Dynamical Predictability of Leading Interannual Variability Modes of the Asian-Australian Monsoon in Climate Models

The Asian-Australian monsoon (AAM) system, which covers more than one-third of the tropics from roughly 40°E to 160°E and contains about half of the global population, exerts strong socioeconomic influences on many countries in the monsoonal region (Wang et al., 2001). Adequate understanding and skillful prediction of the AAM anomalies have become important issues. In recent years, major advancements have been made in examining the typical features and mechanisms of the AAM. For example, some studies have revealed that the AAM tightly interacts with the El Niño-Southern Oscillation (ENSO)(e.g., Normand, 1953; Mooley and Parthasarathy, 1983; Zhang et al., 1996; Webster et al., 1998; Wang et al., 2008b; Wu and Li, 2008). Monsoon-warm pool interaction has also been found to be a vital factor regulating AAM variability (Wang et al., 2003, 2004; Kumar et al., 2005; Wu and Kirtman, 2005), which operates on multiple timescales.

Wang et al. (2008b) identified two statistically distinguishable interannual variability modes of the AAM using seasonal-reliant Empirical Orthogonal Function (SEOF) analysis (Wang and An, 2005). The first mode exhibits a salient biennial tendency coincident with the transition of El Niño from warming to cooling in the eastern-central equatorial Pacific, while the second one acts as a precursor leading the ENSO warming by about one year. The two distinguished major modes of the AAM interannual variations represent the predictable part of the variability.

In addition to observational analyses, numerical models are effective tools for investigating the AAM. Many studies have been dedicated to evaluating the performance of current climate models in simulating or predicting the AAM (e.g., Wang et al., 2008a; Wu and Li, 2008; Zhou et al., 2009; Li et al., 2018; Jin et al., 2019; Ma and Jiang, 2020; Zhou et al., 2021). These studies confirmed the importance of the key driving factors, such as ENSO and monsoon-warm pool ocean interaction, in forming the AAM interannual variability. Wang et al. (2008a) assessed the capability of 10 coupled global climate models (GCMs) to predict the AAM modes and found that the multimodel ensemble (MME) could well capture the two leading modes of AAM precipitation variability but at the expense of overestimating the fractional variance. Wu and Li (2008) evaluated the performance of the Grid Atmospheric Model of IAP LASG (GAMIL) and found a reasonable one-month lead prediction, with the first mode better predicted than the second. Ma and Jiang (2020), Ma et al. (2020) applied the stochastic multi-cloud model (SMCM) to ECHAM6.3 (the sixth generation of atmospheric general circulation model ECHAM, developed by the Max Planck Institute for Meteorology, Stevens et al., 2013), and found that incorporating the SMCM can improve AAM precipitation simulations. Moreover, some prior studies have projected future changes in the AAM using climate model datasets in the Coupled Model Intercomparison Project phase 5 (CMIP5) (Wang et al., 2014; Chevuturi et al., 2018).

Although current dynamical climate prediction models have advanced from the uncoupled two-tier prediction approach to the coupled one-tier approach, predicting AAM interannual variability remains a challenging task. At present, dynamical models have been widely utilized for short-term climate prediction, and some centers worldwide can routinely produce and issue seasonal-interannual predictions with lead times of up to 6–12 months (Weisheimer et al., 2009; Wang et al., 2015; Ren et al., 2017; Dunstone et al., 2020). This allows us access to the long-range forecasts covering 1–12 months for directly studying questions regarding predictions and predictability of the leading interannual variability modes of the AAM. Based on the hindcast data from the four operational climate prediction models, including the Beijing Climate Center Climate System Model version 1.1 with moderate resolution (BCC_CSM1.1M: Wu et al., 2014), National Centers for Environmental Prediction/Climate Forecast System version 2 (NCEP CFSv2: Saha et al., 2014), Japan Meteorological Agency/Meteorological Research Institute Coupled Prediction System (CPS) version 2 (JMA CPSv2: Takaya et al., 2018), and the European Centre for Medium-range Weather Forecasts (ECMWF) System 4 (ECMWF System 4: Molteni et al., 2011), the dynamical predictability of the leading interannual variability modes of AAM are systematically examined. In this study, efforts are made to address the following specific questions: (1) What is the performance of the current dynamical prediction models in predicting how the major AAM interannual variability modes vary across different lead times? (2) What is the main role of ENSO in influencing the dynamical predictability of the leading AAM modes?

The remainder of this paper is organized as follows. Section 2 introduces a brief overview of the data and methodology. In section 3, the performances of climate models in simulating the leading modes of AAM interannual variability are assessed, and plausible impact factors contributing to AAM predictions are analyzed. Finally, a summary and discussion are presented in section 4.

In this study, the AAM region considered (40°–160°E, 30°S–40°N) covers South Asia and Australia as well as the nearly entire Indo-Pacific warm pool region. To verify the model hindcasts, the following observed datasets are used. The monthly mean zonal wind observations come from the ERA-Interim reanalysis dataset (Dee et al., 2011), with a horizontal resolution of 2.5° × 2.5°. The sea surface temperature (SST) data comes from the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation (OI) SST version 2, with a horizontal resolution of 1.0° × 1.0°. The precipitation data is sourced from version 2.3 of the Global Precipitation Climatology Project (GPCP, Adler et al., 2003, 2018), with a horizontal resolution of 2.5° × 2.5°. The four fully coupled operational seasonal prediction systems from different international centers, referred to as BCC_CSM1.1M, NECP CFSv2, ECMWF System 4, and JMA CPSv2, are used in this study which focuses on the period 1991–2017. The variable anomalies are calculated by removing the climatology of individual model hindcast data over the entire period, which are also used to conduct the MME mean through an arithmetic average. A brief description of all the models is provided in Table 1.

In this study, the phrase “1-month lead” means that the forecast was made from the initial conditions at the beginning of one month for the next. For example, the 1-month-lead forecast, which uses the initial conditions from May, is the forecast for June. It follows that the seasonal prediction indicates the average of three months, within which each of the three months is initialized from the month before: for example, the seasonal forecast for the JJA period is initialized, consistent with the one-month lead time, in May, June, and July, respectively. The remaining lead times are defined analogously.

To extract the leading modes of the AAM, the SEOF analysis method is adopted, which can capture the characteristics of AAM seasonal evolution throughout a full calendar year (Wang and An, 2005; Wang et al., 2008b). The idea of SEOF analysis is similar to that of extended EOF analysis except that the SEOF specifically addresses a seasonally dependent evolution that references the annual cycle, as opposed to an arbitrary four-season sequence, which can start from any individual season for each year. Four different seasonal sequences are used in this work, spanning from boreal spring [March−April−May, MAM(0)], summer [June−July−August, JJA(0)], autumn [September−October−November, SON(0)], and winter [December−January−February, DJF(0/1)] of Year 0 to the winter [DJF(0/1)] of Year 0, the next spring [MAM(1)], summer [JJA(1)], and autumn [SON(1)] of Year 1, respectively. To distinguish among these SEOFs, they are denoted as SEOF-frMAM, SEOF-frJJA, SEOF-frSON, and SEOF-frDJF, respectively. This method constructs a covariance matrix using four consecutive seasonal mean anomalies for each year. Then the derived spatial pattern for each SEOF mode will contain four sequential patterns representing the seasonal evolution of the U850. Taking SEOF-frMAM as an example, we treat the anomalies for MAM(0), JJA(0), SON(0), and DJF(0/1) as a “yearly block”. After the empirical orthogonal function decomposition is performed, the yearly block is divided into four consecutive seasonal anomalies so that one obtains a seasonally evolving pattern of monsoon anomalies in each year for each eigenvector. The four-season sequential patterns share the same yearly value in their corresponding principal component (PC). The SEOF is applied to the observed anomalies and predicted anomalies, respectively.

The BCC_CSM1.1M supports a 12-month prediction. Thus, it is possible to generate a prediction for an entire year based on each initial month. The yearly forecast is for the complete 12-month period following the initial month: in the February initial conditions example, the forecast is for the MAM-JJA-SON-DJF period. Then we project the data from the whole period onto the two observed SEOF structures to get the AAM PC indices (hereafter referred to as AAM1 and AAM2). The performance of BCC_CSM1.1M in predicting these indices has been evaluated in section 3.5.

The Temporal Correlation Coefficient (TCC) and the Pattern Correlation Coefficient (PCC) are used to quantify model predictability. We define $ {x}_{i,j} $ and $ {f}_{i,j} $ as the anomalies for observation and prediction in space (i) and time (j); M is the number of space samples, and N is the number of time samples. They are calculated as follows:

The range of the TCC and PCC is from –1.0 to 1.0, and a large positive (negative) value indicates a highly similar (opposite) correlation between prediction and observation.

Considering the pronounced variations in the AAM region, the focus of this study is to investigate whether the first two leading interannual variability modes of AAM are predictable with definitions starting from different seasonal sequences and how well the operational climate models can predict the spatiotemporal characteristics of these modes at different lead times. By comparing the observed two leading modes in terms of zonal wind anomalies at the 850-hPa isobaric level (U850) in the AAM region, we first examine the performance of the model predictions with different lead times in capturing the major AAM modes of interannual variability and then explore the possible connection of the AAM leading modes with ENSO.

Figures 1 and 2 first present the seasonally evolving spatial patterns of the first two SEOFs in reanalysis with different initial seasons. The first SEOF (SEOF1), initiated from boreal spring, summer, autumn, and winter, explains 29.2%, 30.1%, 25.4%, and 24.8% of the total variance, respectively. It is clearly seen that the seasonal evolutions of SEOF1 in terms of four sequences are basically consistent with each other. The westerly anomalies over the western North Pacific (WNP) develop and persist from MAM(0) to JJA(0), extending from the Maritime Continent to the Arabian Sea, as shown in the patterns associated with the SEOF1-frMAM (Fig. 1a). The easterly anomalies over the Indian Ocean intensify from JJA(0) to SON(0), persist into DJF(0/1), and then decay rapidly in MAM(1), as shown in SEOF1-frJJA. The wind anomalies feature opposite variations between the JJA(0) [SON(0)] pattern of the SEOF1-frMAM (SEOF1-frJJA) and the JJA(1) [SON(1)] pattern of the SEOF1-frSON (SEOF1-frDJF). These features are quite analogous to those of Wang et al. (2008b).

Figure 1.  The first SEOF spatial patterns (from the first to the fourth row) and principal components (the bottom row) of AAM U850 anomalies (units: m s^–1) as derived from different initial seasons in ERA reanalysis data: (a) SEOF1-frMAM; (b) SEOF1-frJJA; (c) SEOF1-frSON; (d) SEOF1-frDJF.

Figure 2.  Same as Fig. 1, but for the second SEOF.

However, we also note some differences in the SEOF1 patterns between season (0) and season (1), which are generated from different initial seasons. Such a distinct feature could be presumably due to the distinguishing monsoonal circulation anomalies between the developing year and the decaying year of ENSO. For example, the patterns of summer rainfall anomalies are quite different between the developing and decaying ENSO phases (Wu et al., 2009). Identifying these distinctions of some SEOF1 patterns would aid in understanding the differences in prediction skills and predictability of the AAM modes, as shown in the next sections.

As seen in Fig. 2, the second SEOF (SEOF2) accounts for 10.8%, 10.8%, 13.3%, and 14.5% of the total variance in terms of four initial seasons, respectively. The seasonal evolution of SEOF2-frMAM and -frDJF is quite different from that of SEOF2-frJJA and -frSON. Notably, the SEOF2-frMAM (SEOF2-frDJF) features the decay of the easterly and westerly anomalies over the Indian Ocean from MAM(0) [MAM (1)] to JJA(0) [JJA (1)], which resembles that of MAM(1) to JJA(1) patterns in SEOF1 (Fig. 1). The SEOF2-frJJA and SEOF2-frSON reflect the evolution of the zonal wind anomalies over the WNP, which were intensified in JJA(0) before decaying rapidly in SON(0). It is noteworthy that the SEOF2 leading ENSO by one year, as identified by Wang et al. (2008b), may cease to exist in the SEOF2-frMAM and SEOF2-frDJF.

To evaluate the dynamical predictability of the AAM interannual variability modes in the four prediction models, the TCCs between the observational PCs and corresponding PCs directly from SEOFs over the model-predicted fields at different lead times are calculated. Figures 3a and 3e show that TCCs vary with lead times for the first two SEOFs-frMAM. Overall, these models demonstrate reasonable performance with TCCs above 0.9 at a 1-month lead and still above 0.7 at a 6-month lead for SEOF1-frMAM. Similarly, TCCs for SEOF1 starting from other initial seasons are still high, where almost all the models show TCCs above the significance threshold at the 99% confidence level within 9 months lead. Particularly, due to a longer forecast length, BCC_CSM1.1M has significant TCCs at the 99% confidence level reaching up to 10- or 11-month lead except for the SEOF1-frDJF, which shows slightly less skill.

Figure 3.  (a) Dependence of temporal correlation coefficients on the lead month for PC1 of SEOF-frMAM predicted by (orange) BCC_CSM1.1M, (green) NCEP CFSv2, (blue) ECMWF System 4, (pink) JMA CPSv2 models, and (red) the ensemble mean of these four models. (b–d) Same as (a), but for the SEOF-frJJA, the SEOF-frSON, and the SEOF-frDJF, respectively. (e–h) Same as (a–d), but for the second SEOF. Dashed light green (purple) horizontal lines denote statistical significance at the 99% (95%) confidence level based on a Student's t-test.

In contrast, the TCCs of the SEOF2 are relatively small compared to the SEOF1, where the smallest ones appear in the results of SEOF2-frJJA. As seen in Fig. 3f, most models have reduced performance. TCCs of BCC_CSM1.1M, NCEP CFSv2, and JMA CPSv2 decrease rapidly at a 2-month lead. Of note, only the ECMWF System 4 can pass the significance test at a 99% confidence level for 1–6 lead months. The TCCs of the SEOF2-frMAM show better results. For the SEOF2-frDJF, the models present just as good of a performance as the SEOF1-frDJF, and the TCCs of the first two PCs at identical leads do not show as much separation as other starting seasons, where the BCC_CSM1.1M even has higher TCCs of PC2-frDJF than PC1 at 2- and 3-month leads.

These results suggest that no matter which season the SEOF is initiated from, the temporal variations of the SEOF1 tend to be more predictable than SEOF2, while the models for SEOF2 initiated from JJA have relatively low performance. Among the four models, the ECMWF System 4 tends to perform best for both the AAM modes and even is superior to the MME of all the models.

Here, we examine the ability of the models to reproduce the spatial patterns for the first two SEOFs. Figures 4 and 5 present PCCs between observations and corresponding predictions at different leads. The results are almost identical to each other in terms of the different initial seasons for defining the first AAM mode only with relatively lower PCCs in MAM (Fig. 4). The models can well reproduce the spatial patterns of the first observed AAM mode at most lead months. The ECMWF System 4 is slightly better than the other three within 6 months lead in representing the patterns of the first leading SEOF modes, with referenced PCCs of 0.6–0.98. The PCCs tend to decrease with lead time increasing, and even negative values appear in the MAM and SON patterns of the BCC_CSM1.1M for the SEOF1-frDJF. In addition, as the BCC_CSM1.1M and the NCEP CFSv2 have longer prediction windows, covering 12-month and 9-month predictions, respectively, the PCCs of these two models show a clear decline trend with the increase of lead time.

Figure 4.  Dependence of pattern correlation coefficients on lead months for the first SEOF-frMAM spatial patterns of AAM U850 anomalies predicted by (a) BCC_CSM1.1M, (b) NCEP CFSv2, (c) ECMWF System 4, and (d) JMA CPSv2 models. (e–h) Same as (a–d), but for the SEOF-frJJA. (i–l) Same as (a–d), but for the SEOF-frSON. (m–p) Same as (a–d), but for the SEOF-frDJF.

Figure 5.  Same as in Fig. 4, but for the second SEOF.

Compared to the SEOF1, the models have a much lower capability in reproducing the patterns of SEOF2 (Fig. 5). The PCCs in SEOF2 are significantly distinctive for different seasonal sequences. For example, relatively lower PCCs occur in SON for SEOF2-frMAM, but for SEOF2-frJJA they occur in JJA. For the SEOF2-frSON, PCCs are lower in SON and DJF, decreasing more rapidly in MAM for the BCC and NCEP models as the lead time increases. For the SEOF2-frDJF, PCCs vary greatly among models and decrease more rapidly in MAM and DJF for BCC_CSM1.1M, while rapidly decreasing PCCs occur in MAM and JJA for NCEP CFSv2.

In brief, the model-reproduced spatial patterns of the first mode are much better than those of the second mode, in which lower PCCs of SEOF1 are always present in MAM, while those of the SEOF2 appear in different seasons. Among these models, ECMWF System 4 best represents the observed spatial patterns.

It is well known that ENSO substantially contributes to the interannual variability of the Asian monsoon. Here, we explore the possible connection of the modes of AAM interannual variability with ENSO. It is also important to evaluate the ability of dynamic prediction models to reproduce the relationship between ENSO and the two SEOFs. Previously, Wang et al. (2008b) conducted the SEOF analysis in terms of the sequence from JJA to MAM and pointed out that the SEOF1 coincides with the developing and mature phases of El Niño and that SEOF2 leads El Niño by 1 year, providing an early signal for ENSO. To confirm the relationships of the first two leading AAM modes from different season sequences with ENSO, Figs. 6 and 7 present the observed and initially simulated lead-lag correlation coefficients between the two PC time series and the SST anomaly (SSTA) index in the Niño-3.4 region (5°S–5°N, 170°W–120°W).

Figure 6.  Lead-lag correlation coefficients of the monthly Niño-3.4 index relative to the SEOF-frMAM (the first column), the SEOF-frJJA (the second column), SEOF-frSON, (the third column), and the SEOF-frDJF (the fourth column) in observation (solid black line) and the models, where the first, second, third, and fourth rows represent the BCC_CSM1.1M, NCEP CFSv2, EMCWF System 4, and JMA CPSv2 models, respectively. Colors are for different lead months. The dashed light green (purple) line denotes statistical significance at the 99% (95%) confidence level based on a Student's t-test.

Figure 7.  Same as Fig. 6, but for the second SEOF.

In observations, the first AAM mode, from different initial seasons, has a strong and positive correlation with the Niño-3.4 index during the winter of the event year [DJF(0/1)] (Fig. 6). Also, the observed modes show a significant negative correlation coefficient after the second summer [JJA(1)]. The negative correlation coefficients are around –0.4 for the SEOF1-frMAM, SEOF1-frJJA, and SEOF1-frSON but are nearly –0.8 for the SEOF1-frDJF. For the lead-lag correlations between ENSO and the SEOF1-frDJF, the BCC_CSM1.1M and NCEP CFSv2 overestimate the positive correlations from JJA (–1) to MAM (0), while the ECMWF System 4 and JMA CPSv2 agree well with observations. Generally, the relationship between ENSO and the SEOF1 is well represented in all the models though the spreads become larger at longer lead months.

For different initial seasons, the lead-lag correlations between ENSO and the second AAM mode are quite distinct from each other (Fig. 7). For the SEOF2-frMAM, the observations show a maximum correlation coefficient during year (–1), suggesting that ENSO may provide a precursory signal for AAM onset. However, the observed SEOF2-frJJA shows a maximum correlation coefficient leading ENSO by about 1 year, consistent with the results of Wang et al. (2008b). Similar to the SEOF2-frJJA, the observed lead-lag correlation coefficient of the SEOF2-frSON is positively correlated with the Niño-3.4 index in the following winter [DJF(1/2)]. For the SEOF2-frDJF, the observed shows maximum correlations (~0.8) from JJA (–1) to MAM (0).

The models reproduce lead-lag correlations between ENSO and the second AAM mode with slightly less skill than those of the first mode. For the SEOF2-frMAM, the models capture the realistic lead-lag correlation with ENSO from year (–1) to year (0) but poorly reflect this during year (+1), with the coefficients being negative in simulations but positive in observations. The SEOF2-frJJA and SEOF2-frSON show a minimum negative correlation (~–0.4) during year (–1) in most models but around 0 in observations. The lead-lag correlations between ENSO and the SEOF2-frDJF tend to be well captured by the models at short leads. BCC_CSM1.1M and NCEP-CFSv2 generally underestimate the correlations from JJA of year (–1) to MAM of year (0) and overestimate from JJA of year (0) to year (+1).

As shown in Table 2, we further summarize the relation between ENSO and the AAM modes from Figs. 6 and 7. It is noted that no matter which season the first SEOF was initiated from, it concurs with the turnabout of ENSO warming to cooling. Due to the strong signals of ENSO, these models are always skillful in predicting the first AAM mode. Moreover, the ENSO signal quickly loses its memory during boreal spring (Ren et al., 2016, 2020; Tian et al., 2019), a phenomenon referred to as the spring predictability barrier. Accordingly, the capacity of models in simulating the MAM spatial features is slightly weaker than the other seasons for SEOF1.

Compared to the SEOF1, the SEOF2 becomes more complex. The SEOF2-frJJA and -frSON leads ENSO by about 1 year, and the SEOF2-frDJF is consistent with the turnabout of the ENSO mature to its decaying phase, while the SEOF2-frMAM is beginning from the ENSO decaying phase. As we can see, there are still ENSO signals favoring predictions of the SEOF2-frDJF and SEOF2-frMAM, but the driving force behind the SEOF2-frJJA and SEOF2-frSON may be less related to ENSO than to the AAM system itself. Hence, the AAM variability is more difficult to reproduce for the SEOF2-frJJA and SEOF2-frSON than the SEOF2-frMAM and SEOF2-frDJF (Fig. 3). Additionally, the PCCs of SEOF2-frMAM are lower than those of SEOF2-frDJF owing to the persistence barrier of ENSO in spring. Indeed, most models fail to predict the corresponding PC of the SEOF2-frJJA since it is in the early development phase of ENSO, during which air-sea interactions are relatively weak. Also, the models show less advantage in simulating the JJA pattern of SEOF2-frJJA, as it is the one furthest from the mature ENSO phase.

The MME mean method is an effective way to aggregate and synthesize forecast information from different models. It has been well-recognized that the ensemble mean can effectively reduce prediction errors in an individual forecast (Krishnamurti et al., 1999; Palmer et al., 2000). In the following subsection, we further analyze the prediction skill and predictability of the AAM modes in terms of the MME mean.

Included in Fig. 3 are TCCs between the observed and MME-mean PCs. For the first two leading SEOF-frMAM, the TCCs of the MME mean are slightly worse than ECMWF System 4 and JMA CPSv2. This is probably due to the skills of BCC_CSM1.1M and NCEP-CFSv2 being much lower than those of ECMWF System 4 and JMA-CPSv2. For the SEOF-frJJA, the MME mean performs well in reproducing the temporal evolution of the first AAM mode but fails to outperform the best individual model in the second mode. For the SEOF-frSON, the MME mean reasonably reproduces the first mode with high fidelity (TCC>0.88). For the second mode, the TCCs of the MME mean are comparable to those of JMA CPSv2, yet much lower than ECMWF System 4. For the SEOF-frDJF, the TCCs of the MME mean for the first two modes are almost on the same level, with correlations around 0.80. Generally speaking, the MME mean does not provide a prominent advantage for increasing the TCC skill scores of the first two AAM modes.

The PCC scores between the observed and MME-mean spatial patterns are reported in Fig. 8. As expected, the MME mean has higher dynamical predictability for the first AAM mode than for the second. Minimal correlations still exist in MAM for the first AAM mode, on account of the persistence barrier of ENSO in spring. For the other seasons, the PCCs range from 0.84 to 0.97, demonstrating some improvement compared to the individual model in capturing spatial features of the SEOF1. For SEOF2, negative PCCs are found in the SON pattern for the SEOF2-frMAM and in the JJA pattern for the SEOF2-frJJA. For the SEOF2-frSON and -frDJF, the MME mean maintains its reliable skill with PCCs ranging from 0.54 to 0.94. Compared with the individual model, the MME mean shows a slightly better performance in capturing the second spatial pattern of the SEOFs, despite its poor skill for SEOF2-frMAM and -frJJA.

Figure 8.  Filled gridded cells for pattern correlation coefficients for the first and second SEOF spatial patterns of AAM U850 anomalies predicted by the MME mean: (a) SEOF-frMAM; (b) SEOF-frJJA; (c) SEOF-frSON; (d) SEOF-frDJF.

As precipitation is a direct consequence of the AAM circulation, the primary purpose of the AAM prediction is to examine the performance of models in capturing the seasonal evolution of the AAM precipitation. Thus, as an extension, we further apply the SEOF analysis to both observed and MME seasonal-mean precipitation anomalies. Figure 9 shows the PCCs of the seasonally evolving spatial patterns in terms of precipitation. Associated with the SEOF1, the precipitation anomaly patterns are well predicted, with PCCs ranging from 0.28 to 0.90. Consistent with previous analyses defining the AAM by 850-hPa wind anomalies, the PCCs of the MAM patterns of the SEOF1-frMAM tend to be lower than in the other seasons. Still, the SEOF2 performs worse than the SEOF1, especially for the SEOF2-frMAM and SEOF2-frJJA. Compared to the results for the U850 wind anomalies, the PCCs of precipitation are generally lower, with the maximum PCC being less than 0.9. However, the general conclusions from different sequences of the SEOF analyses in U850 and precipitation are in basic accord with one other.

Figure 9.  Same as Fig. 8, but for AAM precipitation.

The predictability demonstrated in this study is potentially useful for operational AAM prediction. Some meteorological centers worldwide can routinely produce and issue seasonal–interannual predictions for up to 12 months every month. Thus, it is possible to give a whole-year prediction to construct a covariance matrix for SEOF analysis each month. Then, by projecting the model prediction field onto the observed SEOF patterns, we can get two indices associated with the two leading AAM modes. The real-time prediction of these two indices can assist future climate services. The BCC_CSM1.1M covered a 12-month prediction, enabling us to further analyze the skills of BCC_CSM1.1M in predicting the AAM1 and AAM2 indices during the period.

The hindcasts initialized in February, May, August and November from the BCC_CSM1.1M are used to generate the predicted AAM1 and AAM2 indices by projection onto the observational SEOF-frMAM, SEOF-frJJA, SEOF-frSON and SEOF-frDJF patterns in terms of AAM U850 anomalies, respectively. Figure 10 shows the time series of the AAM1 and AAM2 indices (the SEOF spatial patterns for BCC_CSM1.1M can be seen in Figs. S1 and S2 in the Electronic Supplementary Material, ESM) and indicates a good performance of the BCC_CSM1.1M in predicting the AAM1 and AAM2 indices. The correlation coefficients between BCC_CSM1.1M and observations are 0.58 (0.63; 0.66; 0.68) and 0.76 (0.63; 0.43; 0.75) for the AAM1 and AAM2 initialized in February (May; August; November), respectively. The skills of the AAM1 show little variation between different initial seasons, but the forecast skill of AAM2 initiated in May and August is much lower than those of AAM2 initiated in February and November. This result is consistent with the relationship between the AAM and ENSO analyzed above.

Figure 10.  The time series of the AAM1 and AAM2 indices obtained from observation (red solid) and BCC_CSM1.1M (blue dashed). Black numbers in the bottom left are correlation coefficients between the BCC_CSM1.1M and the corresponding observation time series. (c, d) Same as (a, b), but for the SEOF-frJJA. (e, f) Same as (a, b), but for the SEOF-frSON. (g, h) Same as (a, b), but for the SEOF-frDJF.

In this study, the dynamical predictability of the leading interannual variability modes of AAM and major factors contributing to prediction results have been investigated based on retrospective prediction datasets from the seasonal forecasting models in four operational centers worldwide. The SEOF analysis is used here to extract the leading modes of AAM with a focus on different seasonal sequences.

Our results reveal that the model predictability of the leading AAM modes is sensitive to their definitions of seasonal sequences, especially for the second mode, concurring with significantly different phases of ENSO for various seasonal sequences. Specifically, models have significant prediction skills for the AAM modes but tend to exhibit lower performance in MAM spatial features, while they have difficulty reproducing temporal features of the SEOF2-frJJA. The dynamical predictability of the two leading AAM modes is model dependent. The ECMWF System 4 always achieves the best performance for the AAM modes. The MME mean demonstrates some advantages in capturing spatiotemporal variations of the AAM modes but has not contributed an apparent improvement compared to the best individual model in predicting temporal features, especially for the SEOF2-frJJA. Analysis of the MME seasonal-mean precipitation anomalies shows that the general conclusions from different sequences of the SEOF analyses in U850 and precipitation are basically in accord with each other, with the predictability of the AAM precipitation generally lower than that of the AAM wind associated with the leading AAM modes.

In this study, the relationship between ENSO and the AAM modes has been checked. Results show a good performance of models in capturing the spatiotemporal features of the leading AAM modes in association with ENSO as an early signal. The first modes, from various seasonal sequences, concur with the turnabout of warming to cooling in the eastern-central Pacific, which is consistent with previous studies (e.g., Wang et al., 2008a, b; Zhou et al., 2009). Due to the strong signal associated with ENSO, temporal variations of the first AAM mode are well-captured in all models. In contrast, the lead-lag correlations between ENSO and the second mode are more complex. The SEOF2-frDJF is consistent with the turnabout of ENSO’s mature to decaying phase. The SEOF2-frMAM begins from the ENSO decaying phase, while the SEOF2, initialized from JJA and SON, leads the warming/cooling by about one year. The SEOF2-frMAM and SEOF2-frDJF have high predictability in models as there is still an ENSO signal ahead of the AAM (Fig. 3). Our results also confirmed that the persistence barrier of ENSO in spring leads to poor model skill in capturing the MAM spatial characteristics of the SEOF1. Similarly, the models demonstrate even worse performance predicting the pattern of the SEOF2-frMAM than the SEOF2-frDJF.

Accounting for the actual forecast demand, it is important to make accurate predictions of AAM as early as possible for signaling climatic disasters, not just in boreal summer. Previous analyses (e.g., Wang et al., 2008a, 2014; Wu and Li, 2008; Zhou et al., 2009, 2021; Li et al., 2018; Ma and Jiang, 2020) on the leading two modes of AAM all examine the seasonal sequence beginning from the summer of a given year to the following spring. Nevertheless, whether the leading modes are sensitive to the initial season has not been well studied. To clarify this issue, our study examined the predictability of leading interannual variability modes of the AAM. Our study uncovered two interesting findings: 1) the model predictability of the leading AAM modes is sensitive to their definitions in terms of seasonal sequences, especially for the second mode. 2) ENSO, as an early signal, is conducive to a better performance of model predictions in capturing the spatiotemporal variations of the leading AAM modes. Still, the persistence barrier of ENSO in spring leads to poor modeling skill in terms of spatial features. These findings here are critical for the operational prediction of AAM. For example, by projecting the model prediction field onto the observational SEOF patterns, we can obtain two indices associated with the two leading AAM modes. Our study has demonstrated that these two indices are quite skilfully predicted by BCC_CSM1.1M (Fig. 10), indicating a positive outlook for future AAM prediction. In addition, the analysis and evaluation results reported in this paper provide valuable guidance for operational prediction. In light of our discovery, one should focus less on the AAM1 prediction results at a specific initial month in MAM and more on the AAM2 prediction results at a specific initial month in MAM/DJF to more accurately predict the AAM. Once more, we note that the AAM mode, with a weak or absent ENSO signal, has not been well represented by the models. Presently, the performance of models for predicting the second AAM mode initialized from boreal summer still cannot sufficiently meet the demands of operational climate prediction, and methods for improving its prediction skill need to be further explored.

Acknowledgements. This work was jointly supported by the National Natural Science Foundation of China (Grant Nos. U2242206, 41975094 and 41905062), the National Key Research and Development Program on monitoring, Early Warning and Prevention of Major Natural Disaster (Grant Nos. 2017YFC1502302 and 2018YFC1506005), the Basic Research and Operational Special Project of CAMS (Grant No. 2021Z007), and the Met Office Climate Science for Service Partnership (CSSP) China.

Electronic supplementary material Supplementary material is available in the online version of this article at https://doi.org/10.1007/s00376-023-2288-2.