A HINDCAST STUDY WITH HIGH RESOLUTION WAM MODEL

Caixin Wang, Zhanhai Zhang and Keguang Wang

National Marine Environment Forecasting Center,

 No. 8 Da Hui Si Haidian District, Beijing, China, 100081

Tel: 010-62173572, Fax: 010-62173620, E-mail: wangcaixin@263.net

Abstract: The primary objective of this work is to develop an operational model to forecast the wave caused by typhoon storm in offshore area of the China Sea. In this paper, the WAMC4 model is employed to hindcast the waves induced by typhoon 9914, which caused the most extensive damage to the Minnan coastal areas after typhoon 5308 during the past 40 years. Because of the limitation of computer, the grid size of 1/6° is chosen in both longitude and latitude, and the domain covers 10~30N in latitude and 110~130E in longitude. As for the regular observation, only the coastal station measurements are available in this area, so in the first step, we compared the simulated significant wave height with that of the observation and find the WAMC4 model can reproduce the growth of the waves effectively. As the further comparison, the simulated results are also compared with the satellite altimeter data, and we find the satellite data is generally greater than the simulated data, even when the Cotton’s calibration functions are adopted. Because the Cotton’s corrections are made according to the comparison of satellite data with US buoy, a new calibration correction in China Sea is needed presenting, which is a major work in the future.

Keywords: WAMC4, significant wave height, hindcast, altimeter data, calibration

1    INTRODUCTION

The WAM model, a third generation wave model developed by WAMDI-group (WAMDI, 1988) and improved by Komen et al. (Komen, 1994), is one of the best-tested wave models in the world. It is widely used for global and regional operational wave forecast in many marine and meteorological centers around the world, such as global operational wave forecasting at the European Centre for Medium-Range Weather Forecast (ECMWF). In recent years, the numerical operational wave forecast in high spatial resolution turns into being with the development of powerful computer as well as the remote sensing techniques, from which plenty of information on sea state becomes available. The wave height data from satellite can further validate the capability of the wave model and improve it, and the wave model can also verify the accuracy of the satellite data on the other hand. To improve the wave forecast accuracy, the spatial resolution for regional study has been already enhanced from 1° to 1/10° and (1/20)°. In the near-shore area the spatial resolution has dropped grid size to 1/96°´1/96° when Mobaliu et al(2000) studied the North Sea with the WAMC4 model in their PROMISE project.

The WAM model with a grid size of 1°´1° in NMEFC(Ji, 1995)was run in a quasi-operational manner during the 8^th Five-Year Plan period in China (1991-1995). To improve the wave forecast accuracy and save the computer time, Cheng et al.(Cheng, 1994) constructed a high resolution regional model system, where the WAM model with a grid size of 0.25°´0.25° was nested into the hybrid model of 1°´1°, to examine the wind waves along coastal area. Liu et al (Liu, 1999) employed the WAMC4 model with a spatial resolution 1/4° to predict the wave over the East China Sea, the Yellow Sea and the Bohai Sea, all the case studies indicated the results encouraging.

In order to perform operational wave forecast using WAM model in NMEFC, still a lot of work should be done. The primary objective of the present work is to develop a framework to forecast the wave in the coastal area. In this paper, the WAMC4 model is employed to hindcast wind waves caused by typhoon 9914. Due to the limitation of the computer, the model domain only covers 110°~130°E, 10°~30°N which include Taiwai Strait and Taiwan Island, parts of the East China Sea and South China sea. The grid size is 1/6° in both latitude and longitude. In section 2 we briefly introduce the WAMC4 model and the typhoon model, some new features of the WAMC4 compared with the previous versions also are mentioned. In section 3 the model results are compared with the data from coastal stations. Comparison between the model results and the wave height data measured by satellite altimeter is shown in section 4. Section 5 gives a summary of the conclusion.

2    THE WAVE MODEL

The WAM model

The WAM model is a state-of-the-art third generation spectral wave model, which solves the wave energy balance equation without any priori assumptions on the shape of the wave energy spectrum. Denoting the two dimensional frequency(f)-direction(q) wave variance spectrum by F(f,q), the model equation reads:

                                  (1)

where v_g is the group velocity, and S is the net source function describing the rate of change of the wave spectrum, which includes wind input(S_in), nonlinear wave-wave interaction(S_nl) and energy dissipation functions due to white capping(S_ds) and bottom friction(S_bf), that is,

                                   (2)

The WAM model used here is the most recent version WAMC4 developed by Komen et al.(Komen, 1994). There is an improvement in this cycle over the earlier cycles. It contains: (1) current-induced refraction (U=0 in this paper), (2) nesting, (3) the wind input term takes into account the feedback of the growing waves on the wind profile, (4) Dissipation due to the white capping, the least well-known source function, is clear now. There is some freedom in redefining the wind input and returning the dissipation constants, the only puzzle is the absolute magnitude of wind input and dissipation. By improving the wind input and dissipation term, the model gives more realistic growth rates of the waves.

The wind model

The wind force is calculated following Wang(1992), which consists of two parts: (1) a symmetric basic wind field (Veno Takeo, 1981); (2) an asymmmetric wind field . It can be expressed as:

                            (3)

The detail can be found in Wang(1992). The wind force is determined by several parameters: storm track, center air pressure and the radius of maximum wind speed. The wind field of every time step is given by linear interpolation of the typhoon parameters every 6 hours, such as the location of typhoon, the pressure etc.

3     CASE STUDY

To investigate the ability of WAMC4 in the China Sea, a hindcast study of waves caused by typhoon 9914 was carried out. The domain covers 10°N~30°N，110°E~130°E(see domain D1 in Fig.1), the grid size is 1/6° in both latitude and longitude. Typhoon 9914 as shown in Fig. 1 caused the most extensive damage to Minnan coastal area after the typhoon 5903 during the past 40 years. When it landed at the Xiamen area, just about the time of astronomical spring tide, the strong storm surge and waves resulted in 72 people dead and the economical losses up to 80 millions RMB in Minnan area (Li, 1999).

Fig. 1    the Track of Typhoon 9914

Fig. 2    Comparison of the hindcasting results with the Coastal Data

                      (a. Chongwu Coastal Station, b. Dongshan Coastal Station）

The hindcast of wave induced by typhoon 9914 was carried out for the period of 6-9 October 1994. The results are compared with the coastal station observations at—Chongwu(24°54¢N, 118°55¢E) and Dongshan(23°47¢N, 117°31¢E ). As seen in Fig. 2, the hindcasted results agree well with the observation data, except that the last three observation values in Fig. 2a are larger than the calculated results, which might be influenced by the special terrain of Taiwan Strait and probably caused by underestimate of swell waves as mentioned by Janssen(1999). When the northeastern or southwestern wind blows, the sea is so rough due to the narrow tube effect in this area that the swell can’t be transported to the observation station of Chongwu. As shown in Fig. 2b, the calculated results are more closely to the observation data in Dongshan since the station is situated in the edge of the strait.

4    COMPARISION WITH THE SATELLITE MEASUREMENTS

To further investigate the simulated results, we compare the model results with the altimeter data of TOPEX/POSEIDON and ERS-2 satellites. In order to ensure the quality of the altimeter data, some measurements were removed when the radar backscatter(s0) was less than 0 dB or greater than 20 dB(which indicates non-oceanlike altimeter returns) or wave heights greater than 25m(Cotton, 1994). The altimeter measured significant wave heights are averaged in each model grid rectangular that the satellite track was scanned, and the simulated results are averaged with four corner points of the rectangular. The nearest time of the satellite data and the model results are chosen to compare.

Fig. 3    Scatter Plot of WAM Significant Wave Height vs. Uncorrected (a) T/P (b) ERS-2

Fig. 3a and 3b show the scatter plot of the WAM model vs. the satellite measurement, where no correction has been made to the satellite data. We find the significant wave heights of the WAM model agree well with the altimeter data. However, the significant wave heights of the WAM model are generally lower than the satellite measurements. This can also be found in the literature of Monbaliu et al(1999) when they used WAM model to study the waves in the North Sea, but the difference is somewhat smaller. The ocean significant wave height is a function of the slope of the leading edge of the altimeter return pulse from the sea surface (Brown, 1977) and can be retrieved to an accuracy comparable to that of buoy data. Here the calibration corrections of Cotton (1998), who applied a principal components regression analysis to generate the calibration corrections for significant wave heights in comparisons with US buoy data, are adopted to correct the satellite data,

            (4)

            (5)

where the subscript T represents the calibrated value, E2 is ERS-2 and P is POSEIDON. Here we use the same calibration to TOPEX and POSEIDON. The corrected results are shown in Fig. 4.

Fig. 4    Scatter Plot of WAM Significant Wave Height vs. Corrected (a) T/P (b) ERS-2

It can be seen from Fig. 4a and 4b that the result has a little improvement for T/P, but no improvement for ERS-2 after corrections adopted. The significant wave heights of the WAM model are still lower than that of the satellite. The statistical variables bias, scatter index (S. I.) and root of mean square error (RMSE) for the data from the WAM model and the satellite with and without correction are given in Table 1. From the table we can find that the statistical variables have been improved after corrected for T/P, but not so satisfactory for ERS-2. The calibration corrections for significant wave height in Northwest Pacific should be further studied in the future. The difficulties, such as rare and discontinuous observation data of wave in Northwest Pacific especially in China Sea, must be settled appropriately.

                      Table 1    Statistics of WAM Model vs. Satellite Data

5    CONCLUSION

The WAMC4 model with a high spatial resolution has been employed to hindcast the waves caused by typhoon storm in the domain 10°N ~ 30°N, 110°E ~ 130°E. A case study was carried out to evaluate the capability of the WAM model. Compared with the coastal stations and the satellite data (T/P and ERS-2), the results are found to agree well with the observation data but not so well with the satellite data. When using the calibration corrections of Cotton to correct the satellite measurement, the improvement is not so satisfactory. This suggests that an adequate correction for the wave height should be explored in the future. In addition, when there is no typhoon storm but other meteorological condition such as cold air affecting the domain, a realistic wind model should be developed.

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.

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