The most severe thunderstorms, producing extreme precipitation, occur over subtropical and midlatitude regions. Atmospheric conditions conducive to organized, intense thunderstorms commonly involve the coupling of a low-level jet (LLJ) with a synoptic short wave. The midlatitude synoptic activity is frequently modulated by the circumglobal teleconnection (CGT), in which meridional gradients of the jet stream act as a guide for short Rossby waves. Previous research has linked extreme precipitation events with either the CGT or the LLJ but has not linked the two circulation features together. In this study, a circulation-based index was developed by combining (a) the degree of the CGT and LLJ coupling, (b) the extent to which this CGT-LLJ coupling connects to regional precipitation and (c) the spatial correspondence with the CGT (short wave) trending pattern over the recent 32 years (1979–2010). Four modern-era global reanalyses, in conjunction with four gridded precipitation data sets, were utilized to minimize spurious trends. The results are suggestive of a link between the CGT/LLJ trends and several recent extreme precipitation events, including those leading to the 2008 Midwest flood in U.S., the 2011 tornado outbreaks in southeastern U.S., the 2010 Queensland flood in northeastern Australia, and to the opposite side the 2012 central U.S. drought. Moreover, an analysis of three Coupled Model Intercomparison Project Phase 5 models from the historical experiments points to the role of greenhouse gases in forming the CGT trends during the warm season.
 Recent devastating floods such as those in the central U.S. (June 2008 “Midwest flood”), in Pakistan (July–August 2010), in eastern Australia (December 2010 “Queensland flood”), and in Brazil (January 2011) have resulted in tremendous societal and economic losses. None of these floods were caused by tropical cyclones and yet, each of the extreme precipitation events was unprecedented in its particular region, not only in the scale of damage but in the magnitude of precipitation that initiated the flooding. Increased extremes in precipitation worldwide have been observed and in many cases have been attributed to increased greenhouse gas (GHG) loadings in the atmosphere leading to moisture intensification [Easterling et al., 2000; Diffenbaugh et al., 2005; O'Gorman and Schneider, 2009; among others]. However, the current understanding of extreme precipitation events remains insufficient for climate prediction to operationally provide an accurate probabilistic assessment as to where and when extreme events will most likely occur. The purpose of this paper is to develop a method of identifying high-threat regions of extreme precipitation under the changing climate.
 Satellite observations such as the Tropical Rainfall Measuring Mission (TRMM) have confirmed that the most intense thunderstorms occur over subtropical and/or semiarid regions, rather than over the heavy-raining tropics [Zipser et al., 2006]. Correspondingly, there are relatively more extreme precipitation events, as well as steeper increases in their magnitude, over the subtropics than the tropics [e.g., Sun et al., 2007; Sugiyama et al., 2010]. The atmospheric conditions conducive to intense convective storms usually involve strong vertical shear, a low-level jet (LLJ), and synoptic forcing by propagating short waves. When they occur in unison, these conditions provide the key ingredients for organized convection: instability, moisture, and lift [Doswell, 2001]. In other words, the observed increase in extreme precipitation likely has occurred in conjunction with certain changes in those factors. Organized convective storms often take place in regions where the tropical moist air meets the midlatitude continental/polar air, with the former providing conditional instability and the latter generating frontal lift. Regions of active mesoscale convective systems (MCSs), for example, are often regions of frequent, diurnally-varying LLJs as well [Stensrud, 1996; Monaghan et al., 2010]. When the evolution of the LLJ is coupled with the propagation of upper level short waves (referred as the 300 hPa level by Uccellini, 1980), the resulting MCSs tend to be stronger and more organized, such as those forming the mesoscale convective complex [Maddox, 1980, 1983]. Extreme precipitation events worldwide are almost always a result of consecutive occurrences of these strong and organized MCSs [Tetzlaff et al., 2012].
 Around the world, regions where tropical and midlatitude air masses interact correspond to the positions of the jet streams. The meridional gradients of the jet streams and their nearly circumpolar extent act as a guide for short Rossby waves [Hoskins and Ambrizzi, 1993], a dynamical process referred to as the circumglobal teleconnection (CGT). One commonly accepted mechanism of the CGT is Rossby wave propagation, in which the jet stream acts as a waveguide to provide an important source of circumglobal teleconnectivity, particularly in winter [Hoskins and Ambrizzi, 1993; Branstator, 2002]. The CGT connects climate anomalies between widely separated regions within similar latitude zones through Rossby wave energy dispersion induced by local vorticity sources [Schubert et al., 2011]. The CGT occurs with a preferred zonal wave-5 structure with its wave amplitudes confined within the jet streak. Although the intensity of the CGT is stronger at the upper levels (e.g., between 200–300 hPa), the circulation anomaly exhibits a vertically uniform (or barotropic) structure [Wang et al., 2010]. Variability of the CGT is uncorrelated with the El Niño-Southern Oscillation (ENSO) but might be connected to the North Atlantic Oscillation [Branstator, 2002; Ding and Wang, 2005; Yasui and Watanabe, 2010]. The CGT can also occur in summer [Ding and Wang, 2005] and spring transition seasons [Wang et al., 2010], as the meridional gradients and nearly circumpolar extent of the summer jets form important guides for Rossby waves as well. Further evidence has been found that the summertime CGT has stronger variability in the subseasonal time scale than the interannual one [Ding and Wang, 2007; Wang et al., 2010; Schubert et al., 2011]—this feature is directly relevant to extreme precipitation events that tend to persist for an extended period of time.
 There has been considerable evidence of the linkage between the CGT and regional climate extremes. For instance, in the central United States, the anomalous circulation with predominant short-wave features modulates summer precipitation [Lau and Weng, 2002] and the Great Plains LLJ [Weaver and Nigam, 2008]. Similar CGT modulations on regional climate extremes have been observed over the past decade, including northern India [Ding and Wang, 2005, 2007], Pakistan [Wang et al., 2011b], East Asia [Krishnan and Sugi, 2001], Eurasia [Matsueda, 2011; Schubert et al., 2011], and the western United States [Wang et al., 2010]. The CGT modulation on regional climate also exists in the Southern Hemisphere [Ambrizzi et al., 1995] affecting South America [Junquas et al., 2012].
 Post-1970s climate change has modified the atmospheric general circulation in two fundamental ways: (a) a weakening and a poleward shift of the jet streams [Archer and Caldeira, 2008] leading to potentially further meandering of the jet [Rivière, 2011] and (b) a widening of the tropical belt and expansion of the Hadley circulation [Seidel et al., 2008; Lu et al., 2009]. Given the CGT's underlying waveguide mechanism, any long-term changes in the jet stream may affect the stationary wave train and, in turn, modify the CGT characteristics. Indeed, recent studies [Wang et al., 2011b; Francis and Vavrus, 2012; Screen and Simmonds, 2013] have found an increase in the amplitude of larger zonal wave numbers (i.e., short stationary waves) along the midlatitudes. Likewise, the widened tropical belt increases the moisture and strengthens the moisture flux toward the midlatitudes; one such response is the enhanced transport of moisture by the LLJ as has been observed in the U.S. Great Plains [Cook et al., 2008; Weaver et al., 2009]. Therefore, in regions where increased moisture transport of the enhanced LLJ interacts with increased transient vorticity source associated with the CGT, the combined increases in moisture and lift are conducive to deep moist convection. These processes, together with warming in the lower troposphere that decreases static stability and holds more moisture [e.g., Gaffen et al., 2000], could enhance the likelihood for extreme precipitation events over those particular regions.
 In order to identify such regions, we developed a technique to diagnose the trend in extreme precipitation threat under the changing climate and its geographical distribution. This technique characterizes the CGT and LLJ dynamics using a set of circulation criteria and regression analyses. The purpose of this analysis is to provide a circulation-based evaluation for global climate models without directly engaging simulated precipitation, which remains considerably biased. The long-term trend of the circulations was examined through an ensemble of modern-era global reanalyses; these are introduced in section 2. Evidence of the enhanced CGT and the analysis procedure are explained in section 3. Interpretation of the diagnostics and the mapping results of precipitation threat are presented in section 4. Possible cause of the changing CGT effects is discussed in section 5. A conclusion from the results is summarized in section 6.
2 Data Sources
 Global reanalysis data sets provide complete coverage over most geographical regions around the world. However, trend analysis using a single reanalysis has led to concerns related to changing observation systems that may introduce spurious trends [Paltridge et al., 2009]. Thus, to obtain a reliable or optimal estimate of any long-term trend, we utilized an array of global reanalyses and sought consensus. For the global reanalysis, we used four post-1979 data sets that cover the satellite era: MERRA [Rienecker et al., 2011], CFSR [Saha et al., 2010], ERA-Interim [Dee, 2011] and the JRA-25 [Onogi et al., 2007]; the acronyms, full names, and description of each data set are provided in Table 1. Previous studies have also raised concerns about the quality of gridded precipitation data over data-poor regions [e.g., Ghosh et al., 2009]. Thus, for the gridded precipitation data sets we used the satellite-enhanced GPCP [Adler et al., 2003] and CMAP [Xie and Arkin, 1997] data combined for the global domain, the GPCC (http://gpcc.dwd.de/) and PREC/L [Chen et al., 2002] data combined overland (owing to their higher spatial resolution), leading to four precipitation data averaged overland at a 2.5° resolution and two over ocean (equally weighted). Again the acronyms, full names, and spatial resolution of the precipitation data are provided in Table 1. All the aforementioned reanalysis and precipitation data sets are for monthly means. For daily precipitation, we used the Climate Prediction Center (CPC) Daily Unified precipitation data at a 0.5° resolution (http://www.esrl.noaa.gov/psd/data/gridded/data.unified.html).
Table 1. Global Reanalysis, Precipitation Data Sets, and CMIP5 Models Used
Full Name and Agency
Modern-Era Retrospective Analysis for Research and Applications, by the National Aeronautics and Space Administration (NASA)
1.0° longitude × latitude
Extrapolated to 2.5
ECMWF Interim Reanalysis Project, by the European Centre for Medium-Range Weather Forecasts (ECMWF)
1.5° longitude × latitude →
Extrapolated to 2.5
Climate Forecast System Reanalysis, by the National Oceanic and Atmospheric Administration (NOAA)
2.5° longitude × latitude
Japanese 25-year ReAnalysis, by the Japan Meteorological Agency (JMA)
2.5° longitude × latitude
Global Precipitation Climatology Project v2, by NASA
2.5° longitude × latitude
Climate Prediction Center Merged Analysis of Precipitation, by NOAA
2.5° longitude × latitude
Global Precipitation Climatology Centre v4
1.0° longitude × latitude
Extrapolated to 2.5°
NOAA's Precipitation Reconstruction over Land
1.0° longitude × latitude
Extrapolated to 2.5°
Climate Prediction Center's Daily Unified precipitation in U.S.
0.5° longitude × latitude
NASA's Goddard Institute for Space Studies (GISS) model
~2.0° longitude × latitude
Centre National de Recherches Météorologiques—CM5 version
~2.0° longitude × latitude
The Canadian Earth System Model
~1.25° longitude × latitude
 In an attempt to attribute the cause of the observed changes in circulation patterns, we examined three climate models that participated in the Coupled Model Intercomparison Project (CMIP5; Taylor et al., 2011): the CNRM, GISS, and CanESM models (see Table 1 for full names). These three models were chosen since each has a distinct jet stream bias (further explained in section 5). For the attribution analysis, we used two sets of the CMIP5 Historical Single-Forcing Experiments, driven by (a) natural forcing only (Natural, including solar and volcano) and (b) greenhouse gas forcing only (GHG). Each experiment produced a five-member ensemble, initialized from long-stable preindustrial (year 1850) control settings up to year 2005 [Taylor et al., 2011].
 Storm reports consisting of gusty winds and hail were compiled by the Storm Prediction Center (SPC) at the Storm Data publication website (http://www.spc.noaa.gov/climo/historical.html). Bias and quality problems inherent in storm data included marked increases in weaker wind and hail reports over the last few decades, due largely to human and population biases. We detrended the data to remove such biases. Following Wang et al. [2011a], we projected wind gusts greater than 50 knots and hail with 3/4 in. in diameter or greater onto a 2° × 2° grid mesh and then accumulated these reports over a 24 h interval for each day. This procedure generated “convective wind and hail frequencies” over the continental United States and designated our criteria for severe weather.
3 Analysis Procedure
3.1 Change in the CGT Pattern
 The CGT typically features a zonal wave-5 pattern confined to the mean jet [Branstator, 2002; Ding and Wang, 2005]; this justifies the use of spatial harmonic analysis in filtering the circulations in order to obtain the CGT signal (following Wang et al., 2010). In addition, the spatial filtering helps isolate climate patterns induced from widespread tropical Pacific forcings, such as ENSO (or ENSO-like decadal variations), which tend to generate the long-wave Pacific-North America (PNA) “arching pattern” [Wallace and Gutzler, 1981]. However, the PNA pattern is dynamically possible only at zonal waves 1–3 [Hoskins and Karoly, 1981]. The filtered result therefore highlights shorter-wave responses that are sensitive to midlatitude forcing terms such as the transient vorticity, divergence, and temperature balances, i.e., processes that are crucial in the CGT maintenance [Schubert et al., 2011].
 Exploring the relationship of the 2010 Pakistan floods with climate change, Wang et al. [2011b] found that the 32 year trend in the upper level circulation exhibited a distinct short-wave feature. Figure 1a depicts such a feature, delineated by the linear trend of the 250 hPa geopotential height in July for the period 1979–2010. Furthermore, the trend in the short-wave component (i.e., filtered with zonal wave-5 and beyond) is significant along the jet stream. Such a character contrasts with circulation trends in some other months, such as March (Figure 1b), which exhibit a dominant long-wave pattern with mostly insignificant short-wave components. Thus, we performed the zonal harmonic (Fourier) analysis on the horizontal distribution of linear trends of the 250 hPa streamfunction during 1979–2010; this identifies the amplitude of each zonal wave number (waves 1–7), leading to a wave spectrum. The spectrum was calculated for each month within a 10° latitude zone starting 80°–70°S through 70°–80°N. The 250 hPa streamfunction was used here instead of geopotential height in order to depict circulation features in the tropics with weak pressure gradients.
 Our analysis was conducted first using the individual reanalysis and then, the ensemble of the four reanalyses. Figure 2 shows the zonal spectra of trends in streamfunction from the ensemble reanalyses at each 10° latitudinal zone; the results of individual reanalyses are shown in the figure in the supporting information. To depict a dominant short-wave response, which more likely reflects the CGT forcing rather than the ENSO-PNA forcing, the amplitude of the combined zonal waves 4–7 was compared against the amplitude of combined waves 1–3. If the amplitude of each of waves 4–7 was larger than that of waves 1–3, the corresponding latitude zone was highlighted (light blue). For these latitude zones with predominant short-wave spectrums to be highlighted, they must appear consistently in all the reanalyses, in order to minimize spurious trends.
 In the Northern Hemisphere (Figure 2), the seasons that feature a pronounced short-wave variability include summer (June–August), late autumn (October–December), and the month of April. Although short-wave variability is noticeably large in February and May, it does not exceed the magnitude of longer waves. The robust CGT pattern in July (Figure 1a) is reflected by the dominant amplitude of zonal wave 5 around 40°–50°N, while the weak CGT signal in March (Figure 1b) is evidenced by the dominant amplitude in waves 1–2. In the Southern Hemisphere, pronounced short-wave variability is distributed more evenly throughout the year than in the Northern Hemisphere, possibly because the jet stream is less seasonally variable. Noteworthy in the Southern Hemisphere is the rather large discrepancy in the short-wave regime among the four reanalyses (see figure in the supporting information) owing to the sparse observations in the Southern Hemisphere. Different assimilation procedures that are sensitive to the sparse observations could also play a role. For instance, CFSR depicts stronger short waves than ERA-Interim, while JRA-25 and MERRA appear to be between CFSR and ERA-Interim in terms of the number of short-wave regimes. Such a discrepancy results in a conservative (smaller) number of short-wave regimes being picked up by the ensemble mean.
3.2 Constructing the Circulation Trend Index—Ψ (psi)
 Given the observed and modeling evidence of an enhanced CGT pattern in the changing climate, we next examined the association between monthly precipitation and circulation anomalies by quantifying the connection between this association and the general circulation's 32 year trend. The quantification involved seven steps, which are illustrated in Figure 3 to facilitate the explanation. These seven steps may seem complicated, but they are essentially a series of regression and correlation analyses applied on the temporal/spatial dimension of the circulation and precipitation fields.
 The quantification begins first by detrending both the monthly 250 hPa streamfunction (S) and the monthly precipitation (P), denoted as S′ and P′ (Step 1); this step eliminates the possibility of spurious trends in the data, especially P. The detrending was performed using a least squares regression. The horizontal S′ was then regressed point-wise on P′ (which is an average of four grid points consisting of a 5° × 5° domain); this produced a series of one-point regression maps of S′ corresponding to each 5° × 5° domain of P′ (Step 2). Next, we computed the linear trending pattern of S, such as that shown in Figure 1 (Step 3). The regression maps from Step 2 are then correlated with the S trend through a spatial correlation analysis. The resulting correlation coefficient is denoted as ρPS,S (Step 4). Interpretation of ρPS,S is provided in section 4a.
 As previously mentioned, regional precipitation anomalies are closely associated with the poleward moisture fluxes representing the LLJ. Taking the U.S. Central Plains for example, the LLJ contributes to more than one-third of the total water vapor during the warm season [Helfand and Schubert, 1995; Higgins et al., 1997]. The LLJ also influences the precipitation variations worldwide, while its strength is modulated by synoptic systems [Stensrud, 1996]. Thus, to depict the LLJ and its association with the tropospheric circulation, we used the column water vapor flux (Q). By subjecting Q to the Laplace inverse transform, one can compute the moisture flux streamfunction, SQ,
and, from there, obtain the rotational and divergent components of Q,
where λ and θ are longitude and latitude [Chen et al., 1996]. Since moisture is concentrated in the lower troposphere, SQ generally resembles the lower tropospheric circulation. Further, since the CGT structure is barotropic, i.e., vertically uniform [Branstator, 2002], we analyzed SQ in conjunction with the upper level streamfunction (S) to detect the tropospheric circulation anomalies that satisfy this structure. Following the approach for constructing ρPS,S (Steps 1–4), the detrended SQ was then regressed upon P′; the regression pattern corresponding to each P′ grid box was then subjected to a spatial correlation analysis. In this case, the resulting spatial correlation is denoted ρPQ,Q (Step 5). We next computed the spatial correlation between the regression map of S′ and P′ and the regression map of SQ′ and P′, denoted ρPS,PQ (Step 6). This step quantified the correspondence (or coupling) between synoptic short waves and the LLJ circulation, as required in the CGT framework.
 Using these regression/correlation factors, a unitless index was developed to assess the extent to which S (upper tropospheric circulation) is coupled with SQ (lower tropospheric circulation and moisture flux) and their association with P′, as well as their correspondence with the circulation trends. We refer to this index as the Circulation Trend Index (Ψ, for wave function), derived empirically as
 At any given 5° × 5° domain, Ψ represents the degree of consistency between (a) the regression patterns of S′ and SQ′ with the precipitation anomalies and (b) the 32 year trends of S and SQ, weighted by the degree of coupling between the upper level circulations and the moisture fluxes (Step 7). Moreover, in order to detect the short-wave signal, we also computed Ψ using spatially filtered S and SQ (i.e., removing zonal waves 0–3). The resulting index for the short-wave regime is denoted ΨS. Since the CGT is a midlatitude phenomenon, the analysis was confined to the latitudes of 20°–60° in both hemispheres. Interpretation of ΨS is provided in section 4.
 The function ΨS, as well as the impact of short-wave regime on the circulation anomalies, is illustrated by calculating the root-mean-square (RMS) of ρPS,S across each 5° latitude band for each month (Figure 4). To avoid arid regions, only grid points with monthly precipitation amounts greater than 2 mm/d were analyzed here. In the Northern Hemisphere (Figure 4a), the difference in ρPS,S between the total and short-wave regimes was significant at the 90% confidence level (analysis of variance test) but did not exceed the 99% level. On the other hand, the difference between the RMS of Ψ and ΨS (Figure 4b) was considerably larger, exceeding the 99.9% confidence level. Such a difference highlights the importance of (a) the coupling between moisture flux and upper level circulation in the short-wave regime (or the CGT) and (b) the profound association between the changing CGT pattern and regional precipitation anomalies. A similar analysis for the Southern Hemisphere (Figures 4c and 4d) shows that the difference in ρPS,S between the total and short-wave regimes was insignificant (not exceeding the 90% confidence level), yet the difference between Ψ and ΨS was again significant at the 99.9% level. Hereafter, we then focus on ΨS given its greater variability and correspondence with the regional precipitation anomalies.
4 The ΨS Diagnosis
4.1 Examples for Interpretation
 To substantiate the implications of ρPS,S and ΨS, three recent extreme precipitation events are demonstrated here, including the June 2008 Midwest floods in the central United States, the April 2011 tornado outbreaks in the southeast United States, and the December 2010 Queensland floods in eastern Australia. Shown in Figure 5a are the anomalous circulations for the June 2008 Midwest floods in terms of the short-wave regime 250 hPa streamfunction (S250, of zonal waves 4 and beyond) and the rotational component of the water vapor flux (QR). A zonally elongated short-wave train is present across 40°N, forming a cyclonic cell in the western U.S. accompanied by the enhanced Great Plains LLJ, revealed by the southerly QR. Such a circulation coupling reflects the classic “dynamical pattern” that is conducive to rainstorms [Uccellini and Johnson, 1979; Johns, 1993]. Meanwhile, Figure 5b shows the regression patterns of the detrended S250 and QR with the detrended precipitation in the Central Plains (averaged within the domain 95°–90°W, 37°–42°N) using the ensemble precipitation data. A wave train is predominant across 40°N and it is in-phase with the June 2008 anomalies, indicating that the June 2008 circulation pattern satisfies the common synoptic setting for above-normal precipitation in the Midwest. Previous studies [e.g., Karnauskas et al., 2008; Weaver and Nigam, 2008] have also found similar wave trains that cause abnormal wet/dry spells in this region. Furthermore, the linear trends in S250 and QR over the 1979–2010 period (Figure 5c) reveal a wave train that resembles both the regression pattern and the 2008 anomaly, suggesting that wet conditions in the Midwest similar to those in June 2008 may have become more common in the changing CGT pattern, further enhancing recent events.
 By comparison, patterns of the long-wave regime (zonal waves 1–3; Figure 6) corresponding to those in Figure 5 are not consistent. The June 2008 circulation anomalies (Figure 6a) do not feature any noticeable long-wave pattern over North America; this is in contrast with the marked, continental-scale cyclonic anomaly revealed in the regression pattern (Figure 6b), which indicates an enhanced jet stream over the Midwest. During the past 32 years, however, there has been a mild trend toward anticyclonic circulations over much of North America (Figure 6c). Together, these results indicate that June precipitation in the Midwest is increasingly modulated by a consistent CGT pattern rather than any systematic long-wave pattern; this also illustrates the better depiction of ΨS over Ψ, as was shown in Figure 4b.
 In the second example—the spring of 2011—we examined the record tornado outbreaks across the southeastern U.S. and flooding in the north. The short-wave regime S250 and QR in April 2011 (Figure 7a) show a wave train that echoes the dynamical pattern, with a quasi-stationary synoptic trough over the western U.S. and an intensified LLJ over the southern plains (vectors). The regression maps of detrended S250 and QR with detrended precipitation (averaged over 90°–85°W, 35°–40°N) also reveal a wave train (Figure 7b) that is in-phase with that of April 2011. Remarkably, the linear trends in S250 and QR during the period 1979–2010 (Figure 7c, i.e., excluding 2011) again depict a wave train resembling both that of April 2011 and the regression pattern (this resemblance is quantified by ΨS in section 4b). Recall that a predominant CGT signal was revealed along 50°N in April (Figure 2). However, in the long-wave regime (not shown), the anomalous circulations do not reveal any coherence between the 2011, regression, and trending patterns. Thus, the marked correspondence among Figures 7a–7c suggests that the abnormality of extreme weather in April 2011 is part of a long-term change involving the CGT.
 Finally, Figure 8 presents an example for the Southern Hemisphere. Beginning in December, 2010 through January 2011, eastern Australia underwent a series of rainstorms followed by devastating floods, resulting in the so-called Queensland flood. The short-wave regime S250 and QR during December 2010 (Figure 8a) again depict a short-wave train along the jet stream, with a cyclonic cell protruding over northeast Australia coupled with poleward anomalies of the water vapor fluxes. The regression patterns (Figure 8b) between precipitation in eastern Australia (147.5°–152.5°E, 30°–20°S) and the detrended S250 and QR show a similar deepening of the trough west of Queensland connected to the short-wave train; the similarity between Figures 8a and 8b suggests a CGT linkage of this and past above-normal precipitation events. While strong La Niña conditions during 2010–2011 have been linked to the extreme precipitation resulting in the Queensland floods [Evans and Boyer-Souchet, 2012], Figure 8b clearly indicates that the CGT played a role. The wave train also resembles the circulation anomaly associated with the Indian Ocean Dipole (IOD) during austral spring [Cai et al., 2011], though the precipitation response to the IOD is located further south over coastal southeastern Australia (in New South Wales and Victoria) rather than in Queensland. Nevertheless, the trending patterns of S250 and QR during 1979–2009 (excluding 2010 here for significance test) reveal a short-wave pattern (Figure 8c) that is in-phase with the regression and the 2010 patterns along the midlatitudes. These results reinforce the proposed connection between enhanced precipitation in eastern-central Australia and long-term changes to the CGT.
4.2 The ΨSIndication of Precipitation Change
 The horizontal distribution of ΨS is shown in Figure 9, derived from the ensembles of precipitation and reanalyses at a 5° grid spacing. For brevity, and to focus on the seasons that exhibit a pronounced CGT signal, only the warm season (April–August) is shown. Color codes reflect significant ΨS while the significance is determined as p < 0.1 in all of the correlations (ρPS,S, ρPQ,Q, and ρPS,PQ); insignificant values are presented as gray dots. Arid regions with monthly precipitation less than 2 mm/d are omitted. The analysis was performed over the period 1979–2010. As shown in Figure 9, a waveform pattern is revealed from the ΨS distributions with positive and negative regions alternating about every 30° in longitude. In April, positive ΨS values over the U.S. Central Plains and northwest of the Appalachian Mountains correspond with the large precipitation anomalies that occurred in 2011 associated with the record tornado outbreaks in the southeastern U.S.; this reflects the correspondence between the different circulation patterns shown in Figure 7.
 Through June, large positive ΨS persists in the U.S. central and northern plains, reflecting the strong coincidence between the regression pattern and the trending pattern (Figures 5b and 5c). Previous studies [Cook et al., 2008; Pryor et al., 2009] have observed an increase in late-spring precipitation over the northern plains accompanied by increased southerly winds and moisture flows. Such a pattern suggests that excessive precipitation in May–June 2008 over the Upper Midwest—and again in spring 2010 and 2011 (see e.g., http://water.weather.gov/precip/)—is consistent with a long-term circulation trend involving the CGT. The positive ΨS pattern in the U.S. reverses in July and August, with negative values in the northern plains and positive values in the southern plains. The feature is consistent with the July circulation trend in Figure 1a, showing an anticyclonic cell over the northwestern U.S. suppressing summer rainfall, which coincides with the rapid onset of the 2012 drought. Although the present analysis is not intended to depict drought, negative values of ΨS do represent enhanced dry conditions associated with the CGT's tendency. The 2011 severe drought in Texas was, in part, linked to the preceding La Niña that induced the PNA long-wave pattern not detectable in the CGT framework. Nonetheless, over the southern plains, positive ΨS do reflect the two consecutive wet Julys in 2009 and 2010 in Texas, and partial wet conditions in southern Texas in 2007. Wet and dry anomalies in the southern Great Plains are known to respond to ENSO, which itself is uncorrelated with the CGT [Branstator, 2002; Ding and Wang, 2005] and therefore may not be depicted by the ΨS diagnosis. Caution should also be taken when interpreting the result as heavy precipitation in the southern and southeastern coastal regions is influenced by hurricane activity that may not be linked to the CGT.
 In Europe and Asia, the ΨS diagnosis reveals several features coincident with recent events. Strong negative ΨS values over the United Kingdom during the month of May (Figure 9) are coincident with, and could be an indication of, consecutive heat waves/dry spells in Britain as was the case in 2011 and 2012. An east-west elongated band of positive ΨS over East Asia in June is in agreement with an observed and projected intensification of the Meiyu rainband [Kusunoki et al., 2011]. Moreover, negative ΨS over western Russia in June–August accompanies recent heat waves in 2010 and again in 2012. The 2010 Russian heat wave has been linked to short Rossby waves that also impacted the 2010 Pakistan flooding [Hong et al., 2011; Wang et al., 2011b; Lau and Kim, 2012]; that flooding was partly attributable to record extreme precipitation during July in northern Pakistan and corresponds to positive ΨS there.
 The ΨS diagnosis for the Southern Hemisphere is presented in Figure 10. For brevity, we show only the warm season of December, January, and March in which the CGT signal prevails (Figure 2). Positive values of ΨS (i.e., wet conditions) over northern and northeastern Australia reflect not only the Queensland flood of December 2010 (Figure 8) but also the observed expansion of the monsoon rainforests due to increased monsoon rains [Bowman et al., 2010]. Moreover, positive ΨS that cluster in southeastern Brazil during December and January appear to be connected with the severe floods there in January 2011, since heavy rainfall in that region has a known association with short Rossby waves extending between the South Pacific and South America [Junquas et al., 2012].
4.3 On Severe Weather
 The ΨS diagnosis can be applied in the examination of changes in severe weather conditions and their linkage with a changing circulation pattern. The analysis here involves the frequency of precipitation extremes, hail and gusty winds, and tornadoes. However, such records of hail and tornadoes are highly influenced by population density and societal developments, making their trend analysis tentative [Anderson et al., 2007]. The use of ΨS overcomes this hurdle because it applies detrended variables for regression analysis (Step 1 in Figure 3) and only considers the trend in the circulation pattern (Step 3).
 We focused on the coterminous United States where comprehensive records of severe weather are available. For the assessment of precipitation extremes, we adopted a simple measure by counting the days in which the grid-scale precipitation of the CPC data exceeds the 95% threshold of its probability density function, yielding an extreme precipitation frequency (F). By regressing F upon the short-wave regime S250 and ψQ, one obtains ρFZ,Z and ρFQ,Q and can use them to derive a new set of ΨS with respect to F; that is, repeating the seven step procedure outlined in Figure 3.
 The result of ΨS with respect to F is shown in Figure 11a for the warm season of April–August. Overall, the distributions of ΨS resemble those derived from monthly precipitation (Figure 8), with positive values over the northern plains during April–June and negative values in July, accompanied by opposite situations in the southern plains. Previous research [e.g., Kunkel et al., 1999; Pryor et al., 2009] has indicated that trends in the mean precipitation and trends in the precipitation frequency are similar, because increased seasonal amounts are often associated with increased precipitation frequency and/or intensity. Noteworthy are the large values near New York in July. According to the 2009 New York City Natural Hazard Mitigation Plan (http://www.nyc.gov/html/oem/downloads/pdf/hazard_mitigation/section_3j_flooding_hazard_analysis.pdf), severe summer rainstorms linked to flash floods have increased over the past decade, with the highest increase occurring in July. As shown in Figure 1a, a distinctive cyclonic cell was situated to the west of the East Coast, signaling increasingly favorable synoptic conditions for convective storms.
 Following equation (3), computing ΨS with respect to the frequencies of hail, gusty winds, and F0–5 tornados reveals a linkage between these phenomena with the changing circulation patterns (Figures 11b and 11c). By following Wang and Chen , the frequencies of hail and gusty winds were combined into one variable to further assess the link with the changing circulation patterns. The frequency of hail and gusty winds is mostly distributed toward the southern or western periphery of high precipitation areas. This is because warm-season storms, which usually travel eastward and/or northward, produce the maximum convection associated with hails and tornadoes prior to generating the maximum precipitation [Wang and Chen, 2009]. As is shown in Figures 11b and 11c, positive ΨS with respect to hail, gusty winds, and tornados during April covers not only the central plains but also the southern plains, where moisture is transported from the Gulf of Mexico by the LLJ. Positive ΨS of tornado frequency over the southeastern U.S. also coincide with the record tornado outbreaks that occurred in April 2011 (not included in this analysis). This correspondence suggests that the extremeness of the April 2011 tornado outbreaks may be part of a long-term trend. During May and June, positive ΨS shifts to the northern plains and the Great Plain including Oklahoma, echoing the elevated tornado activities in 2010 and 2013. In July, positive ΨS only appears in the hail and gusty wind frequencies over the southern Great Plains but not in the tornado frequency. Instead, negative ΨS of tornado frequency covers the northern plains in correspondence to the decreased extreme precipitation frequency corresponding to the recent (2012–13) summer droughts. In August, only mild trends are observed across the U.S.
 Two factors are at play in creating such a strong ΨS contrast between spring (April–June) and summer (July–August): (a) an increasingly coupled pattern in spring, such as that revealed in Figures 5c and 7c, in comparison to the increasingly decoupled pattern in summer as was suggested in Figure 1a; and (b) the intensified Great Plains LLJ in spring versus the weakened LLJ in summer [Cook et al., 2008]. For the latter, the weakened LLJ leads to deceased moisture flux convergence in the northern plains while shifting the convergence over to the southern plains, causing corresponding changes in severe weather conditions.
5 Possible Cause of the CGT Trend
 Here we present a modeling attribution analysis for the possible cause(s) of the CGT trend by using the CMIP5 single forcing experiments for the historical period. In Figure 12a, the observed trend in the July short-wave streamfunction at 250 hPa is closely distributed along the climatological jet stream (isotach of u and v winds), consistent with the jet waveguide theory. We next computed the linear trends for the simulated streamfunction from the GHG experiment of the CNRM, GISS and CanESM model ensembles over the comparable 32 years (1974–2005), shown in Figure 12b. Changes in the CGT pattern are clearly discernable in the simulations of all three models, even though each model has its own bias in the jet stream ranging from being too strong (GISS), to reasonable (CNRM), to too weak (CanESM). All three models simulated the intensification of the climatological short waves across North America and the North Atlantic, although only CanESM depicted the Eurasian wave train and only CNRM captured the North Pacific wave train. By contrast, in the Natural experiment (Figure 12c) the trends in the short-wave regime are universally and considerably weaker than those in the GHG experiment. Similar contrasts were also revealed in June and August (not shown) although the contrast between the GHG and Natural experiments is strongest in July.
 The result of this analysis delineates the likely impact of anthropogenic forcing (i.e., GHG) on the perceived changes in the climatological short-wave pattern and the associated CGT effects. It also confirms recent observational studies [Francis and Vavrus, 2012; Screen and Simmonds, 2013] that the so-called Arctic amplification (as part of the global warming) has amplified short-wave circulations that could lead to enhancement of extreme weather. Rivière  found that climate projections under increased GHG produced a poleward shift of the eddy-driven jets, an intensification and poleward shift of the storm tracks, and a strengthening of the upper tropospheric baroclinicity. Rivière  also point out that the jet stream would break more easily under increased baroclinicity. However, Barnes and Hartmann  suggest that wave breaking on the poleward flank (cyclonic side) of the jet has already reached its poleward limit and will likely become less frequent if the jet migrates any further with increased GHG loading, in essence stopping the jet from its poleward shift. Therefore, though the results presented in Figure 12 provide a logical indication that increased GHG loading may result in a weakened and increasingly meandering jet stream, more sophisticated analysis using the full archive of CMIP5 models is necessary to draw a firmer conclusion.
6 Concluding Remarks
 What are the implications and value of this ΨS formulation for precipitation and extreme weather trends? One benefit is the ability to connect and quantify trends in certain circulation patterns (in this case the CGT) and associated changes in precipitation. Another advantage is the reduction of multiple parameters to a single index, avoiding uncertainties in the trends of precipitation and storm activity (e.g., tornado frequency) trends. The results, as presented here, indicate that ΨS captures these trends concisely and ascribes to them a dynamical mechanism; this method may also provide a guideline for predicting extreme climate events, as both the CGT and extreme precipitation events have a strong subseasonal signal [e.g., Wang et al., 2010; Schubert et al., 2011]. Although current operational weather/climate prediction models have limited skill in forecasting precipitation, they have shown a reasonable ability in forecasting subseasonal variability of circulations both in the tropics [e.g., Waliser, 2005] and in the midlatitudes and associated precipitation extremes [e.g., Jones et al., 2011a]. It has been demonstrated that seasonal forecasts of circulation patterns can be applied to predicting precipitation extremes [Jones et al., 2011b] and, with the aid of empirical modeling, small-scale phenomena such as valley temperature inversions [Gillies et al., 2010].
 Caution should be exercised when interpreting the ΨS results. First, the index does not reflect any long-term change in precipitation, hail, gusty winds, or tornados, as those variables have been detrended during the computation. Thus, the diagnoses presented here only apply to precipitation changes that are linked to circulation anomalies relevant to the CGT. For instance, it is known that the U.S. southwest monsoon has intensified in conjunction with increased precipitation amounts and broadened spatial coverage [Anderson et al., 2010]. However, this feature is not evident in either the monthly precipitation (Figure 9) or the precipitation frequency (Figure 11a) during July and August. Such a discrepancy apparently results from the lack of connection between the southwest monsoon and the CGT. Second, tropical influences should be taken into account. As shown in Figure 8, extreme precipitation events tend to occur with deepened and intensified midlatitude troughs extending toward the tropics; this is in contrast to the fact that CGT trends are confined within the jet stream latitudes. The mechanisms of such a deepening and intensification of local circulations are somewhat different case-by-case, requiring further analysis. Finally, the 32 year period beginning in 1979 may be modulated by certain decadal-scale oscillatory modes in either the Pacific or the Atlantic. The selection of post-1979 analysis was merely based on the best possible data coverage and quality of the reanalyses.
 Regardless, the ΨS diagnosis may provide a useful metric in the evaluation of climate model simulations and projections. ΨS as a single index would reveal not only the extent of simulated circulation changes but also the geographical distribution of any associated changes in the precipitation and extremeness. Apart from the application perspective, the ΨS diagnosis presented here also illustrates the CGT's importance to midlatitude weather/climate extremes and associated trends. Future work should focus on the exploration of the dynamical mechanisms leading to the different CGT responses in different seasons. Of similar importance is the assessment of climate model projections for possible changes in the CGT.
 This study was supported by NASA grant NNX13AC37G and the Agricultural Experiment Station, Utah State University, and approved as journal paper 8542.