Wavelet Analysis on the Variability, Teleconnectivity, and Predictability of the Seasonal Rainfall of Taiwan

162 MONTHLY WEATHER REVIEW VOLUME 138

CHUN-CHAO KUO Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan, and Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada

THIAN YEW GAN Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada

PAO-SHAN YU Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan

(Manuscript received 10 July 2008, in ﬁnal form 5 July 2009)

ABSTRACT

Using wavelet analysis, the variability and oscillations of November–January (NDJ) and January–March (JFM) rainfall (1974–2006) of Taiwan and seasonal sea surface temperature (SST) of the Pacific Ocean were analyzed. From the scale-average wavelet power (SAWP) computed for the seasonal rainfall, it seems that the data exhibit interannual oscillations at a 2–4-yr period. On the basis of correlation fields between decadal component removed wavelet PC (DCR-WPC1) of seasonal rainfall and decadal component removed scale- averaged wavelet power (DCR-SAWP) of SST of Pacific Ocean at one-season lead time, SST of some do- mains of the western Pacific Ocean (July–September SST around 08–308N, 1208–1608E; October–December SST around 08–608N, 1258E–1608W) were selected as predictors to predict seasonal NDJ and JFM rainfall of Taiwan at one-season lead time, respectively, using an Artificial Neural Network calibrated by the Genetic Algorithm (ANN-GA). The ANN-GA was first calibrated using the 1975–99 data and independently vali- dated using 2000–06 data. In terms of summary statistics such as the correlation coefficient, root-mean-square error (RMSE), and Hanssen–Kuipers (HK) scores, the prediction of seasonal rainfall of northern and western Taiwan using ANN-GA are generally good for both calibration and validation stages, but not so for southeastern Taiwan because the seasonal rainfall of the former are much more significantly correlated to the SST of selected sectors of the Pacific Ocean than the latter.

1. Introduction tends to spill downstream, causing water shortages if sub- sequent seasons happen to be dry. In Taiwan, dry seasons For Taiwan and East Asia, there have been various (usually November–April in Taiwan except in the north- studies focused on their summer rainfall prediction eastern Taiwan) on the average received about 32% of (Chan and Shi 1999; Chien et al. 2002; Chien and Jou annual rainfall (Water Resources Agency 2008). This 2004; Shiao and Juang 2006; Li and Zeng 2008) but sel- usually posts problems to water resources management dom studies on its winter and spring rainfall prediction. of Taiwan, especially its agriculture sector, which has Summer, as the wet season, tends to receive more rainfall about 70% of consumptive use. Therefore, dependable than other seasons of an average year in Taiwan. How- seasonal prediction of rainfall for the dry season will be ever, the capacity of many reservoirs in Taiwan is general useful to Taiwan’s water resources management. limited due to the steep terrain so that excessive water Past studies provide an overview of the teleconnection patterns of East Asia with respect to large-scale climate phenomena such as El Nin˜ o–Southern Oscil- Corresponding author address: Thian Yew Gan, Department of Civil and Environmental Engineering, University of Alberta, lation (ENSO; e.g., Xu et al. 2004; Yang and Lau 2004), Edmonton, AB T6G 2W2, Canada. but different teleconnection patterns exist in East Asia E-mail: [email protected] (Li et al. 2005), so it should be useful to investigate the

DOI: 10.1175/2009MWR2718.1

Ó 2010 American Meteorological Society Unauthenticated | Downloaded 10/02/21 02:46 AM UTC JANUARY 2010 K U O E T A L . 163 connectivity between local areas and large-scale cli- tivation of paddy field begins in January and so decisions mate phenomena, especially for a small area such as on water release schedule are usually done at the begin- Taiwan. Besides ENSO, some past studies also link ning of the farming season (January–February). Besides precipitation of Taiwan to large-scale natural variabil- the effect of SST, the spring rainfall of Taiwan starting in ity of sea surface temperature (SST) and Pacific decadal April is subjected to more atmospheric dynamics and cir- oscillation (PDO; Lu and May 2003; Chen et al. 2003; culation and so it will be more challenging to predict the Jiang et al. 2003; Hung et al. 2004). Three precipitation spring rainfall using the Artificial Neural Network cali- associations for Taiwan, Guam, and northwest Australia brated by the Genetic Algorithm (ANN-GA) approach. from January to March have been identified by Lu and First, the spatial, temporal, and frequency variability May (2003). The first type gives rise to wet conditions of the dominant oscillations of the rainfall fields of over Taiwan but dry conditions over the Philippine Sea Taiwan using wavelet analysis and Principal Compo- and northwest Australia, and vice versa by the second nent Analysis (PCA) are examined. Then, sectors of type, but under the third type both Taiwan and north- seasonal SST in the Pacific Ocean that are strongly west Australia will be dry but the Philippine Sea will be correlated to the seasonal rainfall (NDJ and JFM) are wet. Jiang et al. (2003) found that spring (February– identified. Third, the wavelet coherence between selected March) heavy rainfall events were positively correlated SST, ENSO indices, and seasonal rainfall are examined. with the cold season (November–March) Nin˜ o-3 SST Fourth, an ANN-GA was calibrated using the seasonal significantly since the late 1970s but not much correla- rainfall and SST data and the calibrated model is vali- tion between the early 1950s and the late 1970s. The dated by assessing the accuracy of the predicted seasonal spring (February–April) rainfall in northern Taiwan was rainfall based on data not used in the calibration experi- also found to fluctuate simultaneously with the PDO ence. Finally, a composite analysis was also applied to since the early twentieth century (Hung et al. 2004), understand how the warm and cold SST episodes affect and positive (negative) PDO tends to be associated with the precipitation patterns near Taiwan. more (less) spring rainfall in northern Taiwan. These studies show some connectivity between the 3. Climate data rainfall of Taiwan and climate anomalies or SST, which probably implies that predicting seasonal rainfall by such Rainfall data from 15 stations of Taiwan’s Central relationships should be feasible. To our best knowledge, Weather Bureau (Fig. 1) collected from 1974 to 2006 was the prediction of rainfall for winter or spring for Taiwan used to evaluate the predictability of 3-month rainfall by the proposed approach has yet been attempted, but (NDJ and JFM) in Taiwan. The Kaplan SST V2 data summer rainfall prediction in Taiwan has been done by (Kaplan et al. 1998; Parker et al. 1994; Reynolds and Huang and Hsu (2005). Through a permutation test, they Smith 1994) of the same period was provided by the identified sectors of the Pacific Ocean where SST is re- National Oceanic and Atmospheric Administration/Of- lated to the summer rainfall of Taiwan. These sectors of fice of Oceanic and Atmospheric Research/Earth System the Pacific Ocean are close to or located within the win- Research Laboratory Physical Sciences Division (NOAA/ dow of the tropical Pacific used to compute the Ninõ-3 OAR/ESRL PSD), Boulder, Colorado, from their Web index. Selected principal components (PCs) on these site (http://www.cdc.noaa.gov/). The monthly SST anom- sectors of SST data are used as predictors to an Auto- aly at 58358 resolution were selected from the Pacific regressive Integrated Moving Average (ARIMA) and Ocean window (258S–608N, 1208E–708W) and averaged to regression model to predict the summer rainfall of 3-month values, namely, JFM, AMJ, JAS, and OND. The Taiwan. They found that the regression model performed geopotential height and wind fields (Kalnay et al. 1996) better than the ARIMA model. are prepared by the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) as a 40-yr reanalysis product and also 2. Research objectives made available online at NOAA/OAR/ESRL PSD’s Web The primary objectives of this study are to analyze site (http://www.cdc.noaa.gov/). These data have a hori- the characteristics of seasonal rainfall of Taiwan, and zontal resolution of 2.5832.58. to predict the seasonal, November–January (NDJ) and January–March (JFM; hereafter all three-month periods 4. Research methodology will be referred to by the first letter of each respective a. Wavelet analysis month) rainfall of Taiwan, which will be useful for de- cision makings in water resources management because The wavelet transform of a real signal X(t), used to November is the beginning of the dry season and the cul- extract time and frequency domain information from

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC 164 MONTHLY WEATHER REVIEW VOLUME 138

where Cd is 0.776 for the Morlet wavelet (used in this paper), dj is the scale interval, which is 0.0833. Using smaller values of dj gives finer resolutions in scales. dt is the sampling interval which is 1 in this paper, and j1 to j2 (e.g., j1 is 2 yr while j2 is 4 yr) represent scales over which SAWP is computed. For the choice of wavelet function, we should choose a wavelet function that can effectively reflect the oscillatory features of a time series, which in our case is the rainfall. A broad (in time) wavelet function will have poor time but good frequency resolutions, and vice versa. The Morlet wavelet (k 5 6) was used because it provides a good balance between time and frequency localizations (Grinsted et al. 2004) and its structure generally resembles that of a rainfall time series. For some other wavelets such as the Mexican hat wavelet, its time resolution is poorer than the Morlet and so it may not represent a rainfall time series as ac- curately as the Morlet. FIG. 1. Distribution of 15 meteorological stations in Taiwan. The Morlet wavelet is defined as

2 c(h) 5 p(1/4)eikhe(h /2), (3) X(t) (climate data) with a mother wavelet c, is a con- volution integral given as where k is the dimensionless frequency and h is the dimensionless time. Because SAWP is a time series of ð 1 T t n average variance in a certain band, it can be used to W (s) 5 pffiffi X(t)c* dt, (1) n examine the modulation of one time series by another or s 0 s the modulation of one frequency by another within the where c* is the complex conjugate of c, t is the time, T is same time series (Torrence and Compo 1998). Having the total length of the time series, s is the scale, n is obtained the SAWP, its leading PC was then used to extract the spatial and temporal variability on the basis of a translated position along the t axis, and Wn(s)isa wavelet spectrum, a matrix of energy coefficients of the SAWP of a specified range of time scale, such as a 2–4-yr decomposed time series. The advantage of using a com- time scale for interannual oscillations. plex wavelet is that we can present both the amplitude Another useful measure, the wavelet coherence that and phase to better capture the oscillatory behavior of can identify cross-wavelet transformed coherence in time a time series. On the other hand, for a real wavelet like frequency space, is defined as (Torrence and Webster the Mexican hat wavelet, the imaginary part is zero, so 1999): the phase is undefined (Torrence and Compo 1998). 2 S[s1WX,Y (s)] Although we did not use the phase information directly 2 n Rn(s) 5 , (4) 1 X 2 1 Y 2 in the wavelet transform, it was used in section 5d. The S[s Wn (s) ]S[s Wn (s) ] magnitude of the wavelet spectrum coefficients repre- X,Y sents the amplitude of a time series. In a rainfall or SST where Wn (s) is the cross-wavelet spectrum of X and Y, 2 time series, the power at each scale is a good measure of S is a smoothing operator, and 0 # Rn (s) # 1. According the magnitude of time series at that scale. In addition to to Jevrejeva et al. (2003), the smoothing operator S(W) power at individual scales, power over a range of scales, is written as ÈÉ the scale-averaged wavelet power (SAWP), which rep- S(W ) 5 S S [W (s)] , (5) resents the mean variance of wavelet coefficients over scale time n a range of scales, might also be used. The SAWP of the where Sscale denotes smoothing along the wavelet scale wavelet spectrum is computed as follows (Torrence and axis (s)andStime smoothing in the time scale (n)(Torrence Compo 1998): and Webster 1999), given by

2 2 j (t /2s ) 2 2 Stime(W)js 5 [Wn(s) 3 c1e ]js, (6) 2 d jdt jWn(s j)j Wn 5 å , (2) C j5j s d 1 j Sscale(W)jn 5 [Wn(s) 3 c2P(0.6s)]jn, (7)

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC JANUARY 2010 K U O E T A L . 165 where c1 and c2 are normalization constants and P is the selected population. After crossover, mutation is per- rectangle function, which has a value of 0 when s is lo- formed to restore the good weights and biases happened cated outside the interval 60.3, but 1 if it falls within the to be eliminated by selection. Only a small percentage of interval 60.3. The factor of 0.6 is the empirically de- population (1%) is randomly chosen for mutation in termined, scale decorrelation length for the Morlet which the mutation point (weights or biases) are ran- wavelet (Torrence and Compo 1998). domly assigned a number within the parameters’ range. The above three operations are repeated for several b. Principal component analysis generations. At each generation, the best neural network is kept until a better solution is found in successive PCA is widely applied in many fields to transform data generations. At the end of the run, the weights and into independent PCs to reduce the numbers of vari- biases of the best surviving network are kept to be used ables by several leading PCs that explain a large pro- for predictions using input data not used for calibration. portion of the total variance. In this paper, PCA is applied to transform the SAWP of rainfall with the decadal component removed (DCR-SAWP) to decadal component removed wavelet PCs (DCR-WPCs) and 5. Discussion of results only DCR-WPC1 is retained for further analysis. PCA is a. Dominant mode of seasonal rainfall also employed in selected SST field to reduce the SST inputs to the ANN-GA model. In each case the number Global and local wavelet spectra for two seasonal of PCs to be retained is based on a scree plot, from which rainfalls (NDJ and JFM) in Taiwan and four seasonal the number of leading PCs to be retained will be obvious. SSTs (JFM, AMJ, JAS, and OND) in the Pacific Ocean were computed and an example is shown in Fig. 2 for c. ANN-GA NDJ and JFM rainfall. The local wavelet spectra represent the changes of wavelet power in terms of scale A brief outline of ANN-GA is described herein (refer with respect to time while the global wavelet spectrum is to Mwale et al. 2004; Mwale and Gan 2005). It is called the time average of all the local wavelet spectra for each ANN-GA because a genetic algorithm (GA) is used to scale. Thick black contours in the figure indicate that calibrate the parameters of an ANN, which in this case is power is statistically significant at the 95% confidence a forward structure with three layers: input, hidden, and level of a white noise process. The dashed line drawn output layers. Through trial and error, a five-node hid- through the wavelet spectrum depicts the cone of in- den layer was adopted in this study, while the number of fluence (COI), out of which the spectra may be affected nodes for the input layer depends on the numbers of by paddings and should be treated with a grain of salt. input variables, and the output layer has only one node, Figure 2 shows higher power in the 1980s and after 1995 which is the seasonal precipitation. The input data were between 2- and 4-yr cycles for both seasons. Although normalized so that its mean is 0 and its standard de- the global (time averaged) spectra do not show statisti- viation is 1. An hyperbolic tangent is used as the sigmoid cally significant oscillations for all periods, the power function in the hidden layer. Model parameters or co- between 2 and 4 yr is still relatively high. Therefore, the efficients for the layers are optimized by the GA by SAWP for rainfall and SST are estimated between the minimizing an objective function that maximizes the 2- and 4-yr cycles. correlation between simulated and observed seasonal rainfall. b. Seasonal rainfall variability The GA consists of these operations: selection, crossover, and mutation. All the neural networks considered Before applying PCA, the decadal component of SAWP are ranked according to their respective performance of seasonal rainfall (NDJ and JFM) of the 15 rain sta- evaluated in terms of objective function values com- tions was removed individually by linear regressions. puted in a descending order. Only the top 85% of the Next, PCA was applied to the DCR-SAWP of seasonal population is retained for further selection. In this study, rainfall and then the DCR-WPCs were obtained. For the population size is set at 200. In the next step, a one- NDJ and JFM rainfall, DCR-WPC1 and DCR-WPC2 point crossover scheme, weights and biases of neural together explain 71% and 92% of the total variances, networks are exchanged in pairs, such that one location respectively, or individually for the NDJ (JFM) rainfall, is randomly chosen in the hidden layer and weights and DCR-WPC1 and DCR-WPC2 explain 39.81% and 30.98% biases on either side of the location are exchanged be- (81.95% and 9.83%) of the total variances, respectively tween the two neural networks. This procedure is re- (Fig. 3). The variances of NDJ DCR-WPC1 were low peated between all other pairs of neural networks in the between 1975 and 1995, but peaked at around 2001 (see

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC 166 MONTHLY WEATHER REVIEW VOLUME 138

FIG. 2. Wavelet spectra constructed for (a) PC1 of NDJ rainfall and (b) PC1 of JFM rainfall. The dashed line is the COI. The thick black contour in the wavelet spectrum represents energy significant with respect to a white noise spectrum at the 95% confidence level. In the global wavelet spectrum, the dotted curve represents the 95% confidence level and peaks above the curve are considered to be statistically significant. The wavelet power is presented by units of normalized variance.

Fig. 3a), which was consistent with the trend of the ob- c. Connectivity between DCR-WPC1 of served rainfall of the northwestern station (number 3) seasonal rainfall and DCR-SAWP of Taiwan (Fig. 9a), which was relatively low between of Pacific Ocean SST 1975 and 1995 with an average standardized rainfall of 20.18 (excluding data of 1982–84). The observed rain- The relationship between four seasonal SSTs of the fall of other stations in northern and western Taiwan is Pacific Ocean (JFM, AMJ, JAS, and OND) and two not shown. (In Fig. 9a the highest peak occurred in 2001 seasonal rainfalls (NDJ and JFM) of Taiwan were exam- and the second highest peak occurred in 1983, which is ined using their DCR-SAWP of a 2–4-yr period. Sectors of also observed in Fig. 3a.) DCR-WPC1 of the JFM the Pacific Ocean whose SST represented by the 2–4-yr rainfall remained high between 1980 and 1986 but re- DCR-SAWP are correlated to the 2–4-yr DCR-WPC1 mained low thereafter except at around 1998 when of rainfall and if the Pearson correlation is either larger a more modest peak occurred, which was also consistent than 10.5 or smaller than 20.5, those sectors will be first with the observed station rainfall of northern and western labeled as the potential SST predictors. Taiwan. As expected, DCR-WPC1 of rainfall is more strongly The contour plots of the correlation between the correlated to the DCR-SAWP of SST at one season than DCR-WPC1 of NDJ rainfall and DCR-SAWP of local at two season lead time, and so the NDJ and JFM stations show strong correlation (;0.6–0.9) from the west- rainfall are linked to the JAS and OND SST, re- ern to northern Taiwan, moderate correlation (;0.3–0.6) spectively (see Fig. 5). By linking JAS SST to NDJ in southern Taiwan, low positive correlation in central to rainfall and OND SST to JFM rainfall, the former SST is southeastern Taiwan (Fig. 4a). Therefore, for NDJ rainfall one month earlier than the latter in the linkage, so that DCR-WPC1 does not represent the rainfall DCR-SAWP we can use the wavelet transform of four standard sea- of Taiwan uniformly, but for JFM rainfall, DCR-WPC1 sonal SSTs (JFM, AMJ, JAS, and OND). did represent the rainfall DCR-SAWP in Taiwan rela- In Fig. 5, correlations above 0.5 and below 20.5 are tively uniformly (Fig. 4b). first shaded in light gray to better identify locations of

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC JANUARY 2010 K U O E T A L . 167

FIG. 3. Time series of DCR-WPC1 and DCR-WPC2 of (a) NDJ and (b) JFM rainfall with a 2–4-yr band. relatively high correlation areas and areas with corre- 2–5-yr scale in the 1980s and a 3–5-yr scale in the 1990s lation ranging approximately 0.5–0.8 are circled with (Fig. 6a). It should be noted that the existence of sig- thick lines which for the NDJ rainfall were located in the nificant coherence between two signals does not neces- western (08–308N, 1208–1608E) Pacific Ocean (Fig. 5a). sarily depend on the existence of significant wavelet The SST data of this particular sector was chosen as the power in both signals. The phase difference shows PC1 predictors for NDJ rainfall because the correlation co- of selected JAS SST generally leads PC1 of NDJ rainfall efficients were much higher than 0.5 or much lower than by 908 for time periods of significant coherence at the 20.5. For the JFM rainfall, the areas with much higher 2–4-yr scale. In contrast, the coherence between JAS or lower correlation coefficients ranging approximately Nin˜ o-3, JAS SOI, and PC1 of NDJ rainfall is mostly 0.5–0.9 are located around the western Pacific Ocean relatively low (not shown). (08–608N, 1258E–1608W) circled with thick lines in PC1 of the selected OND SST shows strong coherence Fig. 5b and so they were chosen as the SST predictor with PC1 of the JFM rainfall at a 2–5-yr scale near the fields for the JFM rainfall. 1980s and after 1993 and generally with an off-phase relationship during periods of significant coherence d. Wavelet coherence and phase differences (Fig. 6b). A high coherence was found between OND In section 5c, sectors of the seasonal SST of Pacific Nin˜ o-3 and PC1 of the JFM rainfall after 1993 at a 2–4-yr Ocean (JAS and OND) that show strong correlation scale and before 1986 at a 4–6-yr scale, with the phase of with seasonal rainfall (NDJ and JFM) of Taiwan were PC1 of JFM rainfall leading that of Nin˜ o-3 by 908 during identified. Next, the wavelet coherence between sea- periods of significant coherence (not shown). Between sonal rainfall and ENSO [Nin˜ o-3 and the Southern Os- cillation index (SOI)] for JAS and OND seasons were also computed to measure the link between them since ENSO activity usually bring extreme climate conditions in many parts of Asia. The PC1 of NDJ and JFM rainfalls with considerable (45.13% and 68.16%, respectively) explained variances are used to represent the regional precipitation. The wavelet coherence of PC2 and PC3 of the NDJ rainfall (21.14% and 12.46% of variance explained, respectively) and the JFM rainfall (13.86% and 5.15%, respectively) with selected sectors of seasonal SST were also explored. Figure 6 demonstrates the wavelet coherence between three leading PCs of seasonal rainfall (NDJ and JFM) and the leading PC of SST (JAS and OND). The thick contours in Fig. 6 enclose periods of statistically significant wavelet coherence with respect to a red noise process determined by a Monte Carlo ex- FIG. 4. Spatial distributions of the correlation field r between the periment (Jevrejeva et al. 2003). DCR-WPC1 of (a) NDJ and (b) JFM rainfall, and the DCR-SAWP PC1 of the selected JAS SST and PC1 of the NDJ of individual stations. Percentage values above the figures repre- rainfall exhibits statistically significant coherence in a sent the total amount of variance explained by each DCR-WPC1.

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC 168 MONTHLY WEATHER REVIEW VOLUME 138

FIG. 5. The spatial distribution of the correlation r between (a) DCR-WPC1 of the NDJ rainfall and the 2–4-yr DCR-SAWP of JAS SST of the Pacific Ocean, and (b) DCR-WPC1 of the JFM rainfall and the 2–4-yr DCR-SAWP of the OND SST of the Pacific Ocean. Light shaded areas in the figure indicate correlation coefficient .0.5 and ,20.5, and the areas that are enclosed indicate sectors of the Pacific Ocean where the SST data were selected as predictors to the ANN model because the correlation coefficients were much .0.5 or much ,20.5.

OND SOI and PC1 of the JFM rainfall (not shown), previous season. Therefore, the above sectors of JAS SST significant coherence exhibits before 1986 at a 2–3-yr and OND SST of the Pacific Ocean are selected as pre- scale and in early 1980s at a 4–5-yr scale, and they are dictors for the statistical model (ANN-GA) for the sea- either in phase or with OND SOI leading PC1 of the sonal prediction of NDJ and JFM rainfall, respectively. JFM rainfall by 908. Figures 6c–f present other co- e. Prediction of seasonal rainfall herences between PC1 of selected SST and PC2–PC3 of some seasonal rainfall. The coherence was generally Given that the seasonal rainfall of Taiwan were lower in those figures except for Fig. 6f, which shows strongly correlated with SST of some areas of the Pacific a high coherence within 2–3, 8–10, and 5–6 yr after 1995. Ocean at interannual time scales, it seems feasible to use The above results reveal that the JAS and OND SST data to predict the seasonal rainfall (NDJ and JFM) ENSO indices have a lower coherence with PC1 of the of Taiwan at one-season lead time. Raw SST data of NDJ rainfall and PC1 of the JFM rainfall at 2–5-yr scales, thick circled areas from the Pacific Ocean in Fig. 5 were while selected JAS SST and OND SST have a higher co- extracted. As an effort to only retain data that explain herence with PC1 of the NDJ rainfall and the JFM rainfall most of the variances to eliminate unnecessary input at 2–5-yr scales, respectively. The results are consistent data, from the scree plot that shows the percentage of with generally high correlation between DCR-SAWP of explained variances of PCs, we found that only the first selected SST and DCR-WPC1 of seasonal rainfall of the three PCs of JAS SST with a total explained variances of

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC JANUARY 2010 K U O E T A L . 169

FIG. 6. Wavelet coherence and phase difference between PC1 of selected (a) JAS SST and PC1 of NDJ rainfall, (b) OND SST and PC1 of JFM rainfall, (c) JAS SST and PC2 of NDJ rainfall, (d) OND SST and PC2 of JFM rainfall, (e) JAS SST and PC3 of NDJ rainfall, and (f) OND SST and PC3 of JFM rainfall. The thick black contours enclose periods of statistically signiﬁcant coherence at 5% level of a red noise process, and the dashed line is the COI. The phase difference is plotted only for time periods and scales with coherence .0.5. Right-pointing arrows indicate that the two signals are in phase while left-pointing arrows are for antiphase signals.

86.90% were necessary and hence retained for predict- 0.8–0.9), but it is poorly correlated (r of 0–0.3) to the ing the NDJ rainfall, and for OND SST, the ﬁrst four DCR-SAWP of individual stations in central and south- PCs, which explained 81.14% of the total variances were eastern Taiwan (Fig. 4a). Similar results are shown by the necessary and hence retained for predicting the JFM RMSE and the Hanssen–Kuipers (HK) scores. rainfall. All input (SST PCs) and output data (seasonal rainfall) of the ANN-GA were normalized before the analysis. Figure 7 shows the structure of ANN model for predicting the seasonal rainfall and the number of input nodes is three and four for JAS SST and OND SST, respectively. The ﬁrst 25 yr of data were used to calibrate ANN- GA and the last 7 yr of data were used to validate the calibrated model for both seasons. At the validation stage, the predicted NDJ rainfall (Figs. 8a–c and 9a,b) showed a Pearson correlation ranging from 0.5 to 0.7 for western and northern Taiwan but the correlation drop- ped to about 0.3 for central to southeastern Taiwan, which is as expected because DCR-WPC1 of NDJ rainfall in the western and northern Taiwan is strongly cor- FIG. 7. The structure of the ANN model for predicting the related to the DCR-SAWP of individual stations (r of seasonal rainfall.

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC 170 MONTHLY WEATHER REVIEW VOLUME 138

FIG. 8. Contour plots of (a),(d) RMSE; (b),(e) correlation coefficient r; and (c),(f) HK scores in validation years between observed and predicted (a)–(c) NDJ and (d)–(f) JFM rainfall of ANN-GA at one season lead time driven by selected windows of JAS SST and OND SST predictor fields from the Pacific Ocean.

The validation of JFM rainfall (Figs. 8d–f and 9c,d) We further presented scatterplots and lag-1 correla- demonstrated high Pearson correlation (r ’ 0.7) cen- tion coefﬁcient (r) between PC1 and PC3 of the sectors tered in the northern and central Taiwan and it similarly of JAS SST selected as predictors, and the NDJ rainfall declined gradually from central to southern Taiwan (r 5 of two stations, station 3 located in northwestern Tai- 0.2), which again is expected because DCR-WPC1 of wan, and station 12 located in southeastern Taiwan; and JFM rainfall is more highly correlated to the DCR- scatterplots and r between PC1 and PC4 of the sectors of SAWP of individual stations in the western and northern OND SST selected as predictors, and the JFM rainfall of Taiwan but less correlated to stations (0.3–0.5) in south- the same two stations, stations 3 and 12 in Fig. 10. On eastern Taiwan. The RMSE of JFM rainfall prediction a whole, Fig. 10 shows the rainfall–SST relationships to also displayed similar spatial patterns as the Pearson cor- be nonlinear, which likely implies that using a nonlinear relation. The HK scores did not exhibit similar spatial model such as the ANN-GA should be more suitable distribution as the Pearson correlation. Apparently, ANN- than a linear model for modeling the rainfall–SST re- GA driven by the selected sectors of SST predictors in lationship of Taiwan. However, because some r are low the Paciﬁc Ocean has good predictability in western and for certain PCs, such as that of station 12 (southeastern northern Taiwan. Taiwan), it is still a challenge calibrating the ANN-GA

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC JANUARY 2010 K U O E T A L . 171

FIG. 9. The observed and predicted time series of (a) NDJ rainfall for station 3, (b) NDJ rainfall for station 12, (c) JFM rainfall for station 3, and (d) JFM rainfall for station 12. The solid and dashed lines indicate the observed and predicted seasonal rainfall. Here rv represents r of the validation stage. to some rain stations of Taiwan even though ANN-GA relation r, and HK score, results for the composite is a nonlinear model. analysis again shows better agreement between predicted and observed seasonal rainfall in the western and f. Composite analysis northern region than in southeastern Taiwan. Composite analysis was used to explore the possible Other than SST, lower-level (850 mbar) geopotential impacts of extreme phases of PC1 of JAS SST (explained height and winds data were also chosen for composite variances of 59.65%) and OND SST (explained variances analysis because Taiwan’s rainfall depends strongly on of 35.58%) on the standardized NDJ and JFM precipi- the direction of the low-level prevailing circulation, and tation of Taiwan, respectively. The extreme phase is de- higher rainfall is expected on the windward than the fined as the lower or upper 33% of the whole SST phases, leeward sides (Chen and Chen 2003). Figures 13a,b show as shown in Fig. 11. The years in the lower and upper 33% the NDJ 850-mbar geopotential height and wind anom- of the whole period were listed in Table 1. Figure 12 aly patterns associated with the PC1 of anomalous JAS demonstrates the composites for all 15 stations of Taiwan, SST. During low JAS SST years, there is a deep trough where a composite value greater than zero means that centered east of Japan and positive height anomalies in the SST anomaly is associated with more precipitation, the mainland China (Fig. 13a) during the NDJ season. and vice versa. PC1 of high (low) JAS and OND SST are Therefore, the phase of lower JAS SST is associated generally associated with a positive (negative) NDJ and with northeasterly flow over Taiwan and southeastern JFM precipitation anomaly in Taiwan respectively, even China. During high JAS SST years, the positive height though there are a few exceptions. Figure 12a shows that anomalies move to the east of Japan (Fig. 13b) during seasonal rainfall of western stations was positively re- the NDJ season. Therefore, higher JAS SST is associ- lated to the high and low phases of SST, but eastern ated with the southwesterly flow over Taiwan. stations (stations 10–15) show the opposite relationship. Figures 13c,d show the 850-mbar, JFM geopotential Generally, high JAS SST leads to more NDJ precipi- height and wind anomaly under an anomalous OND tation in western Taiwan and low JAS SST leads to less SST. Under low OND SST, a strong positive height NDJ precipitation in western Taiwan. Figure 12b shows anomaly center is observed in the northern center of the a more distinct difference between JFM rainfall com- Pacific Ocean and a negative height anomaly is observed posites and PC1 of low and high OND SST among the in the western Pacific Ocean and northeastern China stations than Fig. 12a. The high OND SST leads to more during JFM (Fig. 13c). The circulation over Taiwan during JFM precipitation in western Taiwan, and vice versa. low OND SST years was dominated by the northeasterly From Fig. 12, it is obvious that composite analysis dem- wind. The high OND SST years exhibit a different cir- onstrated that high or warmer SST will lead to more culation pattern during JFM. Interestingly, the location water vapor in the atmosphere, and hence more NDJ of high pressure center during low OND SST turns out and JFM rainfall is expected. In terms of RMSE, cor- to also be the location of a low pressure center during

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC 172 MONTHLY WEATHER REVIEW VOLUME 138

FIG. 10. Scatterplots of the PCs of (a)–(f) JAS SST and NDJ rainfall and (g)–(n) OND SST and JFM rainfall. high OND SST (Figs. 13c,d). The positive height 2003). The warm OND SST episodes cause the westerly anomaly was located in the western Pacific Ocean and flow over Taiwan that brings in more precipitation to the East Asia (Fig. 13d). Apparently high OND SST is as- western side of Taiwan (Fig. 13d). The eastern side of sociated with westerly flow over Taiwan. The composite Taiwan receives less precipitation than the western side analysis shows that high and low OND SST are associated with different 850-mbar geopotential height and wind anomaly patterns in the following JFM season. The northeasterly winter monsoon cold surges are the most important transient disturbances affecting Taiwan during winter (DJF; Boyle and Chen 1987; Chen et al. 2002). They bring in more precipitation along the northern and northeastern coast at the windward side, at the expense of precipitation of the western side of Taiwan (Chen and Huang 1999). From Fig. 13b, high JAS SST episodes lead to southwesterly flow in the NDJ season that brings in warm moist air to Taiwan, which may bring more precipitation to the western sides of the island. On the contrary, the northeasterly flow (Fig. 13a) during low JAS SST PC1 episodes leads to less precipitation during NDJ particularly for western Taiwan. In February and early March, the southwesterly wind at the 850-mbar level commences over the northern Taiwan Strait and it gradually extends eastward cover- ing the whole island, leading to the west Pacific sub- tropical high moving east in late March (Chen and Chen FIG. 11. The definition of the extreme phase.

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC JANUARY 2010 K U O E T A L . 173

TABLE 1. Years included in the composite analysis of NDJ and SAWP of the selected SST sectors and the DCR-WPC1 JFM precipitation for estimating the PC1 of high (upper 33%) and rainfall. Seasonal JAS (OND) SST data in these iden- low (lower 33%) SST of the Pacific Ocean. tified sectors of the Pacific Ocean were used in an PC1 of Years included in ANN-GA model to predict the seasonal NDJ (JFM) Season composite SST compositing precipitation of Taiwan at one-season lead time. Com- NDJ Low JAS 1982, 1984, 1989, 1996, 1997, posite analysis was also employed to examine the re- 1999, 2000, 2002, 2004, 2006 lationship between the rainfall of Taiwan and low and High JAS 1976, 1977, 1978, 1983, 1986, high SST episodes of the Pacific at a seasonal lead time. 1987, 1991, 1993, 1995, 1998 The SST fields chosen were located around 08–308N, JFM Low OND 1982, 1984, 1989, 1996, 1999, 2000, 2001, 2002, 2004, 2006 1208–1608E for the JAS SST to predict NDJ rainfall and High OND 1977, 1978, 1980, 1983, 1986, around 08–608N, 1258E–1608W for the OND SST to 1987, 1992, 1993, 1994, 1995 predict JFM rainfall, respectively. Results show that ANN-GA gave good performance in the western and northern Taiwan for NDJ (RMSEs between 0.9 and 1.3, partly because the Central Mountain Range (CMR) of correlation between 0.3 and 0.7, and HK scores between Taiwan blocks the westerly wind from reaching the east- 0.2 and 0.5) and JFM (RMSE between 0.7 and 1.0, cor- ern side. relation between 0.3 and 0.7, and HK scores between 0.2 and 0.4) rainfall. Composite analysis shows that high (low) SST is as- 6. Summary and conclusions sociated with more (less) seasonal rainfall, which is ex- This study investigated the seasonal predictability of pected as high SST means more atmospheric water vapor rainfall (NDJ and JFM). First, seasonal rainfall and Pacific and so more rainfall and vice versa. Furthermore, analysis Ocean SST were wavelet transformed. Decadal compo- of the geopotential height and wind patterns during high nent removed scale-average wavelet power (DCR-SAWP) and low SST episodes also show changes in the circula- and its DCR-WPCs were computed. Further, wavelet tion patterns, and the shifting of the low pressure center transformed NDJ and JFM rainfall between 1974 and closer and farther away from Taiwan also attribute to 2006 in Taiwan exhibit strong 2–4-yr cycles. From the the observed precipitation regime. correlation field between the DCR-SAWP of SST and Our results demonstrate a fairly significant relation- theDCR-WPC1ofseasonalrainfall of the following ship between the seasonal Pacific SST anomalies and season, sectors of the Pacific Ocean where SST showing seasonal rainfall from November to March in Taiwan, strong correlation with the rainfall of Taiwan (jrj . 0.5) and the connectivity was well captured by an ANN-GA were identified. High wavelet coherence was also found model. The seasonal rainfall predicted at one-season between the selected SST and seasonal rainfall, which is lead time can be disaggregated to more refined time consistent with the correlation analysis between DCR- steps and used to drive certain hydrologic models to

FIG. 12. Composite (a) NDJ seasonal precipitation associated with high and low JAS SST PC1 (explained variances of 59.65%), and (b) JFM seasonal precipitation associated with high and low OND SST PC1 (explained variances of 35.58%), of the selected sectors (circled with thick lines) of the Paciﬁc Ocean shown in Fig. 5.

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC 174 MONTHLY WEATHER REVIEW VOLUME 138

FIG. 13. Composite of anomalies of (a),(b) NDJ and (c),(d) JFM 850-mbar geopotential height and wind vector associated with (a) low PC1 of JAS SST, (b) high PC1 of JAS SST, (c) low PC 1 of OND SST, and (d) high PC1 of OND SST. The geopotential height is in m and the wind speed is in m s21. predict the seasonal streamflow of the same river basins APPENDIX (Mwale and Gan 2009). Such information should benefit the water resources management of Taiwan particularly Performance Indices during dry seasons. Our future research will focus on the seasonal streamflow prediction of river basins of Taiwan. To evaluate the performance of ANN-GA, three indices (i.e., the Pearson correlation, the Hanssen-Kuipers Acknowledgments. This project was funded by the (HK) skill score, and RMSE) were used. The Pearson National Science Council (NSC 97-2221-E-006-150- correlation r is given as MY3 and NSC 096-2917-I-006-016) of the Republic of n China, Taiwan. The first author was also partly funded by Natural Science and Engineering Research Council å (obsk obs)(predk pred) r 5 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik51 , (A1) of Canada. The rainfall data were provided by Central n n Weather Bureau in Taiwan. Kaplan SST V2 data and 2 2 å (obsk obs) å (predk pred) NCEP reanalysis data were provided by the NOAA/ k51 k51 OAR/ESRL PSD, Boulder, Colorado from their Web site online at http://www.cdc.noaa.gov/. The source codes where obsk and predk are the observed and predicted of wavelet analysis were made available by Terrence rainfall of sample k, obs and pred are their respective and Compo (http://atoc.colorado.edu/research/wavelets/) means, and n is the sample size. Here r varies between 1 and A. Grinsted (http://www.pol.ac.uk/home/research/ and 21. To compute the HK skill score, the predicted waveletcoherence/). The comments of two anonymous and observed rainfall data are grouped into three cate- reviewers helped improve the quality of our manuscript. gories: dry, near normal, and wet. Percentages of the

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC JANUARY 2010 K U O E T A L . 175

normalized NDJ and JFM rainfall below 33%, 33%–67%, Huang, W. Y., and N. J. Hsu, 2005: Rainfall prediction for Taiwan and above 67% were used to deﬁne the categories in a area using global sea surface temperature (in Chinese with contingency table: English Abstract). J. Chin. Stat. Assoc., 43, 371–386. Hung, C. W., H. H. Hsu, and M. M. Lu, 2004: Decadal oscillation (H E ) of spring rain in northern Taiwan. Geophys. Res. Lett., 31, HK 5 c , (A2) L22206, doi:10.1029/2004GL021344. (T Em) Jevrejeva, S., J. C. Moore, and A. Grinsted, 2003: Inﬂuence of the Arctic Oscillation and El Nin˜ o-Southern Oscillation (ENSO) where H is the total number of correct forecasts, T is the on ice conditions in the Baltic Sea: The wavelet approach. total number of correct forecasts obtainable with a per- J. Geophys. Res., 108, 4677, doi:10.1029/2003JD003417.

fect forecast model, Ec is the number of correct hits Jiang, Z. H., G. T. J. Chen, and M. C. Wu, 2003: Large-scale circulation patterns associated with heavy spring rain events over expected by chance, and Em is the marginal number of Taiwan in strong ENSO and non-ENSO years. Mon. Wea. correct (observation) hits expected by chance. For an Rev., 131, 1769–1782. L 3 L contingency table, the HK score may be ex- Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Re- pressed in terms of probabilities as analysis Project. Bull. Amer. Meteor. Soc., 77, 437–471. Kaplan, A., M. A. Cane, Y. Kushnir, A. C. Clement, M. B. L L Blumenthal, and B. Rajagopalan, 1998: Analyses of global sea surface temperature 1856-1991. J. Geophys. Res., 18 567– å p(obsi, predi) å p(obsi) p(predi) 103C, HK 5 i51 i51 , (A3) 18 589. L Li, F., and Q. C. Zeng, 2008: Statistical prediction of East Asian 2 summer monsoon rainfall based on SST and sea ice concen- 1 å [p(obs j)] j51 tration. J. Meteor. Soc. Japan, 86, 237–243. Li,Q.,S.Yang,V.E.Kousky,R.W.Higgins,K.M.Lau,and where obsi and predi are the ith observed and predicted P. Xie, 2005: Features of cross-Pacific climate shown in the values. The HK score values range from 21to11. Perfect variability of China and US precipitation. Int. J. Climatol., forecasts receive a score of 1, random forecasts receive 25, 1675–1696. Lu, M. M., and R. J. May, 2003: The January-March precipitation a score of 0, and forecasts inferior to random forecasts in the region of Asian-Australian monsoon (in Chinese with receive negative scores. In this paper L is equals to 3. English abstract). Atmos. Sci., 31, 307–331. The root-mean-square error is computed as Mwale, D., and T. Y. Gan, 2005: Wavelet analysis of variability, tele- "#connectivity, and predictability of the September–November n 1/2 1 East African rainfall. J. Appl. Meteor., 44, 256–269. 2 ——, and ——, 2009: Integrating wavelet empirical orthogonal RMSE 5 å (obsk predk) . (A4) n k51 functions and statistical disaggregation for predicting weekly streamflow from seasonal oceanic variability for Kafue Basin, Central Southern Africa. J. Hydrol. Eng., in press. ——, ——, and S. S. P. Shen, 2004: A new analysis of variability and REFERENCES predictability of seasonal rainfall of central southern Africa Boyle, J. S., and G. T. J. Chen, 1987: Synoptic aspects of the winter- for 1950-94. Int. J. Climatol., 24, 1509–1530. time East Asian monsoon. Monsoon Meteorology, C. P. Chang Parker, D. E., P. D. Jones, C. K. Folland, and A. Bevan, 1994: and T. N. Krishnamurti, Eds., Oxford University Press, 125–160. Interdecadal changes of surface-temperature since the late- Chan, J. C. L., and J. E. Shi, 1999: Prediction of the summer mon- 19th-century. J. Geophys. Res., 99, 14 373–14 399. soon rainfall over South China. Int. J. Climatol., 19, 1255–1265. Reynolds, R. W., and T. M. Smith, 1994: Improved global sea- Chen, C. S., and J. M. Huang, 1999: A numerical study of pre- surface temperature analyses using optimum interpolation. cipitation characteristics over Taiwan island during the winter J. Climate, 7, 929–948. season. Meteor. Atmos. Phys., 70, 167–183. Shiao, C. H., and H. M. H. Juang, 2006: Sensitivity study of the ——, and Y. L. Chen, 2003: The rainfall characteristics of Taiwan. climate simulation over East Asia with the CWB regional Mon. Wea. Rev., 131, 1323–1341. spectral model. Terr. Atmos. Oceanic Sci., 17, 593–612. Chen, G. T. J., Z. H. Jiang, and M. C. Wu, 2003: Spring heavy rain Torrence, C., and G. P. Compo, 1998: A practical guide to wavelet events in Taiwan during warm episodes and the associated analysis. Bull. Amer. Meteor. Soc., 79, 61–78. large-scale conditions. Mon. Wea. Rev., 131, 1173–1188. ——, and P. J. Webster, 1999: Interdecadal changes in the ENSO– Chen,T.C.,M.C.Yen,W.R.Huang,andW.A.Gallus,2002:AnEast monsoon system. J. Climate, 12, 2679–2690. Asian cold surge: Case study. Mon. Wea. Rev., 130, 2271–2290. Water Resources Agency, 2008: Hydrological year book of Tai- Chien, F. C., and B. J. D. Jou, 2004: MM5 ensemble mean pre- wan, Republic of China—2007 total report (in Chinese). cipitation forecasts in the Taiwan area for three early summer Ministry of Economic Affairs, Republic of China, 38 pp. convective (mei-yu) seasons. Wea. Forecasting, 19, 735–750. Xu, Z. X., K. Takeuchi, and H. Ishidaira, 2004: Correlation between ——, Y. H. Kuo, and M. J. Yang, 2002: Precipitation forecast of El Ninõ-Southern Oscillation (ENSO) and precipitation in MM5 in the Taiwan area during the 1998 mei-yu season. Wea. South-east Asia and the Pacific region. Hydrol. Processes, 18, Forecasting, 17, 739–754. 107–123. Grinsted, A., J. C. Moore, and S. Jevrejeva, 2004: Application of the Yang, F. L., and K. M. Lau, 2004: Trend and variability of China cross wavelet transform and wavelet coherence to geophysical precipitation in spring and summer: Linkage to sea-surface time series. Nonlinear Processes Geophys., 11, 561–566. temperatures. Int. J. Climatol., 24, 1625–1644.

Unauthenticated | Downloaded 10/02/21 02:46 AM UTC