With the increasing occurrence of metrological disasters in recent years, there has been growing attention on subseasonal-to-seasonal (S2S) forecasts, as these forecasts bridge the gap between weather and climate forecasts and reduces disaster risks through early warnings. In November 2013, the WWRP/WCRP S2S prediction project (Phase 1) was launched, with the principal objectives of enhancing S2S forecast accuracy and advancing our comprehension of its dynamics and climate drivers. Then, work on S2S research continued in Phase 2, from 2018 to 2023. The whole project has made a significant contribution to the development of S2S prediction.

The Madden–Julian Oscillation (MJO) (Madden and Julian, 1971) is a crucial predictability source of S2S forecasts. It is a significant tropical oscillation with a period of 30–60 d, characterized by expansive cloud masses and precipitation systems that propagate eastward along the equatorial regions. Accurate S2S prediction requires a good representation of MJO. Many studies have clarified the relationship between the MJO and global weather and climate, such as monsoons (Goswami, 2012; Hsu, 2012; Lau and Chan, 1986; Wheeler et al., 2009; Liu et al., 2022), tropical cyclones (Bessafi and Wheeler, 2006; Ferreira et al., 1996; Hall et al., 2001), and the El Niño–Southern Oscillation (ENSO; Lau and Waliser, 2012; Zhang, 2005). The convective and circulation anomalies associated with MJO establish intricate connections across global weather and climate systems on the S2S timescale. Being able to accurately forecast the MJO can have a positive impact on the forecast of other related systems (Cassou, 2008; Vitart and Molteni, 2010; Wu et al., 2007). Achieving an accurate forecast of MJO has become a primary objective in the field of S2S forecasts.

With an enhanced comprehension of the underlying physical mechanisms governing the MJO and the continuous improvement of numerical models, remarkable advancements have been achieved in the MJO forecast. In Coupled Model Intercomparison Project Phase 6 (CMIP6), models that exhibited lower forecast skills (Hung et al., 2013) in Coupled Model Intercomparison Project Phase 5 (CMIP5) have demonstrated noteworthy improvements in the simulation of MJO (Chen et al., 2022). Generally, the models in CMIP6 simulate more realistic eastward propagation and precipitation over the Maritime Continent (MC) region (Ahn et al., 2020).

However, for S2S forecasts, the improvement of model physics is one aspect of advancing S2S forecasts, as various factors impact MJO forecast skills, such as initialization and ensemble generation (Kim et al., 2018). The forecast skills of the MJO in most models are typically 3–4 weeks (Vitart, 2017), while the estimate of predictability of MJO is approximately 5–7 weeks (Waliser et al., 2003; Neena et al., 2014). These facts underscore the persisting challenges in the S2S forecasts.

The realistic forecast of MJO eastward propagation is one of the challenges that have been repeatedly mentioned in recent years (Jiang, 2017; Kim, 2019; Lim et al., 2018; Wang and Lee, 2017). The MJO propagation skill is closely related to the forecast of the state in the Maritime Continent (MC) region (Gonzalez and Jiang, 2017). Many studies have pointed out the “MC barrier” (Hendon and Salby, 1994; Rui and Wang, 1990; Vitart et al., 2017) during the MJO's propagation through the MC region. The MC barrier refers to a notable deterioration of the MJO signal when it traverses the MC area, but this phenomenon is usually amplified in the climate models (H.-M. Kim et al., 2014; Neena et al., 2014; Xiang et al., 2022, 2015), showing the model's limitation in preserving MJO propagation within the MC region. The moisture mode theory (Raymond and Fuchs, 2009) has been proposed to explain this phenomenon. It suggests that the advection of seasonal mean moisture by the MJO-related circulation anomalies in the lower troposphere is crucial to MJO's propagation through the MC region (Jiang, 2017; Kim, 2019). In models that struggle to capture the realistic propagation of MJO, the mean low-troposphere moisture amplitude over the MC is underestimated, resulting in a weakened horizontal moisture gradient (Gonzalez and Jiang, 2017; Kim, 2017). This discrepancy in moisture advection hinders MJO propagation.

The Institute of Atmospheric Physics at the Chinese Academy of Sciences (IAP-CAS) has been actively involved in climate model development and applications since CMIP1 in the 1990s. As for the IAP-CAS model, it has already shown a significant enhancement in MJO simulation in CMIP6 compared to CMIP5 (Chen et al., 2022), but the performance of the S2S system in IAP-CAS remains uncertain and requires comprehensive evaluation. Therefore, the objectives of this article are fourfold. Firstly, we introduce the S2S forecast system of the IAP-CAS model. Secondly, we evaluate the forecast skills of the IAP-CAS in the MJO forecast. Thirdly, we analyze the evaluation results to identify the sources of forecast errors, facilitating further improvements in the MJO forecast. Lastly, we hope that the verification and analysis process can provide some valuable insights for other models.

The structure of the paper is as follows. A thorough review of the IAP-CAS model and S2S ensemble forecast system is introduced in Sect. . Section  describes the observation data and primary methodology utilized in the article. Section  assesses the overall MJO forecast skills in IAP-CAS. Section  focuses on analyzing the propagation details of the fast-propagating and slow-propagating MJO. After that, in Sect. , we discuss the potential causes of any bias observed in the MJO forecast. In Sect. , we summarize our findings and discuss the results.

The architecture of the IAP-CAS S2S ensemble forecast system is depicted in Fig. . In this section, we give a thorough description of the S2S system, covering the model, initialization methods, ensemble generation approaches, and the resulting datasets.

The evaluation in this section is conducted for the annual MJO events. Figure  demonstrates the overall MJO forecast skill in the IAP-CAS model and the improvement brought by the time-lagged ensemble method. Figure a shows the forecast skill of the ensemble mean is 24 d with the criterion of ACC exceeding 0.5, while the skill of individual members is about 21–22 d. Meanwhile, the ensemble mean RMSE reaches 2 at 21 d, and the individual members exhibit a larger RMSE, reaching 2 at 16 d (Fig. b). The solid blue line in Fig. b represents the ensemble spread (Leutbecher and Palmer, 2008) of IAP-CAS. When this ensemble spread approaches the RMSE of the ensemble mean (solid red line), it indicates that the ensemble members are sufficiently dispersive. Figure b illustrates that the ensemble exhibits an underdispersive characteristic in the early stage of the forecast. We have also observed similar issues of underdispersiveness in many other models (Rashid et al., 2011; Neena et al., 2014; H.-M. Kim et al., 2014; Xiang et al., 2015), and addressing this aspect may be a focal point for future model enhancements.

Increasing the number of ensemble members within a certain range proves to be effective in forecasting the uncertainty in weather and climate (Hou et al., 2001). We employed the time-lagged ensemble method to further augment the ensemble members. The time-lagged ensemble includes the ensemble members generated on the forecast day and from lag times. For instance, by incorporating ensemble members with a lag of i (i=0,1,2,…) days, the total number of members becomes 4⋅(i+1). Upon examining the relationship between lag i days and forecast skill, it was found that the skill increases as i increases at first, but then it reaches a plateau when i>3 (see Fig. ). This suggests that the forecast skill of the 16 members may represent the limit of the time-lagged ensemble method in IAP-CAS. Figure d shows the ensemble of 16 members is more dispersive than that of 4 members, which is illustrated by less distinction between the RMSE and spread in the 16-member system. The ensemble mean of 16 members achieves a skill of 26 d, surpassing the skill of 4 members by 2 d (Fig. c).

Numerous prior investigations have demonstrated that MJO forecast skill is sensitive to the MJO amplitude in many models (Lin et al., 2008; Rashid et al., 2011; Wang et al., 2014; Xiang et al., 2022), and this characteristic is also evident in the IAP-CAS model. We classify an MJO case as an initial (target) strong case if its initial (target) amplitude is greater than 1, while an event with an initial (target) amplitude less than 1 is classified as an initial (target) weak case. Figure a and b show that in the IAP-CAS model, the forecast skills of strong MJO cases are generally higher than those of weak cases, especially in the target strong (weak) cases.

The amplitude and phase of MJO serve as additional indicators for a detailed assessment of MJO forecast performance. For initially strong MJO cases, we analyze the MJO amplitude and forecasted phase angle error (Fig. b and c). The individual member has a stronger amplitude than the observation, which leads to a relatively strong amplitude in the ensemble mean during the initial 40 d. However, as the noise rapidly increases, the phase error of the individual members also escalates (as shown in Fig. c). The phase error results in a mutual cancellation in positive and negative phases of MJO among ensemble members, leading to a rapid weakening of the amplitude in the ensemble mean. In Fig. d, the phase error of the ensemble mean indicates that the speed of forecasted MJO tends to decrease at first and then starts increasing around the 10th day. A more detailed investigation into the speed of propagating MJO events is described in Sect. .

We present a qualitative diagnostic of a 20-year hindcast experiment to evaluate the overall forecast skills of IAP-CAS in Sect. . This analysis provides us with preliminary insights into the performance and biases of the system. Given that the MJO is more pronounced during boreal winter, our focus is concentrated from November to the following April. Based on Wang et al. (2019), we aim to conduct further investigations into different types of boreal winter MJO events to explore the physical explanation of system biases.

In Sect. , we describe the methodology for classifying MJO events and results. Figure  compares the composited propagation patterns of precipitation and U850 between the observation and forecast for four different MJO types. In observations, the fast-propagating MJO (Fig. a) and slow-propagating MJO (Fig. b) exhibit a consecutive eastward propagation structure from the Indian Ocean across the MC region to the Pacific Ocean. The primary distinction between the two types lies in their propagation speed. The fast-propagating MJO demonstrates a faster speed, with a velocity of 4.58 ms-1, compared to the slow-propagating type, which moves at 4 ms-1. The standing MJO (Fig. c) remains relatively stationary over the Indian Ocean and does not continue to propagate eastward. The jumping MJO (Fig. d) shows a convective system that bypasses the MC region and directly jumps from the Indian Ocean to the Pacific Ocean. Here, fast MJO and slow MJO are considered propagating MJO events, while the latter two types are regarded as non-propagating MJO events.

The observed U850 displays a coupled structure characterized by equatorial westerly anomalies of the Kelvin wave component located west of the convection and easterly anomalies of the Rossby wave component located east of the convection (Rui and Wang, 1990; Adames and Wallace, 2014; Wang and Lee, 2017). As illustrated in Fig. , a distinct contrast between propagating MJO and non-propagating MJO can be found in the circulation at the low level: in the propagating MJO events, the Kelvin wave response is strong and tightly coupled with the center of convection, which is shown in the stronger and eastward-extending easterly wind component, particularly prominent in fast MJO events. Many previous studies (Benedict and Randall, 2007; Hsu and Li, 2012; Wang and Lee, 2017) have also indicated that the presence of low-level easterly winds is a key signal that contributes to the eastward propagation of MJO by inducing low-level convergence and premoistening to the east of the major convection. In the non-propagating MJO events, the easterly wind is weak and tends to decouple from the major convection.

The model accurately reproduces the propagating morphology of the MJO and exhibits coupled signals of Kelvin and Rossby waves (Fig. e and f). However, a noticeable acceleration in speed is evident, particularly in the case of fast MJO, reaching speeds of 6 ms-1, while the simulated slow MJO moves at 5 ms-1. Figure g also shows that the forecast for standing MJO remains somewhat imprecise. This aspect is also evident in the MJO forecast skill depicted in Fig. , where the standing MJO has the lowest skill (13 d). For each MJO type, we consider the skill as the ACC of the cases initiated from day -20 to day 15 (Xiang et al., 2015). Figure  shows that the fast MJO achieves the highest skill at 32 d, while the jumping MJO and slow MJO exhibit skills of 23 and 21 d, respectively.

Additionally, from the Hovmöller diagram of observed propagating MJO (Fig. a and b), a significant change in convection is observed after crossing the MC region, which is marked by a decrease in intensity and a slower propagation speed. This change is roughly delineated by 135° E, which is commonly referred to as the MC barrier. As mentioned above, the MC barrier effect is usually amplified in climate models. In the IAP-CAS model, the forecasted convective signal of slow MJO appears to stop after crossing the MC region. Could this indicate an amplification of the MC barrier issue in the IAP-CAS model? However, this phenomenon is less pronounced in the simulation of fast MJO. Due to the zonal averaging in the Hovmöller diagram, some information may be obscured. Further investigation is required to determine the detailed characteristics of the propagating MJO simulated by the model.

Figure  presents the evolution patterns of propagating MJO. In the first 10 d, it is noticeable that the forecasted precipitation intensity of propagating MJO is significantly higher than observed, especially in the case of fast MJO. Coupled winds in 850 hPa also exhibit stronger magnitudes, with a larger zonal scale. The forecasted location of the major convection is relatively biased towards the east, which further confirms that there is an overestimation of the propagation speed. On the 15th day, the MJO convective system crosses the MC region and reaches the eastern Pacific. It is worth noting that the forecasted negative phase of MJO exhibits a significant development, with an accelerated speed, gradually intruding into the positive phase (Fig. b and d). By the 20th day, the development of the negative phase has further intensified, extending its influence into the tropical eastern Pacific region, while in the observation, the negative phase remains east of the MC region. In the later stages, as the negative phase intrudes, the forecasted convective signal in the positive phase is almost absent due to the inherently weaker convection in slow MJO. The disappearance of the slow MJO signal observed in the Hovmöller diagram after crossing the MC region may stem from the intrusion of the negative phase. This might differ from the commonly defined issue of MC barrier amplification observed in many models.

In Fig. , simulations also show that both standing MJO and jumping MJO exhibit overall enhanced convective intensity. However, they accurately capture the non-propagating characteristics of the observed MJO, such as the weak coupling of Kelvin waves and the strong coupling of Rossby waves.

Section  highlights some biases observed in the forecast of propagating MJO, which include stronger amplitude and faster propagation speed in the IAP-CAS model. These biases are also mentioned in Sect. . In this section, we aim to unravel the physical mechanisms underlying these biases.

As a large-scale convective system, MJO's genesis, evolution, and dissipation are intricately linked to atmospheric moisture (Wang, 1988; Kemball-Cook and Weare, 2001; Maloney, 2002; Wang and Lee, 2017). Given that the model forecasts exhibit a systematic bias of stronger amplitude, we start with the diagnosis of the background state in moisture. Figure  shows the winter mean specific humidity averaged over 10° S–10° N. A clear positive bias of the background moisture state in the IAP-CAS model is observed (Fig. c), which can enhance the convection in the MJO. However, the distribution of this moisture bias is non-uniform. Figure c illustrates that the positive moisture bias is more pronounced towards the western Indian Ocean and the central-eastern Pacific, and this bias gradually spreads to the upper levels. However, in the MC region, the positive moisture bias is smaller and primarily concentrated in the low level. We speculate that higher evaporation fluxes in the model may be the reason for the positive moisture bias. Therefore, the reduction in oceanic surface area within the MC region contributes to a decrease in this positive bias.

Figure  displays the precipitation-induced condensational heating (Q2) during fast MJO and slow MJO events. The condensational heating serves as a proxy for the distribution of convection, which was estimated by the moisture sink defined as 11Q2=-Lv∂q∂t+V⋅∇q+ω∂q∂p, where q is the specific humidity; V is the horizontal circulation; ω is the vertical pressure velocity; and Lv is the latent heat at condensation, which is a constant here. The vertical distribution of Q2 reveals that both fast MJO and slow MJO events in the model forecasts trigger stronger convection, particularly in the fast MJO events. Furthermore, the enhanced convective heating leads to a strong response in the coupled-MJO-related circulation (Fig. ). From the 1st day to the 10th day, there is a gradual strengthening process observed in the simulated convection, particularly pronounced in the fast MJO, with its intensity peaking on the 10th day.

To further understand the propagation and intensity variations in MJO in the IAP-CAS model, it is necessary to comprehend the underlying physical processes associated with it. Under the framework of the moisture mode, Jiang (2017) performed a moisture budget analysis on the latest generation of general circulation models (GCMs) and identified the key processes for the eastward propagation of MJO. This research revealed that the advection (V′⋅∇Q‾) of the seasonal mean moisture (Q‾) by the MJO anomalous circulations (V′) plays a crucial role in the propagation of MJO. By increasing moisture eastward and decreasing it westward of the MJO convection, the advection regulates the propagation. (D. Kim et al., 2014; Adames and Kim, 2016; Jiang et al., 2018). Among the two determining factors (V′ and Q‾), the role of the moisture gradient term is further emphasized. Many studies (Gonzalez and Jiang, 2017; DeMott et al., 2018; Ahn et al., 2020) have demonstrated that the mean moisture's horizontal gradient plays a crucial role in determining the propagation of MJO (Fig. a). It is well forecasted in the models that simulate MJO well, leading to realistic horizontal mean moisture gradients and, thus, well-forecasted horizontal moisture advection associated with the MJO (Hsu and Li, 2012; D. Kim et al., 2014; Nasuno et al., 2015; Adames and Wallace, 2015; Gonzalez and Jiang, 2017). The IAP-CAS model is capable of reproducing this gradient, although there is an overall stronger moisture bias (Fig. b). Here, the Q‾ presented is the winter mean specific humidity at 850 hPa (Q‾850). Research has indicated that Q‾850 is representative (Kim, 2019), and subsequent analysis also focuses on the 850 hPa level.

Figure  shows the composite equatorial U850 anomalies averaged over 15° S–15° N for fast MJO and slow MJO, respectively, and depicts the transition from westerly to easterly winds in the MC region (as enclosed by the two dashed blue lines), leading to the change from positive advection to negative advection. On the 1st and 5th days, the MC region is predominantly occupied by easterly winds, while from the 10th to the 20th day, the region is primarily characterized by westerly winds in both fast MJO and slow MJO. However, the forecasted amplitude of low-level wind is significantly stronger, which can be caused by the enhanced MJO convection as explained earlier.

The MJO anomalous circulation patterns in the MC region result in a positive moisture advection on the eastern part of the MJO during the early stages of the MJO's development, which facilitates the propagation of convection in the positive phase. We refer to this process as the “developing phase”. Figure  provides a detailed illustration of this process. Conversely, during the later stages, there is a negative moisture advection on the western side of the MJO, which leads to the propagation of convection in the negative phase and promotes the dissipation of the MJO. We refer to this process as the “decaying phase” (Fig. ). Compared to the observation, the stronger amplitude of the low-level moisture advection (V′⋅∇Q‾) in the model explains the gradual enhancement of convective moist phases during the early stages and the amplification of convective dry phases during the later stages (Fig. ). The model's moist environment leads to intensified convection, triggering the strengthening of coupled wind fields, which in turn enhances the moist phase in the early stage and the dry phase in the later stage of convection. Consequently, during the development phase of the MJO, its amplitude gradually strengthens. Conversely, during the decaying phase of the MJO, the intensity of the dry phase also progressively increases.

As the simulated propagating MJO gradually intensifies, we observe an enhancement of easterly winds on the east of the convective center, accompanied by an overestimation in zonal scale, indicating the triggering of stronger Kelvin waves (Fig. b and d). According to Wang et al. (2019), MJO with a larger zonal scale will experience an increased eastward propagation speed since the phase speed is inversely proportional to the wave number. This phenomenon is also observed in the observation, where the Kelvin wave response to fast MJO exhibits a larger zonal scale compared to slow MJO. Subsequently, during the decay phase of the propagating MJO, the model exhibits a pronounced Rossby wave response triggered by the MJO, leading to the intrusion of convective negative phases and facilitating the dissipation of the MJO.

In addition to examining the winter mean moisture state (Q‾), we analyzed MJO-related moisture anomalies (Q′) as well (Fig. ). By comparing the evolution pattern of moisture anomalies between slow MJO and fast MJO, it is found that the moisture anomalies in the eastern part of fast MJO are more intense compared to the slow MJO. This results in stronger low-level moisture transport towards the convective region, thereby also facilitating the intensification and acceleration of the MJO. Moreover, there is a significant distinction in the spatial correlation between fast and slow MJO, and it happens as early as the first day. As the forecast lead time progresses, the accuracy of the moisture forecast deteriorates, while fast MJO events display comparatively better performance. The disparity in moisture anomalies is possibly a pivotal factor contributing to differences in forecast skills between the fast (32 d) and the slow MJO (21 d). This underscores the significance of improving moisture forecast in the MJO forecast.