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Influence of Pacific Decadal Oscillation on global precipitation extremes

While the influence of the Pacific Decadal Oscillation (PDO) on precipitation has been extensively studied, its influence on precipitation extremes remains not well-known. Based on a series of generalized extreme value modeling experiments, this paper demonstrates some distinct regional patterns of the PDO’s influence on precipitation extremes worldwide. In eastern China, the well-known ‘southern flood (drought) and northern drought (flood)’ pattern in summer corresponds well to the positive (negative) phase of the PDO. In Australia, there tends to be a tripole pattern, with positive correlation between precipitation extremes and the PDO in the central region, and negative correlation in both eastern and western Australia. The precipitation extremes in northwestern Europe and western Russia roughly hold positive correlation with the PDO. These regional patterns of the PDO’s influences are explained via comparative analyses of the atmospheric circulation conditions between cold and warm PDO phases. Certain precipitation extremes tend to be missed or happen more than once during different phases of the PDO at more than 2/3 of stations in a typical region. The cold phase tends to exert more consistent influences than the warm phase in these typical regions. These findings not only indicate different risks of extreme precipitation for the typical regions during different phases of the PDO, but also have important implications for the near-term projection of variable regional climate extremes under global warming.


Introduction
Extreme precipitation events, with their devastating consequences such as flooding, waterlogging and landslides, have always attracted extensive attention worldwide (e.g. Easterling et al 2000, Groisman et al 2005, Kenyon and Hegerl 2010, Li et al 2018. A hot topic currently is whether there is a mechanistic relationship between precipitation extremes and global warming. A few studies have pointed out a tendency towards more frequent and intense precipitation since the mid-late twentieth century at many stations worldwide and attributed the increasing trend in precipitation extremes to global warming (Alexander et al 2006, Min et  However, there were complex regional patterns of changes in extreme precipitation during the past decades (Manton et al 2001, Zhai et al 2005, Simpson and Jones 2014. More complicatedly, for some regions such as North China, the total precipitation of the summer monsoons decreased but the precipitation extremes enhanced during some decades (Tu et al 2010). These results indicate that internal climate variability might play an important role in the observed variability of precipitation extremes.
The influence of internal climate variability associated with various large-scale climate modes on the occurrence and magnitude of extreme precipitation has been investigated for many regions. By fitting the generalized extreme value (GEV) distribution to the winter maximum daily precipitation with El Niño-Southern Oscillation (ENSO), North Atlantic Oscillation (NAO) and Pacific Decadal Oscillation (PDO) indices as covariates, Zhang et al (2010) showed that, during El Niño and the warm phase of the PDO, the likelihood of extreme precipitation increases over a vast region of southern North America and decreases over the northwestern United States, the Great Plains, Canadian prairies and the Great Lakes. Min et al (2013) found less intense extreme rain over northeastern Australia and the southern coast during El Niño and the positive phase of the Indian Ocean Dipole in the cold season and more intense extreme rain over much of the eastern continent in summer during the positive phase of the Southern Annular Mode. Based on daily precipitation records in Beijing during 1951, Pei et al (2017 found that all extreme events, similar to or more severe than that on 21 July 2012, happened during negative phases of the PDO, indicating a negative association between the PDO and extreme precipitation over North China. Kenyon et al (2010) analyzed global patterns of the influences of ENSO and the NAO on precipitation extremes and the influences of North Pacific Index (NPI) on winter precipitation extremes over the Northern Hemisphere. They suggested that ENSO exerts influences throughout the world, while the NAO mainly influences the Eurasian continent and the NPI is similar to ENSO but mainly influences the Pacific Rim.
In short, although there is an increasing or decreasing trend of extreme precipitation in association with global warming, it accounts for a relatively small proportion of the variability in extreme precipitation for many regions. A large proportion of the variability in extreme precipitation arises from the internal climate variability associated with large-scale climate modes at different time scales, such as ENSO and the PDO. The PDO (or Interdecadal Pacific Oscillation, IPO, in case the whole Pacific is taken into account) is one of the most influential decadal to multidecadal climate modes, with dominant impacts on multidecadal variability of precipitation in many regions over the world. Several studies suggested that the PDO influences annual precipitation over eastern China and the US by inducing an anti-cyclonic anomaly circulation over the North Pacific in the lower troposphere during PDO cold phases, which lead to dry and cold northwesterly winds and below-normal precipitation over much of the west US (Dai 2013, Dong andDai 2015) but wet and warm southeasterly winds and above-normal precipitation over North China (Yang et al , 2019. Song and Zhou (2015) found that the IPO affects the decadal variation of relationship between the East Asian Summer Monsoon and ENSO through the western North Pacific subtropical high, resulting in more precipitation in southern China during positive IPO phases. Similar modulation of PDO on the relationship between El Niño and northeast Asian summer monsoon (NEASM) was also found by Yoon and Yeh (2010), who suggested that the summer rainfall over northeast Asia was usually above-normal following an El Niño winter and such relationship was intensified when the El Niño was accompanied by a positive PDO in the previous winter. They further proposed that the PDO modulated the relationship between El Niño and the NEASM through changes in the extratropics-related rainfall, which was associated with the atmospheric circulation, such as the Eurasian pattern. For the precipitation in eastern Australia, it has been found that the asymmetrical ENSO-precipitation relationship in this region is only robust in negative IPO phases due to an eastward shift in the Walker circulation and the convection center near Australia's east coast during the positive IPO phases (Power et al 1999, Cai et al 2010, Cai and Rensch 2012. Although the patterns of sea surface temperature (SST) anomalies associated with the PDO and ENSO appear similar and the latter has some contribution on the formation of PDO (Schneider and Cornuelle 2005), they are not the same phenomenon. The PDO not only has longer time scales, but also has relatively strong variability of SST in the northern Pacific, while ENSO has major variability of SST in the tropical Pacific. Therefore, their influences on global precipitation extremes are not necessarily the same. It is beneficial to study the impacts of PDO on global precipitation extremes.
The aim of the present study is to provide a global overview of the influences of the PDO on precipitation extremes at multidecadal timescales. Section 2 describes the data and methods used to identify the regions where extreme rainfall is significantly affected by the PDO. The results and alteration of certain extreme events between PDO warm and cold phases are demonstrated in section 3. Section 4 summarizes the main conclusions.

Data and processing
The 'maximum five-consecutive-day precipitation' (RX5day) index, defined by the Expert Team on Climate Change Detection and Indices (Klein Tank et al 2009), is adopted as the extreme precipitation index in this study. With regard to the different regional rainy seasons over the world, it is defined within a year and calculated by the following procedures: (a) for each day of the year, calculate the accumulated fiveconsecutive-day precipitation centered on that day, (b) select the maximum value for the year. This index is closely related to severe floods and has important implications for designing infrastructure.
The daily dataset used in this study to calculate the RX5day index is from the Global Historical Climate Network-an integrated database of climate summaries from land surface stations across the globe. It comprises records from numerous sources that have been integrated and subjected to a common suite of quality-control procedures (Menne et al 2012). The daily precipitation records from a total number of 105 309 stations are available at www.ncdc.noaa.gov/ghcnd-data-access. We chose a set of stations containing records with a length of at least 60 years between 1900 and 2018. The station records are not necessarily continuous. The record length varies among the chosen stations with a range from 60 to more than 118 years. From the chosen stations, two subsets of data were extracted for use in the present study: one with station records with a length of at least 100 years starting from 1900, and the other with station records with a length of at least 60 years starting from 1940. The data before the start year were not used to facilitate the comparative analysis among stations. The relationship between the PDO and precipitation extremes in these two subsets of different record lengths and geographical coverages was investigated separately and a comparison was made to help analyze the stationarity of the relationship for the regions with overlapped data.
The monthly PDO index, defined as the leading principle component of North Pacific monthly SST variability (poleward of 20 • N), was obtained from the University of Washington (http://research.jisao.washington.edu/pdo/) and averaged within a year to form the yearly time series. A nine-year running mean was applied to the yearly PDO series to remove the interannual variability, leaving mainly multidecadal variability for the present study ( figure 1(a)). Based on the monthly SST records from the COBE-SSTs dataset (Ishii et al 2005), the contrast of the mean annual SST anomalies between the PDO warm and cold phases shows the typical PDO pattern with strong variability in the northern Pacific (figures 1(c) and (d)) as indicated in previous studies (Mantua et al 1997), different from the typical SST pattern of ENSO, which has its major variability in the tropical Pacific.
Considering the RX5day index is the largest value of the moving 5 day-precipitation accumulation in a year, it can be appropriately modeled with the GEV distribution, which has the form as following: where the three parameters −∞ < µ < ∞, σ > 0 and −∞ < ξ < ∞ are termed location, scale and shape parameters, respectively. Conditioned on ξ > 0, ξ < 0 or ξ = 0, the distribution belongs to Fréchet, Weibull or Gumbel distribution, respectively. The three types of extreme value distribution not only differ from their shapes but also the lapse rates in their tails, which determine the decreasing rates of probabilities in very large extremes. Given the samples such as the RX5day time series, the GEV distribution is usually determined by an estimation of the parameters with the maximum likelihood method. In this estimation, a stationary GEV model is obtained if its parameters are seen as constants. Letting the parameters vary with some variables such as the PDO index, we obtain the non-stationary GEV model. Two modeling strategies were applied independently to explore the relationship between the PDO and precipitation extremes. One was the non-stationary GEV model, which introduces a smoothed PDO index into the GEV model as a covariate (referred to as the NGEV method hereinafter) to see whether it significantly improves the modeling compared with the GEV model without this covariate . The other comprised two steps: (a) fit the RX5day index to a stationary GEV model within a 30 year moving window to obtain a series of stationary GEV models; and (b) regress the smoothed PDO index to the GEV location parameter time series to see whether there is a significant relationship (referred to as the MGEV method hereinafter). More details about the two strategies and how to estimate and select the models can be found in the supplementary material (available online at stacks.iop.org/ERL/16/044031/mmedia). Figure 1(b) shows an example result of the MGEV method. It is clear that the magnitude of the extreme precipitation at the station exhibits significant multidecadal variation roughly out-of-phase with the PDO, although such a relationship might not consistently exist in the interannual variability. The two modeling strategies were applied to the RX5day samples for each station. To check the validity of a fitted GEV model, the Lilliefors' test was applied to compare the empirical distribution and fitted GEV distribution. For the NGEV method, if the selected model is non-stationary, the samples were firstly standardized by the fitted model, then compared with the standard Gumbel distribution (Coles 2001). After model checking, typical regions showing a consistent relationship between the PDO and extreme precipitation were identified. Since we carry out the significance test for each station at a significance level of 0.05, for a region with many stations, there is a probability distribution of proportion of stations with positive or negative relationship between the PDO and extreme precipitation for a random field of data with no relationship with the PDO. To see whether the observed proportion of stations with the same relationship in the region is larger than a criterion of random results, a field significance test using the Monte Carlo method of Livezey and Chen (1983) was applied to ascertain the observed regional patterns to be statistically significant. More details about the goodness-of-fit test and field significance test are provided in the Supplementary Material.
The monthly data from the 20th Century Reanalysis (20CR) datasets version 2 (Compo et al 2011) and The ECMWF twentieth century reanalysis (ERA-20C) (Poli et al 2016) were used for circulation analysis. The spatial resolution of the 20CR reanalysis dataset is 2 • × 2 • and covers a time period of 1871-2012. The ERA-20C has a spatial resolution of 1 • × 1 • and covers 1900-2010. The variables used include sea surface pressure, horizontal winds, and geopotential height. The Southern Oscillation Index (SOI) commonly used to represent the interannual variability of ENSO was taken from the website of Working Group on Surface Pressure, Global Climate Observing System (https://psl.noaa.gov/gcos_wgsp/Timeseries/SOI/).

Global pattern of the relationship between the PDO and extreme precipitation
Four sets of results were obtained, by applying the NGEV and MGEV methods to the 100 year and 60 year subsets (figure 2). The goodness-of-fit tests show that the GEV distribution is an appropriate distribution for modeling the RX5day data (figure S1). For the NGEV methods, 97.5% of the stations in the 100 year dataset show no difference to the fitted GEV distribution in their empirical distribution for RX5day (the proportion in the 60 year dataset is 96.7%). For the MGEV method, 97.2% of the stations consist of at least 90% of insignificant tests (indicating a good match between the empirical distribution and the GEV distribution) in the 100 year dataset (the proportion in the 60 year dataset accounts for 97%). Therefore, the models are good representation of the data and the patterns in figure 2 are reliable. These results are quite consistent for those regions with common stations in the different subsets and for the same subset by using different methods of detection. Specifically, comparing figures 2(a) and (c) or figures 2(b) and (d), we can see that the spatial patterns of the relationship between the PDO and extreme precipitation explored by the different methods are almost the same, indicating that both methods are effective and the influential signals of the PDO are significant for many stations. A comparison between figures 2(a) and (b) or figures 2(c) and (d) reveals plausible stationary relationship between the PDO and extreme precipitation in the regions with common data coverages in the two subsets of different lengths and it suggests that, during a warm PDO phase, most of the contiguous United States experiences enhanced extreme precipitation, except the northwestern corner; eastern Australia shows distinct negative correlation; and northwestern Europe to a large part of western Russia mainly shows positive correlation. A further comparison between figures 2(a) and (b) or figures 2(c) and (d) shows more stations with consistently significant PDO-RX5day relationship in the 60 year subset (figure S2), indicating more consistent regional patterns during the second half of the 20th century in those regions.
Comparing between figures 2(b) and (d), a notable fact is that the relationship explored by the NGEV method exists at fewer stations across the world than that explored by the MGEV method. The reason is that the MGEV method more directly explores the relationship at the multidecadal scale, while the result of the NGEV method also involves the relationship for interannual variability. Consequently, some regionally significant relationships are detected by the MGEV method that are diminished by the NGEV method, such as in eastern China. To facilitate discussion on the multidecadal relationship between the PDO and extreme precipitation worldwide, we focus the following analysis on the result from the 60 year dataset (after 1940) produced by the MGEV method ( figure 2(d)).
According to figure 2(d), there are some distinct regional patterns of the relationship between the PDO and extreme precipitation. Eastern China exhibits a north-south dipole pattern, where extreme precipitation over the southern part is positively correlated with the PDO and that over the northern part is negatively correlated. The well-known 'southern flood northern drought' pattern in eastern China in terms of annual/summer total precipitation and its relationship with the PDO has long been studied (e.g. Wang 2001, Zhu et al 2003, Zhou et al 2009Yang et al 2017).
Here, we emphasize that such a pattern extends in particular to that of extreme precipitation. Australia exhibits a tripole pattern, i.e. extreme precipitation is weakened (enhanced) over the eastern and western parts, but enhanced (weakened) over the central region, during the warm (cold) phase of the PDO. The contiguous United States shows a more complex but roughly dipole pattern, with positive correlation between extreme precipitation and the PDO at most of stations over the southeast, and negative correlation over the northwestern corner. Positive correlation between the PDO and extreme precipitation also exists in northwestern Europe and western Russia.
To confirm whether these regional patterns of climate relationships are statistically significant, we applied the field significance tests for each of these regions using the 60 year dataset. The regional boundaries are shown in figure S3 in the supplementary material. Except for the contiguous United States, all the aforementioned typical regional patterns are statistically significant. A significant pattern means that the observed proportion of stations with positive or negative relationship between the PDO and extreme precipitation (referred to as positive or negative ratio hereinafter) for a given region is larger than the 95th percentile of distribution for the same quantity generated by a random field with no relationship with the PDO. The results indicate statistically significant relationships between the PDO and extreme precipitation over most these regions at a significance level of 0.05 (figures 3(a)-(g)). Specifically, the dipole pattern over eastern China, the tripole pattern over Australia, and the consistent positive influence from the PDO over northwestern Europe and western Russia, are robust. The observed positive ratio is larger than the threshold for the southeastern United States (figure 3(i)), but the observed negative ratio for the northwestern United States remains within the range of random noise (figure 3(h)), implying that the influence of the PDO on extreme precipitation is not quite consistent over this region.
To illustrate more directly the relationship between the PDO and extreme precipitation for the identified regions, we have calculated the regional mean time series of RX5day and plotted them against the nine year smoothed PDO index (figure 4). It can be seen that all identified regions show consistent relationship between their regional mean time series of RX5day and the PDO with what we have found in the analysis above, although for some regions such relationship is not statistically significant (e.g. South China and central Australia). For the US and eastern Australia where the data records span a century, we have investigated the relationship before and after 1960 respectively. The PDO-RX5day relationship was more significant after the 1960 in eastern Australia and southeastern US (figures 4(c) and (h)), and the northwestern US even shows some opposite relationships between the two periods ( figure 4(i)). These suggest a non-stationary relationship between PDO and regional precipitation extremes due to influences from other factors, as implied in recent studies (Curtis 2008.

Atmospheric circulation anomalies
It is interesting to discuss possible physical links underlying the statistical relationship. To do so, we have examined the atmospheric circulation anomalies associated with the PDO-related SST pattern. Considering that the precipitation extremes occur in different seasons for different regions, we first examined the most likely season of RX5day in different regions ( figure S4). It is found that extreme precipitation events most frequently happen in boreal summer for most regions over Eurasia, while most regions in southern Hemisphere experience the extreme precipitation event in boreal winter. The seasonal times for precipitation extremes over North America are complex, but boreal summer remains the most likely season for extreme precipitation events in general. Hence, a composite analysis of the atmospheric circulation anomalies between the PDO warm and cold phases in boreal summer (June-July-August, JJA) for northern Hemisphere and in boreal winter (December-January-February, DJF) for southern Hemisphere was performed respectively to obtain a global view of the PDO's effects on circulation anomalies in different regions. Here, we used the seasonal mean circulation anomalies to help analyze possible physical links between the PDO and precipitation extremes under the assumption that the The histogram is an estimation of the distribution of positive/negative ratios under the hypothesis that the extreme precipitation field is a random field and unaffected by the PDO. The red points are the observed positive/negative ratios. When the red points are larger than the 95th percentile (black dashed lines), significant consistent influences of the PDO on the extreme rainfall over these regions are determined at a significance level of 0.05. probability of precipitation extremes depends on the mean circulation states. Before applying the composite analysis, the ENSO-related atmospheric circulation anomalies, which were obtained by regressing the original fields onto the SOI in DJF, were subtracted from the original atmospheric circulation anomalies to further remove possible effects of ENSO. For northern Hemisphere, the SOI in DJF was shifted to correspond to the RX5day index in the following summer to account for the delayed effect of ENSO on the precipitation extremes in the boreal summer (Wang et al 2000).
Based on the 20CR monthly data during 1900-2010, the differences of atmospheric circulation anomalies between PDO warm  and cold  phases in the second half of the 20th century were first calculated by a composite analysis (figure 5). For the regions in northern Hemisphere, it can be found that, in boreal summer, eastern China is dominated by a significant circulation anomaly dipole in the lower troposphere with an anomalous anticyclonic (cyclonic) flow over North China (South China), while an anomalous cyclonic flow was found over the western Russia and northwestern Europe ( figure 5(a)). Such low-level circulation anomalies match the observed PDO-RX5day relationships over these regions. In the middle level of the troposphere, a wave train was found along the northern mid-latitude ( figure 5(b)), linking the variation of precipitation extremes in different regions with the PDO. Over the western North Pacific, an anomalous cyclonic flow was found during the PDO warm phase (figure 5(a)). As well-known, the western North Pacific subtropical high (WNPSH) is over there and its seasonal evolution dominates the meridional shift of the rain belt over eastern China. The existence of the anomalous low there indicates weakening of the WNPSH with less northward and westward extension than usual, leading to a dry condition over North China in boreal summer. The weakened and eastward retreat of the WNPSH in boreal summer after the 1970s has been observed and possibly attributed to the forcing of the PDO (Huang et al 2015, Tong et al 2020. The US roughly saw a west-east dipole of circulation anomaly but not very consistent, especially for the western US. This explains the insignificant PDO-RX5day relationship over the northwestern US. In austral summer, an anomalous high accompanied by an anomalous anti-clockwise flow in the low-level troposphere was found over eastern Australia, while an anomalous low accompanied by an anomalous clockwise flow located in the Northwest of the continent (figure 5(c)). Such atmospheric circulation anomalies suppress the convective activity and reduce the rainfall over the eastern Australia due to the anomalous high there and increase the rainfall in the central to northwestern Australia due to the anomalous horizontal wind shear and moisture convergence. The formation of the anomalous high over eastern Australia was due to the eastward shift of the South Pacific Convergence Zone during a warm PDO phase with similar SST anomaly patterns and atmospheric forcing with the El Niño event (Power et al 1999, Cai et al 2012. Southwestern Australia was more affected by the anomalous high to its west ( figure 5(c)), leading to anomalous downward flow and moisture divergence in this region during a PDO warm phase. This anomalous high over southern Indian Ocean was part of the wave train associated with the PDO in the southern mid-high latitudes ( figure 5(d)). Thus, the tripole pattern of the PDOextreme precipitation relationship over Australia was explainable in the atmospheric circulation anomalies associated with the PDO.
To consider possible uncertainty in one reanalysis dataset, we performed the same composite analysis of SLP from the ERA-20C for the same period and found similar spatial patterns of atmospheric circulation anomalies, though the strength and significance vary among different regions ( figure S5). This further corroborated the observed PDO-extreme precipitation relationships over those typical regions. Analysis of the circulation difference between warm and cold phases in the 1922-1977 cycle (figure 1) in the two reanalysis datasets suggests that the observed PDO-RX5day relationships also hold for this early period for some regions, such as eastern China and US (figures S6(a) and (c)). Meanwhile, there was nonstationary PDO-RX5day relationship in other regions such as western Russia to northwestern Europe. Over this region, an anomalous low was found in the second half of the 20th century (figures 5(a) and S5(a)). But this anomalous low was largely reduced to an insignificant level or shifted westward in this early period (figures S6(a) and (c)).

Quantifying the influence of the PDO on certain extreme events
Having explored the global pattern of influence of the PDO on extreme precipitation, we next extend the analysis to certain extreme events for those regions with robust pattern of relationship to see how their frequencies or magnitudes change between positive and negative PDO phases. The 30 year return value derived from the GEV model fitting to all RX5day samples over the study period was used as a baseline. For each station, we calculate the return periods of this baseline value for GEV models fitted to moving 30 year samples, and then compare the return periods between positive and negative PDO phases. A statistically significant difference is determined by the t-test after a cubic root is applied to the return periods. The distributions of the mean return period in warm/cold PDO phase for those significant stations are summarized in the boxplots in figure 6 and table 1 for each region.
The influence of the PDO on precipitation extremes is consistent with the patterns we have discussed so far, with shorter (longer) return periods at most stations in the regions of positive (negative) correlation with the PDO during a warm PDO phase, and vice versa (figure 6). Specifically, during the cold phase of the PDO, about 65% stations over northern East China show the return periods of the baseline values decreasing to below 30 years (figure 6(b)); while during the warm phase of the PDO, 60% stations in the same region have the return periods of the same extreme events increasing to above 30 years ( figure 6(a)). For southern East China, the return periods of the baseline values increase to above 30 years at 53% stations during the cold phase of the PDO, while these decrease to below 30 years at 51% stations during the warm phase of the PDO (table 1). Note that a 30 year period is the typical duration for a warm or cold phase of the PDO on the multidecadal time scale. For those stations with their return periods of the baseline values above 30 years during a warm/cold PDO phase, such extreme events  The PDO also exerts strong influence on extreme events over eastern and western Australia. During warm PDO phases, 64% and 63% stations increase the return periods of the baseline values, respectively, leading to fewer such extreme rainfall events in the corresponding periods (figure 6(a) and table 1). On the contrary, extreme rainfall events happen more frequently over these two regions with decreasing return periods of the baseline events at most stations (65% and 60%, respectively) during cold PDO phases (figure 6(b) and table 1). Central Australia experiences the opposite, with 55% of stations with decreased return periods during warm PDO phases (figure 6(b) and table 1) and 57% of stations with increased return periods in cold PDO phases (figure 6(a) and table 1).
Similar alternation happens in the other typical regions. The warm PDO phase corresponds to more stations with shorter return periods of the baseline values (more intense precipitation extremes) over western Russia and northwestern Europe (figure 6(b) and table 1), while the cold PDO phase reverses the situation over these regions (figure 6(a) and table 1).
A notable finding is that the influence of the PDO on extreme precipitation is asymmetric. Comparing the first two rows or the last two rows in table 1, we can see that the typical regions have more stations with changing extremes in the cold PDO phase than those in the warm PDO phase. This suggests that the extreme conditions induced by the cold PDO phase are more severe than those induced by the warm PDO phase for the typical regions. The negative PDO phase tends to induce a more consistent response of extreme precipitation than the positive PDO phase. Previous studies have also shown similar asymmetry between the influences of cold and warm PDO phases on extreme precipitation over eastern Australia (King et al 2013). Here, we find that such asymmetry extends to almost all the typical regions with a certain relationship between the PDO and extreme precipitation. These findings have meaningful implications for these regions in their efforts to tackle the different risks in different PDO phases.

Conclusions and discussion
In this study, we examined the influence of the PDO on extreme precipitation worldwide. The main conclusions can be summarized as follows: (a) The PDO significantly influenced extreme precipitation at most stations on the multidecadal time scale, with some distinct regional patterns. In particular, eastern China exhibited a dipole pattern, i.e. extreme precipitation over the southern part was positively correlated with the PDO, while that over the northern part was negatively correlated. Australia exhibited a tripole pattern, with two negative correlation centers in the east and west and a positive one in the middle. Northwestern Europe and western Russia showed a roughly positive relationship overall between the PDO and extreme precipitation. These typical regional patterns of the relationship were explained via comparative analyses of seasonal mean circulation anomalies between the different phases of the PDO in corresponding rainy seasons. (b) The influences of the PDO on certain extreme rainfall events over these typical regions were quantified. Given the once-in-30 years events derived from all samples during the study period as baseline events, such extreme events would barely happen at as many as 2/3 stations in the typical regions during a PDO phase when extreme rainfall is suppressed (e.g. North China and eastern Australia in a warm PDO phase; northwestern Europe and western Russia in a cold PDO phase). On the contrary, 2/3 of stations in the typical regions would experience such extreme events more than once during a PDO phase when extreme rainfall is enhanced (e.g. North China and eastern Australia in a cold PDO phase; western Russia in a warm PDO phase). These impose quite different risks of extreme precipitation over the typical regions during different phases of the PDO. (c) The influence of the PDO on extreme precipitation was found to be asymmetrical between the warm and cold PDO phases. For almost all typical regions, the proportions of stations with changing extreme events in a cold PDO phase were larger than those in a warm PDO phase, indicating that the cold PDO phase exerts more extensive and consistent influence.
Due to limited availability of long-term daily observations, the influence of the PDO on extreme precipitation for regions such as Africa, South America, India and the central Eurasian continent remains unclear. However, the effects of the PDO on extreme precipitation over some of these regions might be inferred from the present global analysis. For example, there appears to be a wave train of positive and negative relationships with the PDO in extreme precipitation across the Eurasian continent (figure 2(d)), with a wave train of circulation anomalies associated with the PDO (figures 5(a) and (b)). These features deserve further investigation when more data become available.
The physical mechanisms underlying the typical regional patterns of the relationship between the PDO and extreme precipitation also deserve further study. Although the seasonal mean circulation anomalies associated with the PDO were consistent with the observed PDO-RX5day relationships over the typical regions, it remains interesting to study how the PDO influences on the large-scale circulation responsible for local precipitation extremes. In addition, as another significant multidecadal climate mode, the effects of the Atlantic Multidecadal Oscillation on global precipitation extremes also deserve noticed. Considering the strong interaction between different ocean basins to form the different climate modes (Cai et al 2019) and the shortage of the observational records, numerical experiments are needed to uncover their combined effects on global precipitation extremes. Sensitive experiments by running an atmospheric general circulation model driven by prescribed SST patterns associated with different multidecadal SST modes or their combinations might provide further evidence of their influences on global precipitation extremes. However, more convincing verification of these multidecadal climate modes' effects on global precipitation extremes needs not only long enough simulations by coupled general circulation models (CGCMs) but also a good enough representation of these modes in the CGCMs.
The asymmetrical effect of the PDO on precipitation extremes is another topic worth further study and it is possibly related to the PDO's modulation of the ENSO's effect on climate worldwide. Some studies have pointed out the asymmetrical or even more complex modulation of ENSO teleconnections by the variability in the oceanic and atmospheric mean state on longer time scales (e.g. IPO and global warming) (Dong et al 2018, Yeh et al 2018. For eastern Australia, King et al (2013) found that La Niña had much greater influence on extreme precipitation than El Niño and during a negative phase of the Interdecadal Pacific Oscillation, such asymmetry appeared more significant. The asymmetrical ENSOextreme precipitation relationship could be explained by a shift of the South Pacific Convergence Zone to enhance convection across eastern Australia during La Niña and to suppress convection during El Niño (Power et al 1999, Cai et al 2010. Our preliminary results suggested that the mid-high latitude circulation anomalies were stronger during PDO cold phase, which caused the asymmetrical influence on extreme precipitation across eastern China, western Russia and northwestern Europe. The mechanisms linking the PDO and different typical regions deserve further studies.
Nevertheless, the regional patterns of the relationship between the PDO and extreme precipitation found in this study are reasonably robust both in statistical and physical contexts. The significant regional patterns of the PDO's influence are meaningful for validation of interdecadal climate modeling and our understanding of the near-term projection of extreme precipitation in these regions. The alternating probability of precipitation extremes between cold and warm PDO phases also provides guidelines for regional response and adaptation measures to relevant climate risks.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.1175/JTECH-D-11-00103.1.