Anindya 3200 Essay

Analysis and modeling of flooding in urban drainage systems

Theo G. Schmitt a,*, Martin Thomas a, Norman Ettrich b

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aFG Siedlungswasserwirtschaft, Kaiserslautern Technical University, Postfach 3049, D -67653 Kaiserslautern, Germany

bFraunhofer Institut fu?r Techno – und Wirtschaftsmathematik ITWM, Gottlieb -Daimler -Stra?e 49, D -67663 Kaiserslautern, Germany


Urban flooding is a global problem and can have significant economic and social

consequences. The main objective of this paper is the development of an integrated planning

and management tool to allow cost effective management for urban drainage systems and

prevention of urban flooding .

This paper follows European Standard EN 752 defining flood

frequen cy as the one hydraulic performance criterion. Dual drainage modeling is used here to

analyze urban flooding caused by surcharged sewer systems in urban areas . A dual drainage

simulation model is described here in details based upon hydraulic flow routing procedures

for surface flow and pipe flow. Special consideration is given to the interaction between

surface and sewer flow in order to most accurately compute water levels above ground as a

basis for further assessment of possible damage costs.

The model application is presented for

small case study in terms of data needs, model verification and first simulation results .

1. Introduction

Climate change is altering precipitation patterns across the globe. Every year, rainstorms and

flooding events are increasing in both frequency and severity. With municipal water utilities

already strained by decades of underinvestment and aging infrastructure, they now face a whole

new spectrum of c hallenges due to climate change and growing urb an populations . So

prev ention of flooding in urban areas has become an important issue. However, drainage

systems designed to cope with the most extreme storm conditions would be too expensive to

build and operate. In establishing tolerable flood frequencies, the safety of the r esidents and the

protection of their valuables must be in balance with the technical and economic restrictions.

According to European Standard EN 752, urban drainage systems should be designed to

withstand periods of flooding in the range of 10 –50 years, d epending on the type of urban area

and traffic infrastructure served . In the following, the major issues of this standard will be

briefly discussed in conjunction with an analysis of urban flooding. A simulation model to

assess the hydraulic performance of sewer systems and the risk of flooding caused by system

surcharge will be described afterwards. Its app lication and data need is demon strated in a case


2. Analysis of flooding phenomena

Flooding in urban drainage systems as defined above may occur at different stages of hydraulic

surcharge depending on the drainage system (separate or combined sewers), general drainage

design charac teristics as well as specific local constraints.

When private sewage drains are directly connected to the public sewer system without

backwater valves, the possible effects of hydraulic surcharge depend on the levels of the lowest

sewage inlet inside the house (basement), the sewer line and the water level during surcharge,

respectively. Whenever the water level in the pub lic sewer exceeds the level of gravity inlets in

the house below street level, flooding inside the house will occur due to backwater effects. In

such a case flooding is possible without experiencing surface flooding. In the same way,

hydraulic surcharge in the sewer system might produce flooding on private properties via storm

drains, when their inlet level is below the water level of the surc harged storm or combined


In both cases, the occurrence of flooding, being linked directly to the level of inl ets versus water

level (pressure height) in the sewer can be ‘easily’ predicted by hydrodynamic sewer flow

simulations, assuming the availability of physical data of the private drai ns and the public sewer


Distinct from the situations described ab ove, the occurrence and possible effects of surface

flooding depend much more on local constraints and surface characteristics, e.g. street

gradient, sidewalks and curb height. These characteristics, however, are much more difficult

described physically, a nd these data are usually not available in practice. In addition, today’s

simulation models are not fully adequate to simulate the relevant hydraulic phenomena

associated with surface flooding and surface flow along distinct flow paths.

2.1 . Consequences of flooding

Flooding in urban areas due to the failure of drainage systems causes large damage at

buildings and other public and private infrastructure. Besides, street flooding can limit or

completely hinder the functioning of traffic systems and has indi rect consequences such as

loss of business and opportu nity. The expected total damage — direct and indirect monetary

damage costs as well as possible social consequences — is related to the physical properties of

the flood, i.e. the water level above ground le vel, the extend of flooding in terms of water

volume escaping from or not being entering the drainage system, and the duration of flooding.

With sloped surfaces even the flow velocity on the surface might have an impact on potential

flood damage .

3. Methodology

I. Rainfall -Runoff Simulation : The RisUrSim model first transforms rainfall into

effective runoff using standard methods for interception, depression storage and soil

infiltration (previous areas only) as described in literature (e.g. Akan, 1993; Ashley et

al., 1999). Surface runoff would then be handled in distinct detail depending on the

specific situation of a single runoff area. For areas not considered for detailed surface

flow simulation, e.g. roof areas, RisoReff uses a unit -hydr ograph method to compute

surface runoff as input to the sub -surface sewer system (‘uni -directional flow’ ).

II. Hydraulic surface flow modeling : The RisoSurf approach includes detailed

hydraulic considerations for areas where surface flow occurs. Hydraulic (sur face) flow

modeling is generally based upon conservation laws of fluid flow expressed in the

Navier –Stokes equations. The fact that in surface flow the vertical dimension is much

smaller than typical horizontal scale allows a simplified two -dimensional

rep resentation, the so -called ‘shallow water flow equations’ (Hilden, 2003). The

application of this detailed hydraulic method would be restricted to small areas only.

Therefore, it only served as a benchmark for a further simplified two -dimensional


Rainfall -Runoff



Surface Flow



Sewer Flow


Coupling of



Interaction of

Surface and

Sewer Flow

III. Dynamic sewer flow modeling: Sewer flow is simulated applying fully

dynamic flow routing of unsteady, gradually varied flow and solving Saint -Venant –

Equations numerically in an explicit difference scheme. The explicit difference

scheme is applied in variable time steps that are permanently adjusted to the

COURANT -criterion, guaranteeing numerical stability (Schmitt, 1986).At each time

step, the proced ure of dynamic flow routing starts by computing flow values for each

conduit (sewer segment between nodes) based upon momentum equation and

instantaneous water levels at the nodes at the end of the last time step. In the next step

of the dynamic flow routi ng procedure the flow volume is balanced at each node,

taking into account inlets from house drains and all surface inlets connected, as well as

inflows and outflows from sewers connected at the nodes. The resulting change of

volume is drawn to free water surface ‘available’ at the node, thus producing a change

of water level at the node. In order to improve numerical stability, the two phases are

applied in a half -step –full -step procedure during each time step as described in

Roesner et al. (1988) and Schm itt (1986). The underground sewer system is

represented by a network of nodes and conduits (sewer segment between nodes). In

contrast to conventional modeling, not only manholes but also street inlets and house

drains are considered as extra nodes to fully achieve the connection of surface and

underground drainage system at all locations where interaction between surface and

sewer flow and potentially flooding might occur. This will be further discussed in

context with the case study below.

IV. Modeling intera ction of surface and sewer flow : The simulation of the

interaction between surface and sewer flow is based upon the definition of exchange

locations. Each runoff area is allocated to one specified exchange l ocation as

illustrated in Fig. 1 . Here, all re levant information for surface and sewer flow

simulation (instantaneous runoff, water level, exchange volume) is available at the

beginning of each time step for all simulation modules and is renewed at the end of the

time step in the following way:

? The hy drologic runoff model RisoReff only supports uni -directional

flow and is applied to all areas not considered for surface flow.

Computed runoff from those ‘hydrologic areas’ is passed to the single

exchange location to which the area is connected. The excha nge

volume would be the runoff volume in the according time step.

? Areas simulated with the hydrologic model approach can be connected

to the underground drainage system in two alternative ways :

(a) ‘hydrologic areas’ directly discharging to the sewer system vi a surface inlets or private

drains (se rvice pipes);

(b) ‘hydrologic areas’ discharging to surface areas where surface flow is considered by

hydraulic model RisoSurf .

? The hydraulic surface flow module RisoSurf allows bi -directional

exchange of runoff volume:

(a) from the surface area to the sewer system, if there is sufficient sewer capacity;

(b) from the sewer to the hydraulic surface in case of sewer surcharge when the water

level in the sewer system rises above ground level.

? In case of surcharge, water level above ground as provided by surface

flow simulation module RisoSurf at exchange nodes would be used by

dynamic sewer flow module HamokaRis in the momentum equation in

the following time step. If the balance of flow volume at the nodes in

HamokaRis results in a w ater level above ground, the associate d surplus

volume would be transfer ed to the surface flow simulation by ‘storing’

this volume in the exchange location

Fig. 1 . Possible links and interaction of surface runoff, Fig. 2 . Procedure to synchronize time steps of

surface flow and sewer flow at exchange nodes. Simulation modules RisoSurf and HamokaRis

in simulation tool RisUrSim.

V. Coupling of modules RisoSurf and HamokaRis : The implementation of

coupled hydraulic flow routing for surface and sewer flow modules RisoSurf and

HamokaRis requires particular consideration of numeric stability and observation of

continuity as well. Numeric stability has been secured by a synchro nized

administration of dynamic time step selection according to F ig 2 .

Fig. 3 . Overall structure of the RisUrSim simulation tool

4. Model application — case study : One of the test areas to prove the concept of the

RisUrSim method is a sub -catchment in th e city of Kaiserslautern (Fig. 4 ). Some of the

houses in the southern street of the test -area have been subject to basement flooding during

heavy rainfall in the past. To prepare the model application, detailed surveying has been

carried out to accurately describe flow -relevant surface a reas. Besides, a flow monitoring

device has been installed to gather data during rainfall events for model calibration under

surcharge conditions. This, however, has not been successful as during the period of

monitoring not a single surcharge or even floo ding event occurred .

Fig. 4 . Test case area KL -Erzhuetten (Germany).

Fig. 5 . Mathematical representation of the street surface in a triangular network in surface flow module RisoSurf.

5. Simulation results : Due to the fact that no surcharge or flooding event could be monitored,

the RisUrSim Software has been applied to a variety of test scenarios using synthetic design storms.

These applications have been done to verify the most crucial model features of hydr aulic surface flow

simulation and the interaction between surface flow and sewer flow under surcharge and flooding

conditions. The simulation results of the real -case system Erzhuetten are shown the Fig. 10 in terms of

water level distribution along the st reet surface at 15 and 25 min simulation time, respectively. In this

system the surface elevation decreases from north -east (right) to south -west (left) while the sewer –

system flow direction is oriented in the opposite direction. This has led to problems w ith flooding in

this area in the past. The representation of simulated water levels in the manholes and on the street

surface illustrates the surface flow pattern from surcharged, flooded manholes to street areas with

lower surface levels (on the left side of the graph). This proves that with the RisUrSim Software the

surface flooding could be reproduced realistically.

Fig. 6 . Water level distribution as simulated for the test case system KL -Erzhuetten during a synthetical design

storm after 15 and 25 min.

6. Conclusions : It has been shown that European Standard EN 752 triggers more intense

consideration of the flooding phenomenon in urban drain flow modeling. In the RisUrSim

approach particular recognition is given to deta iled surface flow simulation and the interaction

between surface and sewer flow during times of surcharged sewers. This approach is ‘dual –

drainage’ concept .


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Science Technology 39 (9), 9 –22. ATV, 1999. Hydraulische Berechnung und Nachweis von Entwa?s -serungssystemen (Hydraulic calculation and

verification of drainage systems.), Arbeitsblatt A 118, ATV -Regelwerk, Hennef, Germany 1999. CEN, 1996. Drain and sewer systems outside buildings —Part 2: Performance Requirements, European Standard,

European Comm ittee for Standardization CEN, Brussels, Belgium 1996. CEN, 1997. Drain and sewer systems outside buildings —Part 4: Hydraulic design and environmental

considerations, European Standard, European Committee for Standardization CEN, Brussels, Belgium 1997. Djordjevic, S., Prodanovic, D., Maksimovic, C., 1999. An approach to simulation of dual drainage. Water Science

and Technology 39 (9), 95 –103. Ettrich, N., Steiner, K., Schmitt, T.G., Thomas, M., Rothe, R., 2004. Surface models for coupled modeling of

run off and sewer flow in urban areas, Conference paper submitted for Urban Drainage Modeling 2004, Dresden,

Germany 2004. Hilden, M., (2003): Extensions of Shallow Water Equations. PhD Thesis, Department of Mathematics,

Kaiserslautern University. Roesner, L .A., Aldrich, J.A., Dickinson, R.E., 1988. Storm Water Management Model User’s ManualManual,

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Agency, Athens, GA, p. 203. Schmitt, T.G., 1986. An efficient met hod for dynamic flow routing in storm sewers, Proceedings Of the

International Symposium on Urban Drainage Modeling, Dubrovnik, Yugoslavia 1986 pp. 159 –169. Schmitt, T.G., 2001. Evaluating hydraulic performance of sewer systems according to European Stand ard EN 752,

Water21, Magazine of the International Water Association, London 2001, pp. 29 –32. Schmitt, T.G., Thomas, M., 2000. Untersuchung zum rechnerischen

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