1. Introduction
The prediction of the East Asian summer precipitation (EASP) has been a great challenge with significant subseasonal variations mainly influenced by the East Asian summer monsoon (Ding 2007). The subseasonal variation of the EASP is often associated with flood or drought disasters in East Asia (Liu et al. 2020; Takaya et al. 2020; Zhou et al. 2021), causing great casualties and economic losses. Therefore, accurate prediction of the EASP is of great value for disaster prevention and mitigation.
However, the prediction of the EASP still remains a great challenge. For example, Wang et al. (2009a) demonstrated insignificant prediction skill (around 0.1) in East Asia at a 1-month lead time from the multimodel ensemble mean of the 14 climate model systems in the Climate Prediction and its Application to Society project by the Asian-Pacific Economic Cooperation Climate Center (APCC/CliPAS). Meanwhile, Liang and Lin (2018) reported a statistically significant skill over the mainland of East Asia in the forecasting system of Environment and Climate Change Canada but only for up to 1 week. Although many efforts have been made to improve the EASP prediction, the prediction skill of the EASP is still unsatisfactory. For example, Wang and Fan (2009) applied a new scheme considering both model predictions and observed spatial patterns of historical “analog years” on six model ensemble hindcasts of the Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction. The spatially averaged anomaly correlation coefficient (ACC) skill of ensemble mean EASP was increased from 0.12 to 0.22 using the new scheme. Gong et al. (2016) revealed that the EASP prediction skill in the Beijing Climate Center Climate System Model has low prediction skill over most of East Asia. They tried three methods to improve the prediction, but the best method only improved the averages of the spatial ACC from 0.03 to 0.22, which was still very low. Thus, the EASP prediction still has much room for improvement.
Typically, there are two kinds of sources responsible for the prediction uncertainties in dynamical systems. First, the low prediction skill is due to initial errors and model errors in the prediction, which can be improved by the assimilation and model development, respectively. Second, the low prediction skill stems from the low intrinsic predictability limit (IPL) in dynamical systems. The IPL is an intrinsic property of dynamical systems and is determined by its nonlinearity and stochasticity, which cannot be improved. The IPL study could help us, on the one hand, to quantify the upper limit of the prediction capability and, on the other hand, to understand the physical processes inherent to predictability sources. One important aspect of the IPL study is the identification of the most predictable pattern, which plays a crucial role in prediction improvement (e.g., Huang et al. 2019; Wang et al. 2015). Through the identification of the most predictable pattern, we can have a more predictable target than conventional ones. Then, the prediction skill of the variability, at least in some areas, could be improved further (e.g., Li and Tang 2021a; Wu and Tang 2019; Xing et al. 2017; Yim et al. 2016).
Previous studies on the EASP predictability focused on the actual prediction skill determined by the model quality and the accuracy of the initial conditions. The EASP is a complex dynamical system inherent to dynamic, thermodynamic, and moisture processes (Miao et al. 2019; Ng et al. 2019; Zhang et al. 2021), which are highly nonlinear and stochastic in nature. Thus, exploring EASP prediction from the IPL perspective is of high interest. It is natural to consider the IPL problem of EASP: whether and how much the IPL impedes our prediction capability of the EASP.
In particular, previous studies have also found obvious differences in the characteristics of the EASP between early summer [May–June (MJ)] and late summer [July–August (JA)], including large-scale circulation (e.g., Li and Zhou 2011; Yu and Zhou 2007), ocean impact (e.g., Li and Zhou 2011), and principal modes (e.g., Wang et al. 2009b). We examined the significance of the EASP difference in the two subseasons using rainfall data from 1999 to 2018. The results are consistent with those obtained by Wang et al. (2009b), who used rainfall data from 1979 to 2007; that is, the climatology of the daily rainfall depicts two distinct patterns (Fig. 1). The large rainfall climatology in MJ is located in South China and the eastern Yellow Sea. Meanwhile, the large rainfall climatology in JA is located in North China, the Korean Peninsula and surrounding waters, and the South China Sea (SCS). Therefore, it is reasonable to divide the EASP into two subseasons: early summer (MJ) and late summer (JA). These results motivate us to examine whether there are differences in the IPL of EASP between early and late summer. In this study, the predictability of the EASP is investigated in MJ and JA, respectively by employing a predictability analysis inherent to the IPL. We first explore the predictable patterns of MJ and JA rainfall, respectively. The predictability sources of the two predictable patterns in early and late summer are then further analyzed and compared.
Climatological rainfall (mm day−1) in (a) May–June and (b) July–August.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
This study is organized as follows. The data and methods are briefly introduced in section 2. Section 3 elucidates the subseasonal predictability (including the prediction skill and most predictable patterns) of the East Asian rainfall in early and late summer. The predictability sources during the two subseasons are further analyzed in section 4. Section 5 provides a summary and discussion.
2. Data and methods
a. Data
The rainfall hindcasts are from the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble hindcasts in the S2S project database (Vitart 2017). The ECMWF model is chosen because of its better skill than others for predicting the subseasonal Asian summer monsoon precipitation (Li et al. 2023). The hindcasts were obtained in the year 2020 by the model version CY47R1. The ensemble hindcast used in this study started on 3 January every year from 2000 to 2018 with an interval of 7 days. Each hindcast lasted 46 days, with an ensemble size of 11. A 4-day averaging window is performed over the daily lead times of the hindcasts, that is, hindcasts averaging over lead times of 1–4, 5–8, 9–12, and 13–16 days (hereinafter referred to as 1–4d, 5–8d, 9–12d, and 13–16d, respectively) are used to explore the issues in this study. The 4-day averaging window is chosen according to the results of our sensitivity experiments: by comparing the rainfall prediction skill of the ECMWF hindcasts with various lead-time averaging windows, it was found that for most regions the 4-day window makes the best use of the useful information in the hindcasts than the others indicated by its relatively higher skill than the others.
The rainfall dataset used as observation is the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis TRMM 3B42, version 7 (TMPA; Huffman et al. 2016). The study domain is the East Asia region (20°–45°N, 100°–130°E). We only focus on the summer rainfall in East Asia; thus, the hindcasts with the initial times in May, June, July, and August are used in this study. All data are interpolated to a 1.0° × 1.0° resolution.
Several reanalysis datasets are used in the predictability sources analysis, including the daily outgoing longwave radiation (OLR) from the National Oceanic and Atmospheric Administration interpolated OLR data (Liebmann and Smith 1996) and the daily sea level pressure (SLP), geopotential height (GPH) at 850 hPa, zonal and meridional winds at 850 hPa (UV850), and relative humidity (RH) from the fifth-generation atmospheric reanalysis produced at the ECMWF (ERA5; Bell et al. 2021). All reanalysis data are from January 2000 to December 2018.
The boreal summer intraseasonal oscillation (BSISO) index is calculated using the multivariate empirical orthogonal function (EOF) analysis using daily OLR and zonal wind at 850 hPa (Lee et al. 2013). The normalized time series of the first and second multivariate EOFs are referred to as BSISOI1 and BSISOI2, respectively, representing the northward propagating BSISO over the Asian summer monsoon region. The Pacific–Japan (PJ) pattern index is defined as the difference in the GPH anomalies at 850 hPa between two grid points: 40°N, 150°E and 25°N, 125°E (Wakabayashi and Kawamura 2004).
b. Predictability assessment metrics
c. APT methods
The corresponding predictable components can be obtained by qTx, where x represents original data. Then, the spatial pattern associated with each component is calculated by projecting the predictable components on the original data x.
In practice, we perform the APT decomposition in a reduced space to avoid the computation of a singular matrix as the spatial points are larger than the sample numbers. The first 13 and 16 principal components (PCs) of the rainfall in MJ and JA, respectively, which approximately explain 70% of their corresponding total variance, are used. It is found that the results are not sensitive to the choice of the number when it is beyond 10 (not shown). For the APT calculation, we use all hindcasts at the lead times averaged over 1–4, 5–8, 9–12, and 13–16 days, beyond which the results remain robust by sensitivity experiments.
3. Predictability of early and late summer rainfall
a. Prediction skill
First, the prediction skill of the EASP in MJ and JA is measured by the ACC. Figure 2 presents the ACC skill of MJ and JA rainfall predictions at all lead times and their differences. For the MJ rainfall predictions, relatively high skill is located over the ocean at the 1–4d lead time. At the 5–8d lead time, the skill is significant only in areas with relatively large rainfall climatology (Fig. 1a) but decrease rapidly to be insignificant in the areas north of 30°N. The skill at the 9–12d lead time is significant only over the middle and lower reaches of the Yangtze River, while there is little significant skill in areas north of 30°N at the 13–16d lead time.
ACCs of the MJ rainfall predictions at lead times of (a) 1–4, (b) 5–8, (c) 9–12, and (d) 13–16 days. (e)–(h) As in (a)–(d), but for the JA rainfall. ACCs = 0.3 are highlighted by white contours. The hatched areas indicate that ACCs are significant at the 95% confidence level. (i)–(l) The differences in ACCs between the JA and MJ rainfall predictions. The stippled areas mean the ACC differences are significant at the 95% confidence level.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
Compared with the MJ skill, the JA skill is higher in most East Asian regions at all lead times (Figs. 2e–h), which could be confirmed by the results in Figs. 2i–l. The higher skill of the JA rainfall is located mainly in North China, the Korean Peninsula and surrounding waters, South China, and the SCS, where the rainfall climatology is relatively large in JA.
The consistency between the prediction skill of the East Asian rainfall in MJ and JA with their corresponding climatology suggests that the skill might be mainly dominated by their signal strength. Thus, to further examine this consistency, we calculate the signal variance of the East Asian rainfall in MJ and JA, respectively, using the ensemble hindcasts at all lead times. The results are presented in Fig. 3. The signal variance of MJ rainfall is large south of 30°N, whereas JA rainfall has relatively large signal variance in North China, South China, and the SCS. The results thus further confirm the dominant roles of the signal strength in the prediction skill of the East Asian rainfall.
Signal variances of the MJ rainfall predictions at lead times of (a) 1–4, (b) 5–8, (c) 9–12, and (d) 13–16 days. (e)–(h) As in (a)–(d), but for the JA rainfall.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
b. Predictable patterns
The predictable patterns of the MJ and JA rainfall in East Asia are investigated in this subsection using the APT method. Their spatial patterns are presented in Fig. 4. The leading predictable pattern (APT1) of MJ rainfall has a tripole pattern with a strong positive center in South China extending to the East China Sea and negative centers in the SCS and lower reaches of the Yellow River (Fig. 4a). In comparison, the APT1 of the JA rainfall has a dipole pattern with a strong positive center in South China extending to Taiwan Island and a weak negative center also in the lower reaches of the Yellow River (Fig. 4b).
The leading predictable patterns of (a) MJ rainfall and (b) JA rainfall in East Asia.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
Figure 5 shows the observed and predicted time series averaged over the 1–4d, 5–8d, and 9–12d lead times for the APT1 of the MJ and JA rainfall, respectively, to examine how the predictable patterns are predicted. For the MJ rainfall APT1, the predicted series catch the main variability of the observed series with a correlation coefficient of 0.57 except for a few strong events, such as that in 2002 (Fig. 5a). Likewise, the JA rainfall APT1 could be well predicted with a correlation coefficient of 0.74 with the observed counterpart (Fig. 5b).
Observed and predicted time series of the APT1s of (a) MJ and (b) JA rainfall averaged over the first three 4-day lead times. The corresponding correlation coefficients are given in the upper-left corner. (c),(d) ACCs and RMSEs, respectively, between the observed and predicted APT1 time series at each lead time.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
Further, we evaluate the APT1 prediction skill of the MJ and JA rainfall as a function of lead times measured by ACC (Fig. 5c) and RMSE (Fig. 5d). The predicted and observed APT1 time series at each lead time are obtained by projecting the predicted and observed precipitation onto the APT1 spatial pattern, respectively. The JA rainfall APT1 is better predicted than the MJ rainfall APT1 at all lead times for both ACC and RMSE. It is noted that the skill difference between JA and MJ in Fig. 5c is statistically significant only at the 1–4d lead time at the confidence level of 95%, suggesting that the advantages in the prediction of the JA rainfall were mostly beneficial at short lead times. The relatively low prediction skill of the MJ rainfall APT1 could be caused by either the large initial uncertainties or the low intrinsic predictability of MJ rainfall. To further examine this issue, we calculated the potential predictability of MJ and JA rainfall, respectively, and found that their potential predictability is almost the same (not shown). Thus, the difference of prediction skill between the two periods can reasonably be hypothesized to be attributed to their different initial conditions.
4. Predictability sources of early and late summer rainfall
The predictability sources of MJ and JA rainfall are explored in this section to reveal the physical processes behind their predictability.
a. Relationship with the leading EOF mode
First, we calculate the leading EOF mode (EOF1) of the ensemble mean from MJ and JA rainfall hindcasts to explore the relationship between the APT1 and EOF1. The results show that the APT1 of the MJ rainfall is very similar to its EOF1, and the same is true for the JA rainfall (Fig. 6). The leading PC (PC1), that is, the time series corresponding to the EOF1, of the MJ rainfall has a correlation coefficient of 0.84 with the APT1 time series, and a higher coefficient of 0.98 for the JA rainfall. It is not surprising that the APT1 has a similar pattern to the EOF1 as the variability with large variance usually provides more signals and is thus more predictable than that with small variance. Previous studies also provide evidence of this consistency (e.g., Wu and Tang 2019).
Leading EOF of the ensemble mean of (a) MJ and (b) JA rainfall hindcasts, and (c),(d) their corresponding PCs.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
The prediction skill of the PC1 is presented as measured by the ACC and RMSE (Fig. 7). The predicted PC1 is obtained by projecting the ensemble prediction onto the observed EOF1. As can be seen in Figs. 7a and 7b, the PC1 prediction skill is higher in JA than in MJ as with the skill differences in the APT1s (Figs. 5c,d). It is noted that although the EOF1 and APT1 patterns of the MJ rainfall resemble each other, the latter prediction skill is higher than the former. For example, at the lead time of 5–8d, the ACC of APT1 is about 0.55, whereas that of EOF1 is approximately 0.4. This suggests that the APT1 of MJ rainfall extracted more predictable components than the EOF1, which is determined by the mathematical differences between the two methods. That is, the former is extracted on the basis of the contribution to predictability, whereas the latter is obtained on the basis of the largest explained variance. In contrast, the skill of JA rainfall EOF1 is comparable with the APT1 (Fig. 5), indicating that the most predictable components of the JA rainfall could be caught mostly by the signal components measured by the ensemble mean of EOF decomposition.
(a) ACCs and (b) RMSEs between the observed and predicted EOF1 of the MJ and JA rainfall at each lead time.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
b. Predictability source analysis
To further explore the predictability sources of the MJ and JA rainfall, linear regression analysis is performed between the relevant variables and the normalized APT time series. Generally, linear regression finds the regression coefficient that minimizes the total error of the predicted value. In this study, the variable regressed on APT indicates how much the variable is related to APT.
The observed SLP and RH at the initial conditions are regressed onto the APT1s of the MJ and JA rainfall, respectively (Fig. 8). In boreal summer, the BSISO, an intraseasonal oscillation characterized by large-scale organized convection arising from the equatorial Indian Ocean and propagating eastward and northward to the northwest Pacific (NWP) through eight phases, is the dominant mode of intraseasonal variability in the tropics (Lee et al. 2013; Wang et al. 2018). By comparison, it is found that the SLP and 850-hPa wind regression maps in MJ (Fig. 8a) resemble the characteristics of BSISO phase 2: the active deep convection is located in the Indian Ocean and is accompanied by an anomalous high from the north Bay of Bengal extending to the SCS and the tropical NWP with an anomalous anticyclonic large-scale circulation over these areas (Lee et al. 2013). The anomalous southwest winds in the lower atmosphere transporting moisture from the ocean to South China provide more vapor (Fig. 8c) and increase the rainfall there. When BSISO is in phase 6 with atmospheric conditions opposite those in phase 2, the rainfall in South China decreases correspondingly. Thus, the MJ rainfall variability (signal) in South China is closely related to the BSISO, which provides predictability sources for the MJ rainfall APT1.
(a) Regressed SLP (Pa) and (c) mean RH over 850–1000 hPa (%) on the predicted APT1 time series of MJ rainfall averaged over all lead times. (b),(d) As in (a) and (c), but for the APT1 of JA rainfall. Stippling indicates that the regression is significant at the 95% confidence level. Regressed winds at 850 hPa significant at the 95% confidence level are also overlain on SLP regression fields in the vectors.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
In boreal summer, the circulation over East Asia is also influenced by the convective activity over the tropical NWP in the form of PJ pattern teleconnection (Kosaka and Nakamura 2006). The PJ pattern is characterized by a dipole of anomalous circulation and rainfall between the tropical NWP and the midlatitudes around Japan. During the positive phase of the PJ pattern, the anomalous cyclone with increased rainfall is located in the tropical NWP, whereas the anomalous anticyclone with decreased rainfall resides in the midlatitudes. The regressed SLP (Fig. 8b) of the JA rainfall APT1 is very similar to the positive phase structure of the PJ pattern. Generally, the PJ pattern is more significant in JA than in the early summer because of a stronger easterly shear of the climatological zonal flow over the tropical western Pacific (e.g., Lu 2004; Tsuyuki and Kurihara 1989). Under the control of the Asian monsoon, the moisture gathers around the SCS and tropical NWP (Fig. 8d), a convergence region in the lower atmosphere (Fig. 8b). The increased moisture anomalies increase the rainfall anomalies (signal) there. Thus, the predictability over the SCS and the tropical NWP is enhanced by these moist processes under the PJ pattern, resulting in the JA rainfall APT1 pattern (Fig. 6b).
A composite analysis is performed to further confirm the above conclusion that the BSISO in phase 2 and the PJ pattern is the main predictability sources of East Asian rainfall in MJ and JA, respectively. Specifically, for MJ rainfall, the relevant observed variables at the initial conditions are composited when the BSISO is in phase 2 (i.e., BSISOI1 ≥ 0.5 and BSISOI2 < 0.5 and BSISOI1 > BSISOI2); for JA rainfall, the variables are composited when the PJ pattern is significantly obvious (i.e., PJ index > 1 standard deviation). Here, the threshold of 0.5 for the BSISO index is chosen considering its significance and the sample numbers. A total of 33 and 21 samples are chosen for the composition in MJ and JA, respectively.
The results are presented in Fig. 9. For the early summer MJ, the composite SLP has an anomalous high over the north Bay of Bengal, SCS, and tropical NWP, with anomalous easterlies around 10°N (Fig. 9a)—that is, the pattern of BSISO phase 2, as in the SLP regression map (Fig. 8a). The anomalous southwest winds also bring more vapor, causing positive RH anomalies in South China and negative RH anomalies in the Bay of Bengal (Fig. 9c). For the late summer JA, a significant dipole pattern (i.e., PJ pattern) emerges in the SLP composition map with an anomalous low pressure center in the SCS–Philippine Sea and an anomalous high pressure center in extratropical NWP (Fig. 9b), which is very similar to the SLP regression map (Fig. 8b), converging vapors to the SCS and tropical NWP to increase the RH anomalies there (Fig. 9d).
(a) Composite SLP (Pa) and (c) mean RH over 850–1000 hPa (%) when BSISO is in phase 2 in MJ. (b),(d) As in (a) and (c), except when the PJ index in JA is one standard deviation larger than its mean. Stippling indicates that the composition is significant at the 95% confidence level. Composite winds at 850 hPa significant at a 95% confidence level are also overlain on SLP composite fields in the vectors.
Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-23-0183.1
In summary, for both MJ and JA rainfall APT1, the SLP, UV850, and RH composition maps (Fig. 9) are all very similar to their corresponding regression maps (Fig. 8), further confirming our interpretation of the APT1 predictability sources for rainfall in both MJ and JA.
5. Summary and discussion
In this study, we investigated the EASP subseasonal predictability in MJ and JA, respectively, considering the distinct characteristics of the East Asian rainfall between early (MJ) and late (JA) summer. We emphasized the elaboration of the leading predictable patterns of the East Asian rainfall in MJ and JA. Their predictability sources were further explored using regression and composition analyses.
The significant prediction skill of MJ rainfall mainly lies south of 30°N at all lead times, whereas those of JA rainfall have relatively large skill in North China, South China, and the SCS. The spatial difference in the prediction skill of the East Asian rainfall between the two subseasons is dominated by the distinctions of their rainfall signal strengths. The distinctions of the APT1s in MJ and JA are also obvious. The MJ rainfall APT1 has a tripole pattern with a strong positive center in South China extending to the East China Sea and negative centers in the SCS and lower reaches of the Yellow River, whereas the JA rainfall APT1 has a dipole pattern with a strong negative center in South China extending to Taiwan Island and a weak positive center in the lower reaches of the Yellow River. Moreover, the prediction skill of APT1s is higher in JA than in MJ.
By comparison with the EOF of the summer rainfall in East Asia, most of the predictability of APT1 is provided by the signal components measured by the leading EOF. Further analysis of the predictability sources for the APT1s reveals that the predictability of the MJ rainfall is related closely to the BSISO signal, which increases the rainfall in South China in phase 2. In contrast, the predictability of the JA rainfall APT1 is closely related to the PJ teleconnection pattern. The rainfall predictability over the SCS and the tropical NWP is enhanced by the PJ atmospheric processes.
Generally, the East Asian summer rainfall is closely related to the monsoon trough, a sea level low pressure convergence zone (Wang and LinHo 2002). The monsoon trough varies at multiple time scales (Harr and Wu 2011). On subseasonal scales, the monsoon trough has been found to interact with equatorial waves (Molinari et al. 2007), cross-equatorial surges (Feng et al. 2017), and the Madden–Julian oscillation (Gao and Li 2011). It is the temporal and geographical variation of the monsoon trough that may cause the different features of the East Asian monsoon rainfall in early and late summer. This study supports the complexity of the East Asian summer monsoon system from a predictability perspective.
Considering the different predictability sources of MJ and JA rainfall, predicting the MJ and JA rainfall separately by using distinctive assimilation schemes and/or ensemble construction approaches may be helpful for improving the subseasonal prediction of the East Asian summer rainfall. Moreover, the improvement of MJ rainfall prediction, which is much lower than that of JA rainfall, should be emphasized.
Acknowledgments.
I thank Prof. Youmin Tang very much for helpful discussion. This work is supported by grants from the National Natural Science Foundation of China (42227901) and the Scientific Research Fund of the Second Institute of Oceanography, MNR (JG2206).
Data availability statement.
This publication is supported by multiple datasets, which are openly available in cited previous studies listed in the reference section.
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