(1)
Li
Jie, Zhang Zhanhai and
Liu Yu
National Marine Environment Forecasting Center, Beijing, China, 100081
Tel: 010-62173572, Fax: 010-62173620, E-mail: lijie@nmefc.gov.cn
Abstract: In this paper, a case study of sea wave generated by typhoon Jelawat is carried out by using the cycle 4 version of the WAM (Wave Model) model (hereafter referred to as WAM4). The model domain currently covers from latitudes 20°N-45°N and longitudes 115°E-135°E, and the model spatial resolution reaches 0.25°. Comparisons among the model results, the buoy observations and the altimeter wave height data from ERS-2 and TOPEX/POSEIDON demonstrate that the model can fairly reproduce the observed characteristics of waves.
Keywords: WAM model, typhoon jelawat, simulation, altimeter wave height
In the last decade the WAM models (WAMDI-group, 1988; Komen et al., 1994) have been widely used not only as a research tool but also in making global and regional wave forecasts, which are useful for many purposes such as ship routing and offshore activities, and for the validation and interpretation of satellite observations. Wave information is of great important in ship navigation and offshore oil production in the East China Sea. The wave model currently in operational use at the National Marine Environment Forecasting Center (NMEFC) is a second generation wave model (Wen et al., 1989). Since the second generation wave model parameterizes the shape of the surface displacement spectrum with a limited number of parameters, it remains difficult to predict wave conditions, especially under rapid changing wind fields. Recently, a research program that aims to improve the operational numerical wave forecast for the China Sea is implementing at the NMEFC. Two important improvements have been made. Firstly, the most recently version cycle 4 of the WAM model was introduced, in which more physically realistic formulation is adopted without ‘a priori’ restriction on the evolution of the shape of wave spectrum. Secondly, the model grid size was decreased from 1° (currently used) to 0.25° so that the model result of high resolution was produced. One would expect a better representation of wave prediction. The test model domain covers from latitudes 20N-45N and longitudes 115E-135E. An earlier study (Liu et al., 1999) showed that these could significantly improve the model result.
In this work a numerical study of ocean wind wave created by typhoon Jelawat is performed by using the WAM4 model. The goal is to investigate the model ability in reproducing observed waves in the East China Sea. Two kinds of data, buoy and satellite altimeter measurements, are used to verify the model output. These data provide valuable information both in time series and two dimensional verifications.
In section 2, we briefly describe the physics of the WAM model, and advantages of this formulation compared to the previous cycles are discussed. Comparisons of the simulated wave heights against buoy observations and altimeter data derived from TOPEX/POSEIDON and ERS-2 are shown in section 3 and section 4, respectively. The final section presents the conclusions and discussion of the future work.
The WAM model is the first model that explicitly solves the full energy balance equation for the two-dimensional surface wave spectrum. In deep water, the energy balance equation reads
(1)
where
is the wave spectrum described by
the frequency fw and the
wave direction q,
is the group velocity, and S
is the source term given by
(2)
where the terms on the right hand side represent the physics of wind input, wave-eave interaction, dissipation due to whitecapping and bottom friction, respectively. The wave spectrum has 25 frequencies and 12 directions at each gridpoint.
The WAM4 model has a certain number of advantages over earlier cycles of the WAM model. First of all, the latest cycle allows the surface stress to be determined, including the dependence on the sea state through the wave-induced stress. Secondly, the high-frequency part of the wave spectrum shows more realistic levels when compared to observations. Thirdly, WAM4 shows reduced dissipation of swell.
The wind force used to drive the wave model is calculated by a typhoon model where the symmetric basic field defined by Takeo’s (1981) is superposed by an asymmetric part (see Yu, 1999). The wind field is expressed as
(3)
where
and
are the moving velocity and the
position of storm center,
is the unit vector vertically
upward,
with j
being the inflow angle,
and
are the functions depending on the
storm track, the center air pressure and the radius of maximum wind speed. Thus,
the wind forcing field is determined by storm track, central air pressure and
maximum wind radius.
The model domain covers the latitudes 20°N-45°N and longitudes 115°E-135°E, and the grid size is 0.25°x0.25°. The wave model is numerically solved by integrating the source term and advection term, and the time step is 15 minutes and is 30 minutes, respectively. The wind force is updated every half hour.
To investigate the ability of the WAM model, a numerical study of wave simulation induced by typhoon Jelawat is made and the model verification compared to buoy observations.
Typhoon Jelawat (200008), was first noticed at 22°N and 151°E of the West Pacific Ocean on August 1, 2000. As shown in Fig. 1, it approached the East China Sea on August 07. The model simulation is performed for a representative period from GMT12, 07 to GMT00, 11 August. High winds and waves were measured by a waverider buoy located at 29.3°N, 124.0°E, which is moored in open sea to measure the deep-water waves avoiding the shallow-water effects. The wave information was recorded every one hour. Fig. 2 shows the comparison between model results and buoy observations. It is seen that the observed winds are realistically reproduced by the typhoon model. This offers a good basis in wave model verification since the quality of the wave model output depends critically on the quality of the modeled surface wind.
Fig. 1 The track of Typhoon Jelawat.
Fig. 2 Comparison between model results and buoy observations. The simulations are started at 12GMT, 07 August 2000 for 84 hours.
As expected, the general trend in the time history of wave heights computed by the WAM4 model fairly follows the observations. The peaks of the calculated waves are in a very close agreement with the observed one. The highest wave height measured at 16GMT 09 August was 8.7 m, the corresponding wave period and wind speed were 11.5 second and 25m/s, respectively. The wind speed and wave height decreased abruptly when the eye of Jelawat passed through the buoy and reduced to 5.7m/s and 3.4m at 00GMT 10, respectively. Then, they increased rapidly when the eye moved away. Comparatively, the calculated wave height and wind speed show a similar pattern. The maximum wave height and wind speed calculated are 8.33m and 27.3m/s, the corresponding troughs of wave height and wind speed are 4.5m and 7.6m/s, respectively. These indicate that the model results could exactly reflect the variety of the observation of wind speed and wave height.
Fig. 3 The TOPEX/ERS-2 Along-Track of significant wave
With the development of modern remote sensing techniques, use of satellite altimeter data in model validation has recently become an important subject in wave modeling. In contrast to the conventional observing systems which could provide only local information on the sea state, altimeter data would be able to provide two dimensional information of wave observation on a global scale. The wave heights calculated by WAM4 are compared to the measurements obtained from the TOPEX/POSEIDON and the ERS-2 satellite altimeters in this section. TOPEX/POSEIDON altimeter data are off-line data (OPR). The ERS-2 altimeter data are the so called ‘fast delivery product copy’(FD), which means that only a limited number of calibrations and corrections of the data were performed by the ESA ground stations. This product is intended for near real-time remote sensing applications, to be disseminated via low rate data links. For the data from the TOPEX/POSEIDON satellite, the outliers were removed. The criterion for removal identified consecutive measurements along the same track which differ more than 50% and more than 100%. The measurements flagged for more than 100% difference were removed automatically. The measurements that differed between 50 and 100% were retained. Krogstad and Barstow(1999) indicate that the accuracy of the TOPEX/POSEIDON altimeter wave heights is similar to buoy data if the systematic bias is removed. The ERS-2 FD altimeter data however display a higher bias and variance and the accuracy is therefore somewhat poorer.
Fig. 6 Comparison of T/P satellite measures and simulation results and corresponding statistical parameters on Aug 10,2000
In order to quantify the comparison we have computed the usual statistical parameters which are displayed in Figs. 4-6 as well. The bias is defined as the difference of the observed data mean and the modeled mean. A positive bias therefore means an underestimation of the model in comparison with the data. The RMSE is defined as the root mean squared of difference between observations and model results. S.I. is defined as the ratio between the RMSE and the square root of the product of the mean of the model results and the mean of the observations.
Averaged satellite measurements at a certain time and model grids are then compared to the wave model output for the corresponding model points and time. At first we find out the calculated grid points that are covered the satellite tracks, averaged model results over the four points are calculated. A satellite data are obtained by the mean of the neighbouring included in the model grid points. Figs. 4-6 show the scatter plots of modeled results vs. satellite measurements. In the figures only the observations over 2m wave height were chosen. The mean difference between modeled and observed wave height are about 14cm, 6cm and 4cm for different tracks, respectively. Modeled wave height may be regarded of high quality because of the low bias. Scatter indices obtained from the wave height comparison range from 20% to 30%. It shows the good performance of the wave simulating system during the chosen period.
A case study of sea wave generated by a storm has been carried out using the WAM4 model and comparison with the buoy measurements and altimeter data have been made. Comparison of calculated wave data with independent buoy observations shows a high quality of the model results. Furthermore, the verifications against altimeter wave height data also indicate good agreement. The statistical verifications of the RMSE, correlation coefficient and scatter index (S.I.) are respectively about 0.98m, 0.84 and 0.26 (the mean of the ERS-2 and T/P). The reasons for this progress are due mainly to the improvement of the spatial resolution and improvements in wave modeling with respect to wind input and dissipation. These strongly suggest the possibility to perform an operational use of the WAM4 model in the East China Sea. Altimeter wave height data have been of great help to provide a first guess of initial sea state and as a validation tool of the wave forecast. Although the present promising validation results encourage us to assimilate buoy and altimeter observation into the wave forecasting system, further experiments would be done on how to calibrate the model result with observations. Generally, this could lead to an improved specification of the wave analysis. At NMEFC, there is a continuous effort to improve wave analysis and forecast. The new scheme would be able to handle the wealth of data from the altimeter which provides information on the surface wind field. The forecast skill has improved by half a day. Since variational assimilation is only beginning, further progress in wind and wave forecasting is expected to occur in the near future.
Acknowledgements
This work is a part of the key project “Development and Implementation of Modeling Disastrous Storm Surge Inundation and Nearshore Waves” supported by the State Planning Commission, which is acknowledged.
References
[1] The WAMDI Group, the WAM Model—A Third Generation Ocean Wave Prediction Model, 1998, J.Phys. Oceanogr., 1775-1810.
[2] Liu Yu etc., Operational Use of Wave Models in NMEFC, China, the Second Workshop on Ocean Models for the APEC Region (WOM-2), October 25-29, 1999, Beijing, P.R. China, OMISAR Project Publication, 1b 1-6.
[3] Wen,S.C., D.Zhang, B.Chen and P Gao, 1989. A Hybrid Model fir Numerical Wave Forecasting and Its Implementation: Part I , the Wind Wave Model, Acta Oceanologica Sinica, 8 1-14.
[4] Veno Takeo,1981. Numerical Computation of Storm Surge in Toss Bay, J. Oceanogr. Society Japan, 37(2), 61-73.
[5] Krogstad, H.E., Barstow,S.F., 1999. Satellite Wave Measurements for Coastal Engineering Application. Coastal Engineering.
[6] Yu Fujiang etc. 1999. A High Resolution Storm Surge Prediction Model for Bohai Sea of China and Its Application To Typhoon 9216, Proceedings of The International Conference on Marine Disasters: Forecast and Reduction, 9-16.