coupled 1d-2d hydraulic simulation of urban drainage

12nd

International Conference on Urban Drainage, Porto Alegre/Brazil, 11-16 September 2011

Paz et al. 1

Coupled 1D-2D hydraulic simulation of urban drainage systems:

model development and preliminary results

A. R. Paz*1, A. Meller

2, and G. B. L. Silva

1

1 Federal University of Paraíba (UFPB), Dept of Civil and Environmental Engineering,

Campus Universitário I, 58059-900, João Pessoa, PB, Brazil. 2 Brazilian National Water Agency (ANA), SPS, Area 5, Quadra 3, Bloco "L",

70610-200, Brasília-DF, Brazil *Corresponding author, email [email protected]

ABSTRACT One of the most powerful tools to improve the planning process of urbanization and to predict

its consequent effects on surface waters and floods is hydrologic modeling. Several models

have been developed and applied for modeling urban waters following different approaches.

This paper shows the initial efforts of developing a modeling system composed by coupling a

1D flow routing model to a 2D-raster based model to simulate urban inundation, with an

additional module to simulate the rainfall-runoff process in contributing areas. As a

preliminary test of the modeling system under development, the urban catchment of Moinho

da Areia (Porto Alegre, Brazil) was simulated by running the 1D and 2D hydraulic models,

off-line coupled on a single direction. Results are evaluated in terms of inundation extent

simulated for design hydrographs of several return periods. The general inundation patterns

were considered coherent to what is known about the region, thus illustrating the potential of

the system under development for modeling urban flooding.

KEYWORDS Inundation extent; overland flow; urban inundation; urban flooding

INTRODUCTION In Brazil, the tendency of population growth on urban centers continues accelerated since the

1940’s and 1950’s decades, but mostly accentuated now in the cities of average size or where

there are regional development centers (Tucci, 2002). The fraction of Brazilian urban

population has shifted from around 40% of the total at those decades for over than 80%

nowadays. In the urban centers in which the urbanization is currently largely accelerated,

inadequate processes of urbanization and environmental impact that have been observed on

the major metropolitan areas are being repeated. Perhaps the clearest evidence of these

inadequate processes is the tendency of increasing impervious area associated to urbanization

growth, resulting in the well-known problems of floods, water and soil pollution, and risks to

population health. As a result, the occurrence of inundation of urban areas still continues to be

considered a chronicle problem in Brazil. This is mostly due to fails in planning urban

expansion and also fails or even lack of integrated environmental and urban drainage system

projects.

One of the most powerful tools to improve the planning process of urbanization and to predict

its consequent effects on surface waters and floods is hydrologic modeling. Application of

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Coupled 1D-2D hydraulic models development 2

hydrologic models allows simulating pipe network functioning according with different

urbanization scenarios, implementation of projected hydraulic structures, and for several

return period rainfall events, i.e. for distinct flood simulation scenarios.

Several models have been developed and applied for modeling urban waters following

different approaches. The choice of which model to use must be according with the purposes

of the studies, the data availability, the characteristics of the study area, and the availability of

human and computational resources (Fread, 1992). If the study aims at investigating the

inundation dynamics and extent over the streets and surrounding surface, a relatively recent

modeling proposal is to use a 1D model to flow routing along the underground drainage

features (pipe networks) and narrow open channels, dynamically coupled to a 2D model to

simulate overland flowpaths (inundation over streets and floodplains) (Hsu et al., 2000;

Phillips et al., 2005; Leandro et al., 2009). This approach follows the more widely applied

coupled 1D-2D models for simulating natural river channels with floodplains (Verwey, 2001;

Horritt and Bates, 2001; Hunter et al., 2007; Chatterjee et al., 2008).

This paper shows the initial efforts of developing a modeling system composed by coupling a

1D flow routing model to a 2D-raster based model to simulate urban inundation, with an

additional module to simulate the rainfall-runoff process in contributing areas. As a

preliminary test of the modeling system under development, the urban catchment of Moinho

da Areia (Porto Alegre, Brazil) was simulated by running the 1D and 2D hydraulic models,

off-line coupled on a single direction. Results are evaluated in terms of inundation extent

simulated for design hydrographs of several return periods.

METHODS

Rainfall-runoff model component

To simulate the hydrologic processes that produce runoff from urban areas, the IPHS1 lumped

hydrologic model is being used. This modeling system was first presented by Tucci et al.

(1989), being composed by several algorithms well known and described in literature, such as

the Horton and SCS algorithms for obtaining the excess rainfall and the Clark and SCS unit

hydrograph methods for surface flow routing, and algorithms for groundwater, reservoir and

river flow routing (Tucci, 1998).

In this research, the SCS method was used to calculate effective rainfall and the SCS

triangular unit hydrograph method, as implemented in the IPHS1 hydrologic model, was used

for obtaining design hydrographs for several annual return intervals. These hydrographs were

considered as input to the macro-drainage pipe network simulated by the 1D hydraulic model.

1D model component

The world-widely applied Storm Water Management Model (EPA-SWMM) is used for 1D

dynamic flow routing through the drainage system composite of pipes and open channels.

The SWMM is a model used in urban and non-urban areas, with several capabilities for

simulating the various hydrologic processes that produce runoff and also the flow routing

through the drainage system network of pipes, channels, storage/treatment units and diversion

structures (Rossman et al., 2005; USEPA, 2007). Flow routing through the 1D drainage

network is calculated using either kinematic or full dynamic wave methods, accounting for

user-defined dynamic control rules to simulate operation and flow behavior of hydraulic

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Paz et al. 3

structures. The SWMM has been used in thousands of urban, and many non-urban,

applications worldwide (Rossman et al., 2005).

2D model component

The simulation of overland flowpaths is performed by a raster-based model with a 2D

kinematic approximation, following Bates and De Roo (2000) and modifications proposed by

Paz et al. (in press), but with adaptations to deal with urban areas.

The proposed 2D model adopts a regular grid discretization of interconnected elements,

which may change flow with neighboring elements and with external sources (Figure 1). At

each time step, the balance between the inputs and outputs on a given element is used to

update its water level (h), through a numerical scheme explicit on time and progressive on

space. The water level h in an element i,j at time t+∆t (where ∆t is the time step) is

determined by:

( )yx

tQQQQQhh

j,i

ex

tj,i

y

t1j,i

y

tj,i

x

tj,1i

x

t

j,itj,itt

∆∆

∆∆

⋅

⋅+−+−+=

−−

+

where x

tQ and y

tQ are, respectively, the discharges in x and y directions between elements;

∆x and ∆y are the element dimensions in the x and y directions, respectively; and ex

tQ means

the flow exchange between the 2D element and the corresponding location (manhole) of the

1D pipe network.

Discharge between two neighbor elements is determined by an adapted version of Manning

equation, as presented by Bates and De Roo (2000):

yx

hh

n

hQ

2/1j,1itj,it3/5

flow

t

j,i

x

t ∆∆

⋅

−±=

+

where hflow is the water depth available for flow routing between the two elements at time t,

which is given as the difference between the maximum water depth of them and the

maximum bottom elevation of them; and n is the Manning roughness coefficient of the

element.

Figure 1. (a) Discretization of surface in 2D model grid cells, indicating which elements are

connected with the 1D network of pipes, according with location of manholes/inlet points; (b)

exchange flows between neighboring cells of the 2D model.

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The 2D urban flooding may be modeled a 2D full hydrodynamic model. However, this may

be infeasible due to numerical instabilities related to small water depths and the wetting and

drying process as well as excessive computational costs. The simplifications adopted in the

kinematic approximation used in this study overcome these difficulties, with the advantages

of being easily integrated into a geographic information system (GIS) (Paz et al., in press).

Coupling 1D and 2D models

Water exchanges between the 1D and 2D domains occur primarily through the manholes of

the pipe network, on both directions: while the conduit capacity of the 1D network is not

exceeded, overland flow may enter the network; on the contrary, surcharged manholes cause

surface inundation. This approach of dynamically coupling 1D and 2D models allows the

modeling of several distinct situations, such as the pond of the surcharged flows in the

surrounding surface, propagation of this excess of water along the surface and even the return

of part of this flow to the pipe network through a downstream and not surcharged manhole.

In the modeling system under development, a decoupled 1D/2D time-step approach is being

considered (Trigg et al., 2009), in which different time steps are set to the 1D (∆t1) and 2D

(∆t2) models. The 1D model is run by 1∆t1 and then the 2D model is run by np times ∆t2,

where np = ∆t1/∆t2. After a time interval of ∆t1, the water exchanges (Qex) between channel

(1D model) and floodplain (2D model) are calculated.

A simplified approach is currently being used for testing the system under development: an

off-line coupling of 1D and 2D models. In this approach, firstly the IPHS1 hydrologic model

is used for obtaining design hydrographs for a given return period, which is then considered

as input to the macro-drainage pipe network modeling. Then 1D and 2D hydraulic models are

run by off-line coupling on a single direction: (i) first, the 1D model is run and the

hydrographs at surcharged manholes are obtained; (ii) secondly, these surcharged

hydrographs are considered as inflows when running the 2D model.

Study case and models application

As a preliminary test of the modeling system under development, the urban catchment of

Moinho da Areia (Figure 2), located in the city of Porto Alegre (Rio Grande do Sul state,

South of Brazil), was simulated. For the hydrologic simulation, the whole data as CNs,

subcatchment areas, time of concentration, slopes and concerning the urban drainage network

for the dynamic wave simulations were extracted from the urban master plan report (IPH,

2002). The 2D model discretized the surface domain by a 5-m square grid, and the surface

topography was represented by a digital elevation model (DEM) with equal spatial resolution.

This DEM was modified by burning the streets path, i.e. reducing the elevation value of the

cells located along the streets by a fixed value of 0.40 m, analogously to the stream burning

procedure commonly used to modify a DEM to reflect known hydrology (Hutchinson, 1989).

This procedure was applied as the available DEM is not detailed enough to represent the

streets, and the 0.40 m value was arbitrarily chosen considering it sufficient to allow such

representation.

Distinct greater manning coefficients were adopted for elements of the 2D model lying bellow

the streets path compared to the rest of them. Manning roughness coefficients were arbitrarily

set as 0.017 for 2D elements representing the streets path and as 0.025 for the rest of the

elements of the 2D domain. The 2D simulation was performed for a time period of 1 h 40

min, with a time step of 1 s to avoid numerical instabilities.

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Paz et al. 5

Figure 2. Location of the Moinho da Areia catchment in the Rio Grande do Sul state and in

the Brazilian territory, and its Digital Elevation Model (DEM) overlaid by streets, with

location of the ten inlet points considered in this study.

Four return periods were considered for obtaining the design hydrographs with the IPHS1

model: 2-year, 10-year, 50-year and 100-year return periods. The corresponding synthetic

hyetographs used as input in the IPHS1 model were generated by the intensity-duration-

frequency curves from the 8º Distrito de Meteorologia rain gauge, using the alternating block

method. The duration time for these hyetographs was set to 60 min, which is the

concentration time of the basin according to the urban master plan studies (IPH, 2002).

The mentioned hydrographs were used for simulating the 1D SWMM model of pipe

networks. The surcharged hydrographs calculated with SWMM at ten manholes/inlets points

were obtained and then used as input for running the 2D model. These procedures were

adopted in the set of simulations A. In the other set (named as B), a slightly modification was

performed in the last step, when preparing the input hydrographs for the 2D model. In this set

B of simulations, it was considered that the manhole number 1, located nearby the catchment

outlet, could serve as a return point of the surface inundation down to the 1D domain, if the

conveyance capacity of such manhole and of its corresponding pipe was not exceeded. The

maximum flow allowed for being conveyed by the pipe downstream of manhole 1 was set as

24.4 m3/s, the maximum capacity of outlet conduit according to the dynamic simulations

carried out with SWMM.

RESULTS AND DISCUSSION By applying the IPHS1 hydrologic model for the design hyetographs of the four defined

return periods, the input hydrographs for simulating the 1D pipe network with the SWMM

model were obtained. The results of running such model are the surcharged hydrographs at

the ten manholes shown in Figure 3, which were then used as input for running the 2D

inundation model. Figure 3 illustrates how the adoption of increasing return periods lead to a

larger number of manholes/inlet points not being able to convey the flow and to an increase in

the surcharged flows. For the 2-year return period, just two manholes (M5 and M9)

surcharged, while this amount increased for seven, nine and ten manholes when the 10-year,

50-year and 100-year return periods were adopted, respectively.

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Figure 3. Surcharged hydrographs at the ten manholes/inlet points according to the return

period adopted (2-year, 10-year, 50-year or 100-year return periods).

Inundation maps expressed in terms of maximum water depth for each return period and for

each set of simulations are presented in Figure 4. These maps are overlaying a RGB color

composite of a satellite image in the background. In the set of simulations A, as no water is

allowed to leave the 2D domain by returning to the 1D domain, or by evaporation or other

losses, the maps of maximum depth also closely indicate the maximum extent of the

inundation. Thus, as expected, it can be seen that both shape and depths of surface inundation

were mostly dictated by the DEM configuration, following the streets path. Accordingly,

results show the increase in flooding extent with increasing return periods.

The adoption of a slightly lower value of the Manning coefficient for the 2D elements lying

bellow the streets path in comparison with the rest of the elements has also contributed to

obtaining these inundation patterns. However, indeed the procedure of stream burning the

original DEM by the streets paths and lowering the DEM by 0.40 m along these paths was the

major influence over the overland flow routing. The extent to which the stream burning

procedure as well the adoption of distinct Manning coefficients has influenced the results may

be further better investigated.

Despite of not having inundation maps from other sources for comparison with our results,

such as inundation extent derived from satellite images, the general pattern of inundation

dynamics obtained in this preliminary test is considered coherent to what is known about

actual inundations occurring in the region. For instance, a large and deep inundation area was

simulated in the upper part of the maps shown in Figure 4. This region, where is located the

PUC University, is well known as commonly being inundated, with water covering both sides

of the main avenue in front of the parking lot of this university. Additionally, in the

inundation maps shown in Figure 4, there is also a preferential flow path in the south-north

direction, located nearby the center of the figure. This is the flow path of the main channel of

the Moinho creek.

Visual comparison of inundations maps between both set of simulations shows that, for

design hydrographs of return periods of 10-years or more, the consideration of water leaving

the 2D domain at manhole 1 resulted in lower water depths in the region surrounding such

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Paz et al. 7

manhole. In terms of inundation extent, pronounced differences between the two sets of

simulations were obtained just for the 10-year return period scenario. This test gives a roughly

idea about the influence of representing the dynamic integration between 1D and 2D domains

when simulating inundation dynamics and extent over urban areas.

Figure 4. Maximum water depth simulated by the 2D model applied to the Moinho da Areia

catchment, considering as input the design hydrographs estimated for four distinct return

periods; simulations set B distinguish from set A because in the former the 2D overland flow

was allowed to return to underground 1D network through the manhole number 1.

CONCLUSIONS Inundation maps along time were obtained for this preliminary test, showing the evolution of

the flood over the surface as a result of the incapacity of the underground pipes to convey the

inflowing water. Results show the increase in flooding extent with the increasing of return

periods. As expected, the shape and depths of the inundation were mostly dictated by the

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DEM configuration, following the streets path. There results were not evaluated by

comparison with inundation maps from other sources (e.g. satellite images), but their general

patterns were considered coherent to what is known about the region, thus illustrating the

potential of the system under development for modeling urban flooding.

Further work will be focused on on-line coupling the SWMM model to the 2D model, and

future simulations will also be conducted for urban areas of João Pessoa, a city of the

Northeast of Brazil where the urbanization process is under strong development, but still

lacking integrated environmental and urban drainage system projects.

ACKNOWLEDGMENT

We acknowledge the LABGEO (Laboratório de Geoprocessamento, Centro de Ecologia) of

the Federal University of Rio Grande do Sul (UFRGS) and prof. Alfonso Risso from IPH-

UFRGS by providing the Digital Elevation Model used in this study.

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coupled 1d-2d hydraulic simulation of urban drainage

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