Potential and limitations of 1D modelling of urban flooding

Journal of Hydrology 299 (2004) 284–299 www.elsevier.com/locate/jhydrol Potential and limitations of 1D modelling of urban flooding Ole Marka,*, Sutat Weesakula,1, Chusit Apirumanekula, Surajate Boonya Aroonneta, Slobodan Djordjevićb,2 a Water Engineering and Management Program, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, Thailand b School of Engineering, Computer Science and Mathematics, University of Exeter, North Park Road, Exeter EX4 4QF, UK Abstract Urban flooding is an inevitable problem for many cities around the world. In the present paper, modelling approaches and principles for analyses of urban flooding are outlined. The paper shows how urban flooding can be simulated by onedimensional hydrodynamic modelling incorporating the interaction between (i) the buried pipe system, (ii) the streets (with open channel flow) and (iii) the areas flooded with stagnant water. The modelling approach is generic in the sense that it handles both urban flooding with and without flood water entry into houses. In order to visualize flood extent and impact, the modelling results are presented in the form of flood inundation maps produced in GIS. In this paper, only flooding from local rainfall is considered together with the impact in terms of flood extent, flood depth and flood duration. Finally, the paper discusses the data requirement for verification of urban flood models together with an outline of a simple cost function for estimation of the cost of the flood damages. q 2004 Elsevier B.V. All rights reserved. Keywords: Cost function; Digital elevation model; Flood map; GIS; Sewers; One-dimensional urban drainage; Stormwater; Urban flooding 1. Introduction The problems arising from urban flooding range from minor ones, such as water entering the basements of a few houses, to major incidents, where large parts of cities are inundated for several days. Most modern cities in the industrialized part world usually * Corresponding author. Address: DHI Water and Environment, Agern All’e 11, DK-2970 Hørsholm, Denmark. Tel.: C45-45169373; fax: C45-4516-9292. E-mail addresses: ole.mark@dhi.dk (O. Mark), sutat@ait.ac.th (S. Weesakul), s.djordjevic@exeter.ac.uk (S. Djordjević). 1 Tel.: C66-2-524-5554; fax: C66-2-524-6425. 2 Tel.: C44-1392-263664; fax: C44-1392-217965. 0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2004.08.014 experience small scale local problems mainly due to insufficient capacity in their sewer systems during heavy rainstorms. Cities in other regions, including those in South/South-East Asia, often have more severe problems because of much heavier local rainfall and lower drainage standards. This situation continues to get worse because many cities in the developing countries are growing rapidly, but without the funds to extend and rehabilitate their existing drainage systems. The extent and frequency of urban flooding in large cities in developing countries make them good case studies for urban drainage modelling, as flood data are available and the impact of alleviation schemes can be evaluated straight away. O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 A few examples of historic urban flood problems are: Mumbai (India), 2000 where nearly 17,000 telephone lines in Mumbai City ceased to function after flooding occurred and electric supply was cut off for safety purposes. The water depth reached 1.5 m at the worst inundated locations and 15 lives were lost in the flood. In Dhaka City (Bangladesh), even a small amount of rain may cause serious problems. Dhaka has often experienced flooding with ankle to kneedeep water in the streets. In September/October 1996, most of the daily activities in Dhaka were nearly paralyzed and heavy traffic jams occurred due to stagnant water. In 1983, Bangkok (Thailand) was flooded for nearly 6 months and it caused the loss of life and infrastructural damages of approximately $146 million (AIT, 1985). In February 2002, five people were killed in Jakarta (Indonesia) as heavy rain extended floods to the city center, deepening a crisis, which forced 200,000 people from their homes and killed 50 nationwide (Bangkok Post, 3rd February 2002). A final example is Houston, Texas (USA)— where the storm ‘Allison’ in June 2001 caused urban flood damages in the order of $2 billion on the Texas Medical Center in the Harris Gully watershed (Holder et al., 2002). 285 is presented in this paper, to provide a first estimate of flood costs. Urban flooding may create considerable infrastructure problems and huge economic losses in terms of production, as well as significant damage to property and goods. The water depth in some inundated city areas is commonly in the order of 50–70 cm. In addition, diseases spread and impose problems to the population, for instance, diarrhoea or Leptospirosis, which can be spread by bacteria in the urine of rats. In September 2000 flooding in the north east of Thailand, 6921 cases of Leptospirosis were reported, 244 of these resulting in loss of human life (Bangkok Post, 20th September 2000). Last, but not least, parasites seem to thrive when urban flooding occurs regularly. Moist soil provides a good environment for worm eggs to flourish, and water flooding open drains spreads eggs to new victims (Kolsky, 1998). Today antihelmintica kills parasites, but the parasites may gradually develop resistance to the drug and impose new and more severe problems. The best way to manage parasite problems is to break the life cycle of the parasites, that is, to remove their natural environment by reducing the frequency and duration of flooding. For example, Moraes (1996) found that reduced flooding reduced the prevalence of roundworm and hookworm by a factor of two and hookworm alone by a factor of three. 2. The impacts on society from urban flooding Water flowing on the urban surface is a problem when it causes damage. The perception of damage varies from person to person. König et al. (2002) divided damages from urban flooding into categories: † Direct damage—typically material damage caused by water or flowing water. † Indirect damage—e.g. traffic disruptions, administrative and labour costs, production losses, spreading of diseases, etc. † Social consequences—negative long term effects of a more psychological character, like decrease of property values in frequently flooded areas and delayed economical development. It is often difficult or impossible to provide an accurate estimate of the cost of the flood damages. Nevertheless, a very basic cost estimation procedure 3. What can be done to understand and reduce urban flooding? With today’s advances in computer technology, many cities in the developed part of the world manage local and minor flooding problems using computerbased solutions. This involves building computer models of the drainage/sewer system, for instance by using software like MOUSE (Lindberg et al., 1989); InfoWorks (Bouteligier et al., 2001) and the SWMM models (EPA SWMM, MIKE SWMM, and XP SWMM), (Huber and Dickinson, 1988). These types of models are used to understand the frequently complex interactions between rainfall and flooding. Once the existing conditions have been analyzed and understood, alleviation schemes can be evaluated and the optimal scheme implemented. Nevertheless, at present there are few studies on urban flooding that 286 O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 Fig. 1. Layout of pipe and street system. deal with both the conditions in the surcharged pipe network and the extensive flooding on the catchment surface. Even fewer projects have dealt with modelling urban flooding in developing countries. Some of the few case studies dealing with of modelling of urban flooding which both includes the pipe system and extended surface flooding are: Bangkok (Thailand) (Boonya-Aroonnet et al., 2002); Dhaka City (Bangladesh) (Mark et al., 2001); Fukuoka and Tokyo (Japan) (Ishikawa et al., 2002); Harris Gully (USA) (Holder et al., 2002); Indore (India) (Kolsky et al., 1999) and Playa de Gandia (Spain) (Tomičić et al., 1999). These studies treated urban flooding as a one-dimensional (1D) problem. Schmitt et al. (2002) considered a 2D model as a benchmark for 1D model. A model, which dynamically couples a 1D pipe flow model with a 2D hydrodynamic surface flood is currently under development (Alam, 2003). If the intake capacity of the drainage system is limited, only a fraction of the water can flow into the pipes and a large runoff volume will be transported on the surface during and after a heavy rainfall. This may happen even if the underground pipe system has sufficient capacity, see Fig. 2. The water in the pipe system may return to the street system if the capacity of the pipe system is insufficient. In this case the water will flow from the pipe system to the street system, causing surface flooding, see Fig. 3. The duration of flooding on the street depends on the intake capacity of the catch pits, the drainage capacity of the pipe system, infiltration and evaporation in the catchment area. In the present modelling approach, the urban drainage system consists of two networks, one 4. A methodology for simulation of urban flooding Urban flooding may be due to various causes. The runoff generally starts as overland flow on the street before entering the underground pipe system through catch pits. Fig. 1 shows a street system connected to a pipe system through manholes/catch pits. Fig. 2. Flow from the street system into a partly full pipe. O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 Fig. 3. Flow to the streets from a pipe system with insufficient capacity. representing the free surface flow in the streets and one for the pipe network. The drainage system is modelled as two dynamically interconnected networks. The hydrodynamic model is based on an implicit solution of the St Venant equations. The two networks route the rainfall runoff simultaneously in the pipes and on the streets. Manholes (network nodes) function as points of flow exchange between the pipe and the street systems. Water from the street system can enter the pipe system by flowing through catch pits or manholes and vice versa. 287 Fig. 4 shows the modelling approach for urban flooding. Two models are needed, i.e. a hydrological model, which simulates surface runoff from rainfall and a hydraulic model describing flows in pipes, streets and storage of water on the surface. In urban flooding simulation, the hydrological process is separated conceptually from the hydraulics of the drainage system. The computation of the surface runoff from rainfall can be carried out by a standard surface runoff model, e.g. a time/area, kinematic wave or linear reservoir model. A surface runoff hydrograph is computed for each sub-catchment. Runoff hydrographs from each sub-catchment are then used as input for the hydrodynamic model, simulating flows in the pipe and street systems. The runoff from the catchments is entered in the model either on the streets or directly in the sewers depending on the local layout of the drainage systems. Hence, the initial flooding will be generated due to insufficient capacity of either the pipes themselves or of the inlets to the piped system. As the pipe and inlet capacities can differ significantly, it is important to get this part of the schematization right. Fig. 4. Interactions between various stages in the modelling approach for a flooded urban drainage system. 288 O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 5. The digital elevation model The digital elevation model (DEM) represents land elevation data, which are essential for estimation of flood volumes on the surface areas. In addition, the result presentation in the form of a flood inundation map is based on water levels from the model simulation in conjunction with the DEM. Thus, quality of the model results depends on the quality of DEM. To generate the DEM, spot elevations (X, Y coordinates and the ground level Z) covering all of the catchments are needed. The data for the DEM can be obtained by field survey data, by digitising a contour map or by some other techniques (Hale, 2003). The interval of spot elevation for analysis of urban flooding should be in the range of 10–40 cm, to achieve a resolution sufficiently accurate to cover all important details in the city area, e.g. the distance between the road and the curb level. For a field survey, it is especially important to obtain the following data in the flood prone areas (Fig. 5): † elevation of bottom and curb level of road system, † elevation and general topography of each catchment, † elevation of low and high spots. The DEM may be developed based on a distance weighted interpolation routine. This means that a Z-coordinate is interpolated from the adjacent X, Y, Z points for each and every grid cell. The resolution of the DEM should be fine enough to cover important details so that the DEM can yield sufficiently accurate representation of elevations along the streets and flood prone areas. The size of a 1!1–5!5 m resolution is recommended for urban flood analysis since it can cover the width of the road, the width of sidewalks, and houses or buildings. However, using a finer resolution like 1 m does not necessarily provide results which are significantly more accurate in terms of flood levels, but does provide a much better visual presentation of the flood extent. A coarser 5!5 m DEM can thus be used for quick assessment of the model results, while detailed analyses should be based on the 1!1 m DEM. It makes sense to create both a fine DEM and a coarse DEM and to use each for various purposes. It is essential to have an accurate description of the streets in the DEM. If the DEM is based on spot elevations on the ground level, e.g. on the sidewalk, the streets must be ‘burned’ into the DEM with an elevation which corresponds to the height of the curb. Major roads in the study area where floods occur must be included in the DEM, as the streets act as drains for the surface flooding. If the water from street rises above the curb level of the street, the water will flow to adjacent areas and cause flooding. Fig. 6A and B show sample DEMs from real models, i.e. a DEM from Dhaka City with and without the street system and a DEM from Ballerup, Denmark—where the houses also have been added to the DEM. The houses are on purpose not included in the DEM for Dhaka City—as it is believed that the water flows into many of the houses during flooding—whereas it is essential Fig. 5. Spot elevation map used for generation of the DEM—case Bangkok City. O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 289 Fig. 6. (A) The DEM for Dhaka City, without and with the road system. (B) A 3D view of the DEM for Ballerup, Denmark, with streets and houses. to include the house in the DEM for Ballerup as only smaller amounts of water flow into the houses during the flood events. A typical procedure is to interpolate and generate the DEM using ground points only, i.e. without taking into account the heights of man-made objects. DEM must then subsequently be corrected, by raising of pixels to include buildings. This operation is called height correction of DEM, and is illustrated in Fig. 6B. The procedure presented in this paper is generic in the sense that when the final DEM has been made, the area–elevation curves are automatically computed based on the DEM (with or without houses) and the correct flood zones will automatically be attached to the model. This method thus provides modelling of flooding with or without flood water inside the houses depending on the reality in the field. 6. Catchment delineation for urban flooding The catchment definition depends on topographical and drainage network data. In urban areas the catchments must be further divided into sub-catchments connected to the appropriate location in the local drainage channel. This means that it will be necessary to overlay different types of mapped information from the study area. Difficulties arise in 290 O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 the flat areas, where the boundaries are unclear, and often determined as much by small local drainage paths as by topography (Kolsky, 1998). The main concept in sub-dividing of catchments is to understand the topography and drainage network to define the areas contributing flows to different portions of the network. Once the draft catchment delineation is sketched on a map, it is important to survey the study area and inspect the past flooded areas to check that the runoff is flowing in the expected direction and that there is an agreement between the model and real life. Apart from a manual procedure, automatic catchment delineation can generally be laid out in three different ways (Djordjević et al., 1999): 1. ‘Distance-based’, i.e. based on the distance to the drainage network. 2. ‘DEM-based’, i.e. based on an algorithm that traces most probable flow paths depending on the information in the DEM concerned terrain aspects and slopes. 3. DEM plus cover image (land use). This is the same as the ‘DEM-based’ procedure, but with the addition of impacts from objects in the digital image, like buildings, cascades, etc. Two types of catchment delineation were evaluated in this study. The first procedure was the manual delineation and the second procedure was ‘distance based’. The manual delineation was applied for Dhaka City, as the catchment is rather small and easy to delineate based on topography and land use maps. The ‘distance based’ delineation was applied for Bangkok, as the model for the downtown area of Bangkok has more than 2000 catchments, but very little information is presently available in a digital form concerning local terrain and land use. Hence, the ‘distance based’ method was convenient for Bangkok to define the subcatchments for each manhole, but at the same time it defined the catchment without considering the topography and land use of the area. This may lead to inaccurate physically unreasonable catchment delineation. For instance, automatic delineation does not consider features, like natural flow paths, houses and hill traces as boundaries for sub-catchment delineation. Hence, the result from the ‘distance based’ delineation must be checked and if necessary, verified through a manual procedure. Fig. 7 shows the sample of manual and automatic catchment delineation. When DEM-based delineation is applied, it is essential to have a reliable DEM created not only for the analyzed catchment, but also for a certain zone surrounding its assumed boundary. This should ensure that the real catchment boundary is precisely determined. 7. Modelling of routing and flooding The drainage network is geographically and topologically fully determined so that a network Fig. 7. Dhaka City catchment: manual delineation (left) and automatic (distance-based) delineation (right). O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 model actually resembles a schematized view of a real system. The flow in a flooded pipe system is complex, and the computations in the present urban flood model are based on an implicit finite difference scheme, adopted from the St Venant equations. Traditionally, when surcharge water from a pipe system flows into the street system, most of the models stores flood water from the underground system in a virtual reservoir and the stored volume returns to the pipe once the system resumes free surface flow. To make a significant advance on this approach, and to model the dynamics of flooding in urban areas reliably, high resolution data on terrain model are needed, as stated by Maksimović (2000). His paper concluded that a new methodology for simulating the storage of surface flooding on the street system is needed, not using a virtual reservoir approach at each computational nodal point on the surface. By the application of GIS features like a DEM and a simulation module, modelling of real storage and routing of surface flooding can be achieved. If water from a pipe network flows through a manhole and reaches the street ground level, then surface flooding takes place. The flooded surface area is gradually increased following the DEM and hence a model can accurately describe the rising water level along the street and its borders, and therefore simulate the surface inundation. An area–elevation relation is required for the surface topography, in order to define the storage capacity for surface flooding—as input of the model, e.g. as a storage function for a basin. This relation is developed from the DEM with the application of GIS. Area–elevation relations must be defined for each sub-catchment connected to the street network. The sub-catchments are assumed to be the adjacent areas around manholes, where surface flooding may spread. Fig. 8 shows a sample of an area–elevation relation, which is used as input of the urban flooding model, in order to simulate storage of water next to the street system. When surface flooding occurs, the flow along the street can be in either direction along the street; it is not necessary that the flow direction in the street coincides with the street slope, or that it is the same as in any buried pipe flow. After all, it is not necessary that the layout of the streets matches that of the buried pipe network. 291 Fig. 8. An example of an area–elevation relation. 8. Flow exchange between the street and the pipe system Water from the pipe system may flow to the streets through a manhole when flooding takes place. On the other hand, when water in the pipe system is drained, surface flooding water in the street system can flow through the manholes to the pipe system. In modelling of urban flooding, the manhole may be described as a broad crested weir, where the crest length of the weir is represented by a perimeter of the manhole and the weir crest is set to the bottom level of the street as described in Fig. 9A and B. Discharge through manholes can also be described by a common Weir equation, which handles both free and submerged flows. The use of a weir for the description of the connection between pipe and street systems ensures that a restriction exists both for water from streets entering the pipe system and for water flowing from pipes to the streets. When the sewer system becomes fully surcharged, it may be more correct to shift the Weir equation to an orifice equation, where the driving head is the difference in head between the pressure in the sewer and the water level on the surface. However, 292 O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 Fig. 9. (A) The principle behind the application of a Weir formula for the description of the flow exchange between pipe and street system. (B) Water flowing into a catch pit in Dhaka City. This is an illustration from real life of the principle behind the application of a Weir formula for the description of the flow exchange between pipe and street system. the orifice equation breaks down in cases where the orifice is not full flowing, e.g. as in Fig. 9B. 9. Model requirements Based on the discussion above of the physical processes involved in urban flooding, the technical requirements in an urban flood model can be summarized as: † Dynamic flow description: when urban flooding occurs, surface water can flow in both street and pipe systems with flow exchange between these two systems through manholes. This means that simulation of backwater effects is needed in modelling of urban flooding. By using a dynamic wave model, the model includes backwater effects and surcharge from manhole including rapid change of water level. † Parallel flow routing: while surface flooding takes place, water from the pipe system flows through manholes or catch pits to street system. Flow along the street (e.g. right above the pipes) can be in either direction along the streets, i.e. it can flow following O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 a slope of the street or against it. It is not necessary that the flow direction in the street has to be the same as the flow direction in the pipe system. † GIS interface: GIS is important in simulation of urban flooding. It is used as a tool to provide input data and display simulation results. Surface storage for simulating surface flooding can be calculated by the application of GIS together with the DEM of the study area, i.e. find area–elevation relation from DEM. In addition, results of the simulation can be easily understood in form of flood inundation maps. Model output in term of water level along the streets are transferred to GIS and with the interpolation routine, water surface is able to be developed. Flood inundation maps can be generated by overlaying of water surface and DEM, introducing flood depth map which is an easy method to visualise flood situations. The importance of these elements has also been realized and pointed out by Maksimović and Prodanović (2001). 10. Other physical processes in urban catchments exposed to flooding Important physical processes like evaporation and infiltration must be considered if they affect the urban flood conditions. In some cities, evaporation and infiltration may be predominant, e.g. depending on the season, the land use, location of the city, soil type, etc. Evaporation happens on all surfaces exposed to precipitation, such as parks, buildings, houses and paved area. However, the evaporation rate depends on temperature, wind and atmospheric pressure. To consider whether evaporation should be included in the model simulation, comparison of accumulated evaporation to accumulated rainfall during the rain and flooding periods is needed. Apirumanekul (2001) found that evaporation was insignificant for the maximum flood depth in Dhaka City during the October flood in 1996 and he found that the evaporation per unit city area was approximately 0.5% of the accumulated rainfall during the 3 days of flood. Hence, if only a little evaporation takes place compared to the accumulated rainfall (the volume of flood water), then it does not affect the simulated maximum flooding. 293 The infiltration term is generally used for two different processes in modelling of urban sewers, i.e. it may be used for seepage from groundwater to the pipe system or to describe seepage of surface flooding water to pipe system and groundwater. The two cases are discussed briefly. Knowledge of the groundwater level is necessary for determining the effect of infiltration into sewer pipes. If the water table level is higher than the level of the drainage pipes, infiltration from groundwater to the pipe system may take place depending on the condition of the pipes. In highly urbanized areas, during small rain events that do not generate flooding, often only a small amount of water from rainfall and runoff infiltrates the soil due to imperviousness of the surface. However, infiltration from surface flooding to ground water is one of the physical processes, which should be considered. This type of infiltration rate depends on other factors like: † land use type—most urban areas are commercial areas, industrial areas and government office areas, which comprise buildings, houses and paved areas—this means that less infiltration may occur in these areas, † soil type—more infiltration can occur in sandy soil compared to clay or silt, † soil moisture content—if the soil moisture content is high, infiltration is less than in dry soil. For Dhaka City, most of the areas are commercial areas and government office areas, which consist of houses, buildings and paved areas and the soil is clayey. Therefore, only a minor flood water infiltration takes place in the central part of Dhaka, e.g. the infiltration rate of clay is in the order of 1–5 mm/day (Daniel, 1980). The groundwater level in Dhaka City is around 25 m below the ground surface (Khan and Siddique, 1999). This is due to accelerated utilization of ground water as a resource for supplying drinking water to the city. At the same time the recharge to the ground water has been reduced due to increased impervious city areas, thus infiltration from groundwater to the pipe system has decreased. In Playa de Gandia, Spain, the city is located along the Mediterranean coastal areas and driven by the booming tourist industry. Because of the intensive 294 O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 impermeabilisation of urban catchments, there is less infiltration of surface water to the pipe system. The drainage conditions in the area are not very favourable. The terrain is quite low, sandy and the groundwater level is high. This means that infiltration effect (from groundwater to pipe system) must be considered. Since the city of Gandia is located over sandy soil, surface flooding water can predominantly infiltrate to groundwater and hence the effect of infiltration to flooding must be considered (Tomičić et al., 1999). 11. Calibration and verification Calibration involves minimization of deviation between observed data and simulated results by adjusting parameters within the model. The urban drainage model calibration can be carried out by calibration of the surface runoff model and subsequently the pipe flow model is calibrated towards measured flow and water level at the specific locations. The surface runoff model can be calibrated by adjusting hydrological parameters, for example time of concentration, until the computed hydrograph agrees closely to observed runoff data. Next, the runoff hydrograph is used as input data for the pipe flow model to simulate discharge and water level in the pipe system by changing pipe flow parameter, such as Manning number. This step is iterated until the calculated discharge and water level outputs are agreeably close to the observed data. The main objectives in calibrating urban flooding models are to match the flood extent and the flood depth. The capacity of a drainage system normally depends on pipe sizes and pumping capacity. However, during flooding the capacity of the system may be totally different because the water flows both in the pipes and on the streets. During a flood, the flow condition for a pipe might be pressurized flow, while the flow condition for the street is open channel flow. The pipe discharge is limited by pipe size and the difference in head between the upstream and downstream end of the pipe, but street flow is only limited by the width of the street and the slope of the water surface. Fig. 10 shows water level and discharge on the street and in the pipe from the simulation of a rain event with a return period of 1 year for Bangkok, Thailand. Water starts to flow in the pipe only in a positive direction (downward). When the downstream node floods, backwater effects retard the pipe flow because of a reduced head difference. From this moment, flow on streets will occur in a negative direction (upward). However, the water from upstream still keeps flowing downward. This upstream water will push both street and pipe flows back to a positive direction. In Fig. 10, at the end of the simulation, the discharge in the street is an order of magnitude higher than the pipe flow. This means that contribution to the drainage capacity from the street network is extremely important to define the flow capacity during urban flooding and that measuring the flow in the pipes provide only a part of the information required for calibration of an urban flood model. Hence, in order to calibrate an urban flood model it is not enough to have only a well calibrated pipe network, but the flow paths, the flow extent and the flow capacity of streets must also be estimated accurately. Model verification is a process of testing the quality of a calibrated model against observed data, using the model parameters derived during the calibration. Another set of data, for instance the water level in a manhole, flow velocity and discharge in specific locations in the pipe system should be recorded for model verification purposes. Model verification may be more cumbersome for urban flooding due to sparse flood data. However, verification is still required in order to have confidence in the modelling results. Model validation requires comprehensive and detailed field data sets. Ideally, these would include rainfall as well as level and discharge measurements at several locations both in the underground pipe system and on the surface. Often the desire to model urban flooding occurs after a flood incident, i.e. flow gauges and water level meters are rarely in place to measure flooding when it occurs. An exception to this is the flood in Bangkok during October 2000, where measurement during a flood incident paralysing Bangkok was carried out (Chingnawan, 2003). If high-tech equipment is not available, the areas affected by flooding and the highest flood levels can be cheaply recorded by tools such as resident gauges and chalk gauges (Kolsky, 1998). Whenever the collection of high quality data was not carried out during a flood event the model may be verified by comparing predicted and observed flood extent and maximum water levels—these data are typically O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 295 Fig. 10. Illustration of the complexity of the flow conditions during the flood event as both the sewer flow and the street flow change direction during the event: at tz13:10 the downstream node is flooded; at tz13:20 the head in the sewer pipe exceeds the water level in the overlapping street. available. An example of a model verified against observed flood extent is the flooding in Dhaka City during October 1996 (Fig. 11). In addition the model was compared to marks of highest flood levels where the accuracy of the model was within 5–10 cm—a very good result. 12. Result presentation and model application The model results are geo-referenced and related through a coordinate system linked to the DEM grid. The results are presented in the GIS interface as flood inundation maps, based on the water levels computed by the urban drainage model. Flood inundation maps provide a most effective medium for visualizing flooding. The water levels on the surface mainly cause flooding on the streets and the adjoining areas. Output of the simulation in the form of simulated water levels along the street system is transferred to GIS. Using interpolation routines, continuous three-dimensional water surfaces can be constructed based on the simulated street water level from the model and the DEM. The DEM elevations are subsequently subtracted from the water level surface delineating inundated areas by flood extent and flood depth. Results (water levels) from the simulation are available along the streets as shown in Fig. 11, which shows a flood inundation map for urban flooding in Dhaka City in 1996. Based on the verified flood model for Dhaka a number of alternative scenarios were evaluated to reduce the flooding of the city. Surprisingly it was found that provision of additional pumping capacity had only a local effect. This was due to the fact that the pipes in the most upstream part of the catchment acted as bottlenecks and that the ground slopes in that area were unfavourable for drainage the floods waters 296 O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 Fig. 11. Flood inundation (maximum flood depth) map for Dhaka City in September 1996—the red bold lines show the flooded areas as they were recorded by the local authorities. in the streets. In other words, the small pipes were the points controlling the drainage of the larger upstream catchments. As a logical consequence it was found that real time control of the pumping station had very little impact on reduction of flooding. For the Bangkok flood modelling study, the flood inundation maps was overlaid on property maps of the city (Fig. 12). A cost function for flood damage per establishment (in Thai baht) for the Sukhumvit 0.4 km2 area in Bangkok has been developed by Tang et al. (1990) as: where a, b, c are parameters given in Table 1, estimated based on previous flood. Hence, even though this is a simple empirical model, it provides very useful information for the city planners concerning cost estimation of the flooding and the return of the investment from implementation of alleviation schemes. Flood damageðbahtÞ Clearly the greatest inaccuracy of the described approach lies in the treatment of street channels as prismatic and of flow in those channels as onedimensional. Irregular street geometry and/or catch pits situated in gutters on two sides of the road may Z a C b  ðdepth of flood in centimetersÞ C c  ðduration of flood in daysÞ 13. Drawbacks and limitations 297 O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 Fig. 12. Flood map for Bangkok on the top of a property map—simulated for a rainfall with a 1 year return period. lead to water in two parallel gutters flowing in opposite directions. When the surface channel is prismatic and the boundary conditions for it are close to the real situation, the limit in validity of the 1D flow assumption is not sharp—roughly speaking, it is reasonably realistic as long as water remains within the street profile. When the curbs are overtopped, not only is the flow no longer 1D, but also the water probably reaches pervious areas where roughness is significantly higher, and where infiltration may be possible. Separation between the hydrological and hydraulic phases of the runoff, outlined earlier, is absolutely acceptable for simulation of events without flooding. However, surface runoff parameters calibrated via measurements during moderate rainfall, might not be valid when the underground system cannot capture all the runoff, since the excessive amounts of water on the surface would induce both decreased hydrological losses and quicker response (shorter ‘concentration times’). In other words, storm sewer overflows interact with surface runoff. One possible approach to handle this was described by Djordjević et al. (1999). The Weir formula describing the link between the pipe network and a surface channel network is only a rough approximation of reality, because one such link represents the holes on the manhole cover and/or several catch pits. So, whichever expression is used to relate discharge as a function of water levels at two nodes (one in the manhole and another on the street), it is never unique. Even in the situation when such a detailed system description is achieved to have one link representing only one catch pit (corresponding to one manhole), depending on the type of the inlet structure, it may have several openings that may work in different regimes in time. Furthermore, during the outflow the pressure force of the water rising in the manhole may easily be able to lift and partly remove the manhole cover (Guo, 1989). Consequently, the surface flow might be strong enough to remove the cover completely. In such situations, it is clearly very complicated to include all those phenomena in the simulation. Local losses in both free-surface and surcharged manholes have been subject to extensive experimental Table 1 Estimated flood damage function parameters for different land use types in Bangkok (Tang et al., 1990) Land use type a b c Residential Commercial Industrial Agricultural K300.5 K2.2 K1739.9 K1047.2 45.4 88.1 522.8 553.5 33.5 – 180.5 – 298 O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 and theoretical research (e.g. Pedersen and Mark, 1990), meaning that they can be included in the model in a fairly accurate manner. However, even when the flows in adjoining street channels are more or less one-dimensional, local flow geometry at street junctions is always complex, so the energy equations for surface nodes are less sound. In particular, this is the case with supercritical flow, having in mind the assumptions on the boundary conditions structure inherent to sub-critical flow applied in the model. It is likely that, during the flooding event, the hydraulic grade lines will reach the ground level first at nodes that are in local depression. At those locations the water initially accumulates (filling the surface storage) before a possible flow further downstream. In such cases, the actual lengths of joining surface channels are in fact variable—they depend on the water level in the storage, and this in turn is almost impossible to include in the model. Where open channels (e.g. small streams) are used as part of a drainage system the chances are high that during floods culverts or bridge openings become partly clogged by large items brought by flooding water and hence in this way obstructing the predefined modelling assumptions. A comparison was made between three different model layouts for the Bangkok sewer system for a rainfall event with a 1 year return period, i.e. 35 mm/h. The comparison included: 1. Simulation by application of a standard approach in commercial urban drainage software as outlined by Maksimović (2000). In other words, no provision of streets and surface routing/storage outside the streets. 2. Simulation by application of a standard approach as described just above but with streets added. 3. Simulation of the urban flooding as suggested in this paper. The maximum simulated water levels are reduced by up to 60 cm when streets are included in the model—proving the statement by Maksimović (2000) that a standard flood simulation without any concern for the surface flood routing and flood storage heavily overestimates the flood depth. The difference in maximum flood depth between the model with and without the provision of flood storage next to the streets is in the order of 10–20 cm—but the model with the flood storage next to the streets gives a significantly better picture of the real flood extent and flood damaged areas, providing more accurate and more valuable information. Engineering predictions always imply some degree of simplification. Urban flooding is certainly a very complex phenomenon, but incapability to include all details in modelling should not discourage attempts to use a 1D approach, at least for internal floods caused by heavy rainfall. Basically, the limitations mentioned in this paper make it very difficult to accurately simulate local conditions on a small scale, whereas simulation of larger scale urban flooding based on the principles outlined in this paper gives very promising results. 14. Conclusion This paper has outlined the potential and limitations of a special modelling technique, where a hydrodynamic urban flood model built in two layers describes the conditions both in the surcharged pipe system and flooding on the catchment surface. It can be concluded that the modelling of urban flooding is feasible on a large scale and the model is a powerful tool combination with GIS. Complex hydrological-hydraulic mechanisms are encapsulated into the model and results can be presented as easily understandable flood inundation maps. This integrated approach for modelling of urban flooding provides a methodology for systematic and consistent analyses of the causes for the urban flooding together with evaluation of flood alleviation schemes. It is believed that the method presented in this paper, a combination of GIS and 1D hydrodynamic modelling, constitutes a cost efficient system for planning and management of drainage systems suffering from urban flooding. 15. Future perspectives Today, a few studies have been carried out to simulate urban flooding by application of mathematical models. In urban areas the flow paths on the surface are often complex to define because of crowded buildings, houses and roads—and during O. Mark et al. / Journal of Hydrology 299 (2004) 284–299 heavy flooding a 1D modelling approach may be insufficient. Future approaches to modelling urban flooding may use a hydrodynamic pipe flow model below ground in conjunction with a full 2D hydrodynamic model in order to describe the surface flow. The results of such a model would be usefully compared with those of a 1D urban flood model to provide insight for the selection of an appropriate approach for modelling of urban flooding. Acknowledgements The last author’s work on this paper was partly supported by the U. K. Engineering and Physical Sciences Research Council (EPSRC), Project No. GR/R14712/01 (the Platform Grant). References AIT, 1985. Flood routing and control alternatives of Chayo Praya River for Bangkok. A report submitted to The National Economical and Social Development Board of Thailand. Alam, J.Md., 2003. Two-dimensional urban flood modeling for real time flood forecasting for Dhaka City, Bangladesh. AIT Thesis no. WM-02-06. Asian Institute of Technology, Thailand. Apirumanekul, C., 2001. 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