The Indo‐Pacific Rim at Risk: How Rossby Waves Contribute to Extreme Precipitation Clustering

Clustering extreme weather events are concurrent or consecutive occurrences of disastrous weather in multiple regions, resulting in cumulative impacts. Here we discovered a significant increasing trend in clustering extreme precipitation events over the Indo‐Pacific rim over the past four decades. This trend can be largely attributable to the increasing frequency of the Rossby wave response, including the circum‐Pacific and cross‐Pacific patterns due to Rossby wave activity propagation, and the Pacific anticyclone pattern due to Rossby wave breaking. The three patterns show remarkable disparity in seasonality, persistence, and hydrological impacts. They can increase the occurrences of most severe precipitation by up to 5, 8, and 25 times, respectively. The Indian Summer Monsoon heat sources and La Niña are identified as key drivers, and the mid‐latitude jet streams are modulators contributing to the events. Our findings suggest that specific Rossby wave patterns may influence the potential evolution of future clustering extremes.


Introduction
Clustering extreme precipitation events, which refers to the concurrent or consecutive occurrences of extreme precipitation over multiple regions in a period.The compound occurrence of abnormal weather conditions can amplify the risks posed by extreme weather, as highlighted by Zscheischler et al. (2020), who proposed a typology to classify compound hazards that include spatially clustering and temporally clustering events.Spatially clustering events can be identified using climate anomalies on a monthly to seasonal time scale (Basconcillo et al., 2021;Leonard et al., 2014), while temporally clustering events refer to consecutive weather events on an intraseasonal time scale in a fixed region (Barton et al., 2016;Dacre & Pinto, 2020).These two types of compound hazards have been extensively studied, providing insights into their identification method and underlying mechanisms (Baldwin et al., 2019;Riboldi et al., 2023).However, the understanding of the same type of extreme weather events clustering occurring in multiple regions remains a knowledge gap.These events can have cascading effects on human livelihoods, leading to growing concerns about their occurrence in succession across multiple regions beyond continental boundaries.Signals for extremes in mid-latitudes can originate from the tropics (Lu et al., 2016), but the detailed circulation patterns that result in cross-latitude clustered extremes have yet to be explored.One typical example of such clustering was observed during the 26th UN Climate Change Conference of the Parties held in 2021 (Wang et al., 2022).The extreme precipitation events consecutively occurred in the Northern Hemisphere, causing record-breaking flooding and blizzard across South Asia, East Asia, and North America.These events are not clustered by coincidence but are found to be organized by two Rossby wave trains stimulated by the "wet India-dry Philippines" dipole heating anomaly.Generalizing such clustering events to identify more cases is crucial to understand the underlying physical processes compared to analyze a single case.How frequently clustering extreme precipitation events occur, and their associated atmospheric dynamics are unclear.Determining the physical links between these events will effectively fill the weather-climate prediction gap (Mariotti et al., 2018) at the sub-seasonal to seasonal (S2S) range and have significant implications for early warning systems to mitigate the impact of extreme weather events.This study investigates the clustering extreme precipitation events along the Indo-Pacific rim.We proposed an approach inspired by event synchronization (Quiroga et al., 2002) to identify clustering extreme precipitation events on a daily timescale for the first time and investigate the driving mechanisms.Our aim is to provide a clear view of the clustering extreme precipitation events across the Indo-Pacific rim and address these major research questions: How many times have clustering extreme precipitation events occurred in the past 42 years ?What synoptic-scale dynamics are responsible for the clustering occurrence?Is the "wet India-dry Philippines" only tailored for the typical event in 2021?First, we constructed an event database and found the increasing trend of clustering extreme precipitation events along the Indo-Pacific rim (Figure 1a).To understand  the atmospheric circulation pattern associated with clustering extreme precipitation events, we employed the Self-Organizing Map technique (Text S1 in Supporting Information S1) to classify the daily 200 hPa stream function anomaly field.The atmospheric circulation responsible for these events exhibits diverse Rossby wave patterns that consist of three types: circum-Pacific Rossby wave train, cross-Pacific Rossby wave train, and Pacific anticyclone due to Rossby wave breaking (Figure 2).The diverse wave patterns play an important role in connecting and modulating extreme weather in mid-latitude regions.The frequency of the three Rossby wave patterns has all increased over the past 42 years, especially for the cross-Pacific Rossby wave train and Pacific anticyclone pattern.Given the increasing risks of clustering extreme precipitation events caused by anthropogenic climate forcing (Zhou et al., 2023), the results of this study have significant implications for policymakers and stakeholders concerned with the impact of extreme weather events on human livelihoods.

Data
The meteorological variables during 1980-2021 are retrieved from the fifth generation of the European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis data (ERA5) (Hersbach et al., 2023) to identify clustering extreme precipitation events and conduct diagnostic analysis.The variables include hourly-1°precipitation, zonal and meridional wind at 200/850 hPa, outgoing long radiation, and sea surface temperature (SST).All of these variables have been aggregated into daily values for analysis.The anomalies fields are computed as the departure from the 5-days-moving-average climatology during the period from 1980 to 2019, where the average is calculated by taking the mean of the variable over a moving window of five consecutive days.The All-India areaweighted mean summer monsoon precipitation index (Singh et al., 2019) from 1980 to 2019, developed by the Indian Institute of Tropical Meteorology, is used to represent the monsoon activity.The ENSO index uses the Oceanic Niño Index (ONI) in the Niño 3.4 region and the Pacific Decadal Oscillation (PDO) index is from NOAA's extended reconstruction of SST.The sensitivity of the results is examined using the Global Precipitation Climatology Project (GPCP) daily precipitation analysis climate data record (Huffman et al., 2001).The results of both data sets show a significant increase trend in clustering extreme precipitation events over the past, and the annual frequency time series of extreme precipitation events identified in the five sub-regions are significantly correlated between the two data sets (Table S2 in Supporting Information S1).Given the above robustness test and a full historical record of the ERA5 precipitation for the study period, ERA5 is used to identify the clustering extreme precipitation events.

Identification of Clustering Extreme Precipitation Events
An algorithm is developed to construct a database of clustering extreme precipitation events spanning five domains, including South Asia (65°E-90°E, 6°N-20°N), China (105°E-122°E, 20°N-42°N), Japan (129°E-146°E, 31°N-45°N), Alaska (145°W-168°W, 55°N-70°N), and the West Coast of North America (WNA) (120°W-140°W , 34°N-60°N) over a period of 42 years.The detailed detection procedure is as follows: 1. First, the algorithm detects rain belts (extreme precipitation with a large spatial scale) in five sub-regions.In each sub-region, daily total precipitation for each grid needs to exceed the local threshold, which is the monthly 90th percentile of wet days (>1 mm day 1 ), and more than eight grids satisfying two-connectivity is defined as a rain belt.Two-connectivity means two grids are connected when they are neighbors in a twoconnected sense.2. Second, the algorithm detects extreme precipitation events as rain belts that persist for at least two consecutive days with a spatial overlap ratio greater than 10%.The algorithm calculates the spatial mean precipitation intensity per day (grid-average precipitation for each rain belt), spatial extent (number of grids) per day, and duration (days) of each event.3. Finally, binarization of time series data is used to identify the extreme precipitation events consecutive occur in South Asia, East Asia, and North America.In this step, South Asia, East Asia (including China and Japan), and North America (including Alaska and the West coast of North America), generate three columns of time series data with a span of 42 years, and all the dates of extreme precipitation events extracted in the second step are labeled as "1," and the dates of no events are "0."The time window begins with the date on which any of the three columns is marked "1" for the first time and ends with the date on which none of the three regions is marked.Boolean indexing is used to check that index "1" has occurred in all three regions, and if index "1" occurs in all three regions, the dates within the time window are extracted as a clustered extreme precipitation event.The time window moves to the next day to detect the next event.

Diverse Rossby Wave Patterns Organize the Clustering of Extreme Precipitation Events
A total of 418 clustering extreme precipitation events occurred across the Indo-Pacific rim during the past 42 years.These events predominantly manifested on intra-seasonal time scales, with durations ranging from 7 to 20 days (Figure 1b).They often occurred between May and November, encompassing the boreal summer season and transitional months (Figure S1 in Supporting Information S1).We observed a discernible increasing trend (0.5 event/decade from Sen's slope estimator) in the time series of clustering extreme precipitation events which were validated by the Mann-Kendall test (Figure 1a).Our analysis (Text S1 and Table S1 in Supporting Information S1) reveals three distinct Rossby wave patterns responsible for these clustering events: circum-Pacific Rossby wave train (369 days, 31%), cross-Pacific Rossby wave train (931 days, 57%), and Pacific anticyclone due to Rossby wave breaking (1,276 days, 57%).The percentage in parentheses indicates the percentage of events for each pattern out of the total number of events in the database.Some events could involve multiple patterns, so the sum of the percentages exceeds 100%.
The composited maps of climate variables for each wave pattern are shown in Figure 2. The circum-Pacific Rossby wave train (Figure 2a) at 200 hPa consists of the South Asia High at Bangladesh, East Asia Low over Japan, Central North Pacific High, Gulf of Alaska Low, and Northwest America High.The wave activity flux from the South Asia High to higher latitudes suggests that the circum-Pacific Rossby waves derive energy from South Asia and central Eurasia, thereby facilitating the northeastward development of this wave pattern.The second pattern identified is the cross-Pacific Rossby wave train (Figure 2c) which features anomalous highpressure centers at 200 hPa fixed in West-central Asia (Pakistan), Japan, the Gulf of Alaska, and the central United States.In comparison to the first pattern, the South Asia High shifts westward from Bangladesh to Pakistan, causing a corresponding westward shift in the phase of the wave trains.Over the North Pacific, the cross-Pacific wave pattern tends to exhibit a more zonally oriented structure and out of phase with the circum-Pacific pattern.The phase shift between these two Rossby wave patterns is due to the different tropical heating source locations (Figures 2b and 2d) and the jet stream dynamics (Section 3.4).The third pattern, known as the Pacific anticyclone pattern, substantially differs from the circum-and cross-Pacific wave patterns.This pattern is formed by a dipole system, consisting of anomalous Aleutian high and Hawaiian low, over the North Pacific (Figure 2e).Anticyclonic wave breaking is defined as the wave tilting in a southwest-northeast direction (Rivière et al., 2010).Meanwhile, a giant high-pressure system dominates Asia with a center in northern India.
The remarkable disparity can be seen in the seasonality and persistence of each pattern (Figures 1c and 1d).It should be noted that seasonality is conditional as the percentage occurrence of each pattern is the occurrence days in each month divided by the total occurrence days.Thus, the calculation is based on the clustering extreme precipitation days, which means there will be more occurrences of each pattern in the wet season.That's why the percentage numbers are all very small from January to May.However, in the wet season, the diverse Rossby wave patterns still exhibit significant seasonality differences.The circum-Pacific patterns often occur from July to December except for October, with a peak in September, while the cross-Pacific patterns prevail during the Indian summer monsoon (ISM) season from June to September (JJAS).The Pacific anticyclone occurrence frequency does not show significant seasonal differences from June to December (Figure 1c).The number of continuous days that the Rossby wave pattern persists in each event is referred to as the phase locking days, reflecting its persistence.The percentages of events that have more than five phase-locking days are about 20%, 10%, and 5% for the Pacific anticyclone, cross-Pacific, and circum-Pacific patterns, respectively (Figure 1d).Among these patterns, the Pacific anticyclone pattern is the most persistent, with the highest number of events with phaselocking days greater than 7 days (Table S1 in Supporting Information S1).Conversely, the phase locking days of the circum-Pacific pattern are shorter, indicating that this wave pattern has greater potential to propagate.
The hydrological impacts of the three distinct Rossby wave patterns exhibit notable differences in East Asia, including China (CA) and Japan (JA), and North America including Alaska (ALA) and the WNA (Figure S2a in Supporting Information S1).Although all these patterns can organize the clustering occurrence of extreme precipitation over the Indo-Pacific rim, they have varying effects on the intensity and area of extreme precipitation in East Asia and North America, especially over ALA and WNA (Figures S2d and S2e in Supporting Information S1).Over China, the cross-Pacific pattern leads to more intense precipitation, while the Pacific anticyclone causes larger spatial-scale precipitation (Figure S2b in Supporting Information S1).For Japan, the cross-Pacific pattern has a more significant impact, resulting in extensive and intensive precipitation (Figure S2c in Supporting Information S1).For Alaska, the circum-Pacific pattern has a different directional impact compared to the other two patterns, resulting in increased precipitation intensity instead of precipitation area (Figure S2d in Supporting Information S1).The circum-Pacific Rossby wave train causes the most intense and large-scale precipitation in the WNA region (Figure S2e in Supporting Information S1).
We examined the event coincidence rates (Kornhuber et al., 2020) to quantify the co-occurrence of precipitation days and each Rossby wave pattern in four mid-latitude sub-regions and found that the presence of wave patterns can significantly increase the probability of more intense and large-scale precipitation events (Figure S3 and Text S3 in Supporting Information S1).The probability of severe precipitation can be increased up to 4.8 times in WNA by the circum-Pacific pattern, and six times in JA by the cross-Pacific pattern.In the case of the Pacific anticyclone, the probability of large-scale precipitation events in ALA can be increased by up to 25 times compared to other days.Overall, the circum-Pacific wave significantly impacts the eastward of JA, as depicted in Figure S4 in Supporting Information S1, and WNA, particularly in Canada, where the main route of atmospheric rivers is activated from East Asia to the west coast of Canada after late summer and makes landfall over Canada.The cross-Pacific wave impacts CA, JA, and north of the ALA more, coinciding with the northward displacement of atmospheric rivers starting from South Asia to East Asia and Alaska (Pan & Lu, 2020) during the ISM season.The Pacific anticyclone wave pattern will significantly influence the spatial scale of extreme precipitation in the four affected regions.

Atmospheric Internal Dynamics That Generate Diverse Rossby Wave Patterns
The development of global circulation patterns is influenced by complex interactions between the tropical and midlatitude regions, which are part of the sub-seasonal to seasonal climate variability.During boreal summer, the boreal summer intra-seasonal oscillation (BSISO) is the primary mode of climate variability (Kikuchi et al., 2012;Wang & Xie, 1997).It is characterized by a concentration of heat sources in India and the Philippines and northward movement (Jiang et al., 2004).The tropics release latent heat through extreme precipitation in South Asia, which acts as a heat source and generates a baroclinic Rossby wave response that creates a South Asia high in the upper level and an opposite polarity in the lower level (Figures 2a,2c,and 2e).Under the easterly vertical shear (easterly increases with height), the baroclinic Rossby wave response is considerably enhanced, and it can generate a barotropic Rossby wave pattern extending further poleward from tropics to midlatitude (Liu & Wang, 2013;Wang & Xie, 1996).Therefore, the tropical thermal forcing is the primary feature that triggers different Rossby wave patterns.Specifically, for the circum-Pacific Rossby wave pattern, in addition to enhanced strong convection in India, the climate mean anomalies for the circum-Pacific Robby wave pattern show suppressed convection in the Philippines (Figure 2b).This dipole pattern is consistent with the "wet India-dry Philippines" dipolar heating that causes Asia/North America teleconnection identified in the previous study (Wang et al., 2022).The cross-Pacific Rossby wave occurs more often from June to September.The dominant diabatic heating source during this period is located in the ISM region.All-India area-weighted mean summer monsoon precipitation can be used to reflect ISM activity.The correlation matrix shows (Figure 3c) that the cross-Pacific wave pattern occurrence has significant positive correlations with monsoon activity indicating stronger BSISO activity can increase the frequency of the cross-Pacific Rossby wave pattern.

External Forcings Causing the Rossby Wave Patterns
Over a much longer timescale, the SST anomaly has a remote control that influences the atmospheric mean state and anomalous diabatic heat sources to change the Rossby wave pattern.The seasonal frequency of the cross-Pacific pattern tends to negatively (positively) correlate with the Nino 3.4 index (monsoon activity) as shown in Figures 3b and 3c.This means that the cross-Pacific pattern is associated with a developing La Niña in the eastern Pacific (Figure 3a) and increased Indian monsoon rainfall (Figure 2d).During La Niña, the frequency of cyclones increases in the Bay of Bengal (Roose et al., 2022), resulting in stronger monsoons and more precipitation (Rajeevan & Pai, 2007;Slingo & Annamalai, 2000).
The frequency of the Pacific anticyclone pattern is modulated by ENSO, as shown by the significant negative correlation between the Nino 3.4 index and the frequency of the Pacific anticyclone (Figure 3e).The SST composite map for this pattern reveals a significantly lower SST in the equatorial eastern central Pacific (Figure 3d).Additionally, the PDO index has a significant negative correlation coefficient of 0.74 with the variability of this pattern (with warm SST anomalies in the interior and cool SST anomalies along the North American coast), indicating that it plays a role as a mechanism of atmospheric forcing in the North Pacific basin (Figure 3f).Previous research has shown that anticyclonic Rossby wave breaking is associated with a warm, moist column extending to a surface anticyclonic circulation (Figure 2e).The surface circulation associated with moisture and temperature advection can generate turbulent heat flux anomalies that may cause interior SST anomalies (Strong & Magnusdottir, 2009) associated with the PDO cool phase.For the circum-Pacific Rossby wave patterns, there are no significant equatorial SST anomalies.However, positive SST anomalies are seen in the Philippine Sea around 20°N (Figure S5a in Supporting Information S1), which corresponds to a dry precipitation anomaly (Figure 2b).Numerical experiment results suggest that the anomalous heat sink over the Philippine Sea plays a significant role in generating circum-Pacific Rossby wave pattern (Wang et al., 2022).Note, however, the SST anomalies in the North Pacific during summer are largely forced by atmospheric circulation anomalies, rather than the other way around.
It is worth noting that, consistent with the trend of the event frequency, the occurrence frequency of all these three Rossby wave patterns has shown an increasing trend over the past 42 years (the green dashed lines in Figures 3b  and 3e, and Figure S5b in Supporting Information S1), indicating that natural variability or climate change has made atmospheric circulation patterns that cause compound disasters more frequent.The increasing trend of the cross-Pacific and Pacific anticyclone patterns is particularly noticeable, and these two wave patterns have a greater ability to amplify the probability of severe precipitation (Figure S3 in Supporting Information S1).In the future, these specific Rossby wave patterns may lead to more extreme weather.

The Impact of the Mean State on Rossby Wave Patterns
Rossby waves and their associated energy propagation on a sphere critically depend on the structure of the basic state westerlies (Hoskins & Karoly, 1981).The westerly jet stream substantially enhances the meridional potential vorticity gradient, favoring the generation of Rossby waves and affecting their propagation speed (Hoskins & Ambrizzi, 1993).It is often called "waveguides" (Wirth et al., 2018).The barotropic instability of the zonally varying mean flow could support synoptic disturbance providing an energy source for low-frequency Rossby wave train pattern (Simmons et al., 1983).The circum-and cross-Pacific Rossby wave patterns initially propagate along the jet stream waveguide but emanate a north-eastward propagation of the Rossby wave train near the dateline when the jet stream weakens (Figure 2).The Rossby waves turn equatorward when they reach a critical latitude in the Gulf of Alaska and form a great-circle Rossby wave energy propagation pattern (Hoskins & Karoly, 1981).Therefore, the propagation of the Rossby wave patterns in mid-latitude regions is driven by the variation of the jet streams and meridional and zonal variations of mean flows.
As shown in Figure 4a, the circum-Pacific Rossby wave train is associated with jet exit "extension" and poleward shift compared to the climatology.The 200 hPa zonal wind is very strong around 40°N-60°N when the circum-  context of a weaker jet stream.The frequency of Rossby wave breaking in the mid-latitude is primarily controlled by the jet stream (Peters & Waugh, 1996).The zonal potential vorticity gradient is small when the 200 hPa zonal wind weakens, so the waves become nonlinear and eventually break (Li et al., 2018;L. Song & Wu, 2021), causing anticyclone in the Pacific.During La Niña, the jet stream is slower than normal (Ryoo et al., 2013), which can increase the frequency of cross-Pacific Rossby wave train and Pacific anticyclone (Martius et al., 2007).

Discussion and Conclusion
In our study, we conducted a comprehensive analysis of clustering occurrences of extreme precipitation along the Indo-Pacific rim and, for the first time, identified this type of event on a daily timescale.The clustering extreme precipitation events cannot be attributed to coincidence.Three key connectors organize these events across multiple regions: circum-Pacific and cross-Pacific Rossby wave trains, and Pacific anticyclone pattern due to Rossby wave breaking.This present study fills the gap in the generalization of clustering extremes and contributes to an improved understanding of their underlying driving mechanisms.Figure S9 in Supporting Information S1 summarizes the key findings of three patterns, highlighting the key weather systems that pave the road for the Rossby waves.Diverse Rossby wave patterns set up favorable atmospheric conditions for extremes to occur over multiple regions.The tropical latent heat anomaly during the BSISO period serves as a first-order driving mechanism for the Rossby wave propagation to higher latitudes.The northward shifting component of tropical convection associated with the South Asian summer monsoon during BSISO (Chen & Wang, 2021;Kikuchi, 2021) is conducive to cause consecutive extreme weather from South Asia to mid-latitudes.In particular, the "wet India-dry Philippines" dipole heating anomaly can make the Rossby wave train more northeastward compared to the simply wet India condition.Then the Rossby waves interact with the jet stream to promote its development.The SST anomaly over the Pacific will affect the atmospheric mean state.With more tropical disturbance and slower mid-latitude background flow, the quasi-stationary patterns of cross-Pacific Rossby wave train and Pacific anticyclone due to Rossby wave breaking will be more frequent during the La Niña year (Figures S9b and S9c in Supporting Information S1).
One reason for the increasing risk of the clustering extreme precipitation events along the Indo-Pacific rim is likely connected to the rising frequency of Rossby waves.The annual frequency of three identified Rossby wave patterns shows a positive correlation with the number of annual days of events (Figure S10 in Supporting Information S1).This suggests that more frequent circulation patterns are likely to increase the frequency of clustering extreme precipitation events (F.Song et al., 2022).The escalating frequency of Rossby wave patterns revealed here will make future clustering extreme precipitation events more frequent and exacerbate their hydrological impacts, posing acute challenges to social, economic, and environmental systems.Notably, the cross-Pacific Rossby wave train and Pacific anticyclone exhibit a more substantial increasing trend, implying that the probability of experiencing the most severe extreme precipitation events could be amplified.Therefore, it is crucial to consider future changes in atmospheric circulation frequency when attempting to predict extreme events through climate change (Faranda et al., 2023).Moreover, the earlier onset of favorable oceanic conditions has resulted in a significant seasonal advance of intense tropical cyclones (TCs) in most tropical oceans (Shan et al., 2023).This seasonal advance increases the likelihood of extreme precipitation events induced by TCs that concurrence with those produced by the summer monsoon system.It raises concerns TCs may cause more clustering extreme precipitation events in the Northern Hemisphere in the future, thereby increasing the compound risk.
Our study provides a new perspective on the future evolution of extreme weather with global warming.The sequential clustering of extreme precipitation events might offer a predictability source because their favorable atmospheric precursors stem from the tropics associated with the rapid La Niña cooling.Thus, we can enhance the predictability of consecutive extreme rainfall events across the Indo-Pacific on a sub-seasonal to seasonal scale.
The identification method provides a technical alternative for investigating similar types of events.Future research could explore the clustering heatwave or the seesaw pattern of clustering disaster events in multiple regions, further contributing to our understanding of extreme weather phenomena.
an increase in the frequency of clustering extreme precipitation events across the Indo-Pacific rim • The consecutive occurrences of extreme precipitation in multiple regions are organized by three diverse Rossby wave patterns • The Indian Summer Monsoon heat sources and La Niña are key drivers of the events and the mid-latitude jet streams are modulators Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.General properties of the clustering extreme precipitation events and three Rossby wave patterns (a) Time series of the annual frequency of the events.The green solid line is the fitted trend line, and the Mann-Kendall trend test results are shown in the upper right corner.(b) Histogram and probability density of the duration of clustering extreme precipitation events.(c) Displays the percentage occurrence of each pattern in each month across the entire clustering extreme precipitation event database reflecting seasonality.(d) Presents the cumulative distribution function of the phase locking days per event for circum-Pacific Rossby wave (red), cross-Pacific Rossby wave (blue), and Pacific anticyclone pattern (green), the p values indicate the likelihood of not exceeding five phase-locking days per event for three Rossby wave patterns.

Figure 2 .
Figure 2. Composite maps of the atmospheric anomalies for three Rossby wave patterns.For (a, b), Circum-Pacific Rossby wave train (c, d), Cross-Pacific Rossby wave train and (e, f), Pacific anticyclone due to Rossby wave breaking, left panels (a, c, e) show 200 hPa stream function anomalies (shading; 10 6 m 2 s 1 ), 850 hPa stream function anomalies (contours at an interval of 10 6 m 2 s 1 , 3 × 10 5 m 2 s 1 , 3 × 10 5 m 2 s 1 respectively), and 200 hPa wave activity flux (vectors).Three patterns show an equivalent barotropic structure except over the source region in South Asia.The yellow contours show the 200 hPa jet axis locations.The right panels (b, d, f) show outgoing long radiation anomalies (shading), 850 hPa wind anomalies (vectors; UV 850) and high Rossby wave source region (red contour region with larger than 20 × 10 11 s 2 ).The white stippling denoting statistically significant differences at the 5% level (Student's t-test).

Figure 3 .
Figure 3. Background sea surface temperature (SST) anomalies associated with the Rossby wave patterns and time-series trends of each pattern (left panel: cross-Pacific Rossby wave, right panel: Pacific anticyclone).Composites of SST anomalies for (a), cross-Pacific pattern and (d), Pacific-anticyclone pattern, white dots over the shading indicate statistically significant values at the 0.1 level and 0.001 level, respectively (Student's t-test) (b), the relationship between cross-Pacific pattern occurrence frequency (black curve) and Nino 3.4 index (yellow and blue bars) during JJAS.The Pearson correlation coefficient r and p-value are shown in the top left corner.The fitted green dashed line represents the trend of the occurrence frequency which is validated by Mann-Kendall test.(c), correlation matrix (Pearson correlation coefficient r) between monsoon activity, Nino 3.4, and occurrences (e), the relationship between all-year Pacific-anticyclone pattern occurrence frequency and Nino 3.4 index.The Pearson correlation coefficient r and p-value are shown in the top left corner.The fitted green dashed line represents the trend of the frequency which is validated by Mann-Kendall test.Panel (f), same as panel (e), but for Pacific Decadal Oscillation index.

Figure 4 .
Figure 4. Jet stream variability for each pattern (a), Circum-Pacific pattern (b), Cross-Pacific pattern and (c), Pacific anticyclone pattern, show the 200 hPa zonal wind anomaly (shading), the composite 200 hPa zonal wind (green contour; m/s) and the climatology 200 hPa zonal wind (black dashed line; m/s).