Introduction

Pakistan and northwestern India experienced extremely wet conditions during June–August (JJA) of 2022 (Fig. 1a). The mean rainfall anomaly in the region 20°N–35°N and 60°E–75°E (hereafter, the Pakistan rainfall (PR) anomaly) was 2.76 mm day−1, i.e., beyond four standard deviations of the year-to-year variations (0.66 mm day-1) in the past 40 years (Fig. 2). A sequence of extreme rainfall events led to severe floods, which killed nearly 1500 people, caused havoc on infrastructure over a wide area, and even reduced crop production by 80–60%1,2. A successful prediction of the extreme flood at least a few months ahead could have helped reduce the socio-economic losses through necessary mitigation measures. Such a research stream is becoming critically important in Pakistan and India, where the frequency of extreme floods is expected to increase due to ongoing global warming3 and the impacts of natural year-to-year climate variability are also becoming more serious.

Fig. 1: Precipitation anomaly in June–August 2022.
figure 1

a Precipitation anomaly from the GPCP observational data averaged in June–August 2022 (mm day−1). The PR, the DMI, and the Niño3.4 regions are shown by black boxes, respectively. b, c Same as (a), but for the prediction issued on early May 2022 by the SINTEX-F2 (108-ensemble mean) and the NMME (82-ensemble mean).

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Fig. 2: Time series of the June–August average of the Pakistan rainfall anomaly.
figure 2

Time series of the June–August average of the PR anomaly from the GPCP observational data (mm day−1; black), the predictions issued on early May by the SINTEX-F2 (108-ensemble mean; red) and the NMME (53-ensemble mean; blue). The pink and light blue shades showed the ensemble spreads of the SINTEX-F2 and the NMME. The standard deviation (σ) from the GPCP data (0.66 mm day−1) is shown by the dashed line. The correlation skills in the 1991–2021 period of the SINTEX-F2 and the NMME prediction from May are shown on the top-left corner.

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It Is known that major sources of seasonal climate predictability are generally rooted in tropical sea surface temperature (SST) anomalies related to climate modes and associated teleconnection patterns4,5. Previous works identified two potential sources of the seasonal predictability of Pakistan’s summer rainfall: ENSO6 and the Indian Ocean Dipole (IOD)7. Ashok et al.8 showed that positive IODs could cause anomalously high rainfall over Pakistan through partial correlation analyses of observational datasets and AGCM experiments. Based on a simple linear argument, this suggests the surplus Pakistan rainfall in 2022 may be due to the La Nina rather than the negative IOD. Jeong et al.9 suggested that the extreme rainfall over Pakistan in 2022 was due to triple-dip La Nina. Hussain et al.10 showed a positive correlation between the IOD and the precipitation in the coastal area and the western region of Pakistan. However, except for the coastal area and western regions, they did not find a significant correlation between the IOD and the precipitation anomalies in the northern regions and the upper Indus Plain of Pakistan. Iqbal and Hassan11 suggested, based on some statistical analyses, that La Niña events often triggered the Pakistani floods before 1970. In contrast, they suggested that positive IOD events, individually or with El Niño, seemed to have caused the Pakistani floods after 1970. For the 2010 serious Pakistan flooding, Hong et al.12 discussed the roles of European blocking and tropical-extratropical interaction and the indirect contributions of the 2010 La Niña, whereas, using a high-resolution AGCM, Priya et al.13 showed that the combined influence of a La Niña and a negative IOD played significant roles in the 2010 Pakistan flooding.

Unfortunately, the extreme event of summer 2022 was not captured by seasonal prediction systems, such as the Scale Interaction Experiment-Frontier version 2 (SINTEX-F2) climate model and the North American Multi-Model Ensemble (NMME), despite their success in capturing the negative IOD and La Niña evolving at the time (Figs. 1, 3). The present study is to explore the origin of the failure and, hopefully, find potential room for improvement in the seasonal predictions by analyzing the co-variability of intermember anomalies and conducting some numerical experiments with the SINTEX-F2.

Fig. 3: SST anomaly in June–August 2022.
figure 3

Same as Fig. 1, but for the OISSTv2 high-resolution data and the SST predictions (°C).

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Results

Diagnostic analysis

We have evaluated the SINTEX-F2 seasonal predictions by comparing them with the observed wetter-than-normal conditions in Pakistan and adjoining northwestern India during the JJA of 2022. As shown in Fig. 1a, b, the ensemble mean of the SINTEX-F2 from early May initialization fails to capture the observed state, although two members predicted PR anomalies above 1.00 mm day−1 (Supplementary Fig. 1). The ensemble mean prediction (+0.19 mm day−1) only captures less than 10% of the observed PR anomalies (+2.76 mm day−1) (Supplementary Fig. 1, Table 1). The NMME mean prediction (+0.52 mm day−1) underestimates the PR anomalies as well, which is less than 20% of the observed PR anomalies (Fig. 1c, Table 1). The above results are not very surprising because of their low performance in predicting the JJA PR anomalies from May initialization. The correlation skills of the SINTEX-F2 and the NMME are only 0.31 and 0.33 respectively based on the 1991–2021 reforecast experiments, which are not statistically significant above the 95% confidence level on a paired t-test (Fig. 3). We note that the SINTEX-F2 as well as the NMME is not skillful in predicting the Indian summer monsoon rainfall from May in spite of its reasonable skill in predicting the tropical SST field (Supplementary Fig. 2).

Table 1 a 2022 June–August average of the PR anomalies from (1) the GPCP observational data, (2, 3, 4, 5) the prediction from early May 2022 by the SINTEX-F2 (108-ensemble mean), the NMME (82-ensemble mean), the NAS_ANOM (108-ensemble mean), and the NAS_OBS (108-ensemble mean). b Same as (a), but for the DMI (°C) by the OISSTv2 high-resolution data and the predictions. c, d Same as (b), but for the Niño3.4 and the SST anomalies in the NAS (°C).
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While both prediction systems did not capture the PR anomalies, they correctly predicted the evolution of a negative IOD and a La Niña at the time (Fig. 3, Table 1). The SINTEX-F2 and the NMME overestimated the negative IOD; the Dipole Mode Index (DMI, the SST anomaly difference between the western pole off East Africa (50°E–70°E, 10°S–10°N) and the eastern pole off Sumatra (90°E–110°E, 10°S–Equator), introduced by Saji et al. 7) was −1.40 °C and −1.16 °C, which is about 180% (150%) of the observed DMI (−0.77 °C). La Niña was well predicted by the SINTEX-F2, whereas the NMME underestimated the amplitude; the Niño3.4 index (SST anomaly averaged in 170°W–120°W, 5°S–5°N) was −0.68°C and −0.38 °C by the SINTEX-F2 and the NMME respectively, which are about 90% (50) % of the observed index (−0.74 °C). As seen in Supplementary Fig. 3a, the observed wetter-than-normal conditions in Pakistan and India were associated with moisture convergence at 850 hPa over the northern coastal Arabian Sea. However, it was underestimated by the SINTEX-F2 (Supplementary Fig. 3b). We note here that the positive SST anomaly (+0.59 °C) in the northern coastal Arabian Sea (60°E–75°E, 20°N–30°N, hereafter referred to NAS) was underestimated by the SINTEX-F2 (+0.22 °C), while the NMME reasonably predicted it (+0.53 °C). The NAS domain is included in the PR domain. We also note that the inter-ensemble correlation analyses in the SINTEX-F2 show that the prediction of the positive PR anomaly is not linked with the prediction of the negative IOD or the La Niña (Fig. 4a). This is also the case in the NMME predictions (Supplementary Fig. 4).

Fig. 4: Inter-ensemble members correlation.
figure 4

a Inter-ensemble members correlation in the 108-members prediction between the PR anomalies and the SST anomalies for the 2022 June–August average issued on early May by the SINTEX-F2. The PR, the DMI, and the Niño3.4 regions are shown by black boxes, respectively. b Same as (a), but for moisture convergence/divergence at 850 hPa. The divergence and convergence are shown in brown and green.

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Interestingly, however, we have found a positive inter-ensemble correlation between the PR anomaly and the SST anomaly in the NAS for the SINTEX-F2 predictions (Supplementary Fig. 5a). It is 0.27 and statistically significant above the 99% confidence level on a paired t-test, considering the degree of freedom for the ensemble size of 108. Although the area of the positive correlation coefficients between the PR anomaly and the SST is small (Fig. 4a), the area of the positive correlation coefficients between the PR anomaly and the moisture convergence/divergence at 850 hPa (Fig. 4b) is relatively large and could cover the NAS. The co-variability may suggest that the warmer SST anomaly in part of the NAS enhances the local convective activity associated with the moisture convergence at 850 hPa in the NAS and around Pakistan. This is consistent with Kumar et al. 14, who showed that the predictability of seasonal mean precipitation is high when SST–rainfall correlation is positive. The NCEP-CFSv2 and the NASA-GEOS5 also show the positive inter-ensemble correlations between the PR anomalies and the SST anomalies in the NAS; the former reaches 0.42 and the latter reaches 0.73 (Supplementary Fig. 5b). Here, as a result of a decreased ensemble size for the NMME with less degrees of freedom, the confidence interval of the significance test is reduced to 95% as against 99% for the SINTEX-F. The two correlations are statistically significant above the 95% confidence levels on a paired t-test, taking into account the degrees of freedom on the ensemble sizes of 32 and 10 with the NCEP-CFSv2 and the NASA-GEOS5 (Supplementary Fig. 4b, c). In contrast, the NCAR-CCSM4 and the GFDL-SPEAR show negative inter-ensemble correlations: −0.60 and −0.27, respectively, although they are not statistically significant above the 95% confidence levels on a paired t-test, with the degrees of freedom on the ensemble sizes of 10 and 20, respectively (Supplementary Figs. 4a, b, 5). The SST differences between the observations and the ensemble mean predictions also appear in other regions (e.g., Atlantic, Fig. 3). However, the inter-ensemble correlations with the PR anomaly are mainly limited to the northern coastal Arabian Sea (Fig. 4a, b). So, we focused on the northern coastal Arabian Sea surface temperatures after that.

Numerical experiments

Deep convection over tropical oceans is generally enhanced above a threshold SST around 26–28 °C15,16. Since the observation shows that the absolute SST in the NAS was about 28–29 °C during the summer of 2022 (Supplementary Fig. 6b), it is possible that the NAS could locally drive the deep convection and contribute to the PR. To examine the hypothesis, we have conducted two sets of sensitivity experiments starting from early May 2022. The first experiment (NAS_OBS) is a 108-member ensemble prediction in which the model SST in the NAS was strongly nudged to the NOAA OISST V2 High Resolution Dataset17 from early May until August at a daily time-scale by a coefficient of 2400 W m−2 K−1 (1-day in the upper 50 m) with a linearly tapering 5° buffer zone that extends to 15°N and 55°E (Supplementary Fig. 6a). The second experiment (NAS_ANOM) is similar to the NAS_OBS, but nudged toward the daily observed SST anomaly of the NOAA OISST V2 High Resolution Dataset (deviation from the daily mean climatology) added to the model predicted daily climatology for the 1991–2020 period. The anomalies in NAS_ANOM are defined as deviations from the mean climatology in the original prediction, while the anomalies in NAS_OBS are defined as deviations from the mean climatology in the 1991-2020 re-forecast experiments in NAS-OBS by 12 members.

In the NAS_ANOM experiment, the number of members predicting the PR anomalies above 1.00 mm day−1 almost tripled, and the ensemble mean prediction (+0.42 mm day−1) was about 220% of that of the original reforecast experiments, capturing about 15% of the observed PR anomalies (Table 1). The difference in the ensemble means between the original reforecast and the NAS_ANOM was beyond the 99% confidence level on a paired t-test. The enhancement of moisture convergence at 850 hPa over the enhanced positive SST anomalies in the NAS seems to be responsible for this (Fig. 5). The orographic rainfall in the Western Ghats also clearly increased, which could contribute to the target area. In the climatological state, the orographic rainfall in the Western Ghats is large relative to the Pakistan rainfall. When we normalized the rainfall anomalies by the climatological rainfall, the effectiveness of the NAS warming in increasing rainfall over Pakistan and the Western Ghats was comparable (Supplementary Fig. 7a). Those features in the NAS_ANOM were enhanced in the NAS_OBS experiment. The ensemble mean prediction (+0.69 mm day−1) captured about 25% of the observed PR anomalies (Table 1, Supplementary Fig. 1a, b, Fig. 5d). Supplementary Fig. 1 shows that a chance of the PR anomalies above 1.0 mm day−1 is also enhanced.

Fig. 5: Pakistan precipitation anomaly in June–August 2022.
figure 5

a, b Same as Fig. 1 (a, b), but for the zoom-in the northern Indian Ocean. The PR region is shown by black boxes. c, d Same as (a, b), but for the NAS_ANOM and the NAS_OBS (108-ensemble mean). For (c, d), dotted are area where the differences between the nudging experiment and the original experiment are statistically significant above the 99% significance level.

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The above results clearly demonstrate the importance of the positive SST anomaly in the NAS in the successful seasonal prediction of the 2022 summer extreme rainfall in Pakistan. This is consistent with Hong et al.18, who indicated the contribution of the Arabian Sea to the 2022 Pakistan flooding. The negative SST bias in the model climatology in the NAS (Fig. 6a) seems to have caused the failure of our prediction. Although the PR has been considered a part of the Indian Summer Monsoon driven by the large-scale land-sea thermal contrast, the present experiments suggest that resolving the regional SST-driven local deep convection may lead to improving the SINTEX-F2 system. Similar to the SINTEX-F2, some of the NMME models show a negative SST bias in the model climatology in the NAS (Fig. 6). Further analyses are needed to understand the cause of this model bias. Increasing the horizontal resolution of the climate model may improve the negative SST bias in the model climatology in the NAS19,20,21,22. The Eastern Boundary Upwelling Systems (EBUS: https://www.clivar.org/research-foci/upwelling) are actively studied because of their climatological and societal importance. We believe that the Western Boundary Upwelling System (WBUS) in the western Indian Ocean, including the NAS, the Gulf of Oman, the Somali Current23 needs to be studied as well.

Fig. 6: Model SST bias for the Arabian Sea.
figure 6

The SST biases (°C) in the June–August averaged climatology prediction (the base period is 1991–2020) by (a) the SINTEX-F2 (108-ensemble mean), (b) the NCAR-CCSM4, (c) the NASA-GEOS5, (d) the NCEP-CFSv2, and (e) the GFDL-SPEAR, relative to the OISSTv2 high-resolution data.

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Interestingly, we found a positive inter-ensemble correlation between the PR anomaly and the temperature anomaly around western Japan using the SINTEX-F2 (Fig. 4a). It may suggest a possible teleconnection pattern from Pakistan to Japan via China along the subtropical Asian jet24. The positive SST anomaly in the NAS may enhance the regional convective activity (Fig. 5) and excite stationary Rossby waves at the upper troposphere, leading to the northward meandering of the subtropical jet around East Asia, as shown by the geopotential height anomalies and the wave activity fluxes at 200 hPa (Fig. 7). The possible teleconnection pattern was enhanced in the NAS_ANOM as well as the NAS_OBS, suggesting that the 2022 devastating flood in Pakistan could partly contribute to a hotter-than-normal summer in East Asia, including China, Korea, and Japan. This is consistent with Tang et al.25.

Fig. 7: Teleconnection to East Asia.
figure 7

Geopotential height anomalies (m; shaded) and the wave activity fluxes (m2s-2; vector) at 200 hPa averaged in June–August 2022 from (a) the NCEP/NCAR reanalysis data, (b) the SINTEX-F2 (108-ensemble mean), (c) the NAS_ANOM, and (d) the NAS_OBS (108-ensemble mean). For (c, d), dotted are area where the differences between the nudging experiment and the original experiment are statistically significant above the 99% significance level.

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Discussions

In 1994, 2006, 2007, 2010, and 2020, the observed PR anomalies were larger than one standard deviation (Fig. 3). Those extremely wetter-than-normal events were not well predicted by both the SINTEX-F2 and the NMME. The composite of the observational SST anomalies in those five events suggests that the positive SST anomaly in the NAS could partly work as a potential source of predictability for the above-normal summer monsoon rainfall in Pakistan, similar to the 2022 case (Supplementary Fig. 8). The scatter plot from 1991 to 2022, based on observational datasets, indicates a significant positive correlation (0.60) between PR anomalies and NAS SST anomalies. This correlation is evident not only in extreme PR events but also in moderate ones (Supplementary Fig. 9). We note that the composite field also suggests contributions from the La Niña, but not from the IOD. The La Nina signal is due to 2007, 2010, and 2020 La Nina years. The disappearance of the IOD signal may be due to the cancellation of positive IOD events (1994, 2006, and 2007) and negative IOD events (2010 and 2020) for the selected five years.

The scatter plot of the SST anomalies in the NAS with the Niño3.4 and also the DMI for the June–August average in 1991–2022 based on the observational datasets, together with their insignificant correlations, suggests that the SST anomalies in the NAS were not introduced by ENSO and IOD events (Supplementary Fig. 10). We also did not find a significant inter-ensemble correlation between the SST anomalies in the NAS and the Niño3.4 for the 2022 summer predictions by the SINTEX-F (Supplementary Fig. 11a). Interestingly, however, we have found a positive inter-ensemble correlation between the SST anomalies in the NAS and the IOD (Supplementary Fig. 11b). It is 0.35 and statistically significant above the 99% confidence level on a paired t-test, considering the degree of freedom for the ensemble size of 108. The co-variability may suggest a pathway of IOD influences on Pakistan rainfall via the NAS SST. The NCEP-CFSv2 also shows a positive inter-ensemble correlation of 0.39 between the SST anomalies in the NAS and the IOD, which is statistically significant above the 95% confidence levels on a paired t-test, taking into account the degrees of freedom on the ensemble sizes of 32. However, other models did not show a statistically significant correlation above that confidence level (Supplementary Fig. 11d). The GFDL-SPEAR shows a negative inter-ensemble correlation of −0.38 between the SST anomalies in the NAS and the Nino3.4, which is statistically significant above the 95% confidence levels on a paired t-test, taking into account the degrees of freedom on the ensemble sizes of 30, although other models did not show a statistically significant correlation above that confidence level (Supplementary Fig. 11d).

Here, we focus on the 2010 event, the second largest in the 1991–2022 period, reached about two standard deviations (Fig. 2). The extremely wetter-than-normal conditions observed in Pakistan were not well predicted by both the SINTEX-F2 and the NMME from early May initialization (Supplementary Fig. 12). The SINTEX-F2 successfully predicted a combination of the negative IOD and the La Niña, although it underestimated the La Niña amplitude (Supplementary Fig. 13). In contrast, the NMME failed to capture the negative IOD but successfully predicted the La Niña (Supplementary Fig. 13). Similar to the case in 2022, the wetter-than-normal conditions observed in Pakistan and India seem to be associated with moisture convergence at 850 hPa over the positive SST anomalies in the northern coastal Arabian Sea (Supplementary Fig. 14). It is also supported by the inter-ensemble correlation analyses in the SINTEX-F2 (Supplementary Fig. 15). The inter-ensemble correlation between the PR anomaly and the SST anomaly in the NAS (Supplementary Fig. 16) is 0.42 and statistically significant above the 99% confidence level on a paired t-test, considering that the degree of freedom is based on an ensemble size of 108. The NCEP-CFSv2 also showed a positive inter-ensemble correlation of 0.44 between the PR anomalies and the SST anomalies in the NAS, which is statistically significant above the 95% confidence levels on a paired t test with a degree of freedom based on the ensemble size of 24, although the NCAR-CCSM4, the NASA-GEOS5, and the GFDL-SPEAR did not show significant correlations (Supplementary Fig. 17 and Supplementary Fig. 16). As similar to the 2022 event, the contribution of the positive SST anomaly in the NAS to the 2010 excess rainfall in Pakistan was also demonstrated by the model sensitivity experiments (Supplementary Fig. 18). In the NAS_ANOM, the ensemble mean prediction (+0.21 mm day−1) was about 300% of that of the original reforecast experiments ( + 0.073 mm day−1) and captured about 16% of the observed PR anomalies (+1.30 mm day−1). The difference in the ensemble means between the original reforecast and the NAS_ANOM was beyond the 99% confidence levels on a paired t test. The enhancement of moisture convergence at 850 hPa over the enhanced positive SST anomalies in the NAS was also seen (Supplementary Fig. 18). The feature was enhanced in the NAS_OBS. The ensemble mean prediction ( + 0.41 mm day-1) has captured about 30% of the observed PR anomalies. Note that the inter-ensemble correlations in the SINTEX-F2 and the NCEP-CFSv2 also suggested the weak contributions of the La Niña event (Supplementary Fig. 15a and Supplementary Fig. 17b), as discussed by the previous studies (see Introduction).

In this study, we have demonstrated that the positive SST anomaly in the NAS may contribute to the successful seasonal prediction of the 2022 summer extreme rainfall event in Pakistan. However, the predicted amplitudes in the two experiments are still not enough to explain the extreme rainfall over Pakistan. In the NAS_OBS and the NMME, there is no ensemble member that predicted the PR anomaly reaching 2.76 mm day−1(Supplementary Figs. 1 and 5b). Further analysis and possible coordinated sensitivity experiments with multi-models are necessary for a better understanding of why the PR anomaly was so extreme (above four standard deviations of the interannual variation) and for improving the prediction. The extreme PR anomaly in 2022 might have reflected the inherently unpredictable nature of atmospheric variability. Since synoptic and high-frequency cyclogenesis activity is beyond the scope of this study, possible interactions between the anomalous seasonal mean SST in the NAS and the anomalous cyclogenesis in the Eastern Arabian Sea might be important factors for the extreme rainfall.

Methods

Reforecast experiments

We have analyzed the monthly reforecast outputs by the 108-member SINTEX-F2 seasonal prediction system from the nine initialized dates (1st–9th) May of 1991–202226,27. The SINTEX-F2 is based on a global ocean–atmosphere–land–sea ice coupled model28,29 with a surface and subsurface oceanic initialization scheme30,31 developed under the EU–Japan collaborative framework. The atmospheric component of the SINTEX-F has a horizontal resolution of 1.125° (T106) with 31 vertical levels, while the oceanic component has a horizontal resolution of about 0.5° × 0.5° with 31 vertical levels. The SINTEX-F2 system is skillful at predicting the mean state of the Indian Summer Monsoon Rainfall (ISMR) and its interannual variations32. To determine the anomalies, we have removed the model monthly climatology for the period 1991–2020 at each lead time. We have also analyzed the NMME outputs [see Kirtman et al. 33]. Here, we have used 53 (82) ensemble members for hindcast (forecast) by four models; 24 (32) members of the NCEP-CFSv2, 10 (10) members of the NCAR-CCSM4, 4 (10) members of the NASA-GEOS5, and 15 (30) members of the GFDL-SPEAR for the 1991–2022 period based on the availability of the outputs. As for the SINTEX-F2, the prediction anomalies were derived by subtracting the individual model mean climatology for the period 1991–2020 at each lead time. Because of some differences in the base period used to calculate the anomalies, the number of ensemble members, and the selected models, the prediction maps by the NMME in the following analyses are slightly different from those on the original website (https://www.cpc.ncep.noaa.gov/products/NMME/).

Observational and reanalysis datasets

To evaluate the prediction results, we used the GPCP34 rainfall data over both land and ocean. It is based on a combination of various satellite data sets over ocean and land, and rain gauges on land. We also used the NOAA OISSTv235 and its high-resolution version17 for SST and the NCEP/NCAR reanalysis data36 for other atmospheric fields. The monthly anomalies were derived through deviations from the monthly climatology calculated by averaging the monthly data from 1991 to 2020.

Inter-ensemble correlation analysis

The inter-ensemble correlation (i.e., correlation in the ensemble phase space) can measure how two predictions co-vary over the ensemble phase space and indicate the linear relationship as a number between −1 and 1. It provides useful insights into possible precursors and teleconnection patterns related to a climate event27,37,38,39,40. Here, we calculate inter-ensemble correlation coefficients between the PR anomalies and a horizontal map of anomalous sea surface temperature (SST) and moisture convergence/divergence at 850 hPa for each grid point among the 108 ensemble members with the SINTEX-F2 system and 82 ensemble members with NMME for the June–August average as

$$R\left(x,y\right)=\frac{\frac{1}{{ne}}\mathop{\sum }\nolimits_{e=1}^{{ne}}(X(e)-\bar{X})(Y(x,y,e)-\bar{Y(x,y)})}{\sqrt{\frac{1}{{ne}}\mathop{\sum }\nolimits_{e=1}^{{ne}}{(X(e)-\bar{X})}^{2}}\sqrt{\frac{1}{{ne}}\mathop{\sum }\limits_{e=1}^{{ne}}{(Y(x,y,e)-\bar{Y(x,y)})}^{2}}}.$$
(1)

Here \({ne}\) is the ensemble size: 108, \(X(e)\) is predictions of the target index (the PR anomalies) and a function of ensemble member (\(e\)), \(\bar{X}\) is the average of \(X\left(e\right)\) by all ensemble members, \(Y(x,y,e)\) is predictions of the target variables (anomalous SST and moisture convergence/divergence at 850 hPa) and a function of two-dimensional horizontal (\(x,y\)), and ensemble member (\(e\)), \(\bar{Y(x,y)}\) is the average of \(Y(x,y,e)\) by all ensemble members, respectively. In this analysis, the large ensemble size has an advantage in finding significant co-variability patterns because the signal-to-noise ratio is generally reduced41.