Energy decay of the 2004 Sumatra Energy decay of the 2004 Sumatra tsunami in the World Oceantsunami in the World Ocean

Alexander B. Rabinovich1,2, Richard E. Thomson2, and Rogerio Candella3

1 P.P. Shirshov Institute of Oceanology, RAS, Moscow, RUSSIA1 P.P. Shirshov Institute of Oceanology, RAS, Moscow, RUSSIA2 Institute of Ocean Sciences, DFO, Sidney, B.C., CANADA2 Institute of Ocean Sciences, DFO, Sidney, B.C., CANADA

3 3 Instituto de estudos do Mar Almirante Paulo Moreira, Arraial do Cabo, RJ, BRAZILInstituto de estudos do Mar Almirante Paulo Moreira, Arraial do Cabo, RJ, BRAZIL

Up-to-now knowledge and conceptionsUp-to-now knowledge and conceptions

E(t) = E0e-t, t > td

Munk [1963]: “…Tsunami energy in the ocean decays in the same manner as sound intensity in a closed room (“acoustic analog model’)”

E0 is the tsunami index;

t0 = -1 is the “decay (e-folding) time”;

td is the “diffusion period” (required for

tsunami waves to become isotropic).

t0 ~ tr = L*/VgH

Munk [1963], Van Dorn [1984, 1987]: “…Main energy losses are associated with absorption during multiple coastal reflections at a rate of ~e-1 per reflection”.

L* is the mean free travel pass.

However, Oh and Rabinovich [1994]: Sea of Japan (1993) 3.1 – 13.3 hrs (probably depending on Q-factors of the respective sites)

Van Dorn [1984, 1987]: Pacific Ocean (1946, 1952, 1957, 1960, 1964) 22 hrs; Indian Ocean (1960) 14.6 hrs; Atlantic Ocean (1960) 13.3 hrs; Sea of Japan (1983) 8.6 hrs.

>

- 2 m

G auge coastalhe ights

M ode l am plitude

7 0 cm6 05 04 03 02 01 00 0.05m

Tsunami of the December 26, 2004 Tsunami of the December 26, 2004 recorded in the World Oceanrecorded in the World Ocean

Observational dataObservational data

(1) Indian and South Atlantic Ocean: 50 stations

(2) North Atlantic Ocean: 5 stations

(3) Pacific Ocean: ~40 stations

(4) Deep-ocean stations (NE Pacific): 4 stations

Quality records were selected with high signal/noise ratio.

Tsunami records and energy decayTsunami records and energy decay

Variances were estimated based 6-hour segments with 3-hour shifts

Examples

Station t (min)

First wave Maximum wave Energy

Arrival

time (UTC)

Travel

time (hr)

Observ.

time (UTC)

Height (cm)

E0Decay time

Cocos Is. (Australia) 103:1

72:18 03:26 59 90 10.1

Paradip (India) 603:2

72:28 06:42 318 3968 13.0

Vishakhapatnam (India) 5+ 03:35

2:36 06:25 291 2558 12.0

Chennai (India) 5+ 03:33

2:34 07:05 324 7350 10.0

Tuticorin (India) 604:2

43:25 04:18 181 1352 14.5

Neendakara (India) 1505:0

84:09 20:15 217 2127 18.6

Kochi (India) 605:4

14:42 07:42 149 1234 13.2

Mormugao (India) 5+ 06:53

5:54 10:00 157 529 18.9

Okha (India) 6+ 09:03

8:04 13:42 45 42 19.2

Hanimaadhoo (Maldives) 204:3

03:31 04:40 217 1127 10.2

Male (Maldives) 404:1

43:15 04:24 215 713 9.3

Gan (Maldives) 404:1

63:17 04:32 139 210 11.9

Diego Garcia (UK) 604:4

53:46 04:54 90 102 11.5

Port Louis (Mauritius) 207:4

66:47 09:26 195 1052 9.7

Pointe La Rue (Seychelles) 408:1

67:17 09:12 278 2671 10.8

Hillarys (Australia) 107:1

46:15 09:52 108 405 12.2

Salalah (Oman) 408:0

87:09 10:04 278 2335 14.0

Lamu (Kenya) 409:5

28:53 10:44 100 311 11.0

Zanzibar (Tanzania) 410:4

09:41 11:24 72 225 14.1

Table 1. Tsunami characteristics estimated for the Indian Ocean

Energy decay in the Indian and Energy decay in the Indian and South Atlantic oceansSouth Atlantic oceans

Five selected regionsFive selected regions

Energy indices in comparison with Energy indices in comparison with simulated resultssimulated results

Decay time as function of the travel timeDecay time as function of the travel time

Coastal stations

Island stations

70.132.8

;104.0548.0

3.855.0

b

a

xbaxy

62.225.12

;148.0588.0

3.1259.0

b

a

xbaxy

Pacific OceanPacific Ocean Station Hmax(cm) t0(hrs) Ttsu(hrs) Easter Island (Chile) 39 27.0 15:27Juan Fernandez I. (Chile) 8 32.3 20:05San Felix Island (Chile) 12 41.3 21:43Antofagasta (Chile) 26 26.0 26:51Arica (Chile) 72 28.7 27:15Callao (Peru) 67 25.7 25:15Manzanillo (Mexico) 89 17.8 32:25Cabo San Lucas (Mexico) 23 11.1 34:30San Diego (CA, USA) 32 38.6 35:44Port San Luis (CA, USA) 53 34.2 35:23Point Reyes (CA, USA) 40 24.6 34:34Crescent City (CA, USA) 61 26.9 ?Pago Pago (US Samoa) 15 42.5 27:00Nawiliwili (HI, USA) 14 43.5 ?

Energy decay in the Pacific Ocean

Decay time: t0 = 50-54 hrs

(1) The principal finding of our analysis is the non-uniformity of the decay time.

This result contradicts Munk [1963] and Van Dorn [1984, 1987] who determined that the tsunami decay time depends only on morphometric characteristics of the basin (mean depth and lateral dimension), and is therefore fairly uniform within each basin.

Main results:Main results:

(2) The observed decay time in general increases with distance and tsunami travel time.

The travel time is a key parameter determining the decay time. The greater the distance, the longer the travel time and the greater the degree of “tsunami forcing” by incoming tsunami wave energy.

(3) The ocean shelf effectively absorbs the tsunami energy; the wider and shallower the shelf the more intensive it absorbs and accumulates the tsunami energy.

Parameters of shelves play the principal role in the rate of the tsunami energy decay.

In general, our analysis for the 2004 Sumatra tsunami illustrates, the energy decay of major tsunamis is a much slower and more complicated process than previously reported. Large-scale topographic irregularities apparently play a principle role in this process with mid-ocean ridges serving as wave-guides that efficiently transmit tsunami energy from the source area to remote regions of the World Ocean. Continental shelves subsequently have the ability to retain tsunami energy leading protracted tsunami ringing along the coast.

Thank Thank you!you!