Tsunami Evacuation Mathematical Model for the City of Padang

Transcription

1 Tsunami Evacuation Mathematical Model for the City of Padang R. Kusdiantara, R. Hadianti, M. S. Badri Kusuma and E. Soewono Department of Mathematics Institut Teknologi Bandung, Bandung Indonesia Department of Civil Engineering Institut Teknologi Bandung, Bandung Indonesia {hadianti, Abstract. Tsunami is a series of wave trains which travels with high speed on the sea surface. This traveling wave is caused by the displacement of a large volume of water after the occurrence of an underwater earthquake or volcano eruptions. The speed of tsunami decreases when it reaches the sea shore along with the increase of its amplitudes. Two large tsunamis had occurred in the last decades in Indonesia with huge casualties and large damages. Indonesian Tsunami Early Warning System has been installed along the west coast of Sumatra. This early warning system will give about minutes to evacuate people from high risk regions to the safe areas. Here in this paper, a mathematical model for Tsunami evacuation is presented with the city of Padang as a study case. In the model, the safe areas are chosen from the existing and selected high rise buildings, low risk region with relatively high altitude and (proposed to be built) a flyover ring road. Each gathering points are located in the radius of approximately 1 km from the ring road. The model is formulated as an optimization problem with the total normalized evacuation time as the objective function. The constraints consist of maximum allowable evacuation time in each route, maximum capacity of each safe area, and the number of people to be evacuated. The optimization problem is solved numerically using linear programming method with Matlab. Numerical results are shown for various evacuation scenarios for the city of Padang. Keywords: Linear Programming, Tsunami evacuation model. PACS: Gg, a, c INTRODUCTION Pacific Earthquake Belt (Ring of Fire) is a horseshoeshaped area that surrounds the Pacific Ocean covering the length of about 40,000 km. Around 90% of earthquakes occurred in this area, in which 81% of them occurred along the Ring of Fire. Large portion of Indonesian archipelago which lies in Pacific seismic belt has been causing earthquakes and volcanic eruptions. Indonesia is also a meeting point between the Pacific plate, the Indo-Australian plate and Eurasian plate. As a result, Indonesia is high-risk to earthquakes and tsunamis [1]. Tsunamis occur due to a disorder that causes the displacement amount of water, caused by: earthquakes, volcanic eruptions, or meteorite that fell to earth. About 90% of tsunamis occurred because of earthquakes under the sea as happened in Aceh and Japan recently[1]. Here are some of the historical occurrence of large earthquakes accompanied by tsunamis in the world: 1. March 11, 2011, earthquake in Japan, 373 km from the city of Tokyo with magnitude 9.0 on the Richter Scale. The earthquake has also caused a tsunami along the eastern coast of Japan[2]. 2. October 26, 2010, large-scale earthquakes in the Mentawai with magnitude 7.2 on the Richter Scale. On November 9, 2010, it was reported 156 people died due to the tsunami[3]. 3. February 27, 2010, earthquake in Chile with 8.8 on the Richter Scale. On March 30, 2010, it was reported 432 people died due to the tsunami. Resulting tsunamis that reach across the Pacific Ocean to New Zealand, Australia, the Hawaii, archipelago states in the Pacific and Japan with the effects of light and medium impact[4]. 4. December 26, 2004, devastating earthquake measuring 9.0 on the Richter scale rocked Aceh and North Sumatra as well as cause a Tsunami in the Indian Ocean. These natural disasters, caused more than 220,000 people died inhabitants[5]. In order to reduce casualties, Indonesian Tsunami Early Warning System (InaTEWS) has been developed by the Government of Indonesia. The system is in direct control by the Indonesian Meteorogical, Climatology and Geophysic Agency (BMKG) in Jakarta. With this InaTEWS, BMKG can transmit a Tsunami alert in case of a potential Tsunami earthquake[6]. The system, which is still further developed by BMKG, provides only a short period of time for evacuees to find safe places for evacuation. Time available after this warning is about 15 minutes. With a very limited time, the main objective here is to find the best scenario for the evacuation of evacuees [7].

2 GEOGRAPHY AND DEMOGRAPHY CITY OF PADANG The City of Padang is the capital city of West Sumatra which is located on the west coast of Sumatra which has coastline of the length about 84 km and area about km 2. The altitude of the City of Padang varies from 0 to 1,853 m above sea level, where 40% of the total area has elevation only from 0 to 5 m. This Tsunami high-risk region is divided into eight kelurahan (the smallest administrative region). The City of Padang has five major rivers and 16 small rivers, with the longest river of the length 20 km along Batang Kandis. These existing rivers should be taken into account in selecting the evacuation routes. TABLE 2. Number of Evacuees in High-risk Area Clus- Village Population Number of ter People in High-Risk Area K1 Air Tawar Barat K2 Air Tawar Timur K3 Ulak Karang Utara K4 Gunung Pangilun K5 Ulak Karang Selatan K6 Lolong Belanti K7 Plamboyan Baru K8 Rimbo Kaluang Jumlah FIGURE 1. Tsunami High-risk Areas The table below shows, the percentage of Tsunami risk in each kelurahan. TABLE 1. Percentage of Tsunami High-risk Areas Cluster Kelurahan Persentage of area with Tsunami high risk K1 Air Tawar Barat 100% K2 Air Tawar Timur 100% K3 Ulak Karang Utara 100% K4 Gunung Pangilun 20% K5 Ulak Karang Selatan 100% K6 Lolong Belanti 70% K7 Plamboyan Baru 100% K8 Rimbo Kaluang 50% of the problem needs to be done to build a mathematical model. Listed below are the assumptions. 1. In each route vehicles run with the same speed. 2. The speed ( v and the density ρ satisfy the relation v = v f 1 2ρ ρ f ), where v f is the maximum allowable speed, and ρ f is the largest density before congestion occurs [8]. 3. Evacuees with no vehicle take separate routes. 4. Every person and transportation vehicles are ready at the Muster(gathering) Points when the evacuation starts. The evacuation process starts immediately after a Tsunami alarm sounds, and evacuees gather at the Muster Point, and then from the Muster Point evacuees are distributed with designated transportation modes into the Safe Area. Table 2 shows the population of each high-risk area. EVACUATION SCENARIO In the evacuation model here, the transportation unit being used is PCU (per car unit), and 1 PCU is equivalent to 1 car with a capacity of 8 persons. From the geographical and demographic we described above, the simplification FIGURE 2. Evacuation Process In FIGURE 2 the small circle represent the people/vehicles who will be evacuated, gathering at the Muster Point and being directed with designated transportation modes toward the Safe Area. In City of Padang, with limited high rise buildings satisfying the building

3 codes for Tsunami, and relatively no empty lands with high altitudes, we find that the total capacity of safe areas is far below the total number of evacuees. In the model here, the scenario of evacuation will utilize high rise buildings and (proposed to be built) a flyover ring road. The letter X above states that there is no access route from the Muster Point to corresponding safe area. MODEL FORMULATION FIGURE 3. The Flyover From the illustration above, it is assumed that flyover can be considered as shared safe area of each cluster. There are five entry points E1-E5 to the flyover with total capacity people. The routes to the entry points are given below. 1. Entry point 1 can be accessed by cluster 1 and cluster Entry point 2 can be accessed by cluster 3 and cluster Entry point 3 can be accessed by cluster 5 and cluster Entry point 4 can be accessed by cluster 6 and cluster Entry point 5 can be accessed by cluster 7 and cluster 8. Here are the distances from each Muster Point to the flyover. As mention before, the evacuees in a muster point will be evacuated with selected mode of transportation to a number safe areas or to the flyover. In the following, we will denote by M i as the muster point, the S j as the safe area, and the E k as the share area (see the following illustration). FIGURE 4. Illustration of The Model Suppose there are n muster points and m safe area, the evacuation time to evacuate N i people/pcus in muster point i to safe area j is Ni l i j x i j 1 d i j + L i j T i j =, (1) v i j

4 where x i j is the portion of people/pcus in muster pointi to be evacuated to the safe area-j along the route (i, j) of the length L i j and with the corresponding speed v i j, l i j is the number of lanes in route (i, j) and d i j = 1/ρ i j. In the following, we derive an optimization model for determining x i j, the optimal proportion of the evacuees in muster point i to safe area/entry point j, i = 1,...,n, j = 1,...,m. The optimization model has the following constraints 1. for every i, m j=1 (x i j) = 1, meaning that all evacuees in each muster point must be evacuated 2. for every j, n i=1 (N ix i j ) C j, meaning that the total number of evacuees to each safe area/entry point must be less than the capacity of the safe area/entry point 3. for every i, j, T i j τ, meaning that all evacuees in each route must be evacuated within τ minutes 4. for every i, j, 0 x i j 1, where C j is the capacity of the safe area j. Further we construct a multi-cluster model which allows evacuees from different clusters share the same safe area or the entry point of the flyover. Now we extend the notation of the decision variables x i jk is the proportion of evacuees from muster point i that will be evacuated to safe area/entry point j within cluster k. Due to the geographical aspects, we see that evacuees in a muster point can only be evacuated to a safe area/entry point within its cluster and its neighborhood. The optimization model has the following constraints m(k) xi jk = 1, 1 i n,1 k K, (2) j=1 n(k) Nik x i jk Cjk,1 j m,1 k K, (3) i=1,(i, j,k)/ SS (i, j,k) SS SS = A a=1ss a, (4) Nik x i jk Ca, a = 1,2,...,A (5) (6) T i jk τ, for every i, j,k, (7) 0 x i jk 1, for every i, j,k, (8) (9) For the multi-cluster model, we induce the evacuation time Nik l x i jk i jk 1 d i jk + L i jk T i jk = (10) v i jk We can choose the total evacuation time K n(k) k=1 i=1 m(k) Ti jk j=1 (11) as the objective function of our optimization model. We then have a linear programming, which is easily to solve. But the solution unrealistic since the parameter L i jk will be regarded as a constant. Where as L i jk must have an important role in obtaining the optimal solution. Since, we prefer to evacuate the evacuees from muster point i to a safe area j in cluster k with small distance L i jk. For that, we choose K n(k) k=1 i=1 m(k) Ti jk Li jk (12) j=1 as the objective function. In the optimization model (12) there is a development in parts related to capacity constraints in which some safe areas are shared by more than one cluster. Here A is the number of joint-safe areas, and for each 1 a A, C a is the capacity of the safe area which can be jointly shared by the corresponding clusters. The list of parameters are given in the following table. N ik is the number of people from muster point i to the safe area j in cluster k, d i jk is the distance between the two unit from the muster point i to the safe area j in cluster k, v i jk is the speed of the unit from the muster point i to the safe area j in cluster k, l i jk is the number of evacuation lines from the muster point i to the safe area j in cluster k, L i jk is the distance from the muster point i to the safe area j in cluster k, SS is the share area who can be access by cluster k, A is the number of share area, C jk is the capacity of the safe area j in cluster k, C a is the capacity of the safe area at cluster k that had been drop and become share area and become member of the SS or the combination of cluster that can access Ca K is the number of the cluster n(k) is the number of the muster point in cluster k, m(k) is the number of the safe area in cluster k NUMERICAL SIMULATION In the following simulation, we use only a single mode of transportation i.e. with cars. Here are the data to be

5 used in the simulation for 8 clusters. We mean by the shortage as the total capacity at safe area minus the total population. Cluster 3 Cluster 1 Cluster 4 Cluster 2

6 Cluster 5 Cluster 7 Cluster 6 Cluster 8 The optimal solution of the optimization problem are given.

7 Cluster 1 Cluster 4 Cluster 2 Cluster 5 Cluster 3 Cluster 6

8 Cluster 7 transportation mode. We propose a flyover as a vertical structure that can be used for evacuation. The solution of the optimization model shows that the flyover will give significant contribution evacuation in case of tsunami. The optimization model can be generalized to a more realistic model with more than one transportation modes. ACKNOWLEDGEMENT Part of this research is funded by Hibah Penelitian Kerjasama Luar Negeri dan Publikasi Internasional DIKTI 2010 REFERENCES Cluster 8 The numerical solution shows that all evacuees in cluster 2 and cluster 8 will be evacuated to safe areas within the cluster. This makes sense since the shortages in these clusters are negative. Meanwhile, although the shortage af cluster 7 is also negative, a number of evacuees in this cluster will be evacuated to share area 5. Since certain muster points in this cluster are closer to the share area rather than to the safe areas. CONCLUSION We derive an optimization model for determining optimal tsunami evacuation plan for the City of Padang, where the evacuation is performed by using cars as the 1. G. Lämmel, M. Rieser, K. Nagel, Hannes Taubenböck, G. Strunz, N. Goseberg, T. Schlurmann, H. Klüpfel, N. Setiadi, Jörn Birkmann, Emergency Preparedness in the case of a Tsunami - Evacuation Analysis and Traffic Optimization for the Indonesian City of Padang, Proceedings of the 4th Conference on Pedestrian and Evacuation Dynamics PED2008, Wuppertal, D.K. Nanto, W.H. Cooper, J. M. Donnelly, R. Johnson, JapanŠs 2011 Earthquake and Tsunami: Economic Effects and Implications for the United States, Congressional Research Service, USA, A. V. Newman, G. Hayes, Y. Wei, J. Convers, The 25 October 2010 Mentawai tsunami earthquake, from real - time discriminants, finite - fault rupture, and tsunami excitation, GEOPHYSICAL RESEARCH LETTERS, 38, G. Pararas, Carayannis, THE EARTHQUAKE AND TSUNAMI OF 27 FEBRUARY 2010 IN CHILE - Evaluation of Source Mechanism and of Near and Far-field Tsunami Effects, Journal of Tsunami Society International 29, Honolulu, Hawaii USA, Thorne Lay, Hiroo Kanamori, Charles J. Ammon, Meredith Nettles, Steven N. Ward, Richard C. Aster, Susan L. Beck, Susan L. Bilek, Michael R. Brudzinski, Rhett Butler, Heather R. DeShon, Göran Ekström, Kenji Satake, Stuart Sipkin, The Great Sumatra-Andaman Earthquake of 26 December 2004, SCIENCE , T. Charnkol, Y. Tanaboriboon,Tsunami Evacuation Behavior Analysis, One Step of Transportation Disaster Response, International Association of Traffic and Safety Sciences 30, 83-96, Japan, R. S. Dewi, N. Salam, S. Suwadi, Remote Sensing for Dissaster Mitigation: Case Study for Tsunami Evacuation Route Modelling in Cilacap-Central Java Indonesia, International Archives of the Photogrammetry, Remote Sensing and Spatial Information Science 38 Part 8, Kyoto, B. D. Greenshields, A Study in Highway Capacity, Highway Reseach Board Proceedings 14; , 1935.