## 1. Introduction

Typhoon activity significantly impacts human populations in many Asian-Pacific countries. The interannual variability in typhoon activity is recognizably complex; contributing to this complexity are the many processes that have been identified as having relationships with typhoon activity, including the El Niño–Southern Oscillation (ENSO) (Camargo and Sobel 2005; Camargo et al. 2007; Chan 2000; Chan et al. 2004; Chen et al. 1998; Chia and Ropelewski 2002; Gray 1984a), the stratospheric quasi-biennial oscillation (Gray 1984a), the Antarctic Oscillation (Wang and Fan 2007), the North Pacific Oscillation (Wang et al. 2007), the North Pacific sea ice cover (Fan 2007), the atmospheric circulation over the western North Pacific (WNP) (Ding 1983; Ritchie and Holland 1999; Zhang and Altschuler 1999; Zhou et al. 2008a,b), etc. For the purposes of operational prediction, it is very important to develop a forecasting tool for predicting typhoon activity over the WNP (Chan et al. 1998, 2001; Cheung and Elsberry 2002). Predictions for Atlantic hurricane activity and intensity have been made in several prior studies (Gray 1984a,b; Thorncroft and Pytharoulis 2001). Chan et al. (1998) that established statistical models for seasonal forecasting of tropical cyclone activity over the WNP. The predictors identified to date for forecasting typhoon activity include indices representing the ENSO phenomenon and the environmental conditions over East Asia and the WNP. However, the model prediction failed partially in 1997 and 1998, during which a warm and a cold event of the ENSO phase occurred during the peak typhoon activity season. Chan et al. (2001) later identified new predictors to improve the statistical model. Furthermore, the recent increase in typhoon disasters in many coastal counties and populations demonstrates the urgent need to find new predictors and new forecasting approaches for typhoon activity.

Recently, Wang et al. (2007) found that the North Pacific Oscillation (NPO) index for July–September is positively correlated with the annual number of typhoons occurring in the WNP and negatively correlated with the annual number of Atlantic hurricanes for the period 1949–98. They suggested that the NPO typhoon linkage may be explained by changes to the upper-level westerly winds in the middle latitudes over the Pacific Ocean, which result in variations of the vertical zonal wind magnitude in the WNP. Fan (2007) further suggested that the appearance of more sea ice covering the Pacific during boreal winter–spring corresponds to a decrease in the number of typhoons in the WNP via the NPO. Thus, both the interannual variation in sea ice coverage over the North Pacific as well as the NPO could be considered to be potential predictors for the interannual variability of the annual typhoon frequency over the WNP.

Fan et al. (2008a,b) proposed a new approach for forecasting the summer rainfall over the middle to lower reaches of the Yangtze River valley (YRV) and north China. They define DY as the difference in any variable between the current year and the preceding year. YR is denoted as the seasonal mean precipitation rate over the middle to lower reaches of the YRV. After analyzing the DY of the atmospheric circulations in the boreal winter/spring that were associated with the DY of the YR, the predictors were identified. The forecast model for the DY of the YR was established and then applied to forecast the YR. The model showed a high level of accuracy for hindcasting the YR rainfall during the period 1997–2006 with an average relative root-mean-square error (RMSE) of 18%. It even reproduced the upward and downward trends of the YR during the periods from 1984 to 1998 and 1998 to 2006, respectively, suggesting that the model can capture both interannual and decadal variations in summer rainfall over the YRV.

Fan et al. (2008b) proposed that the rationality of this approach may arise from the existence of a tropospheric biennial oscillation (TBO) in the Asian monsoon and monsoon rainfall (Meehl 1997; Meehl and Arblaster 2002), as well as ENSO (Gray 1984a), and so on. The standard deviation of the DY for the YR is much larger (1.98 mm day^{−1}) than that for the YR itself (1.48 mm day^{−1}), which could be useful for capturing the prediction signal.

In this paper, we aim to exploit a new statistical model based on the above approach to forecast the typhoon frequency over the WNP.

## 2. Method and dataset

We take the following steps: 1) We use the DY to denote the difference between the current year and the preceding year in any variable, and the WNPTF corresponds to the annual number of typhoons over the WNP. For example, the DY of the WNPTF in 1998 represents the difference in the WNPTF between 1998 and 1997. 2) We analyze the DY of the atmospheric circulation variability associated with the DY of the WNPTF in order to identify predictors. 3) We establish a statistical forecast model to predict the DY of the WNPTF. 4) We validate the statistical model.

Since the peak tropical cyclone activity season over the WNP covers July–October (JASO), the selected predictors would be taken from data available before the peak typhoon season.

The essential criteria for defining a typhoon include maximum wind speeds exceeding 33 m s^{−1}. The dataset for the annual number of typhoons is obtained from the Joint Typhoon Warning Center (JTWC). The region of the WNP is confined to the area of 5°–45°N, 105°E–180°, including the South China Sea. The Hadley Center for Climate Prediction and Research’s monthly mean sea ice concentration, with a horizontal resolution of 1° × 1°, is also taken into account. The National Centers for Environmental Prediction–National Center for Atmospheric Research’s (NCEP–NCAR) monthly atmospheric reanalysis data, with a resolution of 2.5° × 2.5°, are used for the atmosphere circulation analyses. The time span of the dataset is 44 yr, covering 1964–2007. The forecast model is established using a multilinear regression method based on data taken from 1965 to 2001. Using the forecast model, we made a hindcast of the typhoon frequency of the WNP for the period 2002–07. A cross-validation test is performed to validate the prediction skill of the prediction model.

## 3. The predictors

In this section, we will try to identify several predictors based on the analysis of the DY of the circulation associated with the DY of the WNPTF, and the independent and dependent variables to be used in the prediction model will be discussed.

Figure 1 shows the local wavelet power spectrum using the Morlet wavelet analysis in which the shaded contours are the normalized variances. The regions outside of the parabola on either end indicate the cone of influence. The cone of influence represents the region of the wavelet spectrum in which edge effects become important and is defined here as the *e*-folding time for the autocorrelation of the wavelet power at each scale. The TBO is one of the significant features of the WNPTF during the period 1965–2006 (see Fig. 1). Thus, the predictand is selected as the DY of the WNPTF, with the standard deviation of the DY for the WNPTF being much larger (5.21) than that of the WNPTF itself (4.08).

### a. Sea ice cover over the North Pacific

As Fan (2007) indicated, the sea ice coverage (SIC) for December–February (DJF) and March–May (MAM) over the North Pacific is confined to the areas of 53.5°–66.5°N, 158.5°E–159.5°W and 44.5°–59.5°N, 140.5°–155.5°E, which correlates well with the annual typhoon frequency over the WNP. We found that the DY of the sea ice cover (SIC) over the North Pacific in DJF also correlated well with the DY of the WNPTF, with the correlation coefficient between the DY of the SIC and the DY of the WNPTF being −0.47 during the period 1965–2001 (above 99% significance level) and 35 degrees of freedom. To evaluate the DY of the SIC in DJF and the DY of the WNPTF, we prepared a composite analysis of the years 1969, 1970, 1974, 1975, 1977, 1979, 1980, 1983, 1986, 1992, 1995, 1998, and 2000 (1966, 1968, 1972, 1978, 1982, 1984, 1991, 1996, 1999, and 2001), which were selected as years with a positive (negative) DY of the SIC anomalies in DJF. The DY of the SLP difference between the positive and negative DYs of the SIC composite was concurrent with the negative DY of the NPO anomalies during DJF–JASO, with an enhanced Aleutian low and subtropical high over the WNP (figure not shown). This is consistent with the findings of Fan (2007), who noted that the SIC anomalies have a relationship with the circulation over the North Pacific, such as NPO, which was associated with the dynamic and thermal condition changes necessary for typhoon genesis over the WNP (Wang et al. 2007). Associated with the positive SIC anomalies, the anticyclonic anomalies and the negative vorticity anomalies at 850 hPa over the WNP (Fig. 2) are related to the weaker monsoon trough over the WNP in JASO (Chen et al. 1998). Elsner and Kocher (2000) found that global tropical cyclone activity has a statistical link to the NAO, but not to the ENSO; however, a complex interaction exists between the NAO and other high-latitude signals and tropical variations. Since the sea ice variability is significantly correlated with the typhoon frequency, it is used as a predictor in the prediction model of typhoons.

### b. The thermal condition predictor

The tropical Pacific Sea surface temperature (SST) and local region pressure have been identified as an important factor for tropical cyclone genesis and frequency (Gray 1984a; Knaff 1998; Kossin and Vimont 2007). Many researchers have shown the impacts of the ENSO on typhoon activity, indicating that ENSO events can modify typhoon occurrence, intensity, landfall incidence, track, and lifetime (e.g., Chan 2000; Camargo and Sobel 2005; Camargo et al. 2007; Dong 1988; Wu and Lau 1992; Wang and Chan 2002; Chen et al. 1998). Lander (1994) indicated that no relationship exists between annual storm totals and ENSO. However, the aforementioned research suggests that ENSO appears to affect, on a larger scale, atmospheric factors related to typhoon activity, but that the relationship between the ENSO and typhoon activity is very complex. As Fig. 3 shows, the changes in the SST in the eastern tropical Pacific for boreal winter/spring are different from those in JASO, which suggests that the relationship between the DY of the WNPTF and ENSO varies with season. So, instead of the Niño-3.4 index or the Southern Oscillation Index (SOI), we hope to seek a better, more seasonally persistent, predictor for the DY of the WNPTF. Since the changes in the SST over the Bay of Bengal and the East Asian marginal seas have good consistency from DJF to JASO, the temperature index at 1000 hPa (IT1000) was selected as a predictor for the DY of the WNPTF. It is defined as the area-averaged DY of the temperature at 1000 hPa over the region of (−20° to 20°N, 90° to 120°E), with correlation coefficients between the DY of the WNPTF and IT1000, both in MAM and in JASO during the period 1965–2001, of −0.76 and −0.74, respectively. On the other hand, IT1000 is associated with local thermal conditions not only over the western tropical Pacific but also for the eastern tropical Pacific, the latter of which is more important for tropical cyclone genesis.

### c. The dynamic condition predictors

Most tropical cyclones form along the shear zone between monsoon westerlies and the trades easterlies. Flow intensification on either side of this monsoon trough increases the low-level relative vorticity and enhances tropical cyclone genesis (Briegel and Frank 1997; Schumacher et al. 2009). The value of the 850-hPa relative vorticity in the tropical WNP, both in June and JASO, corresponds to the increase in the WNPTF. This suggests that a stronger monsoon trough results in increased typhoon activity. The index of vorticity at 850 hPa (IVOR850) is defined as the area-averaged 850-hPa vorticity in the region (15°–20°N, 125°–140°E). Since the correlation coefficients between the DY of the WNPTF and the DY of the IVOR850 in June and for JASO are 0.51 and 0.64 during the period 1965–2001, respectively, the DY of the IVOR850 in June was selected as a predictor.

Another dynamic condition factor for the WNPTF is the vertical shear of the zonal wind between 200 and 850 hPa. The magnitude of the wind shear (MWS) could be defined as the absolute value of the zonal wind difference between 200 and 850 hPa. The WNP is a region with a weak MWS in terms of climatology during the major typhoon activity season (JASO). Negative correlation coefficients are prominent east of 140°E in the tropical WNP during June and JASO, which is favorable for the increase of the WNPTF (figure not shown). Therefore, the area-averaged MWS in the region (5°–10°N, 145°–170°E) in June was selected as a predictor for the DY of the WNPTF, with a correlation coefficient between the DY of the WNPTF and the DY of the MSW in June (JASO) of −0.49 (−0.6) during the period 1965–2001.

### d. The summary of predictors

After analyzing the circulation related to the DY of the WNPTF, five predictors were identified: *X*_{1} is the DY of the SIC, which is the index of sea ice coverage over the North Pacific in DJF based on the findings of Fan (2007); *X*_{2} is the DY of the IT1000, which is the area-averaged temperature at 1000 hPa in the western tropical WNP in MAM, which reflects the local thermal condition for WNPTF; *X*_{3} is the DY of the IVOR850, which is the 850-hPa vorticity over the WNP; and *X*_{4} is the DY of the MWS, which is the magnitude of vertical shear of the zonal wind between 200 and 850 hPa in the tropical WNP in June. Both *X*_{3} and *X*_{4} represent the dynamic condition. The fifth predictor, *X*_{5}, is the DY of the SLPWP, which is the area-averaged sea level pressure in the region 10°–20°N, 135°E–150°W in June, indicating that the negative SLP anomalies over the WNP should be favorable for typhoon genesis with a correlation coefficient between the DY of the WNPTF and *X*_{5} in June (JASO) of −0.59 (−0.65) during the period 1965–2001. The definitions of predictors are described in Table 1. It should be noted that the predictors have been related to the DY of the Niño-3.4 index in DJF, which is an important factor for the WNPTF; however, the DY of the Niño-3.4 index is not taken into account in the prediction model, because the relationship between the ENSO index and the WNPT varied with season, with correlation coefficients between the DY of the WNPTF and the DY of the SOI (Niño-3.4) for DJF and JASO of 0.65 (−0.68) and −0.38 (0.55), respectively, during 1965–2001, with a better than 95% significance level. Therefore, it is very difficult to predict the abnormal WNPTF of 24 for 1997 and 9 for 1998 based on the predictor of the Niño-3.4 or the SOI index in DJF before the typhoon peak season in which the El Niño of 1997–98 collapsed rapidly during May 1998 so that, in June, an anomalously cold condition enveloped the east-central equatorial Pacific.

Therefore, the above five predictors are selected based on two considerations: one is attributed to their significant correlation with the DY of the WNPTF for DJF–JASO during 1965–2001 and the physical link to typhoon activity. The other is that the predictors are correlated with the SOI in DJF, and thus they may capture the precursor signal of a warm (cold) ENSO year (see Table 2). Figure 4 shows the time series of the DY of the predictors and the DY of the WNPTF, suggesting that their good agreement is responsible for the better prediction for the WNPTF in 1997 and in 1998.

## 4. A seasonal forecast model for the DY of the WNPTF

*y*stand for the DY of the WNPTF, we get the following forecast model in which all the variables are normalized:

Figure 5a illustrates that the DY of the WNPTF exhibits TBO features just as like those of the summer rainfall over the Yangtze River valley, which supports the hypothesis of the year-to-year increment approach (Fan et al. 2008a).

## 5. Validation of the forecast model

The modeled WNPTF is obtained by adding the preceding year’s observed WNPTF to the modeled DY of the WNPTF. The simulated WNPTF and actual WNPTF exhibit reasonable agreement both qualitatively and quantitatively over the training period 1965–2001 (Fig. 5) and the validation period 2000–07 (Fig. 6). We define some quantities for validation of the forecast model:

- the simulated (predicted) annual typhoon frequency,
- the percentage of the relative error of the simulation (prediction),
- the absolute error of the simulation (prediction),
- the average relative RMSE of the simulation (prediction),
- the average absolute RMSE of the simulation (prediction),
SS = (RMSE1 − MMSE2)/RMSE2,

*y*is the simulated (predicted) DY of the WNPTF,

*y*

_{0}is the observed WNPTF,

*y*is the simulated WNPTF,

*N*is the length of the sample, and SS represents the prediction skill score of model 1. If SS is greater than 0, the prediction skill of model 1 is better than that of model 2.

The forecast model yields an average relative RMSE of 16%, an average (RMSE) of 2.85, and an average mean absolute error (MAE) of 2.29 for the years from 1965 to 2001. The model effectively simulates the larger anomalies of the WNPTF in 1966, 1968, 1977, 1979, 1990, and 1991, with simulated values that are quite close to the observed values. The model exhibits reasonable skill in predicting the variation for the years from 1996 to 2001. The model’s simulated (observed) typhoon numbers for 1996–2001 are 19 (21), 21 (24), 10 (9), 15 (12), 13 (15), and 17 (20), with the average number of typhoons being 17. The percentages of relative error (MAE) in the WNPTF for 1996–2001 are small, taking on values of −11% (3), −17% (3), 6% (1), 17% (3), −17% (2), and −23% (3).

Using the forecast model, we made a hindcast of the WNPTF during 2002–07, a period in which the typhoon numbers are normal except for 2004. The predicted (observed) values during 2002–07 were 17 (16), 17 (17), 22 (21), 15 (16), 16 (15), and 16 (15). Notably, the predicted values are quite close to the observed values, including the higher typhoon occurrence frequency in 2004, with an average relative RMSE of only 6%, an RMSE of 1.3, and an MAE of 1.2 during the period 2002–07. The percentages of relative error (MAE) for the WNPTF are quite low during 2002–07, at 5.8% (1), 0 (0), 5.8% (1), −5.8% (1), 5.8% (1), and 5.8% (1). The forecast model therefore exhibits potential for application in predicting the WNPTF.

## 6. Further verification of the model through the cross-validation test

We apply cross validation to test the prediction model. Cross validation may be applied by removing each year (along with the previous year from which differences are calculated), one at a time, from the training set and generating a new set of coefficients based on the retained years. The process could be repeated to generate blind forecasts for each year of their entire dataset. Figure 7 shows the time series of the DYs of the WNPTF and the WNPTF using the cross-validation test. The predicted DY of the WNPTF (WNPTF) by the cross-validation test fits well with the observed DY of the WNPTF (WNPTF). The correlation coefficient between the predicted WNPTF by cross validation (without cross validation) and the observed WNPTF is 0.78 (0.72) during 1965–2007 (43 yr), with an MAE of 2.4 (2.1) and an RMSE of 3.0 (2.6) during 1967–2007 (40 yr). The model created by cross validation successfully captured the abnormal typhoon activity during 1982–83 and 1996–2000. The predicted (observed) WNPTF values are 20 (19) and 12 (8) during 1982–83 and are 19 (21), 20 (24), 10 (9), 16 (12), and 12 (15) during the period 1996–2000 (see Table 3). Therefore, the prediction model has good predictive ability for the WNPTF.

## 7. Comparison with other models

To further illustrate the superior abilities of the new approach and the prediction skill of M-DY, we performed a comparison among different models. First, the DY predictors are taken in the models of M-DY, M-DY-x6, M-DY-x7, and M-DY-x8, respectively. Second, we used the same predictors in the original form to construct M-Y1 and M-Y-x6. The descriptions of the models are shown in Table 4. New predictors have significant correlation with the predictand (see Table 5). The DY of the SLPWA (SLPWA) is defined as the area-averaged DY of the SLP (SLP) in the region (70°–90°N, 240°–300°E) in MAM.

### a. Significance test

We use the different degrees of freedom to construct different models for the WNPTF, and we calculate the values of the statistic *F* [*F* = *R*^{2}/*p*/(1 − *R*^{2})/(*n* − *p* − 1)] for the significance test, in which R is the correlation coefficient in the prediction model, p is the number of predictors or the degrees of freedom in the prediction model, and n is the length of the sample. The prediction model is significant (*α* = 0.05) when *F* > *F _{α}*. Here,

*F*is the

_{α}*F*value when

*α*= 0.05, and there are

*p*degrees of freedom for the numerator, and

*n*−

*p*− 1 degrees of freedom for the denominator. The larger

*F*value in the prediction indicates greater significance. All of the prediction models are established during the period 1965–2001 (

*n*= 37). M-DY contains five predictors (

*p*= 5), M-DY-x6 contains six, M-DY-x7 contains seven, M-DY-x8 contains eight, and M-Y-x6 contains six. Although all of the prediction models are significant at a 0.05 or 0.01 confidence level, the

*F*value of the M-DY model is the largest and is therefore the most significant among the prediction models. Clearly, the

*F*values decrease when more predictors are taken into account in the regression models. Both the

*F*value of M-DY (M-DY-x6) and the correlation coefficients between the predicted WNPTF and the observed WNPTF are much larger than those of M-Y1 (M-Y6), illustrating the superiority of the year-to-year increment approach (see Table 6).

### b. Comparison of the models by the cross-validation test

We compare the prediction skill of the DY models by the cross-validation test. The M-DY model has a better level of prediction skill (see Table 7), although the prediction skill of the M-DY-x6 model is comparable to that of M-DY. To further illustrate the superiority of M-DY and M-DY-x6, we construct M-Y1 and M-Y-x6, whose predictors are in their respective original forms. The prediction skill of M-DY (M-DY-x6) is still better than that of M-Y1 (M-Y6) (see Table 7). M-DY could better capture the interannual variability of the observed WNPTF (Fig. 7). The correlation coefficients between the predicted WNPTF and the observed WNPTF using the cross-validation test during the period 1965–2007 are 0.7 (52% of variance) for M-DY, 0.6 (36% of variance) for M-Y1, and 0.57 (32% of variance) for M-Y-x6. The values of the MAE during the same period are 2.4 for M-DY, 2.5 for M-Y1, and 2.6 for M-Y-x6. The values of the RMSE are 3.0 for M-DY, 3.1 for M-Y1, and 3.3 for M-Y-x6 (see Table 7).

### c. The models established by using the data from 1977 to 2007

We noted that the prediction failures of the WNPTF for 1965, 1967, and 1971, which might partially arise from the incorrect amount of typhoon data and other available data in the presatellite era (Black 1993), have a big influence on the overall prediction score of M-DY. Therefore, both M-DY_{31} and M-Y_{31y} were established on the training period 1977–2007 (31 yr). The correlation coefficients between the predicted WNPTF and the observed WNPTF are 0.84 (71% of variance) for M-DY_{31y} and 0.76 (58% of variance) for M-Y_{31y}. The values of the RMSE (MAE) are 1.92 (1.67) for M-DY_{31y} and 2.9 (3.8) for M-Y_{31y} during 1977–2007 (see Table 8 and Fig. 8). In the cross-validation test, the correlation coefficients, RMSE, and MAE are 0.76 (58% of variance), 2.4, and 2 for M-DY_{31y}, respectively, and 0.64 (41% of variance), 2.9, and 3.8 for M-Y_{31y}, respectively. Relative to the prediction skill of M-Y_{31y}, the SS of the M-DY_{31y} (0.17) is greater than zero (see Table 9 and Fig. 8).

Chan et al. (1998) considered a larger amount of potential predictors, including the ENSO indexes and large-scale circulation and climatology–persistence predictors, which are monthly values from April of the previous year to March of the current year, and subsequently used the projection pursuit regression technique to establish the prediction models. The prediction model predicts partial failures in 1997 and 1998. The model predicted 19 ± 2 typhoons for 1997 and 20 ± 2 typhoons for 1998, which for 1998 is far from the observed number of 9. Chan et al. (2001) provided an updated prediction model by considering two new predictors related to the ENSO and by incorporating monthly values of the predictors selected in April and May of the current year. Comparing our proposed model with the forecast methodologies of Chan et al. (1998, 2001), our new approach might be easily applied due to its smaller number of predictors and a simple prediction equation. In M-DY, the model includes ENSO-related predictors (not the Niño indexes or the SOI, which means we consider the ENSO index implicitly), and the model can predict the WNPTF well, including the prediction of 20 (10) typhoons for 1998 (1997). The ENSO indexes are taken explicitly in the M-DY-x6, M-DY-dx7, and M-DY-dx8 models; however, these models could not improve on the prediction skill of the WNPTF.

This new approach has some advantages, which include the following.

This approach makes it easier to deal with the trend in the variables because the DY of

*x*=*x*(0) −*x*(−1). If*x*(0) =*x*(0)_{detrend}+ trend, then*x*(−1) =*x*(−1)_{detrend}+ trend, and the DY of*x*=*x*(0) −*x*(−1) =*x*(0)_{detrend}−*x*(−1)_{detrend}. In addition, the trend of the predictand is more easily captured by the M-DY approach because the accumulation of the DY is the trend. Unfortunately, this advantage cannot be seen because there is almost no trend in the WNPTF series, with the correlation coefficients between the WNPTF and the detrended WNPTF during 1965–2007 at 0.97. Only recently did we predict summer rainfall over the Yangtze River valley in north China using the year-to-year increment approach (Fan et al. 2008a,b). It was found that the year-to-year increment approach does capture the trend of the predictand because the accumulation of the predicted DY of summer rainfall in China reflects the linear trend. In this paper, because the linear trend of the WNPTF is insignificant during the period 1965–2007, there is no trend captured by M-DY.It is easy to identify the predictors of the DY of the WNPTF. In this paper, only five DY predictors are used, and all of them have a clear, physical link to the DY of the WNPTF. Even though only five predictors are selected, the skill of the prediction is satisfactory as compared to M-Y1 containing the same predictors for the current year.

## 8. Conclusions

In this paper, a new approach that contains only five predictors is proposed for predicting the WNPTF. By investigating the year-to-year increment in the WNPTF and its associated year-to-year atmospheric circulation increment, a new prediction model is established for the DY of the WNPTF and, by extension, for the WNPTF. The model performs with reasonable accuracy for the period of calibration and validation, including for the larger variability in typhoon frequency in the WNP during 1997 and 1998 and the smaller variability of the WNPTF during 2002–07.

The MAE (RMSE) for the hindcast of the WNPTF in 2002–07 is only 1.2 (1.3). To further test the prediction skill of the new approach, we performed the statistical test of the prediction model using the cross-validation method. The correlation coefficient between the predicted WNPTF by cross validation and the observed WNPTF is 0.72, which explains 52% of variance during the period 1965–2007 (43 yr), with the MAE (RMSE) at 2.4 (3). The prediction model can reproduce the extreme typhoon activity in 1997–98 or 1982–83 (Fig. 7 and Table 4).

In comparison, results from the significance test show that the predictions of the M-DY model are more significant than other prediction models. The ENSO indexes taken explicitly in the M-DY-x6, M-DY-dx7, and M-DY-dx8 models could not improve the prediction skill of the WNPTF. M-DY can reproduce the interannual variability of the WNPTF better than that of M-Y and M-Y-x6, which are established with the original variables instead of the year-to-year increment of variables.

In addition, when the prediction models are established using the data of 1977–2007 (when the quality of the data is much better than that of the presatellite era), M-DY demonstrates a much higher level of prediction skill than that of M-Y, whose predictors are in the original form, with an SS of 0.17, and a correlation coefficient, RMSE, and MAE of 0.76 (58% of variance), 2.4, and 2 for M-DY_{31y}, respectively, and of 0.64 (41% of variance), 2.9, and 3.8 for M-Y_{31y}.

M-DY is not based on the perfect autocorrelation between this year and the past year. The M-DY approach is not the same as the prediction model and includes the previous-year predictors and the current-year predictors. Because there is no relationship between this year’s WNPTF (0) and the past year’s WNPTF(−1) during the period 1965–2007, with a correlation coefficient of 0.2 (far below the 95% significant level), with no significant correlation coefficients between the WNPTF and the WNPTF(−1), the SIC(−1), the IT1000(−1), the IVor850(−1), the MWS(−1), and the SLPWP(−1); however, the WNPTF is significantly correlated with the SIC(0), the IT1000(0), the IVor850(0), the MWS(0), and the SLPWP(0) in the M-Y2 model. It should be noted that M-DY has been established on the significant correlations between the DY of the WNPTF, the DY of the SIC, the DY of the IT1000, the DY of the IVor850, the DY of the MWS, and the DY of the SLPWP. The results above show that the predictors for the WNPTF(0), the WNPTF(−1), and the DY of the WNPTF exhibit many differences. Therefore, the meaning of the M-DY model is not the same as that of the model including the current- and the previous-year variables.

However, M-DY needs to further improve the prediction skill for the WNPTF, which failed to predict the WNPTF for 1965, 1967, and 1971. A possible reason might be the incorrect data available during the presatellite era. Our research suggests that it is feasible to predict the year-to-year increments of a predictand instead of directly predicting the predictand itself. This was borne out in the prediction of summer rainfall in China and of the number of typhoons.

The new approach is easily applied in climate prediction. It would be interesting to apply this approach to the prediction of summer rainfall, the ENSO, monsoons, and other circulation systems in which the TBO signal is significant. Year-to-year variable increments may produce amplified signals, thereby facilitating the capture or identification of marginal changes in the underlying variables.

## Acknowledgments

This research was jointly supported by the National Natural Science Foundation of China (Grants 40775049 and 40631005), the Major State Basic Research Development Program of China (973 Program) under Grant 20009CB421406, and the IAP Key Innovation Program IAP07117.

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Definitions of the predictors of M-DY.

Cross-correlation coefficients among various variables during the period 1965–2001 (37 yr) with 35 degrees of freedom. Correlations significant at 95% (99%) are indicated with italics (bold face).

The results of the cross-validation test of M-DY.

Description of the prediction models.

Correlation coefficients between the new predictors, the DY of the WNPTF and the WNPTF, during the period 1965–2001 (37 yr). Correlations significant at 95% (99%) are indicated with italics (boldface).

The correlation coefficients between the predicted and observed WNPTFs during 1965–2001 along with the *F* values for the different models.

Correlation coefficients between the predicted WNPTF by the cross-validation test and the observed WNPTF during the period 1965–2007 along with the RMSE and MAE.

Comparison of M-DY_{31y} and M-Y_{31y} during 1977–2007.

Comparison of M-DY_{31y} and M-Y_{31y} using the cross-validation test during the period 1977–2007.