Results and Discussion
Figure 1 shows the variations of sea surface heights in China Yellow Sea, East China Sea and South China Sea from October of 1992 to June of 1998, respectively. A traditional harmonic analysis is applied to the variations of sea surface heights to determine the amplitude and phase of annual, semi- annual, seasonal and two-month period, respectively. A FFT analysis is also applied. The results of harmonic and FFT analysis are shown in Table 2. The amplitudes of annual period are largest in all of the three interest regions which means the contributions of annual period are greatest and can be seen easily in Figure 1. The smoothing curves without marks in Figure 1 indicate the sum of the contributions of annual and semi-annual period. The straight lines indicate the secular contributions of the variations in the sea surface heights. However, the contributions of semi-annual and seasonal period are different in three interest regions. In Yellow Sea the contribution of seasonal is greater than that of semi-annual, in South Sea the case is inverse, and in East Sea there is equivalent between the contribution of semi-annual and that of seasonal. What we are surprised is that an about two month period exists obviously in all three interest regions and its amplitude exceeds that of semi-annual and seasonal in Yellow Sea and East Sea. This phoneme is proved in the following wavelet analysis.

Fig. 1 The variations of sea surface heights
(indicates China Yellow Sea, indicates China East Sea, X indicates South China Sea)



Table 2. The amplitudes of the variations in sea surface heights using the harmonic and FFT analysis (unit: mm)

Period	Annual		Semi-annual		Seasonal		60 days
	Harmonic	FFT	Harmonic	FFT	Harmonic	FFT	Harmonic	FFT
Yellow Sea	81.02	63.36	15.25	11.77	28.41	36.29	45.33	37.11
East Sea	75.75	59.31	18.19	12.39	14.70	12.19	69.76	52.06
South Sea	54.83	11.91	22.04	19.05	9.00	7.50	10.93	9.90

The anomalies in the variations of sea surface heights, i.e., sea level anomalies or variations of mean sea level, are what we focus on. Figure 2 shows the sea level anomalies by removing the contributions of secular, annual and semi-annual periods from the variations of sea surface heights, and low-pass filtering with a bandwidth of seasonal, i.e., 90 days to reduce the effects of high frequency. The dash line in Figure 2 indicates the ENSO index (Nino3) from NCEP of NOAA (http://www.cpc.ncep.noaa.gov). From the comparison between the sea level anomalies and ENSO index, we found that the effect of ENSO on the sea level anomalies in South China Sea is the largest. Furthermore, the 1997-1998 El Nino, which is the greatest in history, has the biggest effect, and causes a maximum negative anomaly of 30 mm. The sea level anomalies and the ENSO index almost become asymmetrical relation in South China Sea, while the respond of sea level anomalies on El Nino in China Yellow Sea and East Sea is an oscillation process and has an about six-month delay.


Figure 2 Sea level anomalies and its relationship to ENSO index
The solution of secular term from the variations of sea surface heights should be carefully carried out. The large contribution from the harmonic cycles should be removed first, such as annual cycle and semi-annual cycle. Then a low-pass filtering should be applied to reduce the random noise. Finally, the secular term can be obtained by linearly fitting the low-pass filtered residuals. The estimated sea level rise in China Yellow Sea, East Sea and South China Sea during 1992– 1998 is +3.44 ± 0.61 mm/yr, +3.12 ± 0.47 mm/yr and –1.41 ± 0.48 mm/yr, respectively. Compared with the global sea level rise +2.1 ± 1.3 mm/yr from 4 years T/P altimeter data (Nerem, et al., 1997), we found the sea level rises vary in different regions of China Seas, and there is a very strong correlation with the strongest El Nino of 1997-1998. For example, the rate in South China sea becomes negative due to the 199-1998 El Nino, while the rates in China yellow Sea and East Sea are almost the same because they are closing to each other.

In recent years, the Wavelet analysis becomes a very useful method in data processing because of its multi-resolution analysis. Wavelet analysis works as a mathematical micro-magnifying glass, so it has a better resolution in local frequency domain as well as in local space domain than common FFT analysis. Here we introduce a new wavelet analysis technique named ‘wavelet amplitude-period spectrum’ (WAPS) rather than the common wavelet energy spectrum analysis (Liu, 1999). WAPS can help to express and reveal instantaneous amplitudes and instantaneous frequencies of quasi-periodical signals. The definition of WAPS is as follows: if the real part of Morlet wavelet is chosen as a wavelet basis y(t), i.e.,

From the definition of WAPS, we prove that when a cosine signal reaches its limits ± A at t=t₀+nT/2, the WAPS of f(t) also reaches its limits ± A at the locate (a=w₀ T , b=t₀ +nT/2). Therefore, when a signal consists of several cosine (sine) periodical components, the limits and their locations of WAPS can definitely determine the amplitude, period and phase of each periodical component. It should be noted that the periods and amplitudes of components in most actual signals usually change. Sometimes when the periods of two components are close to each other, there is a coupling so as difficult to separate the two components. In this case, the scales and locations of the limits in WAPS of the signal will affect each other. Of course, when the amplitudes and periods of components are stationary, and the periods of each component are discrete large enough, the scale and locations of the limits in WAPS can definitely express and reveal instantaneous amplitudes and instantaneous frequencies of each periodical component.