Wattana Kanbua, I Ming Tang, Benchawan Wiwatanapataphee

Department of Mathematics, Faculty of Science, Mahidol University,

E-mail : oceansky12@hotmail.com

In 1997 Typhoon LINDA occurred in the South China Sea and reached typhoon intensity shortly after entering the Gulf of Thailand. The cyclone turned northwestward following steering from the subtropical ridge. The impact of Typhoon LINDA caused strong winds, heavy rainfall and big wave, especially in the coastal zone of eastern part and east coast of southern part. It swept marine plant and animal, coastal erosion etc. After that the system weakened slightly to 50 knots (92.65 km/hrs) prior to striking Thabsakae district, Prachuap Khiri Khan province, Thailand on 4 November 1997. Crossing the southern part of Thailand, Typhoon LINDA was weakened as it encountered the mountains. WAM model was used to forecast significant wave height, which the domain covers from longitudes 90E to 115E and from latitudes 0 to 25N, which encompasses Andaman Sea, Gulf of Thailand and South China Sea. The significant wave and wave spectral methods are the major tools to make wave analysis and forecast in the operation run. WAM model is third generation which follows the physical formulation but with different numerics and different tuning. This model has been applied in many hindcasting studies. During the procedure to make wave forecast charts. The final forecast charts are made based on the observed wave. A case study has been made. Comparison between the model results and the observation data such as moored buoys in the Gulf of Thailand and Andaman Sea under SEAWATCH project demonstrates that the model call fairly reproduces the observed characteristics of waves.

In 1997 Typhoon LINDA occurred in the South China Sea and reached typhoon intensity shortly after entering the Gulf of Thailand. The cyclone turned northwestward following steering from the subtropical ridge. The impact of Typhoon LINDA caused strong winds and heavy rainfall, especially in the coastal zone of eastern part and east coast of southern part. After that the system weakened slightly to 50 knots (92.65 km/hrs) prior to striking Thabsakae district, Prachuap Khiri Khan province, Thailand at 1900Z on 3 November. Crossing the southern part of Thailand, LINDA further weakened as it encountered the region’s 3000 ft (914 m) to 5000 ft (1524 m) mountains.

Typhoon Linda from GMS-05 Satellite image


Best Track of Typhoon LINDA

As the Typhoon LINDA passed the Gulf of Thailand, strong winds were experienced north of the typhoon track. The center mean sea level pressure was only of the order 5 hPa lower than the undisturbed pressure field. Consequently the storm surge that was seen along the shoreline north of the standing point was due to the strong onshore wind, piling up the water mass. There was used ocean model (SEAWATCH 3D) in order to estimate the maximum surge to be 61 cm due to wind stress. If the tide were included, the maximum surge height would be 90 – 100 cm, calculated somewhere north of Cha-Am in the upper Gulf and WAM model had run to forecast significant wave height. There are moored buoys in the Gulf of Thailand, they measured meteorological, oceanography data, especially Hua-hin buoy measured meteorological parameters including significant wave height as 3 - 4 meters.

Buoy Location

Comparison of significant wave height between
wave observation and WAM model at Hua-hin moored buoy



1. The significant wave method

Sverdrup and Munk were the pioneers to develop the wave-forecast technique in terms of significant idea. After that, this method was extensively modified by Bretschneider who developed semi-empirical wave forecasting relationship using graphic solution to make forecast and sometimes called SMB (Sverdrup, Munk and Bretschneider) method. However the SMB method is mostly for local forecast. It is inefficient for two-dimension area by numerical techniques. Therefore, Peng (1991) proposed a scheme for computing the wave height and period in the grid point to make forecast for next time step over the ocean. The modified scheme is to interpolate the growth, decay, and propagation of wave energy based on the semi-empirical wave forecasting relationships to the grid point and then to integrate with time to compute the next time of wave height and period. The numerical processes contain four steps with initial value defined, wave growth and decay, wave propagation, and wave interpolated at grid point. Refer to Peng (1991) for details.

2. The second generation wind wave spectrum model

The numerical techniques of the second-generation wave model are based on the Golding (1983) and Chao (1993) proposed structure. According to Hasselmann (1962), the evolution of the spectrum can apply the energy balance equation to demonstrate sea state condition. If the sea water depth changes are taken into account, the group velocity and propagating direction will change as time elapses during the evolution process of the wave energy spectrum. The equation can be written as


where Sin indicates the wave energy induced by the wind, Sds is the wave energy induced by whitecapping and the effect due to sea bottom topography, Snl is a new redistribution of wave energy induced among waves spectrums due to the nonlinear waves and the conservation among wave interactions.

3. Introduction of WAM

3. Introduction of WAM

The WAM-model is a third generation wave model which solves the wave transport equation explicitly without any presumptions on the shape of the wave spectrum. It represents the physics of the wave evolution in accordance with our knowledge today for the full set of degrees of freedom of a 2d wave spectrum. The model runs for any given regional or global grid with a prescribed topographic dataset. The grid resolution can be arbitrary in space and time. The propagation can be done on a latitudinal - longitudinal or on a carthesian grid.The model outputs the significant wave height, mean wave direction and frequency, the swell wave height and mean direction, wind stress fields corrected by including the wave induced stress and the drag coefficient at each grid point at chosen output times, and also the 2d wave spectrum at chosen grid points and output times.
The model runs for deep and shallow water and includes depth and current refraction. The integration can be interrupted and restarted at arbitrary times. The source terms and the propagation are computed with different methods and time steps. The source term integration is done with an implicit integration scheme while the propagation scheme is a first order upwind flux scheme. The wind time step can be chosen arbitrarily.
Subgrid squares can be run in a nested mode. In a course grid run the spectra can be outputted at the boundaries of a subgrid . They can then be interpolated in space and time to the boundary points of the fine subgrid and the model can be rerun on the fine mesh grid.
Hasselmann in the Max-Planck Meteorological Institute, Hamburg, originally developed WAM. Then WAMDI group (The WAM Development and Implementation Group), headed by Hasselmann after years of researches and revision, announces the third generation of this model. The document now applies the fourth revised edition (Gunther et al., 1992). Within the WAM model, the basic equation is wave energy equation in relation to any specific spot on the sea surface, whose spectrum E (j ,l , f,q , t), where (j ,l ) are latitude and longitude of any specific spot on sea surface, is a wave field of two-dimensional frequency (f) and direction (q ).


where (Cj , Cl , Cq ) are the phase speeds of wave energy propagation on (j , l , q ) coordinates, Sin is the wave energy influx transferred to waves from winds, Sds is the depletion flux of wave energy, and Snl is the energy propagation flux induced by the nonlinear effects caused by component waves.


The big significant wave height and swell associated with severe tropical cyclones stand out as by far the most damaging among natural disasters. They must be regarded as a serious threat to life and property in our coastal areas. Many disasters are involved in the formation and propagation of waves, such as the strength and size of the storm, bottom conditions where the surge comes ashore, and the position of the storm center relative to the shore. In addition the ecosystem, fishery industry, environment and tourism industry are also impact from big waves and storm surge. With high concentration of population near the coasts, demand for quantitative estimates of vulnerability to big waves and storm surges of different coastal stretches have increased during recent years.
Wind speed and direction at 10 meters            Significant wave height and direction


Progress has been forecasting and warning in cyclone, it is still inadequate. If we can forecast and warning this situation, it will reduce the damage of life and property.

    [1] Bretschneider, C.L., 1958: Revisions in wave forecasting: Deep and shallow water. Proc. 6th Int. Conf. Coastal Eng. , ASCE, 30-67.
    [2] Chao, Y.Y., 1993: Implementation and evaluation of the Gulf of Alaska Regional Wave Model. NMC OPC Office Note, 35pp
    [3] Golding, B., 1983: A wave prediction system for real time sea state forecasting. Quart. J. R. Met. Soc.109, 393-416.
    [4] Gunther, H., K. Hasselmann and P.A.E Janssen, 1992:Report NO.4, The WAM Model Cycle 4, Edited by Modellberatungsgruppe, Hamburg.
    [5] Hasselmann, K, 1962: On the nonlinear energy transfer in a gravity-wave spectrum. 1. General theory, JFM, vol. 12, 481-500.
    [6] Peng, S.P., 1991: On the numerical prediction model of ocean waves caused he numerical prediction model of ocean waves caused by monsoon.M. S. thesis, National Cheng Kung University.
    [7] Sverdrup, H.U. and W.H. Munk, 1947: Wind, sea and swell: Theory of relations for forecasting. Publication 601, Hydrographic Office, U.S. Navy, 50 pp.