INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 19: 1255–1265 (1999) PREDICTION OF THE SUMMER MONSOON RAINFALL OVER SOUTH CHINA JOHNNY C.L. CHANa,b,* and JIU-EN SHIb,c Department of Physics and Materials Science, City Uni6ersity of Hong Kong, Tat Chee A6enue, Kowloon, Hong Kong, People’s Republic of China b Centre for En6ironmental Science and Technology, City Uni6ersity of Hong Kong, Tat Chee A6enue, Kowloon, Hong Kong, People’s Republic of China c Beijing Meteorological College, Beijing, People’s Republic of China a Recei6ed 23 May 1998 Re6ised 22 February 1999 Accepted 23 February 1999 ABSTRACT The objective of this study is to derive an operational statistical prediction scheme for forecasting the summer monsoon rainfall (SMR, defined as the total rainfall between April and June) over South China (SC). The region of SC is first identified by applying the techniques of cluster analysis and factor analysis to the SMR of 43 stations over China for a period of 47 years (1951–1997). This procedure suggests 13 stations along the SC coast as having similar rainfall characteristics. Subdivisions of these into six stations in the east and seven in the west are also made. The predictands are therefore the average SMR over these stations. The potential predictors include: (a) indices that serve as proxies for the El Niño/Southern Oscillation (ENSO); (b) indices that represent the planetary-scale circulation and (c) the trend and periodicities in the rainfall time series. All predictors are monthly values from March of the previous year to February of the current year. The technique of projection pursuit regression is applied to derive prediction equations for each predictand using individual predictors. Only those equations in which the predicted (obtained from the jackknife technique) and observed SMR are significantly correlated ( ]95%) are retained. The predictions from individual predictors are combined using a weighted average (based on the magnitude of the correlation coefficient) to produce a final forecast, which is found to be superior to those from the individual ones. An operational prediction of the SMR made in March 1998 suggested a below-normal season. However, the actual results indicate an above-normal one. Reasons for this apparent failure are discussed. Copyright © 1999 Royal Meteorological Society. KEY WORDS: South China; regression techniques; long-range rainfall forecast 1. INTRODUCTION Summer rainfall over SC generally has a bimodal structure, with one peak appearing between April and June and another between August and September (see Figure 4 for an example). The first one is associated with the summer monsoon while the second is mainly contributed by the passage of tropical cyclones (TCs). In general, heavy rain due to the summer monsoon can last for an extended period of time and covers a much larger area while that from TCs is more transitory. The amount of rainfall that can be expected from the former is therefore of great importance in terms of disaster preparedness. In addition, an examination of the parameters that can be used to predict the monsoon rainfall can provide insights into understanding the physical mechanisms responsible for the interannual variability of the summer monsoon. It is for these two reasons that the present study is undertaken. Specifically, the objective here is to develop an operational statistical prediction scheme for forecasting the summer * Correspondence to: Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, People’s Republic of China; e-mail: Johnny.Chan@cityu.edu.hk CCC 0899–8418/99/111255 – 11$17.50 Copyright © 1999 Royal Meteorological Society 1256 J.C.L. CHAN AND J-E. SHI monsoon rainfall (SMR) over SC, which is defined as the total rainfall between April and June averaged over a number of stations over SC (to be identified objectively in Section 2). A number of studies has been taken in the past on the SMR over SC. For example, Bell (1976) developed a statistical forecasting algorithm to predict the SMR over Hong Kong using parameters that primarily relate to the winter conditions in the Northern Hemisphere. Huang (1982) also described the characteristics of the heavy rain associated with the SMR over SC. For a detailed review of studies related to this problem, the reader is referred to Tao and Chen (1987) and Ding (1994). The techniques of cluster analysis and factor analysis are employed in Section 2 to group the stations over southern and central China into clusters in which the SMR has similar characteristics. Potential predictors are described in Section 3. Prediction equations are then developed in Section 4 using the technique of projection pursuit regression, a robust statistical method that has been recently applied in many areas of climate studies (Chan and Shi (1997), Chan et al. (1998) and the references therein). The validity of these equations is tested using the jackknife technique. Operational predictions of the SMR over SC for 1998 were then made in March 1998. These predictions and the verifications are discussed in Section 5. A summary and discussion are given in Section 6. 2. RAINFALL CLIMATOLOGY OF SC 2.1. Defining the SC region for the SMR While it is generally recognised that the SMR over SC is the highest within China, an objective identification of this rainfall-intensive region has yet to be made. To do this, the monthly rainfall of 42 stations from the mid and lower reaches of the Yangtze River to the southern coast of China for the period 1951–1997 are obtained from the National Climate Center of China and that of Hong Kong from the Hong Kong Observatory. For each individual station, the annual rainfall between April and June are then totalled from which the anomaly percentage is derived. Applying the Ward’s method and the K-means method in cluster analysis (Hartigan, 1975; Everitt, 1993) to these percentages, three characteristic rainfall regions can be identified (Figure 1). They are the mid and lower reaches of the Yangtze River, the ‘South of the River’ region and the SC. Note that in Figure 1, two different symbols are used for the SC region. These are the subregions identified by the rotated varimax method discussed below. The cluster analysis groups these two subregions as one. To verify the results from the cluster analysis, the rotated varimax method in factor analysis (Gorsuch, 1983; Richman, 1986) is also applied to the same anomaly percentages. The first factor loading, which explains about 30% of the variance, gives a centre near the mid and lower reaches of the Yangtze River Figure 1. The locations of the 43 rainfall stations used in this study. The symbols indicate the various regions identified by the rotated varimax technique: open diamond: mid-low reaches of the Yangtze River; filled diamond: South of the River; open square: east subregion of South China; and filled square: west subregion of South China Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) SOUTH CHINA SUMMER RAINFALL PREDICTION 1257 Figure 2. Plots of the values of the first four factor loading in relative units: (a) first loading; (b) second loading; (c) third loading and (d) fourth loading. Solid—positive values; dashed — negative values; thick solid — zero line (Figure 2(a)) while the second (with 16% of the variance) divides the entire region into two, with the other centre being over SC (Figure 2(b)). The third loading (7.5%) gives the same three regions as those identified from the cluster analysis (Figure 2(c)). A further division of the SC region into east and west can be made based on the fourth loading (6.5%) (Figure 2(d)), which is again consistent with the results in Figure 1. The consistency in the results from the two analysis techniques lends credence to the grouping of the rainfall stations. Three separate prediction equations will therefore be derived, one for the entire SC and one for each of the two subregions (with six stations in the east and seven in the west). The 13 stations that constitute the SC region are plotted in Figure 3. Note that the SMR accounts for anywhere from 29% to almost half of the annual rainfall, which further highlights the importance of predicting the SMR. Figure 3. The 13 stations that constitute the South China region. The number next to each station indicates the percentage of the summer monsoon rainfall relative to the annual rainfall of that station Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) 1258 J.C.L. CHAN AND J-E. SHI Figure 4. Mean monthly rainfall (mm) averaged over the 13 stations of South China 2.2. Characteristics of SC rainfall The monthly rainfall averaged over the 13 stations of SC for the period 1951–1997 shows two peaks, one in June and the other in August (Figure 4). The total rainfall during the period April–September accounts for about 80% of the annual amount (Table I), with each of the two subperiods (April–June) and (July–September) having a similar share. For the rest of this paper, the former, i.e. the SMR period, will be the focus. 3. PREDICTANDS AND PREDICTORS 3.1. The predictands As mentioned in Section 2, the SMR over the entire SC as well as the east and west regions will be studied. Thus, three predictands are established: anomaly percentage of SMR averaged over all 13 stations (RA13), anomaly percentage of SMR averaged over six stations in the east (RA6), anomaly percentage of SMR averaged over seven stations in the west (RA7). Table I. Mean monthly rainfall (mm) for the 13 stations that constitute the SC region Month Rainfall (mm) January February March April May June July August September October November December 36.9 61.6 85.6 152.7 239.8 279.8 223.8 252.1 179.8 79.9 44.7 29.1 Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) 1259 SOUTH CHINA SUMMER RAINFALL PREDICTION Table II. Definitions of the predictors to be tested Predictor Description Source SOI NINO12 NINO4 HC011 HC046 HC047 HC061 HC062 HC070 Standardised Southern Oscillation Index SST anomalies in the NINO1+2 region SST anomalies in the NINO4 region Index of the area of subtropical high over the Pacific Ocean (110°E–115°W) Index of the area of the polar vortex in the Asia sector (60–150°E) Index of the area of the polar vortex in the Pacific sector (150°E–120°W) Zonal index over Eurasia (0–150°E) Meridional index over Eurasia (0–150°E) Index of the frequency of cold-air intrusion into China during September–December and January–May Trend and 3–8 years variations of the predictand NOAA/CACa NOAA/CAC NOAA/CAC NCCb NCC NCC NCC NCC NCC CLIPER Derived from data All values are monthly means. a NOAA/CAC: National Oceanic and Atmospheric Administration/Climate Analysis Center (now the Climate Prediction Center), USA. b NCC: National Climate Center, China. The east and west stations can be found from Figure 1. The normals used in calculating the anomalies are the 45-year mean SMR (1951 – 1995) for the respective predictand. 3.2. Potential predictors Three types of predictors are identified: indices related to the El Niño/Southern Oscillation (ENSO) which include: (a) the Southern Oscillation Index (SOI) calculated as the difference in the standardised anomalies in mean-sea-level pressure between Darwin and Tahiti; and (b) the sea-surface temperature (SST) anomalies over each of the ENSO-affected areas (i.e. NINO1+2, NINO3, NINO4 and NINO3+ 4); indices related to the planetary-scale circulation of the atmosphere (see Table II for a complete list of these predictors; their definitions are given in Appendix A); and the climatology and persistence of the SMR, including possible trends and periodicities (see Appendix A). All the predictors are monthly values and for the period from March of the previous year to February of the current year. 4. DEVELOPING THE PREDICTION EQUATIONS 4.1. The projection pursuit regression (PPR) method Huber (1985) introduced the general method of projection pursuit (PP) as an alternative to the traditional principal component technique to reduce a high-dimensional dataset into a lower-dimensional one. Since then, a number of applications of this method has been introduced (see Chan and Shi (1997) and the references therein). One such application is in regression analysis (Friedman and Stueltzle, 1981), which has been demonstrated to be superior to the traditional multiple linear regression by Chan et al. (1998) because the PPR technique is capable of identifying nonlinear relationships between the predictand and the predictors. A simplified and brief description of this technique is given in Appendix B. For details, the reader is referred to the original paper (Friedman and Stueltzle, 1981) or Chan et al. (1998). To illustrate how this technique is applied, consider the example of developing a regression equation between the predictand RA13 and the predictors which consist of monthly SST anomalies in the NINO1+ 2 area for the period from March of the previous year to February of the current year. Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) 1260 J.C.L. CHAN AND J-E. SHI Figure 5. Plot of the linear combinations of the first projection of the NINO12 predictors against the predicted values for the RA13 predictand. The straight line is the least-square fit Applying the PPR technique, only the anomalies in the months of June, September, October, November and December are found to be significantly correlated. The PPR technique is then applied one more time to only the anomalies of these five months to search for the best projection directions. The first one a T1, is found to be: a T1 =(0.31, −0.52, − 0.06, 0.68, −0.41) The plot of the predictand y ( =RA13) and the first projected factor z1 (= a T1x) (Figure 5) shows essentially a linear relationship between the two. Writing this relationship as g1(a T1x), the residual from the first projection, i.e. g(x) = y − g1(a T1x), can then be correlated with the second projected factor z2 (= a T2x). The plot in Figure 6 suggests a nonlinear relationship (say g2(a T2x)) between the two. The final prediction is then given by g1 +g2. This procedure is then repeated for all the potential predictors listed in Section 3.2. Figure 6. Plot of the linear combinations of the second projection of the NINO12 predictors against the residual from the first solution for the RA13 predictand. The curved line is the least-square fit Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) SOUTH CHINA SUMMER RAINFALL PREDICTION 1261 Table III. Parameters that are found to be significantly correlated with each of the three predictands Predictor 13 Stations (RA13) East 6 stations (RA6) West 7 stations (RA7) NINO12 NINO4 HC011 HC046 HC047 HC061 HC062 HC070 CLIPER ** ** ** * ** ** ** ** ** * * * *** * *** *** *** Correlation significant at the 99.9% level. ** Correlation significant at the 99% level. * Correlation significant at the 95% level. 4.2. Tests for significance For each predictor set identified, a prediction equation for each of the three predictands is derived using the entire sample of 47 years. To test whether the resulting predictions are significant, the jackknife method is applied (see Miller (1974) for a review; Chan (1995) also provides a brief description of the procedure). That is, the predictors and the corresponding predictand for 1 year are removed before deriving the regression equation. This new equation is then used to predict the value of the predictand for the removed year. The procedure is then repeated for all 47 years. These ‘independent’ predictions are then correlated with the observed values. Only those predictor sets with correlations significant at or above the 95% level are retained. These sets are listed in Table III. It is worth noting that among all the predictors, the climatology-persistence predictor shows the highest correlation for all the three predictands. This result suggests that the SMR rainfall has a rather strong climatological signal. 4.3. The final prediction equations The predictions from the individual predictors can be combined to form a single prediction equation for each predictand by a weighted average. That is, the final predicted value, yf, is given by: p % wkyk yf = k=1 p % wk k=1 where wk is the correlation coefficient between the predicted values of the predictand made by predictor yk and the observed, and p the number of predictor sets. Table IV. Correlations, absolute and standard deviation errors (anomaly percentages) and the measure of agreement of the final predictions (compared with the observed) for the 47-year sample Predictand Correlation Absolute error S.D. Error Measure of agreement RA13 RA6 RA7 0.81 0.77 0.84 9.8 12.2 10.4 12.2 15.0 12.3 0.5774 0.6004 0.7002 Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) 1262 J.C.L. CHAN AND J-E. SHI Table V. Forecasts and verifications of the 1998 SMR for the SC region and both subregions Predictand Predicted anomaly (%) Observed anomaly (%) RA13 RA6 (east) RA7 (west) −7.6 −8.0 −13.3 32.8 35.5 30.6 The correlations between yf and the observed values of the three predictands are found to be quite high (Table IV), which are generally higher than those obtained from individual predictors (usually between 0.3 and 0.8). The absolute error and the standard deviation error are all around 10 (%). The measure of agreement, r, which is proposed by Mielke et al. (1996) as another measure of the accuracy of the predictions, also has relatively high values. Therefore, the weighted-average prediction for each of the predictands is chosen to be the final prediction equation. 5. PREDICTION OF THE SMR OVER SC FOR 1998 Based on the results from the last section, a real-time prediction of the SMR over SC for 1998 was made in late March of 1998. The results (Table V) suggest that for each of the two subregions, the SMR should be below normal by about 10%, which is consistent with the prediction for the entire SC, even though the predictors are not exactly identical (Table III). However, the observed anomalies indicate the rainfall in 1998 was above normal (Table V). While a detailed investigation to this failure has yet to be made, it appears that the main reason for the failed forecasts probably lies in the abrupt termination of the El Niño and the subsequent start of the La Niña. Xie et al. (1998) have identified these two phenomena to be related to the summer monsoon onset over the South China Sea. In a La Niña year, onset tends to be early so that the length of the rainfall season would be longer and would result in higher rainfall amounts. Unfortunately, both phenomena occurred after February and no precursor signal of these phenomena has been identified. Their effects therefore cannot be reflected in the predictions. Although the prediction for 1998 failed, the methodology presented here should still be applicable in other years in which the ENSO effect is not so dominant. Efforts are currently being made to identify other predictors that may be related to the onset of the warm and cold phases of the ENSO. They will be included in future modifications of the prediction equations. 6. SUMMARY AND DISCUSSION The monthly variation of rainfall over SC is generally bimodal, with a peak around April to June and another around August or September. The first one is related to the summer monsoon and the other to TCs. This paper attempts to derive an operational statistical prediction scheme for the former, that is, the summer monsoon rainfall (SMR, defined as the total rainfall for the months April–June) over SC. To provide an objective identification of the SC region, the techniques of cluster analysis and factor analysis are applied to the monthly rainfall for the period 1951–1997 of 43 stations over the area from the mid to lower reaches of the Yangtze River to the coast of southern China. Both techniques suggest that of these, 13 stations in the southern part of China have similar SMR characteristics. This batch of stations can further be grouped into east and west stations. Using parameters related to the ENSO, the planetary circulation and the climatology and persistence of the SMR of these stations, prediction equations are derived using the technique of projection pursuit regression, which has been demonstrated to be superior to the traditional multiple linear regression technique. For the predictions to be operationally useful, only those parameters from March of the Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) SOUTH CHINA SUMMER RAINFALL PREDICTION 1263 previous year to February of the current year are used. The jackknife method is then applied to test the validity of these equations. Retaining only those parameters that can give a significant correlation (] 95%) between the predicted and the observed values, the final predictions of the SMR (for the entire SC as well as for the subregions) are then obtained as a weighted average of the forecasts made from these parameters. These final predictions are found to explain around 70% of the variance of the observed SMR. Although an operational forecast for 1998 made in March failed probably because of the abrupt change from the warm to cold phase of the ENSO, the technique presented here should still be applicable in years when the ENSO effect is not so dominant. Further study is necessary to include predictors that can indicate the possible onset of either a warm or cold phase. In addition, while this study has provided a set of prognostic equations for predicting the SMR over the SC and its subregions, the physical reasons for the interannual variability of the SMR still require further investigation. For example, the dominance of the climatology-persistence predictor suggests the trend and periodicities of the SMR should be studied further. The physical explanations of the relationship between the various indices and the SMR should also be sought. These will be topics of future investigations. ACKNOWLEDGEMENTS The authors would like to thank the National Climate Center of China for providing the rainfall data and the planetary-circulation indices for the project and the Hong Kong Observatory for providing the rainfall data for Hong Kong. The help of Meihua Wang in preparing the figures and performing some of the calculations is gratefully acknowledged. This research is partly supported by the Strategic Research Grant of the City University of Hong Kong Grant 7000536. APPENDIX A. DEFINITION OF PREDICTORS With the exception of the predictors related to ENSO (SOI, NINO12 and NINO4) that have been defined in the text (Section 3.2), the detailed definitions of the predictors related to the planetary-scale circulation Table A1. Detailed definitions of the predictors related to the indices related to the planetary-scale circulation of the atmosphere Predictor Definition HC011 Area enclosed by the 5880 m geopotential height contour (characteristic height of the subtropical high) on the 500 hPa monthly mean chart within the area (10–50°N, 110°E–115°W) Area enclosed by the characteristic geopotential height contour of the polar vortex (which varies from 5480 m in January to 5720 m in July and August) on the 500 hPa monthly mean chart within the longitude band 60–150°E As in HC046 except within the longitude band 150°E–120°W Zonal index IZ over Eurasia defined as HC046 HC047 HC061 (Z , (f where (Zis the longitudinal average within the longitude band (0–150°E) of the 500 hPa monthly mean geopotential height within each latitude band (10° latitude) and f is the latitude (from 45 to 65°N) Meridional index IM over Eurasia (0–150°E) 1 (Z 1 n IM = % , n j = 1 cos f (l j IZ = HC062 HC070 )# $) where Z is the 500 hpa monthly mean geopotential height, l the longitude, f the latitude and indicates an average within each area j of 20° latitude×30° longitude (from 45 to 65°N) Frequency of cold air intrusion into China during September–December and January–May. An occurrence of a cold air intrusion is defined as when 8 out of 15 stations over China (evenly spread around from north to south) have a temperature drop of ]5°C within the same 3 days Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) 1264 J.C.L. CHAN AND J-E. SHI of the atmosphere are given in Table A1. The CLIPER predictor is value of the predictand predicted by the trend (not necessarily linear) and periodic functions with periodicities identified from the time series of the predictand using the variance analysis method. APPENDIX B. THE PROJECTION PURSUIT REGRESSION (PPR) TECHNIQUE A simplified discussion of the PPR technique is given here for information of readers who would like to know the basic principles of the technique. For more details, the reader is referred to the original paper by Friedman and Stueltzle (1981) or the description in Chan et al. (1998). The classic linear regression model expresses the response variable y (for simplicity, only one variable is considered here although in general, this can be applied to a set of response variables) as linear functions of the predictor variables xj (1 5j 5p): p y(x1, . . . , xp ) =a0 + % aj xj, j=1 where the values of the aj are estimated by least squares. In the PPR technique, the response variable is expressed in the form: M y(x1, . . . , xp ) =a0 + % zm (a Tmx), m=1 where x is the column vector of the predictor variables (x1, x2,..., xp ) and a Tm is the row vector of the coefficients a (mj), j= 1, 2,..., p. That is: p a Tmx = % a (mj)xj j=1 and zm are single-valued (ridge) functions and M the number of such functions (i.e. the number of projections). In other words, instead of modelling the response as a linear combination of the predictor variables (as in linear regression), the response is expressed as a sum of functions of linear combinations of the predictor variables in the PPR technique. The parameters of the linear combination a Tm as well as the functions zm are estimated by least squares. In the illustration given in Section 4.1, two projections (i.e. M =2) are used (which are generally found to be sufficient) with the coefficients a T1 listed for the five predictor variables (i.e. p= 5). REFERENCES Bell, G.J. 1976. ‘Seasonal forecasts of Hong Kong summer rainfall’, Weather, 31, 208 – 212. Chan, J.C.L. 1995. ‘Prediction of annual tropical cyclone activity over the western North Pacific and the South China Sea’, Int. J. Climatol., 15, 1011–1019. Chan, J.C.L. and Shi, J.E. 1997. ‘Application of projection – pursuit principal component analysis method to climate studies’ Int. J. Climatol., 17, 103–113. Chan, J.C.L., Shi, J.E. and Lam, C.M. 1998. ‘Seasonal forecasting of tropical cyclone activity over the western North Pacific and the South China Sea’, Wea. Forecasting, 13, 997–1004. Ding, Y. 1994. ‘The summer monsoon in East Asia’, in Monsoons o6er China, Kluwer Academic Publishers, pp. 1 – 90. Everitt, B.S. 1993. Cluster Analysis, John Wiley and Sons Inc., 170 pp. Friedman, J.H. and Stueltzle, W. 1981. ‘Projection pursuit regression’, J. Am. Stat. Assoc., 76, 817 – 823. Gorsuch, R.L. 1983. Factor Analysis, Lawrence Erlbaum Associates Inc., 425 pp. Hartigan, P.J. 1975. Clustering Algorithms, John Wiley and Sons Inc., 351 pp. Huang, S.-S. 1982. Hea6y Rainfall in South China in Pretyphoon Season, Guangdong Institute of Tropical Meteorology, 87 pp. (in Chinese). Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999) SOUTH CHINA SUMMER RAINFALL PREDICTION 1265 Huber, P.J. 1985. ‘Projection pursuit’, Ann. Stat., 13, 435 – 525. Mielke, P.W. Jr., Berry, K.J., Landsea, C.W. and Gray, W.M. 1996. ‘Artificial skill and validation in meteorological forecasting’, Wea. Forecasting, 11, 153–169. Miller, R.G. 1974. ‘The jackknife—a review’, Biometrika, 61, 1 – 15. Richman, M.B. 1986. ‘Rotation of principal components’, J. Climatol., 6, 293 – 335. Tao, S. and Chen, L. 1987. ‘A review of recent research on the East Asian summer monsoon in China’, in Chang, C.P. and Krishnamurti, T.N. (eds), Monsoon Meteorology, Oxford University Press, pp. 60 – 92. Xie, A., Chung, Y.-S., Liu, X. and Ye, Q. 1998. ‘The interannual variations of the summer monsoon onset over the South China Sea’, Theor. Appl. Climatol., 59, 201–213. Copyright © 1999 Royal Meteorological Society Int. J. Climatol. 19: 1255 – 1265 (1999)

1/--страниц