, to the fraction of permeable area. For GK we also observe that the actual evapotranspiration drops significantly from the summer months to (GK1) to autumn (GK2), but is, on average a sub- stantial element of the water balance. The simulated annual actual evapotranspiration at RIS for the years 1995 and 1996 is 196 mm and 200 mm, respectively. These estimates cannot be verified against ob- served data at the catchment scale, but are in good agreement with the long term (1983–2012) mean of actual evapotranspiration of 204 mm/
year, estimated for an area of 9 km2, which comprises RIS, by a gridded rainfall runoff model using a Penman-Monteith formulation and gridded meteorological input (Huang et al., 2019).
4.1. Saturation excess overlandflow
InFig. 6 we observe that for prolonged, but not necessarily very intense precipitation events at RIS, the contribution from the P-areas suddenly becomesflashy (30th of January 1997,Fig. 6a, and 30th of March 1997,Fig. 6b).
Fig. 7shows the saturation deficit for the same time period as in Fig. 6, and illustrates that for theseflashy events, the deficit becomes zero, i.e. the subsurface isfilled to capacity and additional precipitation is routed to the river network as overlandflow. Theflood peak late March 1997 (Figs. 6 and 7b) is the highest peak on record for RIS in the period 1993–1998. Although this peak is not simulated particularly well, we see that runofffrom the impermeable areas alone is not suf- ficient to explain the observedflood peak. Additional quick runoffis needed. These are examples of theflood generating process termed
“saturation excess overlandflow”(Dunne and Black, 1970).
InFig. 8, we have plotted the hydrograph and precipitation together with the relative contribution of runofffrom P- and IP areas for two events at RIS (30th of January 1997, a, b, and 8th of June 1995, c, d) In Fig. 8b we see that at peakflow the contribution of runofffrom P areas is about 30–40% of the peakflow and almost 60% for the second peak, whereas forFig. 8d the runoffcontribution from the P areas at peak flow is very small. These results emphasize thatflood generating pro- cesses in urban areas include overlandflow from permeable areas, and that models need to include subsurface processes in permeable areas in order to simulate the dynamics of saturation and their contribution to peakflows.
4.2. Snow and snowmelt
Fig. 9shows an example of observed and simulated runoffduring the snowmelt season at RIS. The blue line in the bottom panel shows simulated snow water equivalent (SWE) and we see that the model si- mulates the observed diurnal variations in runoff due to snowmelt while SWE > 0. Thefirst half of the melting season seems adequately simulated, but the model does not fully capture the reduction in melting intensity at mid-melting season. The accumulated volumes of simulated and observed snowmelt appear to be in reasonable agreement, but the melt-out in the model is too early. It must be noted that changes in the spatial distribution of snow caused by the snow removal (clearly most
(caption on next page) 9
important for the roads, i.e. the IP-areas), have not been accounted for in DDDUrban.
4.3. Calibrated subsurface velocities
Table 4shows the calibrated values ofGshandGsctogether with the corresponding estimates of mean subsurface velocity. We apply Eq.(2) and the meanΛis estimated asGsh*Gsc.
The calibrated mean velocities for GK and RIS are quite similar and the calibrated velocity at GK is close to the saturated hydraulic con- ductivity measured by Solheim (2017) using a double ring in- filtrometer. The calibrated velocity for RIS is in the range of measured saturated conductivity reported byMuthanna et al. (2018)although the values in the study ofMuthanna et al. (2018)vary considerably (i.e. by an order of magnitude, 1.5*10−6 – 5.5 *10−5 m/s). These results, nevertheless, suggest that carefully measured saturated hydraulic con- ductivity may serve as an estimate of the mean subsurface velocity that can be used in the model and hence make the model less dependent on calibration.
4.4. Comparison withHailegeorgis and Alfredsen (2018)
The model of H&A (2018) was calibrated for different time periods (Summer (S) and Autumn (A)) from RIS and was then used to in- vestigate how well the calibrated parameter set performed for times series not used in the calibration, i.e. a model validation. The time periods used for validation in H&A (2018) are within the validation periods in this study, andTable 5compares the Nash-Sutcliffe efficiency criterion (NSE) of H&A (2018) and DDDUrban. The average perfor- mance of DDDUrban is slightly better, but the comparison is not straightforward in that when calibrating the DDDUrban we optimized KGE, not NSE which does not penalize bias.
4.5. Modelling the effect of raingardens (LIDs) at the catchment scale We tested the model for raingardens at GK by assuming that 10, 30 and 50% of the IP-area is managed by raingardens (Fig. 10).Fig. 10b) shows the reduction in peakflows for the six significant peaks seen in Fig. 10a).Fig. 10a) also shows the effect of 30% of the IP-area managed by raingardens by comparing a simulation using 177 raingardens with a simulation without raingardens. The raingardens effectively delay the runoffthat would otherwise be rapid runofffrom IP areas. InFig. 10b) we see that for raingardens with a depth of 1 m, there is a significant reduction in peak flow even with relatively few raingardens and the reduction increases with the number of raingardens. If, however, we reduce the depth of the raingarden to 0.5 m there is an increase in peak flow for precipitation events that follow thefirst event closely. This is because the raingardens arefilled to capacity during thefirst event and produce overlandflow during the subsequent precipitation event. This
overlandflow comes in addition to the delayed response of the rain- gardens from thefirst event. This result highlights the importance of including antecedent moisture conditions in the design of LIDs.
5. Discussion
As stated in the introduction a tool for assessing urban hydrology at data-scarce sites is needed, and this poses problems that are similar to those encountered when predicting runoff at ungauged sites (see Blӧschl et al., 2013on theory for prediction in ungauged basins (PUB)).
In this respect it is interesting to study the sensitivity of the two para- meters calibrated for DDDUrban in this study and evaluate the errors if these parameters were to be estimated without model calibration. The sensitivity of the shape and scale (Gsh andGsc) of the gamma dis- tributed subsurface velocity was therefore tested by keeping the pro- duct (Gsh×Gsc) constant, but varyingGsh(andGsccorrespondingly) between 0.5 and 3.0. This corresponds to the case in which we have an estimate of the mean subsurface velocity from infiltration measure- ments or some other source but need tofix the shape and scale para- meters of the gamma distribution for the simulation.Fig. 11shows, for RIS3, how the KGE criterion and the subsurface capacity M, change with the shape parameter of the velocity distribution.
KGE values are acceptable for all the simulations but are clearly best forGshvalues above 2.0. The effect of changing the shape parameter of the distribution on the subsurface capacity M, is quite dramatic in that M forGsh= 3.0 is reduced by more than 50% compared to that for Gsh= 0.5. This could have consequences for the number of times the catchment in subject to overlandflow from the permeable areas, but we see that M stays relatively constant forGshvalues above 2.0.
An important set of model parameters that is determined somewhat subjectively control the density of the GIS derived river network. We have used GRASS GIS in this analysis and this tool suggests a value for the contributing upslope area (CA) necessary to initiate channelised flow. The proposed value is the minimum area required for the derived flow accumulation. (https://grass.osgeo.org/grass78/manuals/addons/
r.threshold.html). However, a different CA can be chosen and the larger the CA the less dense the corresponding river network. In DDDurban, the choice of a CA value and the subsequent configuration of the river network is very important since it determines the DDs and hence the subsurface velocities, subsurface reservoir capacity, frequency of overlandflow from permeable areas and evapotranspiration. We have calibrated DDDUrban at GK for different river networks (different CAs), andTable 6shows the effects on KGE, calibrated velocities, subsurface reservoir, mean distance for P areas and subsurface reservoir capacity, M.
We see fromTable 6that the choice of CA has an impact on per- formance (KGE) and the estimated physical properties of the catchment.
With generally longer travel distances for higher CA (less rivers), the velocity of subsurface water has to increase in order to match the Fig. 5.Simulated and observed runoffat GK a), and RIS b). The black line, Q(Observed) is the observed runoffwhereas the magenta line Q(Simulated) is the simulated total runoff. The green line Q(SimPermable) is the runofffrom P- areas and the red line Q(SimImpermeable) is the runofffrom the IP areas. The horizontal blue line inFig. 5a (GK) represents the waste-water contribution which is significant at GK(a) and zero at RIS (b). The skill scores KGE and NSE are for the time periods shown in the plots. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)
Table 3
Skill score (KGE), bias, evapotranspiration and average fraction offlow from P-areas for RIS and GK. Bold face indicate timeseries used for calibration.
Period KGE Bias Ea/Precip Average fractional contribution offlow from P areas
RIS1 1993–1-1 00:00–1994–10-4 15:20 0.56 1.03 0.29 0.46
RIS2 1994–10-12 15:50–1997–7-25 18:50 0.62 1.05 0.21 0.48
RIS3 1997–7-28 11:00–1997–9-23 07:20 0.92 1.03 0.19 0.45
RIS4 1997–11-18 16:00–1998–8-31 23:50 0.6 0.86 0.30 0.45
GK1 2010–6-30 10:0–2010–8-31 23:50 0.69 1.04 0.42 0.57
GK2 2010–9-1 00:00–2010–11-15 12:20 0.81 0.90 0.16 0.70
Fig. 6.Runoffand saturation excess overlandflow from P areas at RIS for January 1997 a) and March 1997, b).
11
Fig. 7.Runoff, saturation excess overlandflow and subsurface deficit at RIS a) for January 1997 and b) March 1997.
observed runoffdynamics. The reservoir capacity increases as an in- verse function of the subsurface velocity as described inSkaugen and Mengistu (2016). The CA suggested by GRASS GIS appears to work well at both GK (CA = 10000 m2) and RIS (CA = 500 m2). For GK, the KGE value is slightly better for higher CA than CA = 10000, perhaps at the cost of unrealistic subsurface velocities. Further investigation on why the suggested CA appears to work well at these sites and the possible dependence of the procedure on the spatial resolution of DEMs needs to be carried out. The sensitivity analysis of the gamma parameters of the subsurface velocity distribution and the CA are promising for the po- tential for applying the model at data scarce sites. Further investigation on how DDDUrban performs at fully ungauged sites will be a topic for future work.
The simple analysis of the travel time distributions of the relevant flow processes at GK was conducted in order to distinguish those pro- cesses that have a temporal resolution that is adequately described given the time step used in the model simulations (see Table 1and Fig. 4). The analysis indicates that infiltration and theflow transport in pipes are very quick processes that are not resolved by a model time step of 10 min and hence do not contribute to the shape of the simu- lated hydrographs. The travel time analysis is simple but illustrates that the hydrological dynamics of urban catchments are largely determined by water transport on surfaces and in the subsurface and that simple routing schemes for the transport of water in the pipes probably suffice.
Saturation excess overlandflow appears to be an importantflood generating process, also in urban areas having zones of permeable surfaces, and highlights the importance of modelling the dynamics of the subsurface processes. The two examples analysed inFigs. 6 and 7 show that runofffrom impermeable areas do not suffice to create the observed peaks and quick runofffrom some other source is needed. In DDDUrban this additional quick runoffis contributed by overlandflow generated from permeable areas that become saturated. This seems very
plausible for this environment and gives confidence in the model structure; i.e. the calibrated velocities determine the subsurface capa- city which again enablesflood generating processes such as saturation excess overlandflow. Urban hydrological models such as SWMM can incorporate various infiltration models (Green-Ampt and Horton, see Rossmann and Huber, 2016) so thatflood generating processes such as infiltration excess overland flow can be modelled. From the results presented in this study, wefind that, at least in the studied area, ex- treme precipitation intensities are needed for such a process to take place in DDDUrban and thatsaturationexcess overlandflow appears to be a more important process to incorporate in urban hydrological models. Testing DDDUrban at sites where the precipitation intensity is more likely to be higher than the infiltration capacity, hence enabling infiltration excess overlandflow, needs further investigation.
In Norway, snow hydrology remains important, also in urban areas.
There are many uncertainties associated with the modelling of snow accumulation and melt. The spatial distribution of snow, for example, has a particularly significant impact on the timing and dynamics of snowmelt (Essery and Pomeroy, 2004). Changes in the spatial dis- tribution of snow through snow removal on roads and snow on roofs exposed to drifting call for a more detailed model of snow accumulation and melt in urban catchments (seeMatheussen, 2004). In this study, the parameterisation of the snow distribution for the RIS simulations is based that for a natural catchment in the Trondheim region. Whether this is the sole reason for the failure in the timing of snowmelt is not clear, but there is clearly a potential for improvements in this compo- nent of DDDUrban if it is to be used in snow-rich areas.
Our DDDUrban simulations indicate that, at least for the two study catchments considered, all of the precipitation that falls within the catchment boundariesfinds its way to the conduits or is evaporated.
The water balance in GK is uncertain, and standard water-use and si- mulated runoffare less than theflow volume measured in the conduits.
Fig. 8.Relative contribution of runofffrom P and IP areas for two events at RIS, 30 th of January 1997 (a, b) and 8th of June 1995, (c, d).
13
If rainfall is somehow was lost in the catchment due to unknown pathways we would expect the simulated runofftogether with water use to be higher than what is measured in the conduits. At RIS, the water balance seems reasonable in that simulated and observed runoff are almost identical for three out of four periods. No correction of the observed precipitation input has been carried out in the simulations, and the evapotranspiration routine has no calibrated parameters.
However, actual evapotranspiration is, of course a function of subsur- face storage at any point in time, and this capacity is indirectly cali- brated through the calibrated velocities (Skaugen and Mengistu, 2016), i.e the parametersGscandGsh. That all non-evaporated water appears in the conduits implies that lateral, subsurfaceflow enters the conduits
through cracks in the pipes and possibly via subsurface drainage sys- tems around buildings that are often coupled to the sewer- or storm- water networks. The intention of the combined sewage stormwater network is to transport only wastewater and possibly runofffrom im- permeable areas to water treatment plants, and water that infiltrates is, in principle, not supposed to challenge the capacity of these facilities.
This study indicates, however, that infiltrated, subsurface water is a significant part of the urban water budget in many areas, i.e. the sub- surface water storage is dynamic and dedicated pathways for these fluxes are also needed.
The comparison of skill scores for DDDUrban and the model of H&A (2018) for the validation periods in Table 5 shows that DDDUrban performs better, both on average and for 3 out of 5 time periods. The time periods of validation are very short (1–2 days), excepting the fourth period which is 4 months in length. The brevity of the time periods means that the comparison is uncertain. The model of H&A (2018) is distributed and highly complex, and simulates many processes assumed to be relevant for urban hydrology, such as infiltration excess, depression storages and two-wayflow between subsurface storage and Fig. 9.Simulated and observed runofffor a melting period at RIS together with simulated SWE (blue line, bottom panel). (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)
Table 4
Calibrated values ofGshandGscand the corresponding velocities (Eq.2).
Gsh Gsc Pmid [m] Mean velocity [m/s]
GK 2.23 0.00029 47.0 5.1*10−5
RIS 2.97 0.00026 31.0 4.0*10−5
Table 5
NSE of H&A (2018) and DDDUrban for time periods of validation. The NSE of H&A (2018) is the averaged value over the different parameter sets.
Period NSE(H&A,2018) NSE(DDDUrban)
RIS1(S) 1993–8-1 00:00–1993–8-1 12:00 0.48 −0.27
RIS1(S) 1994–9-28 00:00–1994–9-30 00:00 0.17 0.61
RIS2(S) 1995–6-9 00:00–1995–6-11 00:00 0.21 0.80
RIS2(SA) 1995–6-1 00:00–1995–10-1 00:00 0.56 0.69
RIS4(S) 1998–8-15 12:00–1998–8-15 20:00 0.41 0.36
Mean 0.37 0.44
the urban drainage network. The model of H&A (2018) performs quite well in calibration, producing NSE values ranging between 0.65 and 0.94. For the validation periods however, the NSE values ranged be- tween−0.46− +0.81. For the fourth, longer period, the calibrated NSE of H&A (2018) was 0.76, whereas for the validation the NSE ranged between 0.23 and 0.81 using the different parameter sets. For this period DDDUrban obtained NSE = 0.69. Such a discrepancy between skill scores for calibration and validation periods suggests a lack of robustness in the model that can be associated with over- parameterization (Kirchner, 2006). DDDUrban only has two parameters to calibrate and we see from Table 3, where the validations are
performed for timeseries of some length that the variability in the skill scores for the validation periods is quite low.
The catchment scale effect of LIDs (raingardens) has been tested and hence addresses some of the unresolved questions put forward byElliott and Trowsdale (2007)and more recently byEckart et al. (2017). They highlight the need for investigating the“scaled-up”effect of LIDs from lot- to catchment and regional scales. InFig. 10we can see that even a quite modest use of raingardens, 60 raingardens in a neighbourhood of 500 houses, attenuates the investigated flood peaks by about 10%, which may make a difference in the number of overflows of wastewater to sensitive recipients. In addition, by varying the number of rain- gardens and their specifications the implementation of the LID module in DDDUrban provides a tool for planning (seeEckart et al., 2017) and more specifically enables quantifying the effect of step 2 in the S3SA.
Such LIDs may be more cost effective for mitigating the effect of in- creased peakflows due to urbanization than increasing the capacity of the urban drainage network. Unofficialfigures suggest a cost of 10 k€ per raingarden and 4 k€ per meter for the installation of pipes (pers.com B. Braskerud at Oslo Municipality). The cost for 60 rain- gardens hence is equivalent to the cost of only 150 m of new pipes. The possible adverse effects of under-designed raingardens, is however, of Fig. 10.a) Observed and simulated runoffwith and without raingardens at GK, and b). Peakflow reduction for different number of raingardens with 1 m depth and 0.5 m depth.
Fig. 11.Sensitivity analysis of how various combinations ofGshandGscin- fluence the performance of DDDUrban and the estimated subsurface capacity M, for RIS.
Table 6
The effect of using different CA and river networks at GK. The CA marked with an * is the suggested CA by GRASS GIS for GK and is the CA applied in the results of this study.
CA [m2] KGE Mean velocity [m/s] M [mm] Mean distance P areas [m]
1000 0.53 9.6*10−6 79.1 13.5
2500 0.6 1.43*10−5 84.1 19.4
5000 0.72 2.88*10−5 79.8 31.9
10000* 0.81 5.1*10−5 63 47.0
15,000 0.82 7.6*10−5 57.8 57.3
20,000 0.84 8.0*10−5 58.7 72.2
25,000 0.82 9.6*10−5 58.9 75.4
15
