Journal of the Meteorological Society of Japan, Vol. 74, No. 6, pp , Wavelet Analysis of Summer Rainfall over North China and India

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1 Journal of the Meteorological Society of Japan, Vol. 74, No. 6, pp , Wavelet Analysis of Summer Rainfall over North China and India and SOI Using Data By Zeng-Zhen Hu1 and Tsuyoshi Nitta Center for Climate System Research, University o f Tokyo, Komaba, Meguro-ku, 153, Japan Manuscript received 20 May 1996, in revised form 30 September 1996) Abstract Localization of interannual and decadal variations of summer rainfall in North China and India and seasonal mean Southern Oscillation Index (SOI) from , and the favored time scales of the significant correlations among them are investigated with the wavelet transform (WT) analysis method. Strong localization and non-stationary evolution in the interannual and decadal variations of the rainfall in North China and India are demonstrated. The dominating time scales in the rainfall variations in North China and India are mainly located in two time scale bands: shorter than 10 years, and years. The correlations between the rainfall variations in North China and India are time-scale dependent. The significant positive correlations are concentrated in two time-scale bands: shorter than 7 years and longer than 14 years. The correlations are insignificant on time scales of 7-14 years. El Nino and Southern Oscillation (ENSO) cycle is a nonstationary process. The dominant time scales for the variation of SOI are shorter than 5-7 years, and the decadal variations are obvious in and There is strong interaction between the Indian summer monsoon and the ENSO cycle. The significant positive correlations are mainly focused on the time scales shorter than years, and the significant negative correlations on time scales longer than 40 years in summer and winter SOI cases. The correlation between the rainfall variations in North China and the ENSO cycle in various seasons are less significant, more scattered and complex, but there are some similarities in the correlation pattern compared with that of India, especially in the shorter time scales. The calculation shows that the summer rainfall variations in North China and India at different time scales are related with different general circulation anomalous patterns in middle and high latitudes of Eurasia and the western Pacific. The correlation patterns over Eurasia and the western Pacific between the summer rainfall variations in North China or India and the geopotential height at 500hPa are similar to the correlation patterns between the geopotential height and the WT results of the rainfall on time scales of about 5 years, but different from those on time scales of about 11 years. Therefore, the similar behavior between the rainfall variations in North China and India may be caused by the similar associations between the rainfall variations and the ENSO cycle and the general circulation anomalies in middle and high latitudes over Eurasia and the western Pacific, and the difference may be related to the different character of these associations. 1. Introduction The important role of the Asian monsoon in global and regional climates and the general circulation variations has been demonstrated by many investigators (see Lau, 1992 and Yasunari, 1991). It is pointed out that the Asian monsoon is an integral component of the climate system and that there is strong interaction between the Asian monsoon and some other components in the climate system, for instance, El Nino and the Southern Oscillation (ENSO) cycle (Yasunari, 1991). The Asian 1 On leave from Institute of Atmospheric Physics, Chinese Academy of Science, Beijing , China. (c)1996, Meteorological Society of Japan monsoon consists of three subregions: the Indian (South Asian) monsoon, the East Asian monsoon and the Southeast Asian monsoon (Shen and Lau, 1995). China and India are located in the Asian monsoon region, but belong to different subregions of the Asian monsoon such as East Asian monsoon and Indian monsoon, respectively. The similarity and difference between the Indian monsoon and East Asian monsoon have been investigated by series studies. Using a rainfall dataset for , Tanaka (1987) pointed out that there exists a relationship between the North China rainfall and Indian summer rainfall. Guo and Wang (1988) also found significant positive correlation between

2 834 Journal of the Meteorological Society of Japan Vol. 74, No. 6 the Indian summer monsoon rainfall and rainfall in North China. Relationships between the ENSO cycle, Eurasian winter snow cover, and Indian summer monsoon rainfall were studied by Yang (1996). Yang (1996) suggested that the ENSO plays a more important role than the Eurasian winter snow cover in influencing the variability of the Indian monsoon. Precipitation fluctuations over semi-arid region in Northern China and their association with the ENSO were examined by Wang and Li (1990). Spectral analysis of China rainfall by Chen et al. (1991) showed that the dominant periods are the quasi-biennial oscillation (QBO), 3.5 years and 5.5 years. A recent study by Nitta and Hu (1996) demonstrated that a decreasing trend, QBO signals and decadal variations are significant in the summer rainfall over China. However, there are few works discussing for which time scales there are close correlations between the rainfall variations in India and North China and the role of the ENSO cycle in this correlation. It is important to reveal different relations at different time scales between them in order to further study the physical mechanism of these correlations. For example, using a temporal filtering method, different contributions from different time scales (2-7 years, 8-25 years and larger than 30 years) to the total variations of global and regional land air temperature are found with a 110-year dataset by Nitta and Yoshimura (1993). In the present paper, with the wavelet transform (WT) analysis approach, we focus on: (1) localization of interannual and decadalscale variations of summer rainfall in North China and India and the SOT; (2) for which time scale that the variations of rainfall in North China and India are closely related each other; (3) the role of the ENSO cycle in the rainfall variations in India and North China at different time scales, and the interaction between the ENSO cycle/general circulation and the rainfall variations in India and North China. In Section 2, we first describe the data and WT methods used in this study. The localization of different-time-scale variations in the rainfall variations over India and North China and their relationships are analyzed in Section 3. The localization of the interannual and decadal variation of the SOI and the interaction between the ENSO cycle and the rainfall variations in India and North China are discussed in Section 4. The association between the rainfall variations and general circulation over the Northern Hemisphere are analyzed in Section 5. Conclusions and discussion are given in Section Data and wavelet transform (WT) 2.1 Data All-India summer monsoon rainfall series (ISMRS) are used in this study. The ISMRS is constructed by using 36 uniformly distributed stations over India in JJAS (June, July, August and September) (Sontakke, et al., 1993). The rainfall of this 4- month monsoon accounts for more than 70% of the annual precipitation over the Indian subcontinent (G. Mudur, 1995). Summer (JJA: June, July and August) rainfall data in Beijing and Tianjin of North China are also used in the present study. According to the research of Yatagai and Yasunari (1995, see their Fig. 1b), more than 60-70% of the annual rainfall over North China is concentrated in summer (JJA). Recent studies of EOF and singular-value decomposition (SVD) analyses by Nitta and Hu (1996, see their Figs. 2 and 6) showed that summer rainfall variations in Beijing and Tianjin generally represent those over North China. Therefore, averaged summer rainfall in Beijing and Tianjin is mainly reflecting the nature of summer rainfall variation over North China. The periods of all the data used in the present work are from 1891 to Seasonal (spring: MAM; summer: JJA; autumn: SON; winter: DJF) mean SO index (SOI) data (Wang, 1992) are adopted as a representative of the ENSO cycle. The winter mean SOI is the average of the SOI in December of reference year and in January and February in the next year following the reference year. The period of the SOI data used in this study is from 1891 to The seasonal mean geopotential height data at 500hPa used in the present work are provided by the Japan Meteorological Agency (JMA) at a resolution of 5 (latitude) x 5 (longitudes). As there are too many missing data in regions south of 20 N before the 1970's, only the data at are used in calculating the correlation between the geopotential height and the rainfall variations in North China and India, and their WT analysis results. 2.2 Wavelet transform (WT) WT is a completely new mathematical analysis method, and a powerful analysis tool well suited to the study of multi-scale non-stationary processes occurring over finite spatial and temporal domains (Lau and Weng, 1995). WT was firstly founded by a petroleum engineer Morlet of France Elf-Aquitaine Company when he analyzed seismic data in WT has become a very active field of science research around the world in the subsequent 15 years. WT has been widely used in the analysis of seismic data, image processing, analysis of sonic signals, fractal, sampling, turbulence, and many study fields in the atmospheric sciences and oceanography. Mahrt (1991) firstly introduced WT into atmospheric sciences when eddy asymmetry in the sheared heated boundary layer was studied. In recent years, WT has been widely used in a series of fields of atmospheric sciences, for instance, analyzing low-level cold fronts (Damage and Blumen, 1993), coherent

3 December 1996 Z.-Z. Hu and T. Nitta 835 Fig. 1. The time series of anomalous summer rainfall in India (solid line) and North China (dashed line) from 1891 to structures at the atmosphere-forest interface (Gao and Li, 1993), microfronts and associated coherent events (Gamage and Hagelberg, 1993), rainfall spatial structure (Kumar and Foufoula-Georgiou, 1993), dispersion of mixed Rossby-gravity waves in a reduced gravity equatorial model (Meyers et al., 1993), period-doubling and time-frequency localization in the satellite infrared radiance data (Weng and Lau, 1994), vertical structure of atmospheric gravity waves (Sato and Yamada, 1994), interannual variability of sea surface temperature (SST) (Mak, 1995), a proxy paleoclimate time series and monthly mean surface temperature in the Northern Hemisphere (Lau and Weng, 1995), interannual and decadal variations of annual rainfall in North China (Hu, 1996), and so on. The definition of WT for function f(x) is Wf(a,b)=<F,Ia,b(x)> =f:pf(x)i[(x-b)/a]dx, where, <F,Ia,b(x)> denotes the projection of f(x) onto Ia,b(x). The function P is chosen so that Wf(a,b) is normalized to be unity. I[(x-b)/a] is called a 'basic wavelet', or 'mother wavelet', or simply, 'wavelet'. b denotes the position (translation) and a(>0) the scale (dilation) of the wavelet. Through the translation (x-x-b) and dilation (x-x/a), the corresponding family of wavelets is obtained. WT is also regarded as a mathematical microscope, the signal is observed in high-dimension space through putting the low-dimension signal into the high dimension space. The singularities of f(x) in various times and positions can be studied, basing on the property that wavelet PI[(x-b)/a] is maximum in position b. The evolution of f(x) in various scales can be probed through regulation dilation scale a. Detail of the concept, theory, applications and problems of WT can be referred to the above references, and related monographs and paper collections (Young, 1993; Schumaker and Webb, 1994; Foufoula-Geogiou and Kumar, 1994; Benedetto and Frazier, 1994; Kaiser, 1994). The 'Mexican hat' wavelet: I(x)=(1-x2)e-x2/2 where, x=(i-b)/a, P=11/a, is used in present work. In order to compare with WT, power spectral analysis is also used in the present work as a traditional method. 3. WT analyses of the rainfall variations over North China and India Correlation between the rainfall in North China and India with a data set of 102 years is 0.36, which is significant at a significance level of 99% (Fig. 1). This result coincides with the conclusion of Guo and Wang (1988). The power spectral analyses show that there is not any significance in the raw data of the rainfall variations in North China and India (Fig. 2). With the traditional analysis methods, we can not discover in which time scale this positive correlation is concentrated. In the present study, the time-scale dependence of this positive correlation is clearly revealed with the WT. In this section, the localization of interannual and decadal variations of the different time scale components of the rainfall in North China and India is firstly analyzed with the WT. Then, the relationship between the rainfall over North China and India is calculated in different time scales based on the WT results.

4 836 Journal of the Meteorological Society of Japan Vol. 74, No. 6 Fig. 2. Power spectral analysis of the time series of anomalous summer rainfall in North China and India (solid lines) from 1891 to The dashed lines are a significance test at a significance level of 95%. Fig. 3. Time series of summer rainfall (mm) in North China from 1891 to 1992 and results of WT. The contour interval in Fig. 3b is 0.4. The regions with values larger than 0.4 are dotted and the regions with values smaller than -0.4 are shaded in Fig. 3b. Comparing with the power spectral analysis, through which only the stationary and averaged significant period over the whole period can be found, WT can give more information related to the nonstationary and localized strong signal. Fig. 3 is the time series of summer rainfall in North China and the corresponding WT results. All timescale (period) component variations are changed with time. Time scales shorter than 6 years are dominant in the variations over nearly all the time domain, especially in , , The variations with the time scales near 7-8 years are strong during The decadal variations with the time scales of years are also relatively obvious in and Fig. 4 is the time series of the ISMRS and its corresponding WT results. Similar to the WT results for the rainfall in North China, variations of all time-scale components are changed with time. However, the details of variations with various time scales are different between them (Figs. 3b and 4b). The variations with the time scales shorter than about 6 years are dominant in and , and those with the time scales of about 8-10 years are significant in The decadal variations with the time scales of years are relatively obvious in The character of time-scale dependence of the

5 December 1996 Z.-Z. Hu and T. Nitta 837 Fig. 4. Same as Fig. 3, but for the rainfall in India. The contour interval in Fig. 4b is 0.2. The regions with values larger than 0.2 are dotted and the regions with values smaller than -0.2 are shaded in Fig. 4b. Fig. 5. Correlations (solid line) between the WT results for the rainfall in North China and India on different time scales. The dashed lines represent the lines of significant correlation at a significance level of 95%. correlations between rainfall variations over North China and India is clearly demonstrated in Fig. 5, which is the correlation between different time-scale components of the WT results in Fig. 3b and Fig. 4b. As significance levels of the correlations strongly depend upon the number of degrees of freedom, and the number of degree of freedom are affected by persistences in the time series which is associated with the time scale, it is reasonable to use the effective number of degrees of freedom in the significance test. In this paper, the effective number of degrees of freedom is calculated based on the method given by Leith (1973) and Chen (1982). From Fig. 5, it is found that the lines of significant correlations at significance level of 95% vary with the time-scales. In Fig. 5, although the correlations are positive in all time scales, the significant correlations at significance level of 95% are concentrated in two timescale bands: shorter than 7 years and longer than 14 years. Insignificant correlations exist in the time scales of 7-14 years. Therefore, from above analysis, we can conclude that the rainfall variations in North China and India are mainly located in two time-scale bands: shorter than 10 years, and years, and the significant positive correlations between them are mainly concentrated in two time-scale bands: shorter than 7 years and longer than 14 years. 4. Association with ENSO cycle In this section, the localization of interannual and decadal variations of the seasonal mean SOI is firstly analyzed with WT, then the association between the ENSO cycle and the rainfall variations in North China and India is examined. The various roles of the ENSO cycle in the rainfall variations in North China and India on different time scales and for different seasons are demonstrated.

6 838 Journal of the Meteorological Society of Japan Vol. 74, No. 6 Fig. 6. Same as Fig. 4, but for the SOI in winter. Fig. 7. Lag cross-correlations between the seasonal mean SOI and the rainfall in North China and India. The symbols of '-' ('+') and '--' ('++') in the abscissa denote the SOI leading (lag) the reference year of the rainfall by 1 and 2 years, respectively. The letters without these symbols in the abscissa denote the reference year of the rainfall. The dashed lines represent the lines of significant correlation at a significance level of 95%. Power spectral analyses for the raw seasonal mean SOT demonstrate that the ENSO cycle is a nonstationary process (Figures are saved). WT results in the winter SOI case (Fig. 6) show that the dominating time scales in the variations of seasonal mean SOI are shorter than 5-7 years. This coincides with the time scales (2-7 years) of the ENSO cycle. Nearly all significant negative (positive) values with periods shorter than 5-7 years correspond to the warm (cold) phase of the ENSO cycle, namely EL Nino (La Nina) event. The decadal variations are also obvious in some time subdomains such as during and Similar results can be found in other seasons. The lag cross correlations between the SOI and the rainfall variations in North China and India are shown in Fig. 7. These correlation patterns are very similar to those between sea surface tem-

7 December 1996 Z.-Z. Hu and T. Nitta 839 : SPRING SOI & INDIAN SUMMER RAINFALL : SUMMER SOI & INDIAN SUMMER RAINFALL (c): AUTUMN SOI & INDIAN SUMMER RAINFALL (d): WINTER SOI & INDIAN SUMMER RAINFALL Fig. 8. Correlations between the WT results of the summer rainfall variations in India and the SOI in spring, summer, autumn (c) and winter (d). The thin dashed lines represent the lines of significant correlation at a significance level of 95%. perature (SST) in eastern (western) tropical Pacific and Indian summer monsoon rainfall given by Yasunari (1991), and between the SOI and time coefficients of EOF for China summer rainfall (Tian and Yasunari, 1992). Significant positive correlations exist between the Indian monsoon rainfall and the SOI in summer (JJA) and the following seasons: autumn (SON), winter (DJF) in the same year, and spring (+MAN) in the following year (Fig. 7b). This coincides with the conclusion that the Indian summer monsoon has a strong interaction with the tropical ocean and atmospheric system in following seasons (Yasunari, 1991 and Yang, 1996). Nearmarginal significant negative correlations exist between the Indian summer monsoon rainfall and the SOT in spring (-MAN) and summer (-JJA) of one year before the reference year of the Indian summer monsoon. These negative correlations in one sense reflect the impact of the ENSO cycle one year previous on the Indian summer monsoon, and in another sense demonstrate the quasi-biennial oscillation (QBO) character in the Indian summer monsoon and the tropical ocean and atmospheric system There are not any significant correlations between SOI and the rainfall variations when the lag year is larger than one year. Although the pattern is similar between Figs. 7a and 7b, significant correlation can only be found between the summer rainfall variations in North China and SOI in the following autumn and winter (Fig. 7a). There are not any significant correlations between the summer rainfall variations in North China and SOI in seasons before summer. Therefore it seems impossible to predict the summer rainfall variations in North China by only considering the ENSO cycle. The strong interaction between the Asian summer monsoon and the ENSO cycle have been demonstrated by Yasunari (1991), Tian and Yasunari (1992), Yang (1996) and the present analysis. However, it is not clear in which time scale they are closely related to each other. Fig. 8 shows the come-

8 840 Journal of the Meteorological Society of Japan Vol. 74, No. 6 : SPRING SOI & NORTH CHINA SUMMER RAINFALL : SUMMER SOI & NORTH CHINA SUMMER RAINFALL (c): AUTUMN SOI & NORTH CHINA SUMMER RAINFALL (d): WINTER SOI & NORTH CHINA SUMMER RAINFALL Fig. 9. Same as Fig. 8, but for the rainfall variations in North China. lations between the WT results for the summer rainfall in India and the SOI in spring, summer, autumn (c) and winter (d). Similar to Fig. 5, the effective number of degrees of freedom is also adopted in the significance test in Fig. 8. The general correlation patterns varying with time scales are similar for different seasons. The positive correlations are on the shorter time scales, and the negative correlations are on the longer time scales. The positive significant correlations exist on time scales of years and shorter than 7.5 years for the spring SOI (Fig. 8a), shorter than 30 years for the summer SOI and the autumn SOI (Fig. 8b and 8c), years and shorter than 7.5 years for the winter SOI (Fig. 8d). Therefore, on time scales shorter than 30 years, there are some similarities between the cases of the SOI in summer and autumn (Fig. 8b and 8c), and between the cases of SOI in spring and in winter (Fig. 8a and 8d). But on time scales longer than 40 years there are some similarities between the cases of the SOI in summer (Fig. 8b) and winter (Fig. 8d). On time scales longer than 40 years, significant negative correlations exist in Fig. 8b and 8d, and the correlations are insignificant in Fig. 8a and 8c. It is also noted that the correlations are insignificant on time scales of years for the cases of the SOI in spring and in winter (Fig. 8a and 8d). The correlation patterns are less significant, more scattered and complex for different seasons in the correlations between the SOI and the summer rainfall variations in North China (Fig. 9), compared with the case of India (Fig. 8). The correlations on all time scales are positive in Fig. 9. The positive significant correlations between the SOI and the rainfall variations in North China are on time scales of 6-12 years for the spring SOT (Fig. 9a), years and shorter than 7.5 years for the autumn SOI (Fig. 9c), and years and shorter than about 6 years for the winter SOI (Fig. 9d). For the summer SOI case (Fig. 9b), correlations are positive on all time scales, but no correlation is significant. So there is not a close contemporary correlation between the rainfall variation in North China and the ENSO cycle in summer.

9 December 1996 Z.-Z. Hu and T. Nitta 841 From the above correlation analyses of the WT results and the lag cross-correlations, it is shown that different time scales make different contributions to the correlation between the ENSO cycle and the rainfall variations in North China and India. There are more coherent significant correlations between the rainfall variations in India and the SOI in various seasons (Figs. 7b and 8) compared with the correlations between the rainfall variations in North China and the SOI in various seasons (Figs. 7a and 9). The general positive significant correlations between the rainfall variations in India and the SOI are mainly focused on time scales shorter than years, and the significant negative correlations exist on time scales longer than 40 years for the summer and winter SOI cases. The mechanisms generating these significant negative correlations are not clear and remained as a future subject. The correlations between the rainfall variations in North China and SOI in various seasons are less significant, and more scattered and complex, but with similar patterns compared to the case of India, especially on the shorter time scales. 5. Association with geopotential height in 500hPa Figure 10 shows the correlation between the geopotential height at 500hPa in JJA and the rainfall variations in North China and their WT analysis results on time scales of about 5 years and 11 years (c). As the large-scale significant correlations are mainly located in Eurasia and the western Pacific, only the correlations over Eastern Hemisphere are shown and analyzed. The correlation patterns in Fig. 10a and 10b are similar, especially in middle and high latitudes over Eurasia and the western Pacific. For example, positive correlations are found in regions around the Korean Peninsula and the Japan Islands and in regions near the North Pole, and negative correlations in the northwestern and northeastern regions to the Baikal Lake and the western Pacific. The correlation patterns in Fig. 10c are similar to Fig. 10a and 10b, but the correlations in Fig. 10c are more significant than those in Fig. 10a and 10b. This kind of anomaly pattern is in favor of above-normal rainfall in North China. The correlation patterns in Fig. 11a and 11b for the Indian case are quite similar to Fig. 10a and 10b of the North China case, especially the positive correlations around the Korean Peninsula and the Japan Islands and the negative correlations around the Baikal Lake. The correlations on time scales of about 11 years (Fig. 11c) are less significant compared with Figs. 10 and Fig. 11a and 11b. Therefore the obvious difference of the correlation patterns in middle and high latitudes between Fig. 10 and Fig. 11 is mainly in the correlations between the geopotential height and the WT analysis results on time (c) Fig. 10. The correlations between the geopotential height at 500hPa in JJA and the rainfall in North China and their wavelet analysis results on time scales of about 5 years and 11 years (c). The contour interval is The regions with correlation values larger than 0.30 and smaller than are dotted or shaded, respectively. scales of about 11 years (Figs. 10c and 11c). These results coincid with the conclusion (Fig. 5) that the correlations between the rainfall in North China and India are significant on time scales shorter than 7 years and insignificant on time scales of 7-14 years. The correlations between the rainfall in North China and the 500-hPa height in a prior winter are similar for the total rainfall case and the cases on time scales of about 5 years and 11 years, but differ-

10 842 Journal of the Meteorological Society of Japan Vol. 74, No. 6 ent from the corresponding correlations for Indian rainfall, especially on time scales of about 11 years (Figures are saved). The correlations are more significant for the case of rainfall variations in North China than that in India on time scales of about 11 years. Therefore the summer rainfall variations in North China on time scales of about 11 years are more closely related with the prior winter anomalies of general circulation in middle and high latitudes over Eurasia and the western Pacific in contrast with that for the Indian summer monsoon. From the above analysis, it is found that the summer rainfall variations in North China and Indian at different time scales are related with different general circulation anomaly patterns in middle and high (c) Fig. 11. Same as Fig. 10, but for the India summer monsoon rainfall. latitudes over Eurasia and the western Pacific, especially on time scales of about 11 years. The correlation patterns between the summer rainfall variations in North China or India and the geopotential height at 500hPa are similar to the correlations between the geopotential height and the WT results of the rainfall at the time scales of about 5 years, but different from those on time scales of about 11 years. The summer rainfall variations in North China are more closely related to the general circulation anomalies in middle-high latitudes of Eurasia and the western Pacific in a prior winter, whereas the Indian rainfall variations are more closely related to anomalies of tropical air-sea interaction, for example, the ENSO cycle and east-west SST contrast in the Arabian Sea (Shukla, 1975). 6. Conclusion and discussions The localization of the interannual and decadal variations of the summer rainfall in North China and India and seasonal mean SOI from , and the favored time scales of the significant correlations among them are investigated with the WT analysis method. The main conclusions of the present study are summarized in the following. (1) Strong localization and non-stationary evolution in the interannual and decadal variations of the rainfall in North China and India are demonstrated. The dominant time scales are shorter than 6 years ( , and ), about 7-8 years ( ), and years ( and ) for the rainfall variations in North China. In the Indian summer monsoon, the dominant time scales are shorter than about 6 years ( and ), 8-10 years ( ), and years ( ). (2) The correlations between the rainfall variations in North China and India are time-scale dependence. The significant positive correlations are concentrated in two time-scale bands: longer than 14 years and shorter than about 7 years. The correlations are insignificant on time scales of 7-14 years. (3) The ENSO cycle is a non-stationary process. The dominant time scales for the variations of SOI in four seasons are shorter than 5-7 years. The decadal variations are obvious in and (4) There is strong interaction between the Indian summer monsoon and the ENSO cycle. The general positive significant correlations between the rainfall variations in India and the SOI are mainly focused on time scales shorter than years, and the significant negative correlations exist on time scales longer than 40 years for the summer and winter SOI cases. (5) The correlations between the rainfall variations in North China and the ENSO cycle in various seasons are less significant, scattered and complex, but there are some similarities in the correlation pat-

11 December 1996 Z.-Z. Hu and T. Nitta 843 terns compared with those of India, especially on shorter time scales. (6) The summer rainfall variations in North China and India at different time scales are related with different general circulation anomaly patterns in middle and high latitudes of Eurasia and the western Pacific. The correlation patterns over Eurasia and the western Pacific between the summer rainfall variations in North China or India and the geopotential height at 500hPa are similar to the correlation patterns between the geopotential height and the WT results of the rainfall on time scales of about 5 years, but different from those on time scales of about 11 years. Therefore, the similar behavior between the rainfall variations in North China and India may be caused by the similar associations between the rainfall variations and the ENSO cycle and between the general circulation anomalies and the rainfall variations over Eurasia, and the difference may be related to the different character of these associations. The rainfall variations in North China and India and their relationship and the interaction between ENSO cycle and the rainfall variations are a complex problem, but only linear relationships are analyzed in the present study. The non-linear interactions are not clear and remain as a future subject. Since time series data with a resolution of one year are used for analysis in this study, the variations with time scales shorter than 4 years where QBO signals and large parts of the ENSO signals are included can not be resolved by the WT method. The results of the present study can not be compared directly with studies based on data with higher resolution. Acknowledgments The authors wish to thank Prof. S. W. Wang and Dr. J. Matsumoto for kindly providing the data of the SOI and summer rainfall in North China, respectively. Hu, one of the authors, is grateful to Prof. R.H. Huang, Prof. S.W. Wang and Prof. S.Y. Tao for their invaluable encouragement through recent years. The authors are grateful to Drs. J. Matsumoto, M. Kimoto and A. Yatagai for their valuable comments and suggestions. Thanks are also due to the JMA for kindly providing the geopotential height data at 500hPa. The figures in this paper are drawn with graphic routines in the GFD-Dennou Library, developed by the GFD Dennou Club. References Benedetto, J.J. and M.W. Frazier, 1994: Wavelets: Mathematics and Applications. CRC Press, 575pp. Chen, W.Y., 1982: Fluctuations in Northern Hemisphere 700mb height field associated with the Southern Oscillation. Mon. Wea. 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