Data-driven investigation on the boreal summer MJO predictability

Data-driven investigation on the boreal summer MJO predictability | npj Climate and Atmospheric Science

Abstract

The summer MJO exhibits different characteristics from its winter counterpart, particularly distinguished by propagation in both eastward and northward directions, which is relatively less understood. Here, we explore the primary sources of the summer MJO predictability using Machine Learning (ML) based on the long-term climate model simulation and its transfer learning with the observational data. Our ML-based summer MJO prediction model shows a correlation skill of 0.5 at about 24-day forecast lead time. By utilizing eXplainable Artificial Intelligence (XAI), we discern Precipitable Water (PW) and Surface Temperature (TS) as the most influential sources for the summer MJO predictability. We especially identify the roles of PW and TS in the eastern and northern Indian Ocean (EIO and NIO) regions on the propagation characteristics of the summer MJO through XAI-based sensitivity experiments. These results suggest that ML-based approaches are useful for identifying sources of predictability and their roles in climate phenomena.

Introduction

The Madden-Julian Oscillation (MJO) is an intraseasonal oscillation, widely recognized as one of the dominant modes in the tropical atmosphere 1, 2. In general, the MJO is a planetary scale disturbance that propagates eastward with a period of 30 to 90 days 3. However, the MJO displays a pronounced seasonality due to the influence of the climatological background states 4, 5, 6. In addition to differences in intensity and period, the propagation features exhibit distinct differences, contributing to its unique behavior 7, 8. During the boreal winter, the MJO typically moves eastward along the equator. Conversely, in boreal summer, it propagates in a more complex manner with a relatively shorter period (30-60 days) and a northwest-southeast tilted rainband, often referred to as the Boreal Summer Intraseasonal Oscillation (BSISO) 4, 9, 10, 11, 12, 13. Specifically, the summer MJO primarily propagates in a northeastward direction, originating from the equatorial Indian Ocean (IO) into the Asian Summer Monsoon (ASM) region and the western Pacific 14. The northeastward propagation of convection that occurs in the IO during the summer season could hold crucial implications for the ASM region 15, 16, 17, which directly influences agricultural activities in South Asia. Hence, an accurate forecast of the summer MJO affecting the ASM is important.

Over the past decade, numerous operational models have made efforts to improve the prediction of the summer MJO 18. Nevertheless, most operational models, with the exception of ECMWF which has the highest skill 19, fail to realize their potential predictability with a skill of less than three weeks 20, 21. It has been considered that the prediction skill of summer MJO is more limited compared to that of winter MJO 19, 22. On the contrary, a recent study has shown that NASA’s Goddard Earth Observing System S2S prediction (GEOS-S2S) exhibits higher predictability of the summer MJO than the winter MJO 23. These contrasts and limitations stem from errors inherent in the operational models, primarily due to our limited understanding of the summer MJO. Understanding the sources of the summer MJO’s predictability plays a pivotal role in improving its forecast skill.

Many studies have devoted to understanding the dynamics of the summer MJO, particularly to elucidate the northeastward propagation which is the most distinctive feature of the summer MJO 13, 24, 25, 26, 27, 28, 29, 30, 31. However, there are several possible mechanisms that emphasize different processes. For example, theoretical studies have found a vital role of the vertical wind shear and mean flow 13, 28, and convective momentum transport 30, 31. Recent studies have suggested that the low-level horizontal moisture advection as a key process for the northward propagation in the column-integrated moisture or moist static energy (MSE) budget 26, 32, 33. Therefore, assessing the relative contributions of the sources of summer MJO predictability will provide important clues to advance our current understanding. In addition, it is important to accurately identify the influences of the predictability sources on the eastward and northward propagation, which are the most distinctive features of the summer MJO.

With the recent increase in the application of Machine Learning (ML) and eXplainable AI (XAI) methods, which interpret ML results, across climate research 34, 35, 36, 37, the MJO community has also made endeavors in this direction 38, 39, 40, 41, 42. Several studies have demonstrated that ML-based MJO prediction models exhibit comparable performance to operational models for the boreal winter MJO 38, 40, 42. In addition, Shin et al. 43 have quantified the contribution of various climate variables to the winter MJO at each forecast lead time using XAI methods. However, the utilization of ML-based approaches to the summer MJO remains relatively limited, with the majority of studies mainly focusing on the winter MJO.

In this study, we aim to provide an ML-based systematic assessment of the source of boreal summer MJO predictability. To achieve this, we adopted the framework established by Shin et al. 43, which built a winter MJO prediction model and investigated the source of winter MJO predictability based on ML and XAI methods. Thus, as in Shin et al. 44, which has improved the ability to simulate the summer MJO from that of the previous version (CESM1) 45. Subsequently, we fine-tuned the ML models using observational data to correct model biases in the CESM2 simulation via transfer learning 44. Therefore, our ML-based summer MJO prediction model can have the advantage of effectively capturing the properties of the summer MJO by leveraging the abundant CEMS2 simulation and fine-tuning it with observational data. After the completion of our ML-based model, we intend not only to scrutinize the sources of summer MJO’s predictability but also to investigate the role of the primary sources on the propagation characteristics of the summer MJO using straightforward and intuitive XAI-based experiments.

Results

Performance of the CNN-based summer MJO prediction model

Figure 1a illustrates the performances of our Convolutional Neural Networks (CNN) 46 for the summer MJO after transfer learning with the observational data (denoted CNNOBS) for each forecast lead time. We used the CNN framework 42 to learn the relationship between five input variables (outgoing longwave radiation (OLR), zonal winds at 200hPa (U200) and 850hPa (U850), precipitable water (PW), and surface temperature (TS) over 20°S-40°N and 0-360°E) and the output variables, Real-time Multivariate MJO (RMM) 1 and 2 indices, during the boreal summer season (May-June-July-August-September-October). The details of the data pre-processing procedures are described in the Methods section.

a The black solid line illustrates the bivariate correlation skills (BCOR) of our CNNOBS after transfer learning for each forecast lead time from 1 to 30 days. The BCOR is exclusively for events with strong initial MJO amplitude \({\boldsymbol{(}}\sqrt{{{{\boldsymbol{(}}{\boldsymbol{RMM}}{\boldsymbol{1}}{\boldsymbol{)}}}^{{\boldsymbol{2}}}{\boldsymbol{+}}{\boldsymbol{(}}{\boldsymbol{RMM}}{\boldsymbol{2}}{\boldsymbol{)}}}^{{\boldsymbol{2}}}}{\boldsymbol{ > }}{\boldsymbol{1}}{\boldsymbol{)}}\). The gray dashed line indicates a skill level of 0.5. The shaded line represents the 95% confidence level, determined using 1000 bootstrap samples. Each colored dot (red; PW, yellow; TS, green; U200, blue; U850, and purple; OLR) represents the skill when removing the effect of a single variable at 5-day intervals from 5 to 30-day forecast lead time. b Bivariate-Mean-Square-Differences (BMSD), the quantified contribution, are computed by comparing the original prediction with a single variable-zeroing prediction for forecast lead times of 5, 10, 15, 20, 25, and 30 days. The gray bars indicate the total sum of BMSDs for all variables. The variables represented by each colored line and dot are the same as in a, and the dots are the ratio of each variable’s BMSD to the total BMSD.

Our CNNOBS exhibits a prediction skill based on the bivariate correlation skill 22, 47, above 0.5 up to about 24 days forecast lead time (Fig. 1a), which is comparable to the prediction skill in the ML-based winter MJO prediction models 42. In addition, our CNNOBS shows slightly superior or comparable performance compared to the operational models with a skill of about three weeks, except for the ECMWF model, in predicting the BSISO 19, 20. We note that GEOS-S2S showed skill in predicting the winter MJO up to 25 days, similar to ours, while it exhibited higher skill in summer (> 30 days) 23. This prediction performance suggests that our CNNOBS successfully learned the relationships between the input variables and the RMM indices, capturing the characteristics of the summer MJO. From the CNNOBS model, we also performed additional transfer learning targeting the OLR-based MJO index (OMI) 48, which leverages a partial similarity of predictability source features between RMM and OMI. Our model for the real-time OMI (ROMI) prediction shows bivariate correlation skill above 0.5 up to 29 days (Supplementary Fig. 1), demonstrating consistent or even better predictability of different MJO index as in the RMM prediction.

Investigation of the sources of the summer MJO predictability

To identify the sources of predictability in the summer MJO, we conducted additional forecast experiments to assess the relative importance of input variables in influencing the forecast skill of the RMM indices. This is done by systematically excluding the effect of each input variable by setting it to zero, and calculating the change in forecast skill. In this way, the importance of a single variable can be linked to the degradation of forecast skill after eliminating its effect. In Fig. 1a, the largest reduction in skill is displayed up to about 20-day forecast lead time compared to the ‘all-variable’ forecast (black line) when the effect of PW is eliminated. Removing TS effects shows the most substantial reduction in skill as the forecast lead time increases. Note that the skill decrease due to the removal of the TS effects is about twice as large as in the winter for more than 20-day forecast lead time, suggesting that the TS information is more important in the boreal summer. In contrast, the remaining three variables exert relatively minor impacts on overall skill. These results remain consistent when the skill is assessed using an alternative root-mean-square error metric (Supplementary Fig. 2).

Furthermore, we quantitatively evaluate the influence of each input variable on the RMM indices themselves by calculating the Bivariate Mean Square Difference (BMSD) 22 in predictions between the ‘all-variable’ prediction and the single variable-zeroing prediction in Fig. 1b. In general, PW is the most influential variable for forecast lead times of 15 days or less. TS becomes the most dominant variable after the 15-day forecast lead time, which is consistent with the results in Fig. 1a. These results suggest that a considerable part of the predictability of the summer MJO comes from PW and TS.

We perform identical investigations on the BSISO1 indices, the first and second modes of the principal component (PC) time series, introduced in Lee et al. 49, using the same CNN architecture based on the RMM index. The prediction skill for the BSISO1 is about 17 days based on a skill of 0.5, which is somewhat lower than the RMM index (Supplementary Fig. 3a). This lower skill for BSISO1 than RMM is consistent with the MJO hindcast results 21, which are related to the high-frequency variability in BSISO1 49. Similar to the results of the RMM index, the relative importance of the input variables on a basis of the prediction skill demonstrates that PW is the most dominant variable up to 20-days forecast lead time, and changes to TS beyond the 20-day forecast lead time in Supplementary Fig. 3a. Likewise, for BMSD, the most influential variable shifts from PW to TS as the forecast lead time increases (Supplementary Fig. 3b). The overall BSISO1-based results in terms of relative importance are consistent with the RMM-based evaluations.

In addition, we employ the Signed-Contribution (SC) map as an XAI method (see Methods) 42, to visualize which spatial patterns in the input variable act as the sources of predictability based on our CNNOBS. In the SC map, the signs indicate the relationship between the input and output variables for each grid, and the magnitude denotes the extent of contribution. Figure 2a, b show the SC maps and the linear lag-correlation maps of the five input variables for RMM1 at a 15-day forecast lead time, respectively. The results for the RMM2 index are shown in Supplementary Fig. 4. Consistent with the results in Fig. 1, strong signals are observed in PW and TS in the SC maps (Fig. 2a). Compared to the linear lag-correlation maps (Fig. 2b), the spatial distribution of the relationship exhibits a general similarity to those of the SC maps, although some differences are observed in certain regions. Specifically, the SC map for PW reveals a notable contribution, characterized by a positive relationship in the Arabian Sea (AS), Bay of Bengal (BoB), and western North Pacific (WNP). However, the linear lag-correlation map for PW shows weak relationships in these northern regions, spanning from the AS to BoB and WNP. In particular, the WNP region presents a weak negative value on the lag-correlation map, featuring a dipole pattern with positive signals in the IO region. This reflects the typical pattern of the moisture anomalies 15 days prior to the peak of RMM1. Despite some of these differences, the general sign pattern is consistent.

The left and right columns are (a) the SC maps and (b) the linear correlation maps for RMM1, respectively. The rows from top to bottom sequentially indicate the maps for PW, TS, U200, U850, and OLR. The black boxes in the SC maps of RMM1 for PW and TS represent the selected regions where strong signals appear.

Interestingly, however, the most striking discrepancy is that the relative importance of the variables appears less pronounced in the linear lag-correlation maps. These results suggest that our XAI-based SC maps not only capture the relationships between input and output variables well, but also represent their relative contributions compared to the linear correlation map. Specifically, although the OLR is correlated with the RMM index comparably to the other variables in Fig. 2b, it displays a minimal contribution in preceding analyses (Fig. 1) and the SC maps (Fig. 2a). Consequently, the distinction between SC maps and linear correlation maps suggests that SC maps are able to identify the sole role of each input variable, excluding cross-relationships between variables.

The positive signals in the SC maps of PW and TS for RMM1 (RMM2) indicate that positive anomalies in the IO (western Pacific; WP) are related to an increase in the RMM1, which has the convection in the MC region from the eigenvector pattern of the combined empirical orthogonal function (CEOF) (RMM2, which has convection in the Pacific region from the eigenvector pattern of CEOF) 50, after the 15-day forecast lead time (Fig. 2a). These strong signals tend to move eastward (closer to the convection) as the forecast lead time decreases (not shown). Interestingly, a salient feature of the summer SC maps is that the signals are concentrated in the northern hemisphere, suggesting that our CNNOBS has learned well the characteristics of the summer MJO, which are distinct from those of the winter MJO.

The effects of major sources on the propagation of the summer MJO

To analyze the impacts of PW and TS on eastward and northward propagation, we conducted additional ML-based experiments. First, we categorized the MJO events based on the RMM indices into two cases (see Methods): those propagating with strong MJO amplitude (referred to as the strong case) and those propagating with weak MJO amplitude (referred to as the weak case). In particular, we focus on events where convection and suppression are located in the IO, indicating MJO phases 2 (P2) and 6 (P6), in order to consider both eastward and northward propagation. The dashed lines in Fig. 3a display the RMM composites on the phase-space diagram for each case initiated in P2 and P6 using the target data (i.e., observational data). The strong cases are characterized by propagating while maintaining the MJO amplitude above 1. In contrast, the MJO amplitudes of the weak cases weaken rapidly to less than 1 within about 5 days.

a The red and blue lines represent the composite of strong and weak cases of the summer MJO from 0 to 24 forecast days, originated in P2 and P6, respectively. The CNNOBS predictions are normalized by each standard deviation (SD) of RMM1 and 2 at each forecast lead time. The dots indicate every 3 days. The dashed and solid lines correspond to the observational data and the CNNOBS predictions. The 0-day value (the first value) is set to the observational value for all cases. The number of cases is represented at the start point of each case. The small and large gray dashed circles are the lines with MJO amplitudes of 1 and 1.5, respectively. b The CNNOBS prediction-based RMM phase diagram after scaling the initial MJO amplitude to 1.5 for the same case classification as in a. The 0-day value is set to the scaled value as 1.5 amplitude using observational data. The predictions are also normalized to each SD for each forecast lead time.

Using the composite of the input variables for these two cases, we conducted predictions using CNNOBS for each forecast lead time as shown in Fig. 3. The prediction values are normalized by dividing the standard deviation (SD) of RMM1 and 2 at each forecast lead time, since the magnitude of the CNNOBS prediction systematically decreases as the forecast lead time increases (Supplementary Fig. 5). In general, as shown in Fig. 3a, the CNNOBS successfully predicts each case (solid line in Fig.

After making the equal initial MJO amplitudes by multiplying each SF to all input variables, we newly predict all events. Figure 3b shows that even after scaling the initial amplitude, there remains a discernible difference between the paths of the RMM index in the strong and weak cases. Therefore, this allows us to further focus on analyzing the influence of specific input patterns on the propagation characteristics of the summer MJO, independent of the initial MJO amplitude variations.

Therefore, based on these predictions, we conducted the XAI-based sensitivity experiments by changing the input variables. To examine the effect of the specific region of the input variable on propagation, we select the regions with strong signals in the SC map of RMM1 (black boxes in Fig. 2a), which are associated with convection in MC regions after 15 days. Again, we focus on events where convection and subsidence take place in the IO (i.e., P2 and P6), enabling us to examine both eastward and northward propagation simultaneously. The first region is the eastern IO to MC along the equator (10°S-7.5°N, 70-130°E; hereafter referred to as EIO), and the second is the northern IO (Arabian Sea to Bay of Bengal) to WP (10-20°N, 50-150°E; hereafter referred to as NIO).

We perform a sensitivity experiment as the XAI method, introduced in Shin et al. 35, which perturbs the PW or TS in the EIO and NIO regions, the initial input variables, by adding or subtracting 1.5 SD for each grid. By examining how the output changes sensitively in response to the perturbations of the specific input region, we can isolate the sole influence of that particular input index on the RMM indices. Figure 4a, b represent the results of the XAI-based sensitivity experiment for the PW and TS in the EIO regions, which are positively related to the RMM1 after 15-day in Fig. 2a. When we added a 1.5 SD perturbation of the PW to the weak case in P2, further moistening of the EIO PW (blue dashed line) results in a well-propagating with strong amplitude compared to the original weak case (blue solid line). Moreover, the response propagates farther than in the original strong case while maintaining a stronger amplitude.

In a and b, the red and blue solid lines are the same as in Fig. 3b. The red and blue dashed lines indicate the results of the sensitivity experiments for strong and weak cases, respectively. Panels a and b represent the results for EIO PW and EIO TS, respectively. For the strong case in P2 (P6), we subtract (add) 1.5 SD of each variable in the EIO region at each grid point. Conversely, for the weak case in P2 (P6), we add (subtract) 1.5 SD of each variable in the EIO region at each grid point. Panels c and d illustrate the latitude-averaged (10°S-10°N) evolution of the reconstructed OLR using multiple regression coefficients between the observational OLR and CNNOBS predictions (RMM1 and 2 indices) in P2. The x-axis is longitude, and the y-axis is time. The contours and shadings indicate the OLR reconstructed by the original predictions and the differences in predictions (sensitivity – original), respectively. Panels e and f also show the latitude-averaged evolution of the reconstructed OLR, but except for the EIO TS. Panels c and e represent the results for the strong case, while d and f are for the weak case.

On the other hand, the drier EIO PW for the strong case in P2 (subtracting 1.5 SD PW; red dashed line) leads to slower propagation with weaker MJO amplitude compared to the original strong case (red solid line). The moisture is known to be an important factor in the development and maintenance of MJO convection, thereby influencing the propagation direction of the summer MJO 26, 32. In other words, elevated moisture may contribute to the moistening of that area, leading to more pronounced propagation and deeper convection. Hence, our results confirm the role of PW in these MJO dynamics within the context of the XAI-based investigations. For P6, we subtract 1.5 SD from the weak case and add 1.5 SD to the strong case due to the subsidence being located in the IO. The overall changes in the direction of the responses for P6 are symmetrical, although the sensitivity response for the weak case is relatively weaker than for P2.

Additionally, the amplitudes of the sensitivity experiment for the P2 weak case steadily increase for all forecast lead times compared to the original strong case. On the other hand, the amplitude decreases in the sensitivity experiment for the P2 strong case much more within ~12 days forecast lead time than the original weak case. However, the decrease in amplitude becomes relatively smaller as the forecast lead time increases. These results indicate that the responses of the strong and weak cases for the same perturbation magnitude exhibit asymmetry with forecast lead times, which needs to be further analyzed to understand these nonlinearities.

Figure 4b represents the results of the identical sensitivity experiments for the EIO TS. In line with the EIO PW, the responses of the EIO TS show that warming (cooling) in the EIO region tends to elevate (reduce) the MJO amplitudes for the weak (strong) case in P2. The warm SST conditions to the east of the convection may affect the propagation of convection by increasing the convective instability and evaporation. In the same manner, the responses of EIO TS are also symmetric in direction in P6. These responses become relatively large for the long forecast lead times, which is consistent with the increased contribution of TS for longer forecast lead times in Fig. 1. However, the overall differences are smaller than those of the EIO PW, suggesting that the EIO PW plays a more critical role in the propagation of the summer MJO compared to the EIO TS.

So far, we showed the effects of EIO PW and TS based on the RMM phase diagram (Fig. 4a, b), which is limited to the representation of the spatial pattern. To identify the propagation patterns, we reconstruct the OLR using multiple regression coefficients (\(\alpha\) and \(\beta\) in Eq. ( 1)) on the observational OLR and predicted RMM indices (Fig. 4c–f) as follows:

Previous studies have suggested that moister and drier conditions on the eastern side of convection and suppression play a crucial role in the eastward propagation of the MJO 32, 51, 52, 53, respectively. Therefore, we identify the evolution of the reconstructed OLR averaged over 10°S-10°N in Fig. 4c–f to focus on the eastward propagation of the summer MJO. Figure 4c, e). In contrast, the eastward propagation rapidly weakens in the weak case (Fig. 4d, f). In the difference pattern resulting from the sensitivity experiment on the EIO PW, the strong case (Fig. 4c) shows a dominant increase in the OLR, reflecting a reduction in the eastward propagation of convection, up to about 20 days. On the contrary, in the weak case (Fig. 4d), OLR decreases dramatically (i.e., convection becomes stronger) until ~20 days as the EIO PW moistens, indicating stronger eastward propagation. The prevailing responses within a 20-day forecast lead time in the sensitivity experiments for EIO PW are consistent with PW being the most influential variable, especially up to about three weeks forecast lead time as shown in Fig. 1. Then, after 20-days in Fig. 4c, the responses for the strong case exhibit a weakening of subsidence (i.e., decrease in positive OLR) in the IO regions, which is related to P6. Conversely, an enhanced suppression is observed for the responses of the weak case in Fig. 4d. These results suggest that the EIO PW may also influence the changes in the MJO phase 54, 55, 56, 57.

Figure 4e, f show the evolution of the reconstructed OLR to explore how warmer and cooler EIO TS conditions cause changes in the pattern of eastward propagation in P2. Roughly, in Fig. 4e(Fig. 4f), cooling (warming) of the EIO TS leads to a weakening (strengthening) of convection in the strong (weak) case, which aligns with the responses of the EIO PW. However, consistent with the RMM phase diagram-based results in Fig. 4a, b, the strength of the responses to the EIO TS is considerably weaker compared to the EIO PW. Interestingly, the EIO warming (cooling) continuously contributes to decreasing (increasing) OLR in the MC and western Pacific for even longer lead times (Fig. 4e, f), which is somewhat different from those in the EIO PW case. These results can be interpreted that the TS is less coupled with the MJO phase compared to the PW, but acts as a long-term boundary condition for the local convection. For P6 in Supplementary Fig. 6, we observe a consistent response to the sensitivity experiments with the opposite perturbations. As a result of the application of the XAI-based analysis, we found that PW exerts a greater influence than TS in the EIO region, and moist conditions play a role in aiding the active propagation of the summer MJO.

Next, we examined the impacts of PW and TS in the NIO region of Fig. 5, which are also positively related to convection near the MC (i.e., RMM1) after a 15-day forecast lead time in Fig. 2a, using the same analysis as in Fig. 4. For both PW (Fig. 5a) and TS (Fig. 5b) in the NIO originating from P2, subtracting 1.5 SD from the strong case results in weaker propagation, while adding 1.5 SD to the weak case leads to well-propagation with stronger amplitude. The responses of the sensitivity experiments in the P6 cases demonstrate the same direction of change as in P2. Interestingly, in the NIO region, the degree of response to PW and TS is comparable to each other. These results suggest that PW and TS in the NIO region have a similar level of influence on the summer MJO based on the RMM index analysis.

Same as Fig. 4, but except for the NIO region (a–f). c–f The evolution of the reconstructed OLR is averaged over the longitude range of 70-95°E. The x-axis is latitude, and the y-axis is time.

Previous studies have highlighted the importance of TS in the NIO region for the northward propagation of the summer MJO based on air-sea interactions 27, 58, 59, 60. Specifically, when convection is located near the equatorial IO, there is more incoming solar radiation and less evaporation as subsidence occurs north of the convection, leading to warmer SST anomalies. These warm SST anomalies provide a favorable condition for convection. In addition, an increase in the NIO PW is known to play an essential role in northward propagation. The interaction between baroclinic and barotropic modes under strong mean easterly shear in summer can explain northward propagation by moisture convergence in the planetary boundary layer (PBL) 13, 28. Additionally, moisture advection in the free atmosphere and PBL can contribute to northward propagation by increasing moisture tendency 13, 26. Hence, we identify the evolution of the reconstructed OLR averaged over 70-95°E to investigate patterns associated with northward propagation. As shown in Fig. 5c-f, the strong case (contours in Fig. 5c, e) clearly exhibits stronger northward propagation compared to the weak case (contours in Fig. 5d, f). The evolution of the differences through sensitivity experiments for P2 cases indicates that drying (Fig. 5c) and cooling (Fig. 5e) of the NIO region in the strong case hinder northward propagation, whereas moistening (Fig. 5d) and warming (Fig. 5f) of the NIO region in the weak case enhance northward propagation. In addition, the responses for P6 also show consistent results with those for P2 (Supplementary Fig. 7). Collectively, our CNNOBS seems to grasp the relationship between NIO TS or PW and RMM indices based on their roles in the literature.

In general, the difference in magnitude between the responses of the sensitivity experiments for NIO PW and TS is smaller than the response difference observed for EIO regions. These findings imply that both PW and TS influence the summer MJO in the NIO regions to a comparable extent. Additionally, in line with the results in the EIO regions, the responses of the sensitivity experiments for NIO PW show a dipole pattern, e.g., the change in responses from weakening of convection to weakening of suppression around the 15-day forecast lead time in Fig. 5c. On the other hand, the responses to the NIO TS persist for the longer forecast lead time. This implies that the TS has a long-term predictability memory of the summer MJO (Fig. 1) as a boundary condition. In addition, consistent with the EIO results, PW is relatively strongly coupled to convection 54, 55, 56, 57 and may contribute to the phase transition, while TS is less linked and thus has a smaller effect on the phase transition. As a result, the NIO PW and TS influence the northward propagation with comparable magnitudes, although the nature of the effects is slightly different.

Variation of moisture over time with changes in the major sources

So far, the present prediction experiments are all based on RMM indices, so it is difficult to ascertain how the indices in the EIO and NIO regions actually affect the northward and eastward propagation of the summer MJO. Previous studies have suggested that the evolution of moisture directly affects these MJO behaviors, so changes in moisture are crucial for the propagation of the summer MJO 13, 26, 28, 32, 33. Therefore, we utilize the concept of the moisture budget equation, which describes the movement of convection into regions of increased moisture tendency, using an ML-based method. In other words, we investigate whether changes in input variables over the EIO and NIO regions can indeed influence the propagation of the summer MJO by modulating moistening in areas associated with eastward and northward propagation (see details in Methods).

We select regions pertinent to the eastward (10°S-10°N, 90-150°E) and northward (5-20°N, 60-100°E) propagation of the summer MJO. In each of these regions, we independently train the relationship between the difference in moisture (\(\Delta q(t)=q\left(t\right)-q(t-{lead\; time})\)) and the five input variables for each forecast lead time (hereafter, we refer to as \({{CNN}}_{\Delta q}\)), using the same CNN architecture except for the output variable. In addition, we only focus on the MJO-related variability by reconstructing \(\Delta q\) based on the RMM indices (see Methods for details). Figure 6a displays the prediction skills of \({{CNN}}_{\Delta q}\) for the eastward and northward boxes at 5, 10, 15, and 20-day forecast lead times. Our \({{CNN}}_{\Delta q}\) exceeds the correlation skill of 0.5 at a 20-day forecast lead time, suggesting that this model can be used to understand the processes for MJO-related moistening. To do this, we perform the XAI-based sensitivity experiments to explore the \(\Delta q\) responses in eastward and northward boxes to the perturbations (i.e., \(\pm\)1.5 SD) of PW and TS in the EIO and NIO regions, respectively, with our validated \({{CNN}}_{\Delta q}\). Through the sensitivity experiments, we investigate whether variations (i.e., \(\pm\)1.5 SD) in PW or TS over the specific regions could induce changes in MJO-related moistening to the east or north of the summer MJO, consequently influencing the propagation.

a The \({{\boldsymbol{CNN}}}_{{\boldsymbol{\Delta }}{\boldsymbol{q}}}\) skills, independently trained with five identical input variables, for the eastward box (black solid line) and northward box (gray solid line). The gray dashed line indicates a skill level of 0.5. The responses of the reconstructed \({{\Delta}}{\boldsymbol{q}}\) in the eastward box (y-axis, sensitivity-original prediction) to the perturbation in the EIO PW and TS for (b) 5, (c) 10, (d) 15, and (e) 20 days forecast lead time. The x-axis is the normalized PW and TS in the EIO region. The green and brown (red and blue) lines represent the responses of the reconstructed \({\boldsymbol{\triangle }}{\boldsymbol{q}}\) when 1.5 SD are added to and subtracted from the EIO PW (EIO TS), respectively. The responses of the reconstructed \({{\Delta }}{\boldsymbol{q}}\) are averaged over values in 0.5 intervals from -2.5 and 2.5. The shaded area indicates a 95% confidence level using a bootstrap method. f–i Similar to b–e, but focusing on the responses in the northward box (y-axis, sensitivity-original predictions) to the perturbation in the NIO PW and TS for (f) 5, (g) 10, (h) 15, and (i) 20 days forecast lead time. The x-axis is the normalized PW and TS in the NIO region.

Figure 6b–e show the \(\Delta q\) responses, original prediction minus new prediction after the sensitivity experiment, in the eastward box resulting from the \(\pm\)1.5 SD perturbations for both EIO PW and TS. When 1.5 SD is added and subtracted to the EIO PW, the averaged \(\Delta q\) responses are clearly separated into increase and decrease, respectively, indicating the positive relationship between the EIO PW and the \(\Delta q\) in the eastward box. In other words, an increase in the EIO PW induces a moistening in the eastward box, implying its contribution to the eastward propagation of the summer MJO. Conversely, a decrease in the EIO PW is associated with the drying of the eastward box, which inhibits eastward propagation. For the EIO TS, warmer (cooler) conditions are related to the increases (decreases) in \(\Delta q\) in the eastward box. Interestingly, \(\Delta q\) in the eastward box represents overall greater responses to the EIO PW perturbation, although some variation can be found depending on the forecast lead time. In particular, the response to the EIO PW is pronounced at the 10-day forecast lead time (Fig. 6c), exhibiting a difference of approximately 1.5 times or more than those of the TS case when 1.5 SD is added. These results suggest that changes in EIO PW have a greater influence on the moistening of the eastward box than TS. This supports the findings from Fig. 4, that the EIO PW exerts a relatively strong impact on the enhanced eastward propagation, by adopting \({{CNN}}_{\Delta q}\) approach.

Figure 6f–i show changes in the reconstructed \(\Delta q\) in the northward box, from \(\pm\)1.5 SD sensitivity experiments for both NIO PW and TS. As in the eastward box, the signs of the responses in the northward box are clearly separated. However, unlike the eastward box, the \(\Delta q\) responses in the northward box are of comparable magnitude for both NIO PW and TS. In other words, using XAI-based methods, it can be interpreted that the increases in the NIO PW and TS contribute to the moistening in the northward box with a similar level of magnitude. Therefore, these results can underlie the comparable influences of NIO PW and TS on the northward propagation as shown in Fig. 5. Consequently, with this approach, we can realize that changes in PW and TS in the EIO and NIO regions can actually affect the eastward and northward propagation of the summer MJO through the modulation of the moistening (i.e., \(\Delta q\)). In addition, we estimate their relative roles in the eastward and northward propagation of the summer MJO. The framework of this method is expected to be scalable and versatile for in-depth investigations to understand dynamics.

Discussion

In summary, we successfully built an ML-based summer MJO forecast model and confirmed that PW and TS exert a substantial influence, especially in the EIO and NIO regions for the 15-day forecast lead time in the SC map, compared to other variables through various XAI approaches. Based on the sensitivity experiments for P2, it is evident that PW is dominant in the EIO region, while both PW and TS influence with comparable magnitude in the NIO region. To complement the RMM index-based interpretation, we independently constructed an ML-based model for the relationship between five input variables and \(\Delta q\) for regions associated with eastward and northward propagation. Our results demonstrate that when the EIO PW (NIO PW and TS) increases, the \(\Delta q\) in the eastward (northward) box also moistens, which facilitates the eastward (northward) propagation of the summer MJO. The significant contribution of TS to northward propagation may also indicate the important role of air-sea interaction in predicting summer MJO propagation in the NIO region. That is, the use of ML allows us to assess the relative importance of input variables, as well as to investigate the role of specific regions with strong signals through various XAI-based tests.

Our investigation on the summer MJO primarily centered on the RMM index, which has limitations in capturing variations across latitudes 61. To address this limitation, we extended our analysis to the BSISO1 index, as shown in Supplementary Fig. 3. Despite a relatively reduced prediction skill due to the inclusion of high-frequency variabilities, both PW and TS remain dominant sources of the summer MJO predictability, with signals appearing in similar regions in the SC maps for PC2 of BSISO1. We utilize the XAI-based sensitivity experiments on BSISO1 for PW and TS in the EIO and NIO regions. In addition, we newly construct the BSISO1-related \({{CNNs}}_{\Delta q}\). Overall, the results of these experiments yield consistent outcomes with the RMM index (not shown). However, there are several indices that represent the summer MJO 25, 48, so our ML-based approaches are flexible enough to be applied in different ways by simply changing the output variable.

We utilize the ML-based framework, introduced in Shin et al. 43, to learn the characteristics of the summer MJO. Our CNN is pre-trained with the long-term CESM2 simulation and then fine-tuned with observational data. The performance of our CNNOBS is comparable to other operational models, but there is room for further improvement if we use the long-term data, which simulates the summer MJO features of the observations better than CESM2. In addition, further optimization of the combination of input variables and model structure for the summer MJO may enhance its prediction skills.

DL is specialized in learning nonlinearities, which are abundant in nature. Understanding these asymmetries can be instrumental in making more accurate predictions. Figure 6 illustrates one of the nonlinearities learned by our CNNOBS. While the responses of the reconstructed \(\Delta q\) generally exhibit symmetry for positive and negative EIO and NIO indices, they show asymmetry for specific forecast lead day (e.g., 10-day for the eastward box). These ML-based results reveal that the same magnitude of perturbations can induce different responses in the targets, depending on the sign of the input index. Further studies are needed to comprehend the nonlinear behavior of the summer MJO.

However, as mentioned in Shin et al. 43, the CNN faces the “time-skipping” feature that learns the relationships for each forecast lead time independently. In other words, while our CNNOBS demonstrates proficiency in capturing changes in the characteristics of the summer MJO in each forecast lead time similar to the observational data in Fig. 3, it is limited in accurately learning the evolution due to the inability to organically utilize information between consecutive lead days. To enhance the model’s ability to learn changes over time, DL techniques such as Long Short-Term Memory 62 and Transformer 63 can be employed. These methods leverage previous information to facilitate learning, thereby improving accuracy in capturing complex evolution.

Methods

Convolutional Neural Networks (CNN) and Transfer learning

CNN is specialized in extracting features from input images. CNN’s inductive bias is advantageous with learning spatial traits that is significant to the summer MJO. With 2-dimensional maps (size of 144 × 25) of five input variables and two numbers as the output, we employed a regression CNN architecture identical to that used in Shin et al. 43. Our CNN comprises three convolutional layers, each with 30 filters (2×2), one hidden layer containing 50 units, and one output layer with 2 units. We used the rectified linear unit (ReLU) as the activation function, the mean square error as the loss function, and Adam as the optimizer. To set the number of epochs, we applied early stopping. We independently trained separate models for each forecast lead time ranging from 1 to 30 days. To stabilize our model outputs, we utilized 20 ensembles, each with different random initial weights. All results presented are based on the ensemble mean, which provides a robust representation of our findings.

Our approach involves two stages of training the CNN to learn the nature of the summer MJO. In the first stage, we train the CNN with long-term simulations generated by CESM2, named as CNNCESM2, using the entire period of 1200 years of data for pre-training. Subsequently, we employ transfer learning, a specialized technique to fine-tune the ML model. During the fine-tuning process, we re-fit our model to the observational data, updating the parameters by fine-tuning the pre-trained model. This step is undertaken to correct for any potential bias in the CESM2, leading to a marked skill increase after the transfer learning (Supplementary Fig. 8). For transfer learning, we divide the observational data into three test data sets in a ratio of 3:3:4 for cross-validation, and the remainder of each ratio is used for training during transfer learning. In other words, the observational dataset of 12, 12 and 16 years were designated as training, validation and test dataset, respectively, ensuring comprehensive skill score for MJO which is less affected by internal variability of dataset. Therefore, we perform transfer learning three times with 20 ensembles. After the transfer learning process, our model is called CNNOBS. The learning rate for CNNCESM2 is 0.005 and CNNOBS is 0.0005.

Data

The pre-processing procedures applied in our study closely follow Shin et al. 43, with the exception of the season of interest, which spans from May to October. To pre-train the CNN, the CESM2 long-term (1200 years) pre-industrial simulation is utilized. We use five input variables, which are the daily mean data of outgoing longwave radiation (OLR), precipitable water (PW), surface temperature (TS), zonal winds at 250hPa (U250), and zonal winds at 850hPa (U850) within the region covering 20°S to 40°N and 0 to 360°E, with a resolution of 2.5°x2.5°. Before using them as the CNN input variables, we preprocess the daily mean fields as anomalies which are removed the mean and the first three harmonics of the climatological cycle. Additionally, each input variable is normalized by its respective domain averaged standard deviation (SD). As output variables, we use the Real-time Multivariate MJO (RMM) 1 and 2 indices, which represent the two leading principal components of the combined empirical orthogonal function. Following the methodology established by Wheeler & Hendon, we apply the same procedure to obtain the RMM indices.

To fine-tune our model to observational data, we use NOAA interpolated OLR, ERA-5 reanalysis U200, U850, PW, and TS from 1979 to 2018 over the same spatial domain. All preprocessing steps for the observational data are identical to the procedures applied to CESM2.

Bivariate-mean-square-difference(BMSD)

We provide a single-variable zeroing test using our CNNOBS to assess how much the RMM indices are affected when we remove the influence of individual input variables (Fig. 1b). To accomplish this, we calculated the BMSD for each input variable (denoted by \({{BMSD}}_{k}\) in Eq. ( 2)), which represents the mean square differences between the original predictions and the predictions after zeroing a single input variable for both RMM1 and RMM2 indices.

where \(f\) is an ML prediction model, the subscripts 1 and 2 indicate the prediction value of RMM1 and RMM2 indices, respectively. \({{\boldsymbol{X}}}_{j}\) is the array of five input variables for the jth sample (N=total number of samples), and \({{\boldsymbol{X}}}_{j}^{k}\) denotes the modified array with kth variables replaced by zero. The total BMSD (Eq. ( 3)) is the sum of the BMSDs for five input variables:

To quantify the relative importance of each input variable, we computed the ratio of each variable’s BMSD (\({{BMSD}}_{k}{ratio}\) in Eq. ( 4)) to the total BMSD as follows:

Signed-Contribution (SC) map

The SC map, as developed in Shin et al. 43, is a valuable tool that provides contribution information about the sign and magnitude of the relationships between input variables at each grid and the output variables. To generate the SC maps, we first predict using test data sets, which we refer to as the original prediction. Then we perform a new prediction while zeroing out a specific grid box (2×2) of a particular input variable, termed the zeroing prediction. To determine the sign information in the SC maps, we subtract the average value of the difference between the zeroing prediction and the original prediction when the input values are greater than 1 SD and less than -1SD. Therefore, the sign of these difference values indicates the relationship between the input variable in the single grid box and the output variable. In addition, we can interpret that the magnitude of the difference in predictions is proportional to the degree of effect of the single grid box on the output variable. Though this zeroing prediction experiment has limitations in fully reflecting nonlinear interactions with variables at other grid points, the SC maps provide useful information for roughly estimating the relative importance of the input variables. The SC maps are the averaged map of all individual SC maps of each ensemble. The details are described in the Methods section of Shin et al.

Sensitivity experiment

We utilize the sensitivity experiment, previously introduced as “contribution sensitivity” in Shin et al. 35. This experiment allows us to assess the response of output variables to small perturbations in a particular input variable within a specific region. By conducting this experiment, we can gain insight into the specific role of individual input indices and estimate how the output variables sensitively respond to changes in these input indices. This experiment is scalable and can be applied in a variety of ways.

CNN-based reconstructed \(\Delta {\boldsymbol{q}}\) model

For a deeper analysis of the MJO dynamics based on ML, we adopt additional CNN and train it independently. Adhering to the concept of convection moving towards regions of increasing moisture tendency, we compute the moisture difference (\(\Delta q\)) for each forecast lead day in the regions associated with the propagation of the summer MJO. To consider only the time scale relevant to the RMM index, we reconstruct the reconstructed \(\Delta q\) using the multiple linear regression coefficients (\(\alpha\) and \(\beta\) in Eq. ( 5)) of \(\Delta q\) and the RMM1 and 2 indices as follows:

The input variables for the reconstructed \(\Delta q\) model (i.e., \({{CNN}}_{\Delta q}\)) are identical to the original CNNOBS. However, we modify the output variable to \(\Delta q\) instead of the RMM index, and the output layer is configured with a single unit. Similarly, we generate 20 ensembles and present the results based on the ensemble mean value. This approach enables us to perform a more comprehensive investigation of the MJO dynamics using a separate CNN.

Case definition of the summer MJO

To investigate the influence of regions with strong signals in the SC map on the summer MJO propagation using the XAI methods, we first divide the summer MJO events into two categories: those that maintain propagation with strong MJO amplitude and those that rapidly decay in amplitude. This categorization is specifically applied to events with an initial phase of 2 or 6, allowing us to consider both eastward and northward propagation. First, we selected events with an initial amplitude of 1 or greater and an initial phase of 2 or 6. If the same phase occurs on consecutive days, only the first day of the consecutive days is selected as a separate event. In addition, each event must be spaced at least 5 days apart to be treated as separate events.

For events spanning approximately 24 days, both strong and weak cases meet the angle condition, i.e., the average angle difference between the first 5 days and the last 5 days is greater than 80 degrees. We then classify those with an average amplitude > 1.2 as strong cases. Conversely, events that do not meethese criteria are classified as weak cases. This systematic classification allows us to examine the behavior of the summer MJO with respect to its propagation characteristics.

Data availability

The CESM2 pre-industrial simulation was from https://esgf-node.llnl.gov/search/cmip6/. The NOAA Interpolated Outgoing Longwave Radiation (OLR) reanalysis data were downloaded from https://psl.noaa.gov/data/gridded/data.olrcdr.interp.html. The ERA5 hourly data on pressure levels are available from https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pres….

Code availability

The codes used to produce the results except for training, test, and SC maps are available from the corresponding author upon reasonable request. The codes related to the CNN can be found in Shin et al. 43.

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Acknowledgements

J.-S.K. was also partly supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (NRF-2022R1A3B1077622). D.Kim was supported by the New Faculty Startup Fund and Creative-Pioneering Researchers Program from Seoul National University, the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2024-00336160), NOAA CVP program (NA22OAR4310608), NOAA MAPP program (NA21OAR4310343), and NASA MAP program (80NSSC21K1495). D.Kang was supported by the Ministry of Science and ICT through the National Research Foundation of Korea (NRF-2021R1C1C2004621). D. Kang and J.-Y.L. were supported by the National Research Foundation of Korea (NRF-2022M3K3A1094114). This work was partly supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) [NO.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)]

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All authors declare no competing financial or non-financial interests. J.-Y.L. serves as associate editor of this journal and had no role in the peer-review or decision to publish this manuscript. D.Kim serves as editorial board member of this journal and had no role in the peer-review or decision to publish this manuscript.

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Shin, NY., Kang, D., Kim, D. et al. Data-driven investigation on the boreal summer MJO predictability. npj Clim Atmos Sci 7, 248 (2024). https://doi.org/10.1038/s41612-024-00799-8

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DOI: https://doi.org/10.1038/s41612-024-00799-8