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COASTAL URBAN FLOOD SIMULATION USING FEM-GIS BASED MODEL Shahapure S.S.1, M.ISH
Kulkarni A.T.2, M.ISH Bharat K.S.R3, M.ISH Eldho T. I.4, F.ISH
Rao E.P. 5
1
Research Scholar, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076. email:
[email protected] 2 Senior Research Fellow, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, email:
[email protected] 3 Former M.Tech. Student, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, email:
[email protected] 4 Professor, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400 076, PH +91 (022)25767339 email:
[email protected] 5 Associate Professor, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400 076, PH email:
[email protected]
ABSTRACT In this paper, a coastal urban flood simulation model is presented using simple mass balance technique for overland flow and diffusion wave equation for channel flow. Finite Element Method (FEM) has been used for solving the diffusion wave equation. Effect of tidal variation is considered as the boundary condition. Geographic Information System (GIS) is used for data management while remote sensing is used for land use classification. The model is applied to an urban catchment of Panvel, Maharashtra and possibility of flooding is investigated for three rainfall events. It is observed from the results, that the model reasonably simulates the water levels in the channel compared to field observations. Parameter based sensitivity analysis showed that model results are reasonably stable for different parameters. It is observed that peak discharge and time to peak are moderately sensitive to land use within the catchment. INTRODUCTION Flooding in coastal urban areas due to heavy rainfall and high tide is now becoming a major concern. Major cities in India have witnessed loss of life and property, disruptions to transport and power and incidences of epidemics during the monsoons, most notable amongst them being Mumbai in 2005, Surat in 2006 and Kolkata in 2007. The annual disasters from urban flooding are now much greater than the annual economic losses due to other disasters. It is estimated that over 600 million people will be living in metropolitan areas in India by 2021, and hence finding better ways to deal with special features of floods in urban areas is crucial (Reddy, 2008). Reasons for urban flooding could be many, right from inadequate drainage system, increase in the paved areas to the impact on precipitations due to climate change phenomenon. The problems are further compounded for urban city located in coastal areas, where the draining of the storm water is governed by tidal levels. Thus, there arises a need for coastal urban flood simulation tool which could indicate, in advance, flooding areas or the flooding of channel nodes of the catchment for a given rainfall event. Numerical methods are the main model building tools in physically based hydrology models. Advantage of FEM is that irregular boundaries can be easily dealt with and the matrices of the assembled system of equations are banded and symmetric. The development of Geographic Information Systems (GIS) has significantly changed the way spatial data is managed. Finite Element Method has been used by many researchers in the simulation of channel flow (Szymkiewicz 1991; Aronica et al 1998; Garg and Sen 2001). Greene and Cruise (1995) developed a GIS based model for an urban watershed in Baton Rouge, Louisiana. Mark et al.
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(2004) simulated the urban flooding by one-dimensional hydrodynamic modelling with GIS for Dhaka city. Aronica and Lanza (2005) have used finite element scheme with triangular elements for urban flood simulation. Smith (2006) used urban flood estimation models integrated with GIS tools and terrain analysis technique. Eldho et al. (2006) developed a coupled model for Badi-Kanjawani watershed for rainfall-runoff simulation using FEM and GIS. Reddy et al. (2007) developed a kinematic-wave based distributed watershed model using FEM, GIS and remote-sensing-based approach for the runoff simulation of Catsop watershed in the Netherlands and Amba watershed in Western Ghats of Maharashtra. Bahremand and De Smedt (2008) applied the GIS based WetSpa for estimating flood runoff to the Torysa river basin located in Slovakia. Hai et al. (2008) developed a 2D finite element model for inundation processes in the floodplains of Tonle Sap Lake with the help of GIS tools. In this paper, a flood simulation model has been presented based on FEM and GIS which can be used for flood modelling in coastal urban areas. The model has been applied for Panvel area in Navi Mumbai, Maharashtra and results are presented. MODEL FORMULATION For the urban flood modelling, the urban area is considered as a watershed. The runoff is considered with respect to overland flow and channel flow. The two basic components of the model are the overland flow model and channel flow model. The infiltration and the initial interception losses are not modelled as the present objective is simulation of flood event after the onset of monsoon. Also, urban areas are predominantly impervious and hence infiltration is negligible. The mathematical formulation for the model is briefly described below. FORMULATION FOR OVERLAND FLOW The overland flow for any sub region can be evaluated as follows using the continuity equation (Rao and Rao, 1988): I− Q=
∂(VOL) ∂t
(1)
Where I= Inflow; Q= outflow; VOL= the detention storage over the sub region. Eq. (1) can be written as; r . A c − q . L = ∆ VOL / ∆ t
(2)
Where r is the excess rainfall which is the inflow for the catchment (which is considered same as the total rainfall for the reasons cited above) and q is the overland flow from the catchment into the stream element. The unit of q is taken to be catchment flow per unit length of the stream. This flow is assumed to be perpendicular to the length of the element. If ∆t is the time step in seconds, L is the length of the stream element in meters, Ac is the area of sub region in km2, r is expressed in mm/hour and d is flow depth in mm obtained by using Manning’s empirical formula. Equation (2) can be written as, 5
K 1d t + ∆ t 3 + 100 d t + ∆ t = K 2
Where
K1 =
LS 1 / 2 ∆ t 2 nA c
and
K
2
5 r + rt + ∆ t = 100 d t + ∆ t t − K 1d t 3 72
(3)
(4)
3
The overland flow q during the time step ∆t is given as q = 1 (q t + q t + ∆ t )
(5)
2
Where n is the Manning’s roughness coefficient and S is the slope of the overland flow. The equation (3) is non linear and is solved by an iterative procedure. FORMULATION FOR CHANNEL FLOW The channel flow can be represented by the following one dimensional gradually varied unsteady flow equations based on Saint Venant’s equations (Ross et al, 1979): ∂A ∂Q − q = 0 + ∂x ∂t
Let
∂Q ∂ + m = ∂ ∂ t x
Q 2 A
;
Q 2 ∂ A ∂x
+ gA ∂ H + S ∂x
(6, 7)
= 0
f
(8)
/ gA
From equations (7) and (8), we have, Manning’s formula can be written as
∂Q + ∂t
S
Q =
∂ H − ∂ x
=
f
1 AR n
2 3
S
1 2
+
m
∂H = − K ∂x
f
(9)
+ m ;
(10) Where
A
=
k
⋅ R
∂ H n ∂ x
+
2 3
m
(11)
1 2
In diffusion wave model, the local and convective acceleration terms in the momentum equation are neglected. Finally, the diffusion wave form, where m=0 (Hromadka et al., 1986) can be expressed as: W
∂H ∂ ∂H K − − q = 0 ∂t ∂ x ∂ x
(12)
Where W is the width of the channel. The FEM Formulation of equation (12) is obtained from Galerkin’s approach. The stage H can be approximated as, H = ∑n H i N i , where N1= (1-x/L), N2= x/L for a line element i = 1
with linear interpolation, L is the length of the element and n is the number of nodes in the element. Equation (12) is approximated by Galerkin’s approach and written as L
∂H T ∫ [N ] [N ]dx 0
Here
K − ∂t W
{H } =
1 2
[N ]T ∂ H
x=L
K + W ∂ x x = 0
[{H }t + ∆ t
+ {H
L
∫ 0
}t ] and
∂ [N ] ∂ [N ] dx {H ∂x ∂x T
1 ∂H = ∆t ∂t
}−
q W
[{H }t + ∆ t
L
∫ [N ]
T
dx = 0
(13)
0
− {H
}t ]
(14)
The equation (13) is integrated over the length of the element using linear interpolation functions and the element matrix is given below.
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K LW 2∆t + 2L K − 2L
LW K qL t t t 2 + 2∆t H 1 − 2L H 1 − H 2 H 1 = qL LW K H 2 LW K t + ∆t H 2t − H 2t − H 1t + + 2∆t 2L 2∆t 2L 2 −
( (
K 2L
) )
(15)
Equation (15) is solved after applying the initial and the boundary conditions to find the unknown head. The initial condition used here are at t=0; Q(x, 0) =Q0; H(x, 0) =H0. The boundary conditions used are: upstream boundary H=H (0, t) or Q=Q (0, t) and downstream boundary H=H (Lc, t) or Q=Q (Lc, t); where H is stage, Q is the discharge through the channel and Lc is the length of the channel. Here, tidal flow is considered and base flow is neglected. The overland flow model and channel flow model, discussed above, are coupled to have an integrated model for event based rainfall runoff simulation of urban watershed. The integrated model simulates water levels (stage) and runoff at any location on the main channel for a watershed for the given rainfall and tidal flow condition. The inputs for the model are given from the database, which is generated from GIS thematic maps. Database for the model is discussed along with the case study below. TIDAL EFFECT In coastal urban areas, the drainage channel joins the creek and the flow depth in the channel depends upon the tidal variation at end node. Tides around the catchment are semi-diurnal (two high waters and two low waters each day). The tidal boundary condition is considered based on a semidiurnal sinusoidal equation in time t (CIDCO, 2003) and is given below: 2π t d = d m + h × sin t p
(16)
Here d is the tidal stage; dm is the mean tidal stage; h is half the tidal oscillation range; t is time; tp is the period for one complete tidal cycle. The values at the boundary condition are based on the above mentioned equation and the daily tidal charts available for the Apollo Bunder, Mumbai. Mean Sea Level (MSL) values at Apollo Bunder are obtained after subtracting 2.50 m from the values in tidal charts. A correction of +0.3 m and lag of 20 minutes is considered while applying the values from the tidal charts of the Apollo Bunder for Panvel Creek. CASE STUDY Panvel located in Navi Mumbai, is one of the rapidly urbanizing coastal areas of Maharashtra. Panvel is located in Gadhi valley with the Gadhi as its main river. The study area lies between 190 00’ 00” N and 190 01’ 19” N latitude and 730 04’ 55” E and 730 08’ 37” E longitude. The catchment area is 8.27 Sq. Km. Fig. 1 shows the study area. The study area has a mix of residential, commercial and institutional spaces along with pockets of barren as well as marshy land. The study area is surrounded by Sion-Panvel expressway on north-west side, Parsik foothills on the eastern side. The catchment outflows into the Panvel creek on the western side. The ground level variation is from 0.0 to 251.0 meters above MSL. The dominant flow direction is to the west. The inputs for the overland flow module of the integrated model are rainfall intensity at specified duration, mean overland flow slopes, roughness values and area for each of the overland flow element. The inputs for the channel flow module are bed levels, channel properties like cross-section area, roughness values, side slopes as well as channel node connection. The tidal variation is considered as boundary condition for the channel flow.
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Mass balance equation is used for overland flow simulation while diffusion wave based FEM for channel flow for quick estimation of flooding depths at the channel nodes. GIS software ArcGIS 9.3 has been used for pre-processing of input data. Image classification software ERDAS Imagine 9.0 is used for classification of land use of the catchment. Manning’s roughness values are assigned based on land use pattern in the ArcGIS environment. The subsequent section briefly describes the steps for developing the database. USE OF GIS AND REMOTE SENSING The topographic map of the catchment area was geo-registered in ArcGIS 9.3. The contour lines were digitized in ArcGIS as a polyline file. The data on spot levels, for the catchment, obtained from CIDCO was used to prepare point files. A Digital Elevation Model (DEM) was prepared using the above mentioned polyline and point shape files, in ArcGIS software. Fig. 2 shows the DEM of the study area and Fig. 3 shows the slope map. In the context of urban watershed, the flow in the mainland is based on the man-made drainage system. Hence the actual delineation of the urban watershed is done subjectively using natural delineation (ArcGIS software) and storm water network layout provided by CIDCO.
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For the purpose of modelling, the catchment area is divided into 38 overland flow elements. Maximum and the minimum area of the overland flow elements are 103.48 ha and 1.26 ha respectively. The slope values are obtained from slope map and grid coverage map using zonal statistics option of ArcGIS. Fig. 4 shows the overland flow grid and the main channel of the catchment. Land use classification for the catchment is carried out using remotely sensed data of IRS-P6 LISS III image dated May 14, 2005 with a spatial resolution of 23.5 meters. The image is classified into four classes using supervised classification option of ERDAS Imagine software. Land use classes are, built up area (69.44%), marshy land (11.02%), forest land (19.47%) and water body (0.07%). The Manning’s roughness values for built-up area, marshy land, forest land and water body considered are 0.015, 0.07, 0.1 and 0.03 respectively (Vieux, 2001). Thus, the classified raster image was further reclassified using reclassify option of ArcGIS to spatially distribute the roughness values to various classes.
The main channel of the catchment has been longitudinally divided into 57 elements with 58 nodes. The total length of the channel is 4750 meters, with the maximum and minimum element lengths of 100 meters and 20 meters respectively. The details on bed levels and other details of the trapezoidal channel were obtained from CIDCO. The average longitudinal slope of the channel is 1 in 1011. The channel Manning’s roughness has been considered as 0.03. The channel flow nodes are shown in Fig.6.
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RESULTS AND DISCUSSION Two rainfall events were simulated and the simulated water levels were compared with the observed, in addition to generation of runoff hydrograph using the above mentioned integrated model. An extreme event of July 26, 2005 has also been simulated to investigate possibility of flooding in the main channel. The tidal level at the start of the rainfall is considered as the initial condition of the channel. The infiltration loss is neglected as it is assumed that soil surface has been sufficiently saturated before the occurrence of these events. A time step of 30 sec has been used and all the events are simulated for 24 hrs. Tidal level is considered at the end node of the channel and hence base flow is not considered separately. The rainfall and initial conditions of the tide is summarised in Table 1. Simulated maximum peak at end node and maximum stage at the start node is shown in the same Table. The simulation results of discharge and stages for the three events, for the simulation period are shown in Fig. 7, Fig.10 and Fig.13 respectively. The channel bed level, the water level profile for different periods and the ground level for three events along the channel length are shown in Fig. 8, Fig. 11 and Fig. 14 respectively. TABLE 1 SUMMARY OF RAINFALL AND RUNOFF FOR THE SIMULATED EVENTS Event No. Event Date Rainfall start time Total Rainfall Volume Total Rainfall Duration Average Intensity Max Rainfall Intensity (RI) Duration of Max. RI Initial Tidal Conditions Tide Level at start of Simulation (above MSL) Phase of tide Results Total Simulation Period from start of rainfall Total Runoff Volume Max. Stage (at Ch 0.00 m) Time of max. stage w.r.t to rainfall start time Peak Discharge (at Ch 4750.00 m) Time of peak w.r.t to rainfall start time Flooding at Channel Node
1
mm mins. mm/hr mm/hr mins. m
mins. mm m mins. m3/sec mins.
2
3
July 23, 2009 September 6, 2009 July 26, 2005 11:00 AM 11:55 AM 3:00 AM 33 38 745 810 180 1260 2 13 35 34 40 76 15 15 60 1.19
1.285
1.639
Rising
Rising
Rising
1440 34.54 6.14 735.5 24.09
1440 36.04 6.53 45.5 22.95
1440 739.57 8.12 600 164.78
269.5 NIL
116 NIL
608 0 to 700 m
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Event 1 of July 23, 2009 starts at 11:00 AM. Rainfall is sparsely distributed with total rainfall of 33 mm occurring over a period of 12 hours. The semi-diurnal tide starts rising from its low water level of 1.99 m below MSL at 06:50 hrs. The tidal level at the start of the rainfall is 1.19 m above MSL and is in rising phase. Fig. 8 shows, that effect of tidal variation is more dominant for the event as the model simulated reverse flow at chainage 3500.00 m from 0 to 2.55 hrs. The maximum simulated stage at chainage 630.00 m was 5.25 m at 12.31 hrs. The overall maximum stage of 6.14 m occurred at chainage 0.00 m at 12.25 hrs due to maximum rainfall intensity of 34 mm/hr occurring at 12th hour from the start of the simulation. The peak discharge of 14.19 m3/sec occurs at 4.48 hrs at chainage 3500.00 m. Subsequent peak discharges of 13.46 m3/sec and 8.532 m3/sec occur at 12.8 hrs and 15.97 hrs respectively at Ch 3500.00 m. No flooding has taken place along the length of the channel as can be seen from Fig. 8. Fig. 9 shows the discrete observed water levels and corresponding simulated water levels. The model has reasonably simulated the flood stage.
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Event 2 of September 6, 2009 lasts only for 3 hours with a maximum rainfall intensity of 40 mm/hr occurring for two 15 minute periods. The semidiurnal tide starts rising from its low water level of 1.22 m below MSL at 06:51 hrs and the tidal level at the start of rainfall is 1.285 m above MSL and is in the rising phase. The peak discharge of 22.95 m3/sec occurred at 1.93 hrs while the maximum rainfall intensity occurred at end of 0.75 hrs, from the start of the rainfall. The maximum stage of 6.53 m occurs at chainage 0.00 m after 0.758 hrs. The model has simulated the reverse flow at the mouth of the channel from 0 hrs to 0.65 hrs and 12 hrs to 14.40 hrs. At chainage 630.00 m, the maximum stage during the simulation was 5.612 m above MSL at 0.8 hrs. No flooding has taken place along the length of the channel as can be seen from the Fig. 11. Fig. 12 shows the discrete observed water levels and corresponding simulated water levels. The model has simulated the flood satisfactorily.
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Event 3 of July 26, 2005 is extraordinary with maximum rainfall intensity of 76 mm/hr occurring over 1 hour period. The semi-diurnal tide starts rising from its low water level of 1.33 m below MSL at 21:42 hrs on July 25, 2005. The tidal level at the start of the rainfall is 1.639 m above MSL and is in rising phase. The peak discharge of 164.78 m3/sec occurs at 10.13 hrs while maximum rainfall intensity occurs at around 9.67 hrs. The reverse flow phenomenon in the channel is not conspicuous because of the high volume of runoff. Fig.14 shows that flooding has taken place after 12 hours from the start of the rainfall for the initial 700 m reach of the channel. SENSITIVITY ANALYSIS Parameter based sensitivity analysis is performed to see how the model responds to changes in parameter values and it also helps to build confidence in the model. In the present model, it is carried out by varying the Manning’s roughness for overland flow, time step and grid size for the rainfall event of September 6, 2009 to see its sensitivity on volume of runoff, peak runoff and time to peak. Overland flow Manning’s roughness is varied from -10% to +10%; time step is varied from 10 sec to 120 sec and channel element length is varied from 50 m to 200 m. Table 2 shows that decrease in the overland Manning’s roughness value (reflecting degree of urbanization) marginally increases the volume of runoff and peak discharge. Increase in Manning’s roughness value has no effect on time to peak. TABLE-2 SENSITIVITY ANALYSIS ON OVERLAND FLOW MANNING’S ROUGHNESS (n) n
n n n n n
m-1/3. sec - 10% - 5% + 5% + 10%
Volume of Runoff mm
% Variation
38.07 38.02 37.97 37.90 37.87
0.28 0.14 -0.17 -0.26
Peak discharge m3/sec 23.19 23.03 22.95 22.77 22.58
% Variation
Time to peak minutes
% Variation
1.02 0.34 -0.81 -1.62
113.5 117.5 116 116 116
-2.16 1.29 0.00 0.00
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Table 3 shows that with higher time step there is a small change in volume of runoff and peak discharge. However, for better results, moderately smaller time step is preferred. TABLE-3 SENSITIVITY ANALYSIS ON TIME STEP VARIATION Time step sec 10 30 60 120
Volume of runoff mm
% Variation
37.77 37.97 38.24 39.52
-0.54 0.71 4.08
Peak discharge m3/sec 23.19 22.95 22.70 22.26
% Variation
Time to peak minutes
% Variation
1.03 -1.09 -3.04
115.5 116 117 115.98
-0.43 0.86 -0.02
Table 4 shows that variation in channel element length has little effect on volume of runoff, peak discharge and time to peak. TABLE-4 SENSITIVITY ANALYSIS ON CHANNEL ELEMENT LENGTH Channel Element Volume of Length Runoff m mm 50 100 200
38.11 37.97 37.60
% Variation
0.36 -0.98
Peak discharge m3/sec 22.75 22.95 23.38
% Variation
Time to peak minutes
% Variation
-0.87 1.86
116 116 120
0.00 3.45
The presented FEM based model can be used to identify flooding area along the channel and can become a handy tool for the decision makers to do urban flood simulation study. It can also be used to do ‘What if’ analysis by the town planners for land use planning and hydrologic impact assessment. CONCLUDING REMARKS Rain induced flooding in coastal urban areas is a severe problem especially during the high tide period. The present study attempted to predict flooding in the channel nodes for an urbanizing coastal area in Panvel, Maharashtra. The case study shows that GIS and remote sensing tools are useful for databse management and land use classification respectively, for the modelling. The simulated water levels are in good agreement with the observed for the two rainfall events considered. From the parameter sensitivity analysis, it is observed that peak discharge and time to peak are sensitive to change in overland flow Manning’s roughness values and hence land use change. ACKNOWLEDGEMENTS The authors acknowledge their sincere gratitude to Department of Science and Technology (DST), Govt. of India, New Delhi for sponsoring a project (09DST033) on Integrated Flood Assessment Modelling for Urban Watersheds using FEM, GIS and Remote Sensing. The authors are thankful to Mr. S.C. Deshpande, Mr. P.P. Joshi, Mr. D.R. Hartalkar, Mr. P.U. Natesh and Mr. V.U. Lathkar, engineers from the City and Industrial Development Corporation (CIDCO), Navi Mumbai, Maharashtra for providing the topographical, hydrological and storm water network layout related data for the study.
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