Tsunami Runup and Inundation Simulation in Malaysia Including the Role of Mangroves Teh Su Yean, Koh Hock Lye, Philip Liu, Ahmad Izani Md Ismail and 3 Lee Hooi Ling School of Mathematical Sciences, Universiti Sains Malaysia, 8 Penang, Malaysia. e-mail: hlkoh@cs.usm.my School of Civil and Environmental Engineering, Cornell University 3 Technip GeoProduction Malaysia
6 December 4 Tsunami
t = 6 s t = s 9 9 8 8 7 7 6 6 Y (km) 5 Y (km) 5 4 4 3 3 3 4 5 6 7 8 9 3 4 5 6 7 8 9 X (km) X (km) t = 8 s t = 4 s 9 9 8 8 7 7 6 6 Y (km) 5 Y (km) 5 4 4 3 3 3 4 5 6 7 8 9 3 4 5 6 7 8 9 X (km) X (km) 3 9 8 7 6 5 4 3 - - -3-4 -5-6 -7-8 -9 - - - -3-3 - - - -9-8 -7-6 -5-4 -3 - - 3 4 5 6 7 8 9 3 Elevation (m)
.4.8..6.4.8..6 Simulated Tsunami Wave Heights. 3 A: Penang B: Langkawi C: Kantang.8 4.4.4 - -4.8 -.5.5.5.5 Elevation (m) 8 4 D: Phuket 8 E: Tasai 4-4 Time (h) -4-8 -8 -
Survey runup heights for the December 6 4 tsunami Location Name Date (5) Lat. (N) Min. Long. (E) Min. Runup Height (m) Distance to Shore (m) B. Ferringhi (Teluk Bayu) B. Ferringhi (Miami Beach) Tanjung Tokong Tanjung Tokong Tanjung Tokong Tanjung Bungah Tanjung Bungah /4 5 8.3 4.6 3.46 9. /4 5 8.7 6. 4. 5.6 /4 5 7.6 8.5 3.65 35.8 /4 5 7.6 8.4 N/A 9. /4 5 7.7 8.5.6 8.3 /4 5 8. 6.7.3 8.38 /4 5 8. 6.7.94 36.
Location Name Date (5) Lat. (N) Long. (E) Runup Height Min. Min. (m) Distance to Shore (m) Kuala Kedah /8 6 6. 6..9 N/A Yan (Kg. K.S. Limau) /8 5 53...7.9 Sg udang /8 5 48...5 N/A Tanjung Dawai /8 5 4...385 75.39 Kota K. Muda /8 5 34.. 3.8.54 Kuala Kurau 3/8 5. 5..93 N/A Pantai Acheh 3/8 5 4...55 3.4 Pantai Tengah (Lanai Hotel) 4/8 6 5. 99 43. 3.66 44.5 Pantai Chenang (Pelangi Hotel) Kuala Teriang Pantai Kok (Mutiara Beach Resort) 4/8 6 7. 99 43. 3.749 54.7 4/8 6. 99 4. 3.9 7.38 4/8 6. 99 4..46 5.84 Pantai Kok (Berjaya Hotel) 4/8 6. 99 4..983 34.879
U = velocity [m/s] η = surface elevation [m] H = depth [m]; ( ) ( ) x η g x u u t u x H η u t η = = -D Runup Model
Staggered Scheme t x u η ( ) ( ) x g x u u u t u u x H H u x u u H t n i n i n i n i n i n i n i n i i n i i n i n i n i n i i n i n i = Δ η η Δ Δ = Δ η η Δ η Δ η η
MBC: Study domain 5 5 h/5. (mm - ) η (m) 3 - -3-5 -7-9 MSL MSL Toe of the slope 4 3 - - h/5. (mm - ) η (m) (a) - -3 5 53 4 55 36 357 48 38 387 394 4 48 x (m) (b) x (m)
Runup Onto Dry Land 5 5 3 3 - - -3-3 -5-5 -7-7 -9-9 - 5 53 4 55 36 357 48-5 53 4 55 36 357 48 5 5 3 3 - - -3-3 -5-5 -7-7 -9-5 53 4 55 36 357 48-9 - 5 53 4 55 36 357 48
Enlarged Runup Frames 5 4 3 - - -3 38 387 394 4 48 5 4 3 - - -3 38 387 394 4 48 5 4 3 - - -3 38 387 394 4 48 5 4 3 - - -3 38 387 394 4 48
Effects of Coastal Vegetation
Rhizophora stylosa
Bruguiera gymnorrhiza
Morison Equation M t x M D gd η x gn MM M = flow flux, m /s; D = (ηh) = total water depth, m; h = still water depth, m; n = Manning coefficient; g = gravitational acceleration, m/s ; C D = drag coefficient; A = projected area of trees under water surface, per m. D MM 7 / 3 C D A D = Drag Coefficient V V CD = 8.4.66.. 7 V V V = total volume of obstacles (m 3 ); V = control volume (m 3 );
P L = leaf porosity; N T = number of trees per m ; N R = number of prop roots per tree; D T = diameter of stem, m; D R = diameter of each prop root, m; D L = diameter of leaf part, m; H R = height of root part, m; H T = height of stem part, m; H L = height of leaf part, m.
.4 Δx = 4. m. Elevation (m).8.6.4. 4 6 8 4 6 8 x (m) n =. n =. n =.
.4..8 (a) Δx =. m.4..8 (b) Δx =. m Elevation (m).6.4. Elevation (m).6.4. -. -.4 -.6 4 6 8 4 6 8 -. x (m) -.4 -.6 n =. n =. 4 6 8 4 6 8 x (m) n =. n =..4..8 (c) Δx = 5. m Elevation (m).6.4. -. -.4 -.6 4 6 8 4 6 8 x (m) n =. n =.
.6.4.6 (a) Δx = 4. m.4 (b) Δx =. m.6.4 (c) Δx =. m....8.8.8 Elevation (m ).6.4. Elevation (m ).6.4. (m ) Elevation.6.4. 4 6 8 4 6 8 4 6 8 4 6 8 -. -. x (m) x (m) -.4 -.4 4 6 8 4 6 8 -. x (m) -.4 -.6 -.6 -.6.6.4 (d) Δx = 5. m.6.4.6 (e) Δx =.5 m.4 (f) Δx =.5 m....8.8.8 Elevation (m ).6.4. (m ) Elevation.6.4. (m ) Elevation.6.4. 4 6 8 4 6 8 4 6 8 4 6 8 -. -. -. x (m) x (m) -.4 -.4 -.4 4 6 8 4 6 8 x (m) -.6 -.6 -.6
Linear Approximation η t = h u x u t = g η x γ h u u γ h u u - R u f = gn h 4 / 3 u u Analytical. Solution u = ae βx sin( σt kx α) η = β abe x sin( σt kx) u u e β x η η e βx
π γ = h R f v 3 / h gn = γ π = π = h gn ) h h gn ( R 3 4 / 3 / f v v = f σ R gh σ k f m ghk R σ = β
R f << σ Case (a) R σ f k = σ gh R f >> σ Case (b) k gh R σ f σ = σ = R f gh R σ f k = β = decay number, m - ; n = Manning coefficient, sm -/3 ; h = water depth, m; T = wave period, s; v = wave maximum velocity, ms - ; x = half distance, m. >> σr f gh β = R f σ ghk = R f σ gh gh σr f = R f σ gh = k n v β = xˆ = ln (.5) / 3 h Th β
Decay number β (n,t) T (min) n (sm -/3 )...3.4.5.6.7 3.64 7.7.9 4.55 8.9.8 5.46.57 5.4 7.7.9.86 5.43 8. 3. 4. 6.3 8.4.5.6 4.7 4.8 3.64 5.46 7.7 9.9.9.73 5.63 3.5 4.88 6.5 8.3 9.76.39 6.48.97 4.45 5.94 7.4 8.9.39
Half distance x(n,t) T (min) n (sm -/3 )...3.4.5.6.7 9.58 95.9 63.53 47.64 38. 3.76 7.3 69.5 34.76 89.84 67.38 53.9 44.9 38.5 3 33.9 65.5.3 8.5 66. 55. 47.6 4 38.6 9.58 7.5 95.9 76.3 63.53 54.45 5 46.5 3.7 4.5 6.54 85.3 7. 6.88 6 466.8 33.4 55.6 6.7 93.36 77.8 66.69
η t M x = M t x M D gd η x gn D MM 7/3 C D A MM D = η = elevation, m; M = flow flux, m /s; H = still water depth, m; D = (ηh) = total water depth, m; n = Manning coefficient; g = gravitational acceleration, m/s ; CD = drag coefficient; A = projected area of trees under water surface, m ; Δx, Δy = spatial grid size, m.
n =.5 * C D A gδxδy D f /3 Leaf porosity PL =.3 Number of trees per m NT = 3 Number of prop roots per tree NR = Diameter of stem DT =.5 m Diameter of each prop root DR =.35 m Diameter of leaf part DL = m Height of root part HR = m Height of stem part HT = m Height of leaf part HL = 8 m Forest width W = m
Elevation (m).6.4..8.6.4..8.6.4. -. 4 6 8 4 6 8 x (m) (a) Time =. hr.6.4..8 Elevation (m).6.4..8.6.4. -. 4 6 8 4 6 8 x (m) (b) Time =.5 hr Elevation (m).6.4..8.6.4..8.6.4. -. 4 6 8 4 6 8 x (m) (c) Time =.3 hr
Elevation ( m ).6.4..8.6.4..8.6.4. -. 4 6 8 4 6 8 -. 4 6 8 4 6 8 -. x (m) (a) Time =.5 hr Mangrove Forest Width W = km Manning n =.3 s/m /3 ( m ) E levation.6.4..8.6.4..8.6.4. x (m) (b) Time =. hr.6 ( m ) Elevation.4..8.6.4..8.6.4. 4 6 8 4 6 8 x (m) (c) Time =.5 hr Elevation ( m ).6.4..8.6.4..8 (d) Time =. hr.6 (e) Time =.5 hr.6.4.4...8.8 ( m ) Elevation.6.4..8.6.6.6.4.4.4... -. 4 6 8 4 6 8 -. 4 6 8 4 6 8 -. x (m) x (m) ( m ) E levation.6.4..8 4 6 8 4 6 8 x (m) (f) Time =.3 hr
Reduction Ratio r η = η for η max max r = u u for max u max r η = reduction ratio of elevation; η formax = maximum elevation with mangrove forest; η max = maximum elevation without mangrove forest; r u = reduction ratio of velocity; u formax = maximum velocity with mangrove forest; u max = maximum velocity without mangrove forest.
. Wave Period T (mins) Reduction Ratio of Elevation r η.8.6.4. r η 3 4 5 6 Wave Period Reduction Ratio of Velocity r u...8.6.4.. 3 4 5 6 7 r u Forest Width W (m) Wave Period T (mins) 3 4 5 6 3 4 5 6 7 Forest Width W (m) vs. Forest Width
. Reduction Ratio of Elevation r η.8.6.4.. r η Wave Period Wave Period (mins) vs. 3 4 5 6 3 4 5 Forest 6 Density Forest Density (trees per m ). Reduction Ratio of Velocity r u.8.6.4.. r u Wave Period (mins) 3 4 5 6 3 4 5 6 Forest Density (trees per m )
. Reduction Ratio of Elevation r η Reduction Ratio of Velocity r u.8.6.4....8.6.4.. r η Forest Density (trees per m ) 3 5 3 4 5 6 Forest 7 Density Forest Width W (m) r u vs. Forest Density (trees per m ) 3 5 Forest Width 3 4 5 6 7 Forest Width W (m)
Penang Case Study
Pantai Mas Mangrove Forest Parameter values Forest Density (trees per m ) 3 P L.3.3.3 N T (trees per m ) 3 N R (roots per m ) 6, 6, 6, D L (m) 4. 3.. D T (m).8.8.7 D R (m).8.8.8 H L (m) 4. 3.. H T (m) 6. 5.5 5. H R (m).8.8.8
Reduction Ratio of Elevation r η.5.4.3....5 Wave Period (mins) 3 4 5 6 5 5 5 3 35 Forest Density (trees per m ) Forest Width r η = m Reduction Ratio of Velocity r u.4.3... Wave Period (mins) 3 4 5 6 5 5 5 3 35 r u Forest Density (trees per m )
Reduction Ratio of Elevation r η.7.6.5.4.3... Wave Period (mins) 3 4 5 6 5 5 5 3 35 Forest Density (trees per m ) Forest Width r η = 5 m.7.6 Reduction Ratio of Velocity r u.5.4.3.. Wave Period (mins) 3 4 5 6 r u. 5 5 5 3 35 Forest Density (trees per m )
Thank you