Please cite as : hen. S., jordjević S., Leandro J. and Savić. (2007). The urban inundation odel with bidirectional The urban inundation odel with bidirectional flow interaction between 2 overland surface and 1 sewer networks Le odèle d'inondation urbain avec interaction des flux bidirectionels entre 2 surfaces éergées et 1 réseaux d'égout lbert S. hen, Slobodan jordjević, Jorge Leandro, ragan. Savić entre for Water Systes, University of xeter Harrison uilding, North Park Road, xeter, X4 4Q, United Kingdo RÉ SUMÉ et article développe un odèle nuérique intégrant surface et égouts pour l'étude des processus de ruisselleent en ilieu urbain. Les courbes précipitations ruisselleent et les conditions d'écouleent dans les réseaux de drainage sont basées sur le odèle 1. Les écouleents en surfaces sont déterines par le odèle 2. ien que les deux odèles soient résolus par des algorithes différents et a des échelles différentes, la connection est possible, par l'interédiaire des bouches d'égouts. Les effluents et influents au travers de ces dernières sont déterines par les équations correspondant aux déversoirs et orifices. fin de garantir un interfaçage adéquats, un soin particulier est consacre a la synchronisation teporelle entre les odèles. STRT n integrated nuerical odel is developed in the study for siulating the runoff processes in urban areas. 1 odel is used for calculating the rainfall-runoff hydrographs and the flow conditions in drainage networks. 2 odel is eployed for routing flow on overland surface. oth odels are solved by different nuerical schees and using different tie steps with the flow through anholes adopted as odel connections. The effluents and influents via anholes are deterined by the weir or the orifice equations. Tiing synchronisation between both odels is taken into account to guarantee suitable odel linkages. KYWORS adaptive tie step, coupled odels, tiing synchronisation, urban flood 1. INTROUTION In urban areas, the stor sewer networks are coonly built for conveying runoffs caused by pluvial rainfall. Therefore, the condition of stor sewer syste is highly related to its perforance with respect to sewer flooding. Many odels have been developed for assessing the hydraulic perforance of drainage networks. The Stor Water Manageent Model (SWMM) developed by the U.S. nvironental Protection gency (Rossan et al. 2005) is coonly used not only for hydraulic evaluation but also for water quality odelling in sewage systes (Ha et al. 2003). ecause SWMM is a freeware, its hydraulic engine is widely used in coercial software, including P SWMM (oputational Hydraulics Int. 2002), XP SWMM (XP Software Inc. 2002) and MIK SWMM (HI Software 2002). In addition, various other software packages that use other hydraulic solvers, such as MOUS (HI Software 2003) and Infoworks-S (Wallingford Software Ltd. 2006), exist. Most of those odels use the water stage-volue curve to deterine the flood depth caused by anhole surcharge, but cannot properly siulate the water oveent on the ground surface. Hence, the dual drainage concept has been often introduced to describe the flow interactions between the above ground and below ground systes (jordjević et al. 1999; Nasello and Tucciarelli 2005). Natural flow paths and retention basins are regarded as the ajor drainage syste for routing the surface flow, while sewer pipes, anholes and inlets are considered as the inor drainage syste for conveying the sub-surface flow. oth drainage systes are odelled by 1 hydraulic odels and linked through anholes and inlets to reflect the bi-directional interactions between subsurface and surface networks (olle et al. 2006; Mark et al. 2004; Schitt et al. 2005). When the ajor drainage syste capacity is insufficient to handle the runoff caused by pluvial events, the overland flow occurs. The 1 odelling approaches are usually liited to circustances where overland flows are confined to predeterined flow paths, while the 2 overland flow odels should be eployed to siulate the oveent of surface runoff caused by large surcharges (arr and Sith 2006; hen et al. 2005; ey and Kaioka 2006; Horritt and ates 2002).
Please cite as : hen. S., jordjević S., Leandro J. and Savić. (2007). The urban inundation odel with bidirectional 2. MTHOOLOY In this study, flows in drainage pipes and over the ground surface were routed by the 1 sewer network odel SIPSON (jordjević et al. 2005) and the 2 overland flow odel UIM (hen et al. 2005), respectively. oth odels use different nuerical schees and tie steps with the discharge through anholes adopted as odel linkages. The drainage runoff and surcharge effluents were calculated by SIPSON for every tie step and treated as point sinks and sources, correspondingly, in the UIM odel within the sae tie interval. ischarges are deterined by weir or orifice equations by taking account of the hydraulic heads at anholes and ground surface. 2.1. SIPSON SIPSON consists of two coponents, the hydrological and the hydraulic odels. The hydrological odel, MUS (Radojković and Maksiović 1984), was developed for coputing rainfall-runoff hydrographs for sub-catchents to be used as inputs for anholes in the hydraulic odel. The hydraulic odel is used to analyse the dynaic flow behaviour in 1 drainage networks. It siultaneously solves continuity equations for network nodes, energy equations for nodes and pipe/channel ends, the coplete Saint Venant equations for flow in conduits and streets, and equations for other link types (pups, weirs, etc.). 2.2. UIM UIM siulates flow oveents on the ground surface. The 2 non-inertia flow equations, which are a siplified for of the Saint Venant equations, are adopted in the odel. The conveyance reduction factor based on the building coverage ratio and the storage volue of underground structures are considered in UIM to reflect the influences caused by buildings on flow oveents. Like any other 2 odels, the coputing of overland flow is tie-consuing when the proposed odel is applied to cases with assive nuber of grids. onsequently, the adaptive tie step is introduced to speed up the siulations. The tie step in the 2 odel is adjusted autoatically based on the ourant criterion (Hunter et al. 2005; Yu and Lane 2006) such that larger tie steps could be chosen whenever the nuerical stability is satisfied. The tie step used in SIPSON is generally larger than the ones used for UIM. The default and upper bound of tie steps in UIM are the sae in SIPSON, i.e., t t 0 1d. y the end of coputation for each tie step, the ourant condition is checked based on the latest calculated water depth and velocities for setting the next tie step: x t 1 (1) gd u t 1 gd y v where, is the index of the tie step; t is the estiated tie step length [s] used in UIM for 1 th step; 1 d h z is the water depth [] of the coputing grid at th step; u and v are velocity coponents [/s] along x and y directions, respectively. Theoretically, qs. (1) and (2) should be verified grid by grid for having the best value over the entire doain, nevertheless, the global axiu values d 2 d _ ax, u 2 d _ ax, and v2 d _ ax are deeed to be satisfactory and are used for saving the coputing effort. 2.3. Model linkage Two distinct odels are cobined for siulating the flow dynaics in sewer networks and on overland surface. The odels are executed individually and linked by exchanging inforation obtained at proper locations and ties for appropriate linkages. In this study, the grids containing anholes are considered as the locations where interactions occur. The tie step used in SIPSON is also regarded as the tiing for odel linkage. 2.3.1. Interacting discharge The bidirectional interacting discharge is calculated according to the water level difference between sewer network and overland surface. The upstrea and downstrea levels for deterining discharge are defined as hu ax hh, h2 d and h in hh, h2 d, respectively, where h h is the hydraulic head [] at anhole and h is the water surface elevation [] on the overland grid. The ground levels acquired fro sewer network dataset usually differ fro the values extracted fro the digital terrain odel (TM). oth values are correct because they represent different attributes of the syste. The ground level z h top [] used in sewer odel reflects the point value on the top of a anhole, whereas, the grid elevation z [] in the overland flow odel stand for the average level of the topography within a grid. Inconsistency between two datasets is often present when the anhole is located at local peak or depression inside the grid as shown in igure 1. z Physical terrain z htop z htop Physical terrain z (2) Surface rid Surface rid igure 1 Inconsistency between top elevation of anhole and averaged grid elevation The crest elevation zcrest ax{ zh, z2 } top d [] is, therefore, defined for coputing the discharge between both odels. Three types of linkages are considered for applying different discharge equations. ree weir linkage
Please cite as : hen. S., jordjević S., Leandro J. and Savić. (2007). The urban inundation odel with bidirectional The free weir equation is adopted when the crest elevation z crest is between the values of the upstrea water level and the downstrea water level h, as shown in igure 2. The discharge is calculated by using q. (3). Q sign h h c w g h z (3) 3 2 h w 2 U crest where, Q is the interacting discharge [ 3 /s], whose positive value eant surcharge flow fro sewer toward overland and negative value eant drainage flow fro surface into sewer; c w is the weir discharge coefficient; w is the weir crest width []; and g is the gravitational acceleration [/s 2 ]. h h igure 2 ree weir linkages Suberged weir linkage The suberged weir equation is used (igure 3) when both water levels at anhole and overland grid are greater than the crest elevation and the upstrea water depth above the crest, hu zcrest, is less than h / w, where h is the anhole area [ 2 ]. q. (4) is eployed for deterining the interacting discharge. 1 2 Q sign h h c w g h z h h (4) h w 2 U crest U h h igure 3 Suberged weir h / w or orifice h / w linkages U h Orifice linkage The anhole is considered fully suberged (igure 3), when the upstrea water depth above the crest hu zcrest is greater than h / w for the suberged weir linkages. The orifice equation is used for calculating the interacting discharge. 1 2 Q sign h h c g h h (5) h o h 2 U where, c o is the orifice discharge coefficient. 2.3.2. Tiing synchronisation The flow dynaics in drainage networks and overland surface are solved by two separate odels using different tie steps. The tiing synchronisation becoe an iportant issue for connecting both odels appropriately, in particular because variable tie steps are used. The exact values in both odels are exchanged at the sae tie, as shown in igure 4, to prevent unnecessary errors being introduced to odel counication. The estiated tie step t, by 1 using qs. (1) and (2), is restricted to q. (6) for atching the next synchronisation tiing. t 2 ax ( d 1 1 1 2 ), synl d i di (6) 1 where, t is the tie step size [s] used for 1 th step; T 1 syn l is tie of the previous ( l th ) synchronisation [s]; t i1 is the total length of tie steps [s] after steps of calculations in UIM; ( T ) i syn t l 1d t i1 is the tie left i [s] before next ( l 1 th ) synchronisation. t 0 t T synl t 1d Synchronised syn l 1 t T Synchronised U h t t t i1 i Synchronised Unsynchronised 3. PPLITION igure 4 Synchronized and unsynchronized tiing between 1 and 2 odels Two exaples are presented: the artificial study area that was eployed to analyse and discuss the detailed flow interactions and odel application to the real world case study. The intention was to test whether the proposed odel can effectively and siultaneously describe the bidirectional flow interactions and the surface runoff oveents. 3.1. Idealised case study The idealised artificial case was used to deonstrate the ability of the proposed odel to siulate bidirectional interactions between the sewer network and overland surface. The 1500 x 1000 2 study area shown in igure 5 consisted of three inclined planes. Surface slopes were 0.002, -0.002 and 0.002 in x-direction and 0.001 in y-direction. Ten anholes and ten pipes were installed for draining the surface runoff and the sub-catchents (shown in igure 5).
Please cite as : hen. S., jordjević S., Leandro J. and Savić. (2007). The urban inundation odel with bidirectional 1 had the lowest elevations of the ground surface and the drainage syste, and was connected to the outlet. 3 was located in a local depression 0.4 below the elevation of the exit point. subcatchent 06 07 08 09 10 levation anhole pipe 01 02 03 04 05 igure 5 levation, drainage network and sub-catchents of idealised case The design rainfall intensity for the drainage syste was 10 /h. six-hour rainfall event was applied herein for siulation. The rainfall intensity started fro zero and increased to 20/h in the first hour, kept constant for four hours, and decreased to zero in the sixth hour. The duration of nuerical experient was 12 hours to siulate the receding process of surface inundation. The rainfall-runoff hydrographs were calculated by MUS and iposed as inflows at anholes. igure 6-(a) reveals that anholes becae surcharged when the inflow discharge had exceeded the design capacities of pipes and the hydraulic head had reached the surface elevation. The surcharged flow spread along the ground surface toward lower elevations and caused surface inundation as displayed in igure 6-(b). The overflow between sub-catchents occurred when the flood extent reached the lowest exit point of the sub-catchent boundary as shown in igure 6-(c). The surface runoff kept oving on overland until it reached a downstrea anhole where the hydraulic head was below the surface elevation and the drainage capacity was available. fter the rainfall stopped, the flows in sewer pipes began decreasing such that the flood extent was reduced as a consequence of the surface runoff had returned to the sewer syste. (a) T = 0.75 h (b) T = 2.00 h (c) T = 5.50 h 3.2. Keighley case study (d) T = 12.00 h igure 6 Siulation results of idealised case The Stockbridge region in Keighley (radford, UK) shown in igure 7-(a) was chosen for practical application. The region between the River ire in the south and the Leeds and Liverpool anal in the north is a flood prone area. The northeast part next to the anal is residential area with dense buildings. The rest of the region is green lands with a pond situated next to the River ire. The ajor stor drainage syste passes along the roads in residential area, as highlighted in igures 7-(b-e),. The fluvial flooding fro the River ire was the ajor factor that led to inundation in the region. Nevertheless, the analysis was focused on the consequence of a pluvial event in this study. n extree rainfall was assued in the upstrea catchents and within the region. The resulting runoff was too large for the drainage syste capacity. The TM with buildings was obtained fro the LiR data, and resapled as 2 x 2 grid resolution for overland flow siulation. The tie steps ranged fro 0.5s to 5s with an average 0.732s which eant that the adaptive tie steps saved around 31% of coputing effort copared to using the unifor iniu step size in UIM. The flow surcharged fro s, and oved along the surface toward lower lying areas. Not only the preidentified pond was filled but also two other inor depressions were inundated. The water was trapped in the ponds and flood extent kept increasing due to the lack of drainage inlets inside ponds. The flow surcharged fro anholes,, and was confined by the buildings and oved along the streets until it reached downstrea anholes where the drainage capacity was available. Part of the water was detained in local depressions next to the buildings near. The siulation results clearly indicated the potential inundation area caused by pluvial rainfall although there was no overbank flooding fro the channels.
Please cite as : hen. S., jordjević S., Leandro J. and Savić. (2007). The urban inundation odel with bidirectional Leeds & Liverpool anal (b) Siulation result at T = 30 in (c) Siulation result at T = 40 in Pond River ire (a) Stockbridge region in Keighley (d) Siulation result at T = 50 in (e) Siulation result at T = 120 in igure 7 Study area and siulation results of an extree rainfall event in the Stockbridge region (sewer pipes shown in yellow, various shades of blue indicate different water depths) 4. ISUSSION N ONLUSIONS The initial rainfall-runoff processes, including fro rainfall to surface runoff, fro surface runoff to drainage inlets, fro inlets to gullies, and fro gullies to ajor anholes, were siplified and calculated by using hydrological odel in the study. In other words, it was assued that the surface runoff was collected and conveyed directly to ajor anholes. onsequently, the overflows occurring at the ost upstrea anholes in both study cases were due to the concentrated runoff and the insufficient capacities of sewer pipes such that the surface runoff could not enter the drainage syste. Those overflows were actually excess runoff rather than surcharges. The surcharged runoff was not allowed to return to the sewer syste until it reached a ajor anhole. The assuption was ade due to lack of detailed inlet inforation and siplifications of the initial rainfall-runoff processes. In reality, the surface runoff in urban area is collected by distributed inlets and conveyed to ajor anhole via gullies. Therefore, if the inlets were taken into account in the Stockbridge case, the flood water in local depressions next to buildings could be drained and returned to the sewer syste. y taking the sewerage flow coponent and the overland runoff coponent into account, the proposed odel siulates the coplex flow processes on overland surface of pluvial flooding cases better than the approach that uses 1 odel only. Presented results illustrate several issues inherent to coupled 1-2 odelling of urban flooding. Linkages between the two odels should be forulated carefully by taking care of the physical situation and by ensuring appropriate tie synchronisation. dequate spatial resolution is iportant, both in ters of the nuber of inlets taken into account (1 odel) and the surface grid size (2 odel). oarse resolution ay cause unrealistic results such as ponds not being drained or the influence of buildings not represented accurately, whereas too detailed resolution ay ake the siulation unacceptably slow. ased on a range of case studies, further research will focus on addressing these issues and on the objective coparison between results obtained by the presented 1-2 approach and different 1-1 odels. 5. KNOWLMNTS The work is supported by the PSR s prograe lood Risk Manageent Research onsortiu: (Work Package 6.1): rant R/S76304/01. LIST O RRNS olle,., euynck,., Willes, P., outeligier, R., osch, M. S., Verwey,., and erlaont, J. (2006) Hydraulic odelling of the twodirectional interaction between sewer and river systes. In: 7UM&4WSU Intl. onf., Melbourne. arr, R. S., and Sith,. P. (2006) Linking of 2 and Pipe hydraulic odels at fine spatial scales. In: 7UM&4WSU Intl. onf., Melbourne. hen,. S., Hsu, M. H., hen, T. S., and hang, T. J. (2005) n integrated inundation odel for highly developed urban areas Wat. Sci. & Tech., 51(2), 221-229. oputational Hydraulics Int. (2002). Introduction for PSWMM 2002. http://www.coputationalhydraulics.co/pcsw.htl, uelph. ey,. K., and Kaioka, S. (2006) n integrated odeling approach to predict flooding on urban basin. In: 7UM&4WSU Intl. onf., Melbourne. HI Software. (2002). MIK SWMM - the new generation SWMM. Hørshol. HI Software. (2003). MOUS Pipe low, Reference Manual, Hørshol. jordjević, S., Prodanović,., and Maksiović,. (1999) n approach to stiulation of dual drainage Wat. Sci. & Tech., 39(9), 95-103. jordjević, S., Prodanović,., Maksiović, Č., Ivetić, M., and Savić,. (2005) SIPSON - Siulation of interaction between pipe flow and surface overland flow in networks Wat. Sci. & Tech., 52(5), 275-283. Ha, S. R., Park, S. Y., and Park,. H. (2003) stiation of urban runoff and water quality using reote sensing and artificial intelligence Wat. Sci. & Tech., 47(7-8), 319-325. Horritt, M. S., and ates, P.. (2002) valuation of 1 and 2 nuerical odels for predicting river flood inundation J. Hydrol., 268(1-4), 87-99.
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