Abstract. 1 Introduction

Transcription

1 Numerical simulation of overland flood flows in an urban bay area M. Takeda, T, Uetsuka, K. Inoue, K. Toda Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto, 611, Japan Abstract Overland flood flows in an urban bay area are studied by means of a numerical simulation model which comprises a 2-D storm surge model and a 2-D overland inundation flow model. First, actual overland flood flows caused by a storm surge are simulated and the accuracy of the simulation results is examined. Next, the main factors of urbanization, buildings, houses and a sewerage system are taken up, and their influence on the characteristics of inundation flood flows is discussed. Through these studies, the validity of the simulation model for inundation analysis is demonstrated and the influence of urbanization on inundation flows is clarified. 1 Introduction Recently, population and property have become increasingly concentrated in urban bay areas both for reasons of convenience, and because of changes in industrial structure. As the social importance of urban areas increases, so does the potential for damage by natural disasters. One of these in urban bay areas is flooding due to storm surges. In order to take effective measures against such disasters, we must first be able to estimate the overland flood flows due to storm surges. Numerical simulation by means of a horizontal 2-D model is an important research method for overland flood flows due to storm surges. Although various numerical experiments for inundation flows have been reported, their results are discussed only in qualitative terms, and their accuracy does not seem to be described in detail. Here, we have simulated the inundation due to storm surge caused by Typhoon Jane, one of the biggest typhoons to have

2 60 Hydraulic Engineering Software attacked the Osaka bay area, and examined the accuracy by comparison of the simulated results with observed data. Secondly, in order to examine the influence of urbanization on inundation by storm surge, we have developed a numerical model considering the effects of buildings, houses and a sewerage system. In this model, the effects of buildings and houses on flood flows are expressed not only by the roughness but by the permeation rate. As for the sewerage system, it is treated as a regulating storage and the exchange between overland flow and sewerage flow is taken into consideration. Both effects are discussed with reference to the simulation results. 2 Governing equations For storm surge analysis, the shallow-water equations can be applied,.9#, c^m 8% TV r_ ^ ^,_,_ -gh-^-- + ^-T- + ^ /N i 9% <9z 0^2 "91/ " a ^. ( "5" + "5~ = 0 (3) % 02 0% where t is time and (x,y) are rectangular coordinates. (u,v) is velocity, h is water depth, (M,N) is mass flux (M uh, N vh), and H is water level. (ex y) are eddy viscosity coefficients in the (x,y) directions. (^^,7^^) and (Tix->Tby) are the wind shear stress at the free water surface and the shear stress at the sea bottom, respectively, p^ is the density of sea water, / is the Coriolis coefficient, and g is gravitational acceleration. Equations for the shear stresses at the water surface are expressed by where p^ is the density of air, 7^ is the friction coefficient at the water surface, and (W.^,Wy) is the wind at 10m above the water surface. In the case that large shear stresses act at the water surface in a storm surge, the equations for the shear stresses at the sea bottom are expressed by Tbx = /9w#?f %\ where n is the Manning coefficient and A: is a coefficient whose value is 0.25 [i]. The Leap-frog method, an explicit method, can be used for discretization of these equations. The forward-difference scheme and Ist-order up-wind difference scheme are applied to the time-dependent terms and advection (4)

3 Hydraulic Engineering Software 61 terms respectively, and for the other terms, the centered-difference scheme is used. Viscosity terms at the sea bottom are treated implicitly considering Vasiliev instability. Pressure and wind distributions are required for representing the typhoon. Here, Schloemer's equation for the pressure distribution is used, where f is pressure, P<, is pressure at the center of the typhoon, Af is the pressure difference at the center, r^ is maximum wind radius and r is distance from the center. Wind distribution is determined by vectorial addition of the wind which occurs due to migration of the typhoon, and the ground wind which is related to the wind caused by pressure gradient. The wind which occurs by migration of the typhoon %), the wind by pressure gradient (%,,.) and the ground wind (%,) are given by, I/ = C, Kexp(-/?r) -^ + fvr = ~ V. = % (7) i pa Or where, %= is the velocity of typhoon, C\, (?2 and /? are 4/7, 0.6 and 7r/(400 x 1000) respectively. The corrected angle between % and %,,, is 30. As inundation flows are caused by overflow or wave overtopping at a coastal dike, both effects are considered in this numerical model. As for the overflow discharge, it is estimated by the following method proposed by Inoue-Iwasa [2]. Assuming that Hr is the sea water level, HQ is the crest level of a dike, and Hf is the water level of the inundation area, when Hr,Hj > HQ and H? > Hf, the overflow discharge QQ can be given by the following equations, 62/61 < 2/3 62/61 > 2/3 % = ^62^(61-62 where // and // are coefficients of perfect overflow and submerged overflow, and in the case of a rectangular dike, their values are 0.35 and 0.91, respectively. 1 is the dike length, 61 = #,. - #o and 63 = #/ - #o- In the case of Hr,Hf > HQ and Hr < Hf, overflow occurs from the inundation area to the sea. As for the discharge due to wave overtopping, the method proposed by Gouda et al. [3] is used. The equations used for the overland flood flow are essentially shallowwater equations, but in the case that the water level is discontinuous, the perfect overflow equation (eqn(8)) or overflow equation at a step (eqn(9)) is used. (9)

4 62 Hydraulic Engineering Software where, //' is the coefficient related to energy loss at a step, and the value is, and ft/, is the higher land level at the step. 3 Model regions and open boundary conditions Three different computation regions were prepared for analysis. Region I where Az (the grid size in longitude) is m and Awaji f}-;'region II A?/ (the grid size in latitude) is Island m is used for storm surge analysis. Region II (Az=286.25m, A%/= m) and region III (Az=57.25m, At/=46.125m) are used for both storm surge and overland flood flow analysis. The open boundary condition in region I is the sum of the water level determined by suction due to pressure reduction (Aftp = * Region I 0.991Ap where Aftpis in cm) and / j\f Jane Typlmon the calculated astronomical tide. Plan Typhoon The calculated astronomical tide 50km consists of M2, 82, KI, d, %, K^ 1 PI, Qi and Sa components. The open boundary condition in region Figure 1: Model regions II is obtained from the computed results in region I at the boundary connecting regions I and II. That in region III is obtained from region II in a similar way. 4 Accuracy of simulation results for inundation due to storm surge Here, we take typhoon Jane which caused one of the largest storm-surge hazards in Osaka, try a simulation of the inundation flow, and verify the validity of the simulation model. The characteristics of the overland flood flow is also examined. 4.1 Analysis condition The computation regions used here are regions I and II. For overland flood flow analysis, the ground level distribution in the inundation area in 1950 was required. As there were no ground level data in existence in 1950, it was estimated by adding the subsidence during 15 years to the map data

5 Hydraulic Engineering Software 63 from Furthermore, as there were about 70 data points which were defined as the ground level in 1950, these were also used for correcting the ground level data. As the data of Sumiyoshi Ward, in the southeastern part of region III, could not be obtained, the present data (in 1995) were substituted instead. Although the T.P. (Tokyo Peil) conversion value of M.S.L.(Mean Sea Level) is also required for analysis, it was not known at that time. Therefore,first,we computed the storm surge on the assumption that M.S.L. is T.P.+O.OOm. The computed maximum tide at Osaka was T.P.+2.40m, and the observed one was T.P.+2.55m. Then, we added the computational case that M.S.L. is T.P.-f0.15m. The above discussion is appropriate, considering that M.S.L. from 1971 to 1990 is T.P.+O.OOm ~ T.P.-{-0.15m. As damage due to inundation flow over the Yodo river was not reported, this time we did not take into consideration the overflow over the banks of the Yodo river. As for the coastal dike, three different crest levels of T.P.+2.2m, T.P.+1.7m, T.P.+0.7m were considered here. The first one is the crest level which was planned in The second one is the determined value on the assumption that the subsidence is about 50cm. The third one is the mean high water springs value. The computational cases are shown in Table 1, and the parameters used are shown below. / is 8.34x10"^ I/sec, r^ is 60 km, /, is , ^ is 1030 kg/nf, ^ is kg/nf, and A/, is 100 nf/sec. The Manning coefficient is 72=0.03 for the sea area and n=0.067 for the inundation area. The discharge of the Yodo river was given a steady value of 3,200 nf/s, as obtained from the Manning Law, based on the data in the typhoon Jane report. 4.2 Results and discussions Table 1: Computational cases CASE I(A) CASE 1(13) CASE I(C) CASE II(A) CASE 1t(H) CASE I1(C) DATA 1 T.P.-fO.OOm T.P.40.15m DATA I : Initial water level DATA 2 : Dam crest level DATA 2 T.P.+2.2m T.P.-fl.7m T.P m T.P.+2.2m T.P m T.P. 40.7m Table 2: Inundation area CASE I(A) CASE I(H) CASE I(C) CASE H(A) CASE 11(13) CASE I1(C) Inundation Area (km^) G To estimate the accuracy of the simulation of inundation due to typhoon Jane, the simulated results were compared with the observed ones. In the simulated results, a much smaller area of the right bank of the Yodo river and Sumiyoshi Ward was flooded than in reality. The reason seems to be the uncertainty of the ground level. The change in ground level due to subsidence was large around the Yodo river at that time, and the present ground level data were used for Sumiyoshi Ward. Therefore, the simulated inundation data were compared with the

6 64 Hydraulic Engineering Software adjusted inundation area of 42.25km^, which is the area obtained by subtracting both the right bank area of the Yodo river and Sumiyoshi Ward, 14km\ from the total observed area, 56.25km^. The adjusted observed area lies between CASE I(A) and CASE I(B), or CASE II(A) and CASE II(B). Figure 2 shows the maximum inundation depth distribution of CASE II(B) and the observed one. The simulated result is in good agreement with the observed one. From the above results, the validity of the numerical model used here has been verified. CASR 11(13) Observed data Computed results Figure 2: Maximum inundation depth 5 Numerical simulation of overland flood flows in urban areas In this section, in order to evaluate the influence of urbanization on flood flow due to storm surge, simulations considering the existence of buildings and houses and a sewerage system are presented. In the Osaka bay area, it seems that inundation hardly occurs as long as the present countermeasures function normally, even if the "planned" typhoon (the typhoon which has the Isewan typhoon course and the Muroto typhoon scale) were to attack. Therefore, in this study, we assumed a worst-case scenario as described below. According to the IPCC report, it is expected that the water level will increase by 30cm ~ 110cm by 2100 due to global warming, and unless some measures are taken, the average water level rise will be 65cm. Considering this prediction, we assumed that M.S.L. is T.P m. Also, we assumed the emergency case that the tidal gates do not work normally. In the simulations here, wave overtopping is not taken into account. 5.1 The influence of structures on overland flood flows

7 Hydraulic Engineering Software 65 Overland flood flows are modified by the presence of structures in urban areas. One method of evaluating the influence of structures in detail is to use a grid size small enough to express them. However, this method needs enormous data and is of no practical use. Although the influence of structures is generally treated by the roughness coefficient n in the viscosity terms at the bottom, this idea is not clear in a physical sense. Here, a method in which both the roughness coefficient and the permeation rate proposed by Nakagawa [4] are incorporated is introduced and the results are compared with those of the generally-used model The method incorporating permeation rate The ratio of the total structure area to the model grid cell area can be expressed by the occupancy of structures \ij (Figure 3), and the permeation rate /%j is Y 1 \ij. As the occupancy of structures increases, the overland flood flows are blocked. From this point, Figure 3: momentum flux is corrected as follows, The concept of A,-j 2+1/2J a = i + 1 a = i (10) Substitution of the corrected momentum flux of eqn (10) into the continuity equation yields,. ^ x^r-^r (1-^) 2^ - + = o (ii) This new continuity equation is used in this section Analysis condition To estimate the influence of structures on inundation, it was supposed that the o ecu pane} of structures A is constant in the analysis area. The simulation was executed with A = 0.00, 0.25, 0.50, 0.75 and n=0.067 (CASE I ~ IV respectively). For the generally used method, A=0.00 and n ==0.100 (CASE la,) were used. The computed area is region III Results and discussions Figure 4 shows the inundation area and Figure 5 shows the ratio of inundation area to the total inundation area and the flood depth distribution. CASE I and CASE 1% are almost similar results, that is, the model with the roughness coefficient only does not show any distinguishable difference. On the contrary, in both figures, as A increases, both the inundation area and

8 66 Hydraulic Engineering Software 2-0 L»-»- 16:00 199G 9/16 20:00 Figure 4: Inundation area 4:00 (%) A=0.00 n= A=0.75 n=0.067 aly ^ 60 t$ < ^o.2 20 " 22:00 0:00 2: /16 9/17 4:00 j= 22:00 0:00 2: /16 9/n ID 0. 0 m o m) 0. 1 ~ a 0. 5 ~ m»h i. l o-. 0 ~ ~ 2. 0 CASE I CAES IV Figure 5: The ratio of the inundation area to the analysis area the inundation depth increase. The area where the inundation depth is more than 1.0m scarcely appears in CASE I, while the area where it is more than 2.0m appears in CASE IV. It is considered that as structures increase, the inundation depth and the inundation area increase. From the above results, it has been shown that the method using the permeation rate can express the influence of structures better than the usual method with n only. 5.2 Influence of sewerage system on overland flood flow Sewerage systems, which are constructed in urban areas for the disposal of polluted water and rain water, are not designed for the disposal of overland flood water. However, when inundation occurs in a closed urban area, it seems likely that overland flood water enters the sewerage system, and that the inundation flow volume depends on it. Therefore, the sewerage system is also an important factor to estimate overland flood flow behaviour. 4:00 (m)

9 Hydraulic Engineering Software The method for representing the sewerage system The purpose of this study is not to simulate the sewerage flow in detail, but to extend the inundation model by incorporating a sewerage system. Here, the sewerage system is treated as a regulating storage, and the exchange between overland flow and sewerage flow and the discharge from pumps are taken into consideration. Inflow into the sewerage is estimated by eqn(9), where L is 2;rr^, and j"rnh is manhole radius. Supposing that Q^ is inflow into the sewerage, Qout is outflow from it, and V^ is pondage, the time variation of pondage is expressed by d% ^" (12) ^9z (K > 0) Qout %% > 0) where g, is inflow at the manholes, <^W system, % is storage capacity, and %, = is the discharge capacity of the Analysis condition The analysis area is Ichioka treatment plant (about 8.26knf ) in region III. The sewerage system was modeled by the sewerage pipeline network, including pipes with radius of more than 1m. The capacity of this sewerage network is about 70,000nf and the total discharge capacity of pumps is about 70nf /s. Manhole radius is 0.5m. The used values of A and n are 0.0 and respectively. This case with the sewerage system is defined as CASE V. =0.00 n=0.067 Sewerage Sewerage -e- No Sewerage 22: /16 0:00 4:00 CASE V 9/17 See Figure 5 _. _,_.... Figure 7: The ratio of the inundation rigure o: 1 he inundation water area to, the,1 analysis i area volume 9/17 4:00

10 68 Hydraulic Engineering Software Results and discussions Figure 6 shows the inundation water volume and Figure 7 shows the ratio of the inundation area to the total analysis area and the inundation depth distribution. In Figure 6. the inundation water volume in CASE V decreases as time goes on, whereas it remains almost constant in CASE I. In Figures 5 and 7, it is found that by considering the sewerage system, the area where the inundation flow depth is small increases and the area where it is large decreases. Actually, it rains heavily when a storm surge comes, and the efficiency of the sewerage system for discharging inundation flow is expected to decrease. Also, there is some question about whether the analysis method is appropriate or not. However, from the above simulation results, it is anticipated that the sewerage system can have an effect in controlling the inundation flow in urban areas. 6 Conclusions The investigation results obtained here are summarized as follows. The validity of the numerical analysis model of overland flood flows due to storm surge used here was demonstrated by comparison of the simulated results with the observed ones in the case of Typhoon Jane. The influence of structures on inundation in urban areas was investigated by means of a model including the roughness coefficient 7? and the permeation rate A. It was concluded that the model with both parameters is qualitatively better than the usual one with the parameter n only. It was expected that the sewerage system in urban areas is to some extent effective for control of inundation flow dispersal. References [1 ] Y.Iwagaki: Coastal Engineering, Kyouritu Publication, p.224, 1982.(in Japanese) [2 ] Y.I was a and K.Inoue: 2-D and 3-D Mathematical Models for Flood Analysis,Proceedings of the Japan-China (Taipei) Joint Seminar on Natural Hazard Mitigation, pp ,1989. [3 ] Y.Gouda, Y.Kishira and Y.Kamiyama: Experimental study for wave overtopping at the dike due to irregular waves, Report of the Institute for Harbors Technology, 14-4,pp.3-44,1975.(in Japanese) [4 ] T.Takahashi and H.Nakagawa: Hazard zone mapping in respect to the damages to wooden houses due to breaking of levee, Bulletin of the Disaster Prevention Research Institute, Kyoto University, Vol.37, Part 2, No.325, June, 1987.