## Tsunami Modeling

The use of numerical modeling to determine the potential run-ups and inundation from a local or distant Tsunami is recognized as useful and important tool, since data from past Tsunamis are usually insufficient to plan future disaster mitigation and management plans. Models can be initialized with potential worst case scenarios for the Tsunami sources or for the waves just offshore to determine corresponding impact on near by coast. Models can also be initialized with smaller sources to understand the severity of the hazard for the less extreme but more frequent events. This information then forms the basis for creating Tsunami evacuation maps and procedures. Sufficiently accurate modeling techniques have been developed in the recent years, and these models require proper inputs on detailed bathymetry and topographic data for the area being modeled.

#### Modeling of Tsunami can be divided into three stages:

• Generation
• Propagation and
• Run-up (inundation)

The parameters and type of model employed at three stages are different and depend on the site conditions.

#### Generation

The generation stage of Tsunami evolution includes the formation of an initial disturbance at the ocean surface due to the earthquake triggered deformation at the sea floor. This initial water surface disturbance is transformed into a long gravity wave radiating from the earthquake source. Modeling of the initial stage of the Tsunami generation is closely linked to the studies of earthquake mechanisms.

Several models are being used worldwide (Okada, 1985; Titov and Gonzalez, 1997) for computation of static sea floor deformation to calculate initial conditions required for Tsunami propagation. The basic parameters required for these models include the fault area (length and width), angle of strike, dip, slip, depth of fracture, dislocation and moment magnitude of the earthquake. The wave form generated varies with these source parameters and, hence, the information on above parameters is essential.

#### Propagation

Tsunamis travel outward in all directions from the generating area, with the direction of the main energy propagation generally being orthogonal to the direction of the earthquake fracture. Their speed depends on the depth of water, so that the waves undergo acceleration and deceleration in passing over an ocean bottom of varying depth. In the deep and open ocean, they travel at speeds of 500 to 1000 km/hr.

The distance between successive crests can be as much as 500 to 650 kilometers. However, in the open ocean, the height of the waves is generally about 30 to 40 cm even for the most destructive distant Tsunamis, and so the waves pass unnoticed. Variations in Tsunami propagation result when the propagation impulse is stronger in one direction than in others because of (i) orientation or dimensions of the generating area, (ii) regional bathymetric and topographic features and (iii) rate of advance. Specifically Tsunami waves undergo a process of wave refraction and reflection throughout their travel. Tsunamis are unique in that the wave disturbance extends through the entire water column from sea surface to the ocean bottom.

#### Run-up (Inundation)

A typical inundation map for Nagapattinam

The propagating Tsunami wave from the deep water undergoes a change, causing increase in the wave height at the coast due to the nearshore bathymetry and coastal morphology such as inlets, sand dunes, water bodies etc. The run up of the Tsunami on land is the most undeveloped part of the Tsunami model, primarily because of lack of two major aspects ï¿½ high quality field measurements for testing the models and fine resolution bathymetry/topographic data (Titov and Synolakis, 1997). In the present study, the high quality bathymetry and topography collected from the field were used.

Most Tsunami models often employ different numerical techniques applied to different segments of the total problem starting from Tsunami generation, propagation and run-up on coastal areas. For example, several numerical models have been used to simulate the interaction of Tsunamis with islands. These models have used finite difference, finite element, and boundary integral methods to solve the linear long wave equations. These models solve these relatively simple equations and provide reasonable simulations of Tsunamis for scientific and engineering purposes. Here, a finite difference code of TUNAMI N2 (Imamura, 1996) was employed to study the Tsunami. Studies have been carried out to validate the model results with December 26, 2004 Sumatra earthquake that indicated an 80 % match. This model has been run for 5 historical earthquakes and the predicted inundation areas are being overlaid on cadastral level maps of 1:5000 scale. The maps for most vulnerable parts of the coastline have been provided to the central and state level departments that are involved in Disaster Management.

#### Open Ocean Propagation Scenario database for Operational Quantitative Tsunami Forecast

At the time of any earthquake only the hypo central parameters and magnitude are available in near real time. The information about fault geometry will be available very much later, which can not be used for real time tsunami prediction for near source regions. In addition, tsunami modeling, especially the coastal inundation, can not be run in real time for generating operational tsunami advisories as the model run takes large computing time. For operational quantitative tsunami forecast, there needs to be a method to quickly estimate the travel times and run up based on the quickly available earthquake parameters (based on magnitude and hypocenter of earthquake only). For the above reasons, the best way to generate quantitative operational tsunami advisories is to create a database of pre-run scenarios.

A "scenario"l is a single tsunami model simulation that is calculated from the required initial seismic deformation condition with the pre-defined input fault geometry parameters of earthquake rupture, i.e., Fault Location, Depth, Length, Width, Displacement, Strike angle, Dip angle and Slip angle. Each Scenario output contains the expected tsunami wave travel times, run-up heights and directivity maps. The fault geometry parameters are carefully selected so that they are likely to represent an actual Tsunamigenic earthquake based on knowledge of the historical earthquakes in two Tsunamigenic source regions of Indian Ocean. The Strike angle is assigned based on those of the pre-historical earthquakes which actually occurred near the simulation point and triggered Tsunami in the past. In case of the parameters of historical earthquakes are uncertain, the strike angle is assigned in such away that it will represent the worst case, i.e., parallel to the coast or along trench near by. For the earthquake faults in global subduction zones, 10 km and 25 degrees are the typical values for the depth (d) and dip angle (Pacheco et al. 1993) respectively. But from sensitivity analysis, 45 degrees is assigned as dip angle and 90 degrees is assigned as slip angle, which assumes that the rupture zone is aligned horizontally and the earthquake mechanism is pure dip-slip reverse faulting, which is the worst case for Tsunami triggering by an earthquake. The fault Length (L), Width (W) and Displacement (D) of the fault are assumed to be represented in terms of empirical formulas as function of magnitude (M) as described (Papazachos B. C., et. al. 2004) as following:

Fault Length L (km) log L = 0.55 M â 2.19; S.D =0.18; 6.7< M < 9.3

Fault Width W (km) log W = 0.31 M â 0.63; 6.7< M < 9.3

Fault area A (sq.km) log A = 0.86 M â 2.82; S.D =0.25; 6.7< M < 9.3

Displacement (cm) log D = 0.64 M â 2.78;

Scenario database of 50,000 scenarios

This scenario database of pre-computed scenarios is generated with the objective use of available real time seismic information as well as sea-level data. The Model Domain that has been setup for Indian Ocean covers 30 N to 40 S latitude and 30 E to 130 E longitudes with a grid spacing 0.0450 degrees approximately (5.01km). According to CFL criterion, the model time step of 5 sec has been taken, to stabilize and to avoid the model blow up. The scenario database consists of approximately 975 ï¿½simulation pointsï¿½, each with separation of half a degree, located all along the subduction zones in two Tsunamigenic source regions of Indian Ocean. From the sensitivity analysis and based historical earthquakes, it is concluded that each of these locations should have multiple scenarios associated with it ï¿½ combination of 6 different depths (10, 20, 40, 60, 80 & 100 km) and 7 moment magnitudes (Mw) (6.5, 7.0, 7.5, 8.0, 8.5, 9.0 & 9.5) and pre-defined unit source scenarios, providing a total number of approximately 50,000 scenarios. Each simulation covers the entire Indian Ocean domain with 15 hours simulation time and a time step of 5 seconds. The tsunami profiles of 15 hours for every 15 seconds are saved at coastal forecast points for each scenario. The coastal forecast points are selected at 30 m bathymetry assuming that till such depth, the computation is linear. About 1800 CFPs are selected for the tsunami domain separated by ~50 km apart covering the entire Indian Ocean rim countries. Arrival times and wave heights at specific coastal locations for each scenario are stored in a database. Travel times and Surge heights on 30 m bathymetry are interpolated to get the values at Coast. Travel Times to coast are calculated by considering the speed of the wave at different depths (30, 20, 15 and 10 M). The distance to coast is divided by the average speed to get the travel times at the coast. Tsunami Wave height (H) at coast is calculated by Greens function which is fourth root of bathymetry depth (h1=30 m) multiplied by the wave height (H1) at 30 m depth

When ever an earthquake occurs, the closest scenario to the event is extracted from the scenario database based on magnitude and hypocenter location to identify the regions at risk. Real time observations of sea level will be used to ï¿½invertï¿½ for slip parameter. This information is used to update the forecast.

The model performance has been validated against the Sep 12, 2007 Tsunami. The pre-run scenario for the September 12, 2007 event was used to calculate the estimated travel time and run up heights at various coastal locations and water level sensors (Tide gauges & BPRs). The directivity map generated from the picked scenarios showed that south-east and south-west Indian coast were likely to be affected by a minor tsunami (~ 20 cm) and Andaman and Nicober Islands (~10cm) which is evident from the observations of tidal stations at Chennai & Portblair.

The estimates from the model scenario matched well with the observations from BPRs and tidal stations as evident from the table below:

Location Estimated
Arrival Time (IST)
Estimated
water level (cm)
Observed
Arrival Time (IST)
Observed
water level (cm)