Abstract

The timing of the changma onset has high impacts on the Korean Peninsula, yet its seasonal prediction remains a great challenge because the changma undergoes various influences from the tropics, subtropics, and midlatitudes. In this study, a dynamics-based statistical prediction model for the changma onset is proposed. This model utilizes three predictors of slowly varying sea surface temperature anomalies (SSTAs) over the northern tropical central Pacific, the North Atlantic, and the North Pacific occurring in the preceding spring season. SSTAs associated with each predictor persist until June and have an effect on the changma onset by inducing an anticyclonic anomaly to the southeast of the Korean Peninsula earlier than the climatological changma onset date. The persisting negative SSTAs over the northern tropical central Pacific and accompanying anomalous trade winds induce enhanced convection over the far-western tropical Pacific; in turn, these induce a cyclonic anomaly over the South China Sea and an anticyclonic anomaly southeast of the Korean Peninsula. The diabatic heating and cooling tendency related to the North Atlantic dipolar SSTAs induces downstream Rossby wave propagation in the upper troposphere, developing a barotropic anticyclonic anomaly to the south of the Korean Peninsula. A westerly wind anomaly at around 45°N resulting from the developing positive SSTAs over the North Pacific directly reduces the strength of the Okhotsk high and gives rise to an anticyclonic anomaly southeast of the Korean Peninsula. With the dynamics-based statistical prediction model, it is demonstrated that the changma onset has considerable predictability of r = 0.73 for the period from 1982 to 2014.

1. Introduction

Precipitation during the changma (the Korean component of the East Asian summer monsoon; the mei-yu and baiu are the Chinese and Japanese counterparts) accounts for more than half of the annual precipitation in the Korea peninsula (Lu et al. 2001). Thus, the month of June, when the changma begins, is important in terms of variation in the annual precipitation, and shifting of the changma onset date is of significant concern (Choi et al. 2012). Figure 1 shows the seasonal evolution of the climatological mean precipitation rate in the Korean Peninsula (35°–40°N, 125°–130°E). From 1982 to 2012, the climatological mean changma onset date was 20 June (pentad 35), where a sudden increase in rainfall is seen and the 5-day averaged precipitation is more than 6 mm day−1 (Wang and LinHo 2002). As a subsystem of the East Asian summer monsoon, however, the changma has very complex properties in both development and progression due to its location in midlatitudes, whereas other monsoon systems are located in the tropics. The changma undergoes various influences from the tropics, subtropics, and midlatitudes such as El Niño–Southern Oscillation (ENSO), the Arctic oscillation (AO), the western North Pacific summer monsoon (WNPSM), the Indian summer monsoon (ISM), snow cover over the Eurasian continent in spring, and nearby sea surface temperature (SST; Ha et al. 2012). Therefore, successfully predicting the timing of the changma is an enormous challenge.

Fig. 1.

Seasonal evolution of the climatological mean precipitation rate in the Korean Peninsula (35°–40°N, 125°–130°E) using GPCP pentad data from 1982 to 2012.

Fig. 1.

Seasonal evolution of the climatological mean precipitation rate in the Korean Peninsula (35°–40°N, 125°–130°E) using GPCP pentad data from 1982 to 2012.

Numerous studies have been conducted on the changma with the main focus on the understanding of its interannual and interdecadal variability (e.g., Lu et al. 2001; Yun et al. 2008; Kim et al. 2011). Also, the objective determination of the onset and withdrawal dates has been investigated by several previous studies (e.g., Seo et al. 2011; Ha et al. 2005; Byun and Lee 2002). For example, Yun et al. (2008) demonstrated that after the peak of ENSO in boreal winter, the activity of the summertime northward propagating intraseasonal oscillation in the East Asian summer monsoon system is enhanced. An intraseasonal structure of the summer rainfall over East Asia including the Korean Peninsula is analyzed to exhibit a regime shift in the mid-1990s (Kim et al. 2011). Regarding the changma onset and termination, Lu et al. (2001) examined extreme cases of the changma onset and withdrawal and emphasized that changma retreats are associated with planetary-scale teleconnection patterns of circulation in the middle and high latitudes. Also, Hirota and Takahashi (2012) suggested the importance of the nonlinear processes in the high latitudes on the East Asian summer monsoon pattern in contrast with the forcing in the tropics. The changma onset and withdrawal have been determined by using annual variations of temperature, precipitation, cloudiness, and insolation (Ha et al. 2005) and the available water resources index, which is the accumulated precipitation amount in which daily reduction of water and the duration of accumulation are quantitatively considered (Byun and Lee 2002). Recently, Tomita et al. (2011) and Seo et al. (2011) revisited the definition of the large-scale front (for the baiu and changma, respectively) by calculating the equivalent potential temperature, which signifies the approximate location of the monsoonal front.

Despite its importance, few studies have been devoted to the prediction of changma rainfall intensity and onset. Recently, Lee and Seo (2013) attempted to predict precipitation amount during the changma period using a multiple linear regression model with global SST anomalies (SSTAs) as a predictor. While the prediction skill of the state-of-the-art global models for the Asian monsoons is extremely low, their statistical model achieved high prediction skill. Choi et al. (2013) developed a multiple linear regression model for the prediction of the changma onset date in the Korean Peninsula using the 850-hPa geopotential height field in the preceding April. However, this study used atmospheric variables that have rather short memory and have relatively low possibility of providing robust and stable dynamical processes associated with the variation of the changma onset. Their study excluded effects from ENSO when verifying the model prediction. The present study utilizes SSTA, one of the slowly varying lower boundary conditions, to provide stable and effective prediction (Wang et al. 2013; Lee and Seo 2013; Lau et al. 2000). Also, the Pacific SST variation is taken into account in the development of an empirical model as ENSO is the most prominent predictability source on the interannual time scale (Wu et al. 2009).

The objectives of this study are to determine the characteristics of the interannual variability of the changma onset by examining its large-scale characteristics and to develop a statistical prediction model using the slowly varying boundary forcing of SSTAs. Furthermore, to provide a robust and stable statistical prediction model, dynamical processes associated with each selected predictor are analyzed using numerical model simulations. This paper is organized as follows. Section 2 describes the data and methods used in this study, and section 3 analyzes the observational preconditions for the changma onset. Section 4 describes the statistical prediction model developed in this study and section 5 discusses dynamic processes in relation to predictors. A summary and discussion are presented in section 6.

2. Data and methods

a. Data

The Global Precipitation Climatology Project (GPCP, version 2.2) precipitation (Huffman et al. 1997) pentad data with a horizontal resolution of 2.5° × 2.5° were used for the period of 1982 to 2012. For SST, the National Oceanic and Atmospheric Administration (NOAA) optimum interpolation (OI) SST version 2 (Reynolds et al. 2007) data from 1982 to 2014 were used. The original OISST daily data with a high resolution of 0.25° × 0.25° were averaged to pentad data and aggregated onto a 1° × 1° grid.

Geopotential height (gpm) and zonal and meridional winds (m s−1) at 850, 500, and 200 hPa were used; these variables were obtained from the National Centers for Environmental Prediction (NCEP)–Department of Energy (DOE) Global Reanalysis (R-2) daily dataset (Kanamitsu et al. 2002), which has a horizontal resolution of 2.5° × 2.5°. These daily datasets were also averaged to pentad data from 1982 to 2012. Anomalies were calculated by the deviation of the 5-day mean from the 31-yr climatology (1982–2012).

b. Changma onset index

To predict the changma onset date, it is important to precisely measure the year-to-year variations of the changma onset. In this study, the changma onset index defined by Seo et al. (2011), hereafter referred to as the Seo index, was used to depict the interannual variation of the changma onset. In their study, the changma onset is determined when the following three conditions are simultaneously satisfied: 1) a negative peak in the meridional gradient of equivalent potential temperature averaged over 122.5°–135°E and 925–700 hPa is located north of 32.5°N for the three consecutive days, 2) the 355-K isotherm of 850-hPa equivalent potential temperature averaged over 122.5°–135°E is located north of 32.5°N for the three consecutive days, and 3) the 5880-gpm isopleth at 500 hPa averaged over 122.5°–135°E is situated north of 32.5°N for the three consecutive days. The third day of these consecutive days is marked as the onset date.

In fact, the equivalent potential temperature reveals the thermodynamical features of air masses and monsoon front (Seo et al. 2011). In addition, the 5880-gpm line of 500-hPa geopotential height represents the edge of the North Pacific subtropical high (NPSH) along which southwesterly winds blow (the thermal low on the Asian continent can also contribute to the development of the southwesterly wind) to supply moist air to the Korean Peninsula. Therefore, the three conditions of the Seo index are used to consider almost all of the related factors of the changma: air temperature, humidity, and winds. As our purpose is to examine the changma onset in the framework of the large-scale dynamical and thermodynamical features (rather than just beginning of the precipitation over the peninsula), we first verify the capability of the Seo index by comparing with the Korea Meteorological Administration (KMA) index. The KMA onset index is based on several factors including low-level moisture flux, precipitation, 500-hPa geopotential height, and insolation amount. Specifically, this index is determined by 1) analyzing circulation anomalies using 200-hPa geopotential height and winds; 2) analyzing 3-day moving average precipitation, surface temperature, insolation, and sunshine duration; 3) checking the effect of low-level moisture flux; and 4) examining the location of the 5820- and 5880-gpm isolines at 500 hPa and the formation of changma front in the surface weather chart.

The correlation coefficient between these two indices is about 0.72 for the data from 1982 to 2012, showing a strong linear relationship. Although the KMA index takes account of various climate variables, we used the Seo index as it can be determined in near–real time, whereas the KMA index is decided after the changma has completely finished. Most of all, the Seo index more strongly reflects a rapid transition of the precipitation at the time of the changma onset (Fig. 2). In the plot, lag 0 represents the pentad that contains onset date. The abrupt increase in precipitation is one of the most distinct characteristics of the changma onset (Wang et al. 2004). Here the Seo index is used without removing the trend since a statistically significant trend is not detected in the data at the 95% confidence level based on the Mann–Kendall test (p value is 0.25). It implies that the interannual variation is much stronger than the linear trend.

Fig. 2.

Composite of the area-averaged (35°–40°N, 125°–130°E) precipitation from 10 pentads prior to the changma onset day to 10 pentads after the changma onset day for the Seo index (above) and the Korea Meteorological Administration (KMA) index (below) from 1982 to 2012. Zero on the abscissa indicates a pentad including the changma onset date.

Fig. 2.

Composite of the area-averaged (35°–40°N, 125°–130°E) precipitation from 10 pentads prior to the changma onset day to 10 pentads after the changma onset day for the Seo index (above) and the Korea Meteorological Administration (KMA) index (below) from 1982 to 2012. Zero on the abscissa indicates a pentad including the changma onset date.

c. Multiple linear regression model

A multiple linear regression model was developed to predict the changma onset. The regression model describes the relationship between two or more explanatory variables and a response variable by fitting a linear equation to the observed data. In this work, three predictors were used to prevent a large overfit of coefficients (Lee and Seo 2013). Several studies have suggested that three or four predictors are adequate for developing a statistical model with useful skill (Hastenrath and Greischar 1993; DelSole and Shukla 2002; Rajeevan et al. 2007).

In the first stage of developing the model, a composite difference map (early onset composite–late onset composite) of SSTAs was constructed relative to the onset date of the changma to screen the potential predictors. The model utilizes persistent behavior of the SSTAs. Next, the temporal tendency fields of the composite difference were examined to include an increasing or decreasing tendency of the SSTAs with time. These are two main sources of prediction skill. Here, SSTAs were considered because several previous studies suggested that climate predictability arises from the forcing in slowly varying lower boundary conditions such as SST (Lau et al. 2000; Wang et al. 2012; Lee and Seo 2013). The three predictors were selected based on the following three conditions. First, each predictor must have a high correlation with the changma onset index. Second, the variance inflation factor (VIF) for each predictor should be less than 2 to make sure that it does not create high multicollinearity. The existence of the high multicollinearity means that a considered variable is redundant (Choi et al. 2013). Last, the correlation coefficients among the three predictors should be less than 0.3 to ensure statistical independence.

To test the predictive capability of the statistical prediction model, a leave-one-out cross-validation method in which six years were omitted was performed to hindcast the changma onset index for the period 1982–2012 (Blockeel and Struyf 2003; Lee and Seo 2013). Blockeel and Struyf (2003) suggested choosing 20%–30% of the data as test data and having the remainder (70%–80%) as a training set for performing regression to prevent the overfitting problem (Wu et al. 2009). Therefore, six years, which is 20% of the entire hindcast period of 31 years, was used.

An evaluation of the prediction skill was done using linear correlation skill and Gandin–Murphy skill score (GMSS). The GMSS rewards for correct forecasts inversely proportional to their event frequencies and assigns penalties for incorrect forecasts directly proportionally to their event frequencies. If the multiple linear regression model has a perfect prediction skill, the GMSS will be 1.0 (Lee and Seo 2013). To visualize the forecast errors, a three-category contingency table was created. Forecasts are compared with observations over the hindcast period based on the grouping of the changma onset dates: early onset, near-normal onset, and late onset cases, which are divided by ±0.43 standard deviation. The off-diagonal cells indicate false prediction.

d. Numerical models

To assess whether the observed atmospheric circulation anomalies occur as a direct response to convective heating related to the selected predictors, numerical model experiments were performed. We used a primitive equation model based on the dynamical core of the Geophysical Fluid Dynamics Laboratory (GFDL) atmospheric global spectral model (Gordon and Stern 1982). The dynamical core model has a rhomboidal 30 resolution in the horizontal and 20 equally spaced sigma levels that change from 0.975 to 0.025. A climatological basic state in June was prescribed in the model. This basic state contains three-dimensional wind, temperature, and surface pressure fields (no moisture) and is integrated for up to 30 days, as described by Seo and Son (2012). For the three-dimensional diabatic heating over the tropical (extratropical) area, an elliptic squared cosine distribution in horizontal and a top-heavy (bottom-heavy) vertical structure is prescribed as in Wu et al. (2009). Observational differences in the vertical diabatic profile over the tropical and extratropical regions are already documented in many previous studies (e.g., Hall et al. 2001; Lin and Derome 1996).

In addition, the NCEP ocean–atmosphere Coupled Forecast System (CFS) model was used in this study to verify whether the observed atmospheric circulations occurred due to air–sea interaction process. As described by Seo and Wang (2010), the atmospheric component of the coupled model was the 2003 version of the Global Forecast System (GFS) model with a spectral truncation of T62 waves in the horizontal and a finite differencing in the vertical with 64 sigma layers. The GFS model (the atmospheric part of the CFS model) contains the nonlocal boundary layer vertical diffusion schemes developed by Hong and Pan (1996). The scheme estimates the height of planetary boundary layer and determines the vertical profile of diffusivity coefficient based on the fluxes at the surface. The oceanic component was the GFDL Modular Ocean Model version 3 (MOM3). A more detailed description can be found in Saha et al. (2006).

3. Preconditions of changma onset

To determine the characteristics of the interannual variation of the changma onset, the differences between the early and late changma onset events are presented in Fig. 3. The early and late onset events are categorized based on the normalized Seo’s changma onset index time series. The standard deviation of the changma onset index is about 7.83 (days). If the time series is greater (less) than or equal to 0.43 (−0.43) standard deviation, a changma event is defined as a late (early) onset event. From 1982 to 2012, 10 early onset events (1984, 1991, 1993, 1996, 1999, 2001, 2008, 2010, 2011, and 2012) and 8 late onset events (1982, 1987, 1988, 1989, 1992, 1995, 2003, and 2005) took place. Normal onset cases which have the index between −0.43 and 0.43 occurred in 13 cases. Again, lag 0 is defined as the pentad that includes the onset date.

Fig. 3.

The composite fields of pentad mean rainfall (shaded at intervals of 1 mm day−1), geopotential height (5880 and 5820 gpm in green contour), and meridional gradient of 850-hPa equivalent potential temperature (−2.5, −2.0, and −1.5 × 105 K m−1 in red contour) for 1982–2012, for (left) early and (right) late changma onset cases from lag pentad −2 to lag 0. Lag 0 is defined as the pentad that includes the changma onset date.

Fig. 3.

The composite fields of pentad mean rainfall (shaded at intervals of 1 mm day−1), geopotential height (5880 and 5820 gpm in green contour), and meridional gradient of 850-hPa equivalent potential temperature (−2.5, −2.0, and −1.5 × 105 K m−1 in red contour) for 1982–2012, for (left) early and (right) late changma onset cases from lag pentad −2 to lag 0. Lag 0 is defined as the pentad that includes the changma onset date.

In Fig. 3, the most notable feature is that the minimum value of the meridional gradient of 850-hPa equivalent potential temperature (red contour) almost concurs with the 5820-gpm isopleth (zonally elongated green contour), which represents the northern range of influence of the North Pacific subtropical high and the strong moist geostrophic westerly wind in the upper troposphere (not shown). Such a structure satisfies a thermal wind relation approximately and implies that the meridional gradient of equivalent potential temperature is a useful diagnostic variable for defining the changma onset (Seo et al. 2011).

An additional feature is that the NPSH expands westward and reaches the South China Sea in the early onset case, although convection around the Philippines blocks the high to move westward for the late onset case at two pentads prior to the changma onset. Moreover, the convection over the western Pacific south of 10°N is stronger in the early onset case compared to the late onset case. These differences between early and late onset cases can be more easily verified in the anomaly fields shown in Fig. 4. Here, anomaly field for early (late) onset case is calculated as the difference between the total composite field of early (late) onset events and corresponding early (late) time climatology field. Contours in each figure indicate statistically significant regions at the 90% confidence level based on the Student’s t test. As can be seen, early onset composite (Figs. 4a,b) exhibits strong convection over the western Pacific south of 10°N and positive geopotential anomaly at ~35°N, 120°E. These features suggest that the NPSH expands northwestward much more and the convection over the western Pacific is much stronger in the early onset cases than the late onset cases. The early and late onset cases show almost antisymmetric features.

Fig. 4.

The composite fields of (a) pentad mean rainfall anomaly (shaded at intervals of 1 mm day−1), and (b) geopotential height anomaly at 500 hPa (shaded at intervals of 5 m) for early changma onset cases at lag 0. (c),(d) As in (a),(b) but for late changma onset cases. Contour represents statistically significant region at the 95% level. The 500-hPa geopotential height anomalies (shaded) have been divided by 5 m to share the color bar; i.e., a 1-m level represents 5 m in (b) and (d).

Fig. 4.

The composite fields of (a) pentad mean rainfall anomaly (shaded at intervals of 1 mm day−1), and (b) geopotential height anomaly at 500 hPa (shaded at intervals of 5 m) for early changma onset cases at lag 0. (c),(d) As in (a),(b) but for late changma onset cases. Contour represents statistically significant region at the 95% level. The 500-hPa geopotential height anomalies (shaded) have been divided by 5 m to share the color bar; i.e., a 1-m level represents 5 m in (b) and (d).

Figure 5 shows the composite difference maps representing early minus late onset cases for the spring and early summer SSTAs over the Pacific and the North Atlantic, respectively. Only these two oceanic regions are shown since the correlation between the Indian Ocean and the changma index is considerably small. From March to June, strong negative SST anomalies (blue shading) appeared over the tropical central Pacific, while strong positive SST anomalies (red shading) developed over the North Pacific. In the North Atlantic region, a tripole-like pattern is pronounced; significant positive SSTAs occurred along the eastern coast of North America and extended northward and another significant positive SSTA region between South America and Africa appeared in the lower latitudes, whereas more or less zonally oriented negative anomalies occurred between two positive anomalies. Among these regions, almost all possible predictors including anomaly field (i.e., persistence) and its time evolution (i.e., tendency) with a horizontal size greater than 10° × 10° are verified based on the three criteria mentioned in section 2 and areas of each selected predictor are shown in Fig. 5 as a box. A statistical model developed with the three selected predictors is detailed in the following section.

Fig. 5.

Composite difference (early minus late onset cases) fields for sea surface temperature anomalies (SSTAs; shaded at intervals of 0.2°C) from March to June. Contours indicate statistically significant regions at the 90% confidence level based on the Monte Carlo test. Boxes represent areas of selected three predictors. North Atlantic: NAdipole index; North Pacific: NPdevelop index; north tropical central Pacific: NTCP index.

Fig. 5.

Composite difference (early minus late onset cases) fields for sea surface temperature anomalies (SSTAs; shaded at intervals of 0.2°C) from March to June. Contours indicate statistically significant regions at the 90% confidence level based on the Monte Carlo test. Boxes represent areas of selected three predictors. North Atlantic: NAdipole index; North Pacific: NPdevelop index; north tropical central Pacific: NTCP index.

4. Predictability of the changma onset

To estimate the predictability of the changma onset, an empirical prediction model was developed using the multiple linear regression method with three predictors that are strongly correlated to the changma onset index. One example of the model constructed is

 
formula

where Y is changma onset day expressed as day of year, NTCP represents the SSTAs averaged from late April to mid-May (24–27 pentad mean) in the north tropical central Pacific region (0°–15°N, 165°–135°W), and NAdipole denotes the developing phase of dipolar SSTAs. The NAdipole index is calculated by both areal and temporal differences; first subtracting the midlatitude North Atlantic (35°–45°N, 65°–50°W) SSTA from the tropical North Atlantic (0°–15°N, 55°–30°W) SSTA and then subtracting late March from early April (18–20 pentad mean minus 15–17 pentad mean). The term NPdevelop, representing the developing tendency of the SST anomalies over the North Pacific (20°–40°N, 180°–140°W) region, is calculated by subtracting early April from late April (22–25 pentad mean minus 17–20 pentad mean) SSTAs. The specific period for each predictor is statistically determined by a forward stepwise regression method (Lee and Seo 2013) with a constraint that the predictors are springtime variables to forecast onset of changma occurring in late June (i.e., at least one month lead time forecast). This method is designed to select the optimal predictors from potential predictors that maximize the correlation coefficient with the onset date and also minimize the internal collinearities among candidate predictors. Note here that the last pentad data available for constructing the prediction model are set as 27 (centered on May 8) in this study because we intend to predict changma onset at least one month ahead. The coefficients of the specific regression model described above were computed using the hindcast period (1982–2011) and used for predictions during the years 2012–14. The calculated coefficients appear to be robust since the sign of each of the coefficients is preserved for five different subsets and even the coefficient ranges are fairly well inside the 10th and 90th percentile thresholds estimated from 2500 random trials (not shown).

The magnitude of regression coefficients, after dividing the equation with the standard deviation of the changma onset index, represents the relative weight among predictors since the predictors are normalized by their respective standard deviations. So NAdipole is seen to have the largest contribution to the predictand. The correlation coefficient between the changma onset index and each predictor is shown in Table 1. All three predictors have significant correlation with the changma onset index at the 95% confidence level. The low correlation coefficients among the selected predictors in Table 2 demonstrate the mutual independency.

Table 1.

Correlation coefficient between the changma onset index and each predictor for the period from 1982 to 2012.

Correlation coefficient between the changma onset index and each predictor for the period from 1982 to 2012.
Correlation coefficient between the changma onset index and each predictor for the period from 1982 to 2012.
Table 2.

Correlation coefficients among the selected predictors for the period from 1982 to 2012.

Correlation coefficients among the selected predictors for the period from 1982 to 2012.
Correlation coefficients among the selected predictors for the period from 1982 to 2012.

To test the predictive capability, a cross-validation method was used to make a hindcast of the changma onset. This cross-validation method sequentially left out six years from the period 1982 to 2012, derived a forecast model using the remaining years, and validated it against unused years. For example, the first six years, from 1982 to 1987, are used for testing and the remaining years, from 1988 to 2012, are used for training the regression equation. The second six years, from 1988 to 1993, are validated using years from 1982 to 1987 and from 1994 to 2012. Surprisingly, the forecast using this method showed that the interannual variation of the changma onset was reproduced considerably well even though all three predictors used only spring SSTAs without summer information (Fig. 6). The temporal correlation coefficient between the observation and the 31 yr of leave-6 yr-out cross-validated hindcast is about 0.73 and the GMSS is about 0.70 (Fig. 6).

Fig. 6.

Time series of the observed (black dashed line) and predicted (red line) changma onset date. The horizontal lines divide early, normal, and late cases, accounting for 33.33% each. The temporal correlation skill between the observation and prediction is 0.73, RMSE is 0.69 (in unit of Julian days), and the Gandin–Murphy skill score (GMSS) is 0.70.

Fig. 6.

Time series of the observed (black dashed line) and predicted (red line) changma onset date. The horizontal lines divide early, normal, and late cases, accounting for 33.33% each. The temporal correlation skill between the observation and prediction is 0.73, RMSE is 0.69 (in unit of Julian days), and the Gandin–Murphy skill score (GMSS) is 0.70.

To diagnose the forecast errors, a 3 × 3 contingency table was used (Table 3). The diagonal cells from the top left to the bottom right indicate the years with successful forecasts, whereas off-diagonal cells indicate false forecasts. The ratio of the number of correct predictions to the total number of years was calculated to be about 71%. In the following section, dynamic processes of each predictor will be analyzed to support the robustness of the statistical prediction model developed in this study.

Table 3.

A 3 × 3 contingency table for the validation of the statistical changma onset prediction model. The abscissa represents predictions, and the ordinate represents observations. Late, normal, and early years were determined by ±0.43 standard deviation thresholds. The ratio of the number of correct predictions to the total number of years is about 71%.

A 3 × 3 contingency table for the validation of the statistical changma onset prediction model. The abscissa represents predictions, and the ordinate represents observations. Late, normal, and early years were determined by ±0.43 standard deviation thresholds. The ratio of the number of correct predictions to the total number of years is about 71%.
A 3 × 3 contingency table for the validation of the statistical changma onset prediction model. The abscissa represents predictions, and the ordinate represents observations. Late, normal, and early years were determined by ±0.43 standard deviation thresholds. The ratio of the number of correct predictions to the total number of years is about 71%.

5. Possible dynamic mechanisms of predictors

a. North tropical central Pacific index

In this section, the relationship between the north tropical central Pacific (NTCP) index (a time series of an area mean (0°–15°N, 165°–135°W) from late April to mid-May, representing anomalous cooling or warming in the tropical central Pacific region in spring) and the changma onset is analyzed using a composite difference method. For the composite difference, weak cases (equivalent to anomalous warm cases) were subtracted from strong cases (equivalent to anomalous cold cases). Seven strong (seven weak) cases were selected from years in which the value of the normalized NTCP index was less (greater) than or equal to −0.75 (+0.75) standard deviation. Figure 7 shows the composite difference maps of SSTAs (left panels), 850-hPa geopotential height anomalies and wind anomalies (middle panels), and precipitation anomalies (right panels) from mid-May to mid-June. The 850-hPa geopotential height anomaly field is used to demonstrate physical processes associated with low-level moisture flux. From May to June, strong negative SSTAs were observed over the tropical central Pacific, whereas positive SSTAs were observed over the subtropical central Pacific. The negative SSTAs sustained over the tropical central Pacific from late spring to early summer can be explained by the positive Bjerknes feedback. Initial negative SSTAs in the equatorial central Pacific increase the east–west SST gradient (warm over the far-western tropical Pacific and cold over the central Pacific) and thus strengthen the Walker circulation (Gill 1980), resulting in stronger trade winds along the equator. The anomalous trade winds, shown in Figs. 7d–f, in turn drive an upwelling that further reinforces the negative SSTAs (Wang et al. 2012; Kug et al. 2009). Therefore, the NTCP index in spring can persist until June and acts as a potential forcing in June.

Fig. 7.

Composite difference maps (strong minus weak cases) of (a)–(c) SSTAs [contour intervals (CI) of 0.3°C], (d)–(f) 850-hPa geopotential anomaly (CI 5 gpm) with 850-hPa wind anomaly, and (g)–(i) precipitation anomaly (shaded with intervals of 2 mm day−1) from late May to mid-June using NTCP index. Shading in the left and middle panels and contours in the right panels indicate statistical significant regions at the 90% confidence level.

Fig. 7.

Composite difference maps (strong minus weak cases) of (a)–(c) SSTAs [contour intervals (CI) of 0.3°C], (d)–(f) 850-hPa geopotential anomaly (CI 5 gpm) with 850-hPa wind anomaly, and (g)–(i) precipitation anomaly (shaded with intervals of 2 mm day−1) from late May to mid-June using NTCP index. Shading in the left and middle panels and contours in the right panels indicate statistical significant regions at the 90% confidence level.

The equatorial easterly wind anomalies from mid-May to mid-June enhance convection over the far-western tropical Pacific and seas near the Maritime Continent; the positive precipitation anomaly is shown in Figs. 7g–i. The anomalous precipitation increased the diabatic heating, which acts to induce a cyclonic anomaly around the South China Sea in June (Gill 1980), and to the northeast of the cyclonic anomaly and southeast of the Korean Peninsula an anticyclonic anomaly was induced. This pattern is consistent with the positive phase of the Pacific–Japan pattern (Kosaka and Nakamura 2008; Yamaura and Tomita 2014). The NTCP index is significantly correlated with the Niño-3.4 index (SSTAs averaged over 5°S–5°N, 170°–120°W) from 1982 to 2012 with r = 0.87 for the month of May. It suggests that the NTCP index reflects a persisting La Niña event signifying a stronger than normal western North Pacific subtropical high, and vice versa. Also, the region of NTCP index coincides with the maximum location of the equatorial central Pacific cooling in Wang et al. (2012), who proposed that the enhanced western North Pacific subtropical high concurs with equatorial central Pacific cooling.

The observed circulation response to the convective forcing over the far-western tropical Pacific and near the Maritime Continent can be confirmed by a dynamical core atmospheric general circulation model experiment as presented in section 2d. To mimic diabatic heating over this region, a heating anomaly with a center at 15°N, 130°E was imposed (Fig. 8). To prevent the model from drifting, the most unstable normal mode has been removed by subtracting the initial field (i.e., the imposed background climatological basic state) from the field after integrated forward just one time step (e.g., Jin and Hoskins 1995; Seo and Son 2012). The model background field is sustained almost as it was initialized by up to days 10–13. So up to this time frame, the anomaly evolution in the model is dominated by the almost linear response to the external forcing. Anomalies in this study are defined as the deviations of the day-15 runs from the initial background field. As a result of the external heating, a negative geopotential height anomaly over the South China Sea and a positive geopotential height anomaly to the south of Japan occurred at the 850-hPa level, which is similar to observation (Fig. 7f). The formation of the anomalous anticyclone is not sensitive to the exact location of a heating anomaly (i.e., forcing at any point in the area 5°S–5°N, 130°–145°E generates an almost identical response). This result clearly demonstrates that the convective heating over the western tropical Pacific affects midlatitude height field by inducing the Pacific–Japan-like wave pattern. The complicated pattern over the eastern Eurasian Continent is due to the growth of unstable baroclinic synoptic-scale waves along the summertime jet stream and their interaction with the circulation response to the forcing.

Fig. 8.

The horizontal shape (at the 850-hPa level) of imposed atmospheric diabatic forcing (red shading, intervals of 0.2 K day−1) for the GFDL model experiment and the 850-hPa geopotential height response to the forcing (contour, intervals of 3 gpm).

Fig. 8.

The horizontal shape (at the 850-hPa level) of imposed atmospheric diabatic forcing (red shading, intervals of 0.2 K day−1) for the GFDL model experiment and the 850-hPa geopotential height response to the forcing (contour, intervals of 3 gpm).

Figure 9 shows the composite difference fields for 850-hPa geopotential anomalies and precipitation anomalies right before the climatological changma onset date (pentad 35). The zonal difference in tropical convection, signifying enhanced convection over the far-western tropical Pacific and reduced convection to its east, is consistent with the tropical central Pacific SST cooling. A strong convection over the far-western Pacific lead to an early changma onset by inducing the anticyclonic circulation anomalies to the southeast of the Korean Peninsula at pentad 34 (15–19 June) (Fig. 9b; see also Fig. 7f), and significant precipitation anomalies appeared over the Korean Peninsula at this period (Fig. 9d), which is one pentad earlier than the climatological mean changma onset date.

Fig. 9.

Composite difference maps (strong minus weak cases) for (a),(b) 850-hPa geopotential height and 850-hPa wind anomalies (contour in gpm; vector in m s−1) and (c),(d) precipitation anomalies (shaded at intervals of 2 mm day−1) (blue is positive anomaly; red is negative anomaly) before the climatological changma onset day using NTCP index. Statistical significance at the 90% confidence level is indicated by shading (left panels) and contours (right panels).

Fig. 9.

Composite difference maps (strong minus weak cases) for (a),(b) 850-hPa geopotential height and 850-hPa wind anomalies (contour in gpm; vector in m s−1) and (c),(d) precipitation anomalies (shaded at intervals of 2 mm day−1) (blue is positive anomaly; red is negative anomaly) before the climatological changma onset day using NTCP index. Statistical significance at the 90% confidence level is indicated by shading (left panels) and contours (right panels).

In summary, a positive feedback of atmosphere–ocean interaction forms favorable conditions for maintaining the negative SSTAs over the tropical central Pacific from May to June. These persisting SSTAs force enhanced convection near the Maritime Continent over the western Pacific. Through the Pacific–Japan teleconnection, an equivalent-barotropic anticyclonic anomaly develops to the southeast of the Korean Peninsula, which helps the NPSH advance northward, resulting in an earlier changma event. Therefore, the convective anomaly located over the far-western Pacific is key in bridging the tropical central Pacific cooling and the earlier changma onset.

b. Dipole North Atlantic index

The dipole North Atlantic (NAdipole) index denotes a time series of the time difference (18–20 pentad mean minus 15–17 pentad mean) and area difference between the tropical North Atlantic region (0°–15°N, 55°–30°W) and the midlatitude North Atlantic region (35°–45°N, 65°–50°W). The positive phase of this index represents the temporal enhancement of dipolar SSTAs with positive SSTAs in the tropical North Atlantic region and negative SSTAs in the higher-latitude region. The composite difference method (strong minus weak cases) was also used to analyze the relationship between the NAdipole index and the changma onset. On the contrary to the NTCP index, six strong (seven weak) years were selected from those in which the normalized NAdipole index is greater (less) than or equal to +0.75 (−0.75) standard deviations.

Figure 10 shows the composite difference maps for SSTAs from mid-April to early June. In relation to the NAdipole index, a prominent tripole-like pattern emerges with the positive SSTAs in the tropical ocean and subpolar region and the negative SSTAs along the East Coast of the United States (in fact, this pattern is closely associated with the negative phase of NAO). The increasing tendency in this signal influences the changma onset. Figure 11 shows a composite difference maps for the 200-hPa (Fig. 11a) and 850-hPa (Fig. 11b) geopotential anomaly fields in June. It appears that diabatic heating and cooling (not shown) related to the NAdipole index generate positive and negative geopotential height anomalies propagating eastward across the Eurasian continent at the upper tropospheric level and this upper-level wave propagation induces and strengthens the lower-level pressure anomalies downstream through a Petterssen’s B-type mechanism (i.e., a mechanism that the upper-level disturbance induces the lower-level disturbance; Petterssen and Smebye 1971; Rotunno and Fantini 1989). The positive 850-hPa geopotential height anomaly to the southeast of the Korean Peninsula contributes to the westward expansion of the NPSH, leading to the changma onset. Similar wave train–like teleconnection patterns have been reported in previous studies (Li et al. 2007; Yamaura and Tomita 2011; Wu et al. 2009; Seo et al. 2012; Lee and Seo 2013).

Fig. 10.

Composite difference fields (strong minus weak cases) of SSTAs (contours, °C) from mid-April to early June using the NAdipole index. Shading indicates statistical significance at the 90% confidence level.

Fig. 10.

Composite difference fields (strong minus weak cases) of SSTAs (contours, °C) from mid-April to early June using the NAdipole index. Shading indicates statistical significance at the 90% confidence level.

Fig. 11.

Composite difference maps (strong minus weak cases) of geopotential height anomaly (contour, gpm) and wind anomaly (vectors, m s−1) using the NAdipole index at (a) 200 and (b) 850 hPa. Shading and wind vectors are statistically significant at the 90% confidence level.

Fig. 11.

Composite difference maps (strong minus weak cases) of geopotential height anomaly (contour, gpm) and wind anomaly (vectors, m s−1) using the NAdipole index at (a) 200 and (b) 850 hPa. Shading and wind vectors are statistically significant at the 90% confidence level.

To verify whether these observed geopotential height anomalies are induced by the diabatic forcing related to the dipolar SSTAs or the tripolar SSTAs over the North Atlantic Ocean, numerical model experiments were conducted. First, the diabatic heating anomalies associated with the dipolar SSTAs were added to the GFDL dynamical core model. The locations are shown in Fig. 12, with red shading indicating the heating anomaly centered at 15°N and 30°W and blue shading representing the cooling anomaly centered at 45°N and 60°W. As a result of the diabatic forcing anomalies, a zonally propagating wave train developed. A positive geopotential height anomaly occurred to the southeast of the Korean Peninsula appeared, similar to the observation (Fig. 11a). To verify whether the diabatic heating/cooling related to the tripolar SSTAs results in a circulation pattern significantly more similar to the observation, an additional experiment was conducted. This time, tripolar diabatic heating/cooling anomalies were used as an external forcing to the model (i.e., the subpolar heating was added to the previous dipolar forcing experiment). The result indicates that the teleconnection feature located between 30° and 45°N is almost identical; only a slight difference appears in the vicinity of the northernmost positive forcing (not shown). Thus, since the Korean Peninsula is located at ~35°N, the dipolar NAO centers below 45°N have much more crucial influence on the changma.

Fig. 12.

Location of external forcing added to the model (red indicates heating, blue indicates cooling, in unit of 0.1 K day−1) and the 200-hPa geopotential response to the forcing (contours, m).

Fig. 12.

Location of external forcing added to the model (red indicates heating, blue indicates cooling, in unit of 0.1 K day−1) and the 200-hPa geopotential response to the forcing (contours, m).

Figure 13 shows composite difference maps of the 850-hPa geopotential height anomaly with the 850-hPa wind anomaly (left panel) and the precipitation anomaly (right panel) prior to pentad 35, the climatological changma onset date. At pentads 33 and 34, a significant positive geopotential height anomaly was located south of the Korean Peninsula with significant southwesterly wind supplying moist air to the peninsula. Enhanced precipitation is apparently seen at pentad 34, one pentad earlier than the climatological onset date. One notable feature compared with the NTCP index (Fig. 9a) and the NPdevelop index (which will be shown in Fig. 16a) is that, at pentad 33 (Fig. 13a), the NPSH expanded significantly toward the west all the way even up into southern China.

Fig. 13.

Composite difference maps (strong minus weak cases) for (a),(b) 850-hPa geopotential height anomaly and 850-hPa wind anomaly (contour in gpm; vector in m s−1) and (c),(d) precipitation anomaly (shading in mm day−1) (blue is positive and red is negative anomaly) before the climatological changma onset day using NAdipole index. Shading in the left and contouring in the right panels indicate statistical significant regions at the 90% confidence level.

Fig. 13.

Composite difference maps (strong minus weak cases) for (a),(b) 850-hPa geopotential height anomaly and 850-hPa wind anomaly (contour in gpm; vector in m s−1) and (c),(d) precipitation anomaly (shading in mm day−1) (blue is positive and red is negative anomaly) before the climatological changma onset day using NAdipole index. Shading in the left and contouring in the right panels indicate statistical significant regions at the 90% confidence level.

To summarize, when a strong dipole SSTA pattern appears in the North Atlantic with positive SSTA in the tropical region and negative SSTA in the extratropical region, zonally propagating waves are excited such that these help the NPSH expand northwestward. This process causes the changma to begin earlier than normal.

c. North Pacific index

The North Pacific (NPdevelop) index is a time series of 22–25 pentad mean minus 17–20 pentad mean SSTAs in the central North Pacific region, particularly to the east of the International date line (20°–40°N, 180°–140°W). Similar to what was done with the NAdipole index, seven weak cases are subtracted from eight strong cases. Strong cases for the NPdevelop index represent enhanced warming over the central North Pacific region with time.

Figure 14 shows composite difference maps for the SSTAs (left panels) and 850-hPa geopotential height and wind anomalies (right panels). The SSTA pattern consists of a prominent warm anomaly south of 40°N extending from 150°W to the coast of Asia through April to June, and a significant cold anomaly along the west coast of North America and weak cold SSTAs around the Sea of Okhotsk. This anomalous warm SST pattern in the central basin of the North Pacific can persist through April to June by air–sea interaction process. Climatologically the westerly winds are dominant at ~30°N from April to June (not shown), so anomalous easterlies in Fig. 14d indicate the weakening of the surface wind. The decreased surface wind speed reduces surface evaporation (not shown, but a significant negative latent heat flux anomaly exists) and thus warms SST. In other words, the negative latent heat flux can act as a warming effect on SST anomaly (Wang et al. 1999). Also the significant negative sensible heat flux anomaly (not shown) indicates that the air temperature is relatively warmer and the heat is absorbed by the ocean which leads to the warm SST anomaly. Also, surface friction caused by the southeasterly wind (Fig. 14d) leads to the meridional advection of the ocean surface; this surface wind stress induces Ekman drift to maintain the positive SST anomalies over the central North Pacific (see Wu and Kinter 2010). So both the surface heat fluxes and wind stress–driven SST advection are important for developing/maintaining positive SST anomalies over the North Pacific (Cayan 1992).

Fig. 14.

Composite difference maps (strong minus weak cases) for (a)–(c) SSTAs (contours in °C) and (d)–(f) 850-hPa geopotential height (contours in gpm) and 850-hPa wind anomalies (vectors in m s−1) from April to June using the NPdevelop index. Shading indicates statistically significant region at the 90% confidence level.

Fig. 14.

Composite difference maps (strong minus weak cases) for (a)–(c) SSTAs (contours in °C) and (d)–(f) 850-hPa geopotential height (contours in gpm) and 850-hPa wind anomalies (vectors in m s−1) from April to June using the NPdevelop index. Shading indicates statistically significant region at the 90% confidence level.

In June, the North Pacific region showed a strong meridional gradient of SSTAs (Fig. 14c) along 45°N (positive SSTAs to the south and negative SSTAs to the north around 150°E160°W). This sharp local gradient of SSTAs can increase near-surface baroclinicity, which in turn can induce westerly flow in midlatitude (Sampe et al. 2010; Lee and Seo 2013). A significant westerly anomaly along 45°N at 850 hPa occurring over this region (Fig. 14f) in June also appeared along 45°N at the middle and upper troposphere (not shown). Related to the westerly wind anomaly, a significant equivalent barotropic cyclonic anomaly was located over the Okhotsk Sea in June (Fig. 14f), implying a weakening of the Okhotsk high. In conjunction with the weakening of the Okhotsk high, the NPSH can progress northward much more easily; then anomalous anticyclonic circulation occurred southeast of the Korean Peninsula in June.

To verify whether these positive SSTAs over the NPdevelop index region and air–sea coupling effect can induce the observed geopotential height anomalies, CFS model simulations using the simplified Arakawa–Schubert (SAS) scheme (Pan and Wu 1995) were conducted. For this, first, a control run of this experiment was performed using the atmospheric model (GFS) by forcing a climatological SST field derived from a coupled run to the model (which corresponds to a decoupled experiment). In the second experiment, 1°C was added to the NPdevelop region (20°–40°N, 180°–140°W) in the previous control run from April to May, and then the ocean and atmosphere were fully coupled without any additional forcing from June onward. The subsurface initial conditions are prepared by separate ocean model integrations using the changed SST field. This experiment is designed to intend to evaluate the effects of the positive SSTAs over the central North Pacific region in spring and the subsequent air–sea interaction process in June. The integration (Fig. 15; the anomaly pattern plotted by subtracting the 15–25 June mean field of the control run from the forced run for the same period) shows the development of an anomalous cyclonic circulation over the Okhotsk Sea (signifying the weakening of the Okhotsk high) and a much stronger anticyclonic circulation anomaly to the east of the Korean Peninsula, supporting the hypothesis that the anomalous warm SSTAs over the NPdevelop index can induce weakening of the Okhotsk high and thus help the NPSH progress northward much more easily.

Fig. 15.

A difference map of 850-hPa geopotential height anomaly (contours, gpm) for the period around the climatological mean changma onset date (15–25 June averaged) between the air–sea coupled CFS run conducted by adding 1°C in the NPdevelop index region (20°–40°N, 180°–140°W) and the uncoupled GFS run forced by climatological SST field produced by a coupled CFS run.

Fig. 15.

A difference map of 850-hPa geopotential height anomaly (contours, gpm) for the period around the climatological mean changma onset date (15–25 June averaged) between the air–sea coupled CFS run conducted by adding 1°C in the NPdevelop index region (20°–40°N, 180°–140°W) and the uncoupled GFS run forced by climatological SST field produced by a coupled CFS run.

Figure 16 shows the composite difference fields for 850-hPa geopotential height anomalies (left panels) and precipitation anomalies (right panels) prior to the climatological changma onset date. At pentad 34, significant westerly winds appeared around 45°N, and cyclonic and anticyclonic circulation anomalies were located to the north and south of the anomalous flow, respectively. Significant southwesterly winds blew along the northwestern edge of the anticyclonic circulation to allow the supply of moist air to reach the Korean Peninsula. In addition, a significant rainband formed on pentad 34, one pentad earlier than the normal onset date.

Fig. 16.

Composite difference maps (strong minus weak cases) for (left) 850-hPa geopotential height anomaly and 850-hPa wind anomaly (contour in gpm; vector in m s−1) and (right) precipitation anomaly (shading in mm day−1) (blue is positive and red is negative anomaly) before the climatological changma onset day using the NPdevelop index. Shading in the left and contouring in the right panels indicate statistical significant regions at the 90% confidence level.

Fig. 16.

Composite difference maps (strong minus weak cases) for (left) 850-hPa geopotential height anomaly and 850-hPa wind anomaly (contour in gpm; vector in m s−1) and (right) precipitation anomaly (shading in mm day−1) (blue is positive and red is negative anomaly) before the climatological changma onset day using the NPdevelop index. Shading in the left and contouring in the right panels indicate statistical significant regions at the 90% confidence level.

Essentially, when strong positive SSTAs over the central North Pacific region develop and persist from April to June by air–sea interaction, an oceanic front forms along near 45°N over the western and central North Pacific. This oceanic front induces near-surface baroclinic instability, and the anomalous westerly wind weakens the Okhotsk high, allowing the NPSH to progress northward. In this way, the changma can begin earlier than the climatological changma onset date.

6. Summary

The changma begins as the North Pacific subtropical high (NPSH) expands northwestward and causes the changma front to progress to the Korean Peninsula. Compared with late onset years, the NPSH in early onset cases expands significantly more northwestward to reach the South China Sea. Moreover, anomalously stronger convection over the far-western tropical Pacific acts to push the NPSH northward. Therefore, investigation of the mechanisms of how the anticyclone moves northwestward is a key for the understanding of interannual variability of the changma onset date.

In this study, a dynamics-based statistical prediction model was developed using the multiple linear regression equation. According to the selection criteria that should possess high correlation with the changma index, low VIF, and mutual independency, three indices (NTCP, NAdipole, and NPdevelop) were selected. The prediction model constructed using these three indices showed considerable predictability. The correlation coefficient between the observation and the prediction was about 0.73 and the GMSS was about 0.70 for the period from 1982 to 2014. Therefore, the selected three SST predictors play a role in the prolonged predictability source.

To ensure robustness and stability of the prediction model, the dynamical mechanisms of each of the predictors were analyzed. First, the anomalous cooling over the NTCP in spring can act as a forcing in June because the anomalous SSTAs persist through June by the Bjerknes feedback. The anomalous cooling over the NTCP and associated anomalous trade winds caused strong convection over the western tropical Pacific and the Maritime Continent. Diabatic heating related to this strong convection in turn induces the Pacific–Japan teleconnection pattern, which produces a positive geopotential height anomaly to the southeast of the Korean Peninsula. Second, when there exists an enhancing tendency in the anomalous dipole SSTA pattern over the North Atlantic in spring (NAdipole) which can persist until June, this can act as a forcing on the initiation of changma. Tropical diabatic heating and midlatitude diabatic cooling related to this dipole pattern created a barotropic structure of positive geopotential height anomaly around 45°N and 25°W. This wave propagated zonally across the Eurasian continent along the waveguide formed by the jet stream, and a positive geopotential height anomaly appeared southeast of the Korean Peninsula. At the lower level, a zonally elongated positive geopotential height anomaly represents both westward and northward expansion of the NPSH.

Last, the developing positive SST anomaly over the central North Pacific region in spring (NPdevelop), which can be maintained through June by air–sea interaction, plays a role in advancing the changma onset. The strongly developed warm anomaly in June creates a steeper meridional gradient of SST in the North Pacific, and thus the enhancement in low-level baroclinic instability. As a result, an anomalous westerly wind was induced along the oceanic front. To the north of this anomalous westerly wind, cyclonic circulation was induced, implying the weakening of the Okhotsk high. Therefore, the NPSH can move northward more easily than during a normal year. It seems that the NTCP and NPdevelop indices force the NPSH to expand northward, and the NAdipole index forces the high to expand both westward and northward.

In this study, a dynamics-based statistical prediction model was developed to predict the changma onset. As the prediction skill of the developed model shows considerable predictability, this statistical model can be used for practical changma onset forecasting since the predictors can be easily monitored and are available in real time.

Note that the two tendency predictors and one persistent predictor (NTCP, NAdipole, and NPdevelop) selected in this work provide an optimal prediction skill, but we present the basic statistics for different predictors. In this case, we selected NTCPdevelop for a tendency predictor and NA and NP for two persistence predictors. The following summarizes the areas and periods for these predictors: (a) the NTCPdevelop index: 5°–15°N, 165°–135°W, 16 May–4 June average minus 21 April–10 May average; (b) the NA index: [0°–15°N, 55°–30°W] − [40°–50°N, 70°–60°W], 16–20 April average; and (c) the NP index: 0°–40°N, 180°–140°W, 21–25 April average. Prediction using the constructed statistical model results in correlation skill of 0.47 and GMSS of 0.43, which are considerably smaller than the skills proposed in the study (0.73 and 0.70, respectively).

In addition, the absolute correlation values between changma onset index and the above predictors range from 0.37 to 0.44, about 20% smaller compared to the original correlations (see Table 1). Also, as done in Table 2, we computed the correlations among the selected predictors. Even though the independence between NTCPdevelop and NA and between NP and NTCPdevelop is guaranteed, NA and NP are not independent. Thus, it is preferable to use NTCP, NAdipole, and NPdevelop as the predictors for the statistical model. However, it should be noted that the statistical model using the selected persistence and tendency predictors in this study is not the only way for the skillful prediction of the changma onset. Other possibilities including use of SSTA over other regions or slowly varying atmospheric signals or soil moisture and snow depth (e.g., Yang et al. 2011) may exist, of course, which will be sought in future work.

Acknowledgments

This work was funded by the Korea Meteorological Administration Research and Development Program under Grant KMIPA 2015–2113. It is also supported by the National Research Foundation of Korea grant funded by the Korean government (MSIP; NRF-2014R1A2A1A11051818). The authors would like to acknowledge the support from the Korea Institute of Science and Technology Information (KISTI). We thank the three reviewers for their constructive and helpful comments and suggestion, which improved the original manuscript.

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