1. Introduction
The Madden–Julian oscillation's (MJO; Madden and Julian 1994; Zhang 2005) convection can initiate and amplify Rossby wave trains (Matthews et al. 2004; Roundy et al. 2010; Weare 2010) that manifest themselves in teleconnections such as the North Atlantic Oscillation (NAO; Cassou 2008; Lin et al. 2009) and the Pacific–North American (PNA) patterns (Kiladis and Weickmann 1992; Higgins and Mo 1997; Moore et al. 2010). The interactions between the MJO and the aforementioned patterns can affect temperature and precipitation over North America (Becker et al. 2011; Zhou et al. 2012; Riddle et al. 2013).
The extratropical impacts may not be the same associated with every MJO event, but such variations have not been explored. This study aims to bridge that gap by focusing on relationships between the MJO and the PNA. Previous studies have used a variety of indices to describe the PNA using fields like sea level pressure or geopotential (Wallace and Gutzler 1981; Barnston and Livezey 1987; Johnson and Feldstein 2010; Riddle et al. 2013). Common to all of these indices are four anomaly centers that resemble a Rossby wave train. They are located in an arc from the tropical western North Pacific to North America. The precise locations of these centers may vary, such that no single pattern can be considered the PNA (Feldstein 2002). The current study develops a new index, termed the multivariate PNA (MVP), which combines information about tropical convective forcing with information about the extratropical wave state. It will be shown that new insights into the temperature response over North America can be gained by using the MVP in conjunction with the real-time multivariate MJO index (RMM; Wheeler and Hendon 2004).
2. Data and methods
a. Data
The National Oceanic and Atmospheric Administration (NOAA) interpolated daily outgoing longwave radiation (OLR; Liebmann and Smith 1996) data were used as a proxy for the tropical convection associated with the MJO. Extratropical patterns were identified with dynamical fields from the daily National Centers for Environmental Prediction–Department of Energy (NCEP–DOE) Reanalysis-2 (Kanamitsu et al. 2002). Streamfunction was calculated from the reanalysis winds using the National Center for Atmospheric Research (NCAR) Command Language (UCAR/NCAR/CISL/VETS 2012). Each dataset was used on a daily 2.5° latitude × 2.5° longitude grid from 1979 to 2011.
b. Calculating the MVP
The goal of this study is to investigate relationships between the MJO and North American temperature anomalies. For that reason, we calculated the combined empirical orthogonal function (EOF) of OLR, 850-hPa streamfunction, and 200-hPa streamfunction over a domain covering 0°–60°N, 120°E–40°W. The results are insensitive to changing these bounds by 10° in either direction or extending the northern boundary to the North Pole. The OLR was chosen as a proxy for the forcing from tropical heating. Meanwhile streamfunction identifies the extratropical Rossby waves state. Other variables, such as geopotential and zonal wind were tested, but the OLR and streamfunction produced the strongest connection between the MJO and North American temperature anomalies.
Each variable was normalized and filtered in time for 20–100 days to focus on the MJO's typical time scales (Waliser et al. 2009), but such data can be difficult to calculate in real time. To demonstrate the forecasting potential of this index, we produced the principal component time series by projecting the filtered EOF onto unfiltered data. This approach was inspired by the combined wavenumber–frequency and time-extended EOF methodology developed by Roundy and Schreck (2009).
c. Compositing method
Composite analyses were used to examine the weather patterns associated with the MJO and the MVP. The composites were constructed from dates when the Wheeler–Hendon (2004) RMM index had an amplitude >1 standard deviation and was in a given phase. These dates were also subdivided by MVP relative to a 0.75 standard deviation σ threshold, which was chosen to ensure sufficient cases in each phase and roughly corresponds with the upper and lower quartiles. These subdivisions will be referred to as the negative (MVP ≤ 0.75σ), neutral (−0.75σ < MVP < +0.75σ), and positive (MVP ≥ +0.75σ) phases of the MVP. Only December–February 1979/80–2010/11 dates were used. To illustrate the predictive potential of the MJO and the MVP, the composites for the North American impacts show the mean for all dates that are 6–10 days after one of the composite dates.
A Monte Carlo test similar to that described by Schreck et al. (2013) evaluated the statistical significance of the composite anomalies. In this case, the composite dates are divided into “events,” which are simply consecutive dates in the composite. Null composites are generated as follows:
Randomly select one of the composite events with replacement and use its initial date.
Generate a new initial date for that event by using the original month and day but randomly selecting a different year from the dataset.
Randomly select one of the composite events with replacement and use its duration.
Repeat the above steps to produce the same number of events as were in the original composite.
3. Results
a. MVP spatial pattern
Figure 1 shows the first EOF, which explains 10.1% of the variance. The second EOF (not shown) only explained 7.9%, and it was not physically associated with the first. Therefore, only this first EOF will be considered hereafter. The 200-hPa streamfunction (Fig. 1a) resembles a Rossby wave train emanating from the tropical western Pacific, extending over North America, and then reflecting back toward the tropical Atlantic. Nondivergent winds flow perpendicular to streamfunction gradients, so the first two wave centers over the Pacific are also associated with variability in the Pacific jet structure.
Leading EOF for (a) 200-hPa streamfunction, (b) 850-hPa streamfunction, and (c) OLR.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-13-00118.1
The 200-hPa Rossby wave train represents a form of the PNA pattern, although the exact positioning of the circulation centers is shifted 5°–10° southward compared with Barnston–Livezey (1987) version that is used by the NOAA/Climate Prediction Center (NOAA/CPC). That shift is insensitive to extending the MVP domain all the way to the North Pole. After projecting the pattern in Fig. 1 onto unfiltered data, the resulting time series has a 0.57 correlation with NOAA/CPC's PNA. While this correlation is significant at the 99.9% level, more than two-thirds of the variance is unique between these indices.
The 850-hPa streamfunction (Fig. 1b) shows the lower-tropospheric reflection of the 200-hPa wave train. The pattern contains an anomaly dipole over the Pacific with one center near 40°N and the other center near the equator. The nondivergent winds inferred from this dipole represent variability in the 850-hPa zonal winds near Hawaii.
A large anomaly near Hawaii dominates the OLR pattern (Fig. 1c). The anomaly represents suppressed convection when the MVP is positive and enhanced convection when it is negative. The anomaly is surrounded by opposite signed anomalies to the north, east, and west. The central anomaly extends northeastward to North America, which parallels the anticyclonic wave breaking (Thorncroft et al. 1993; Ralph et al. 2011) suggested by the 200-hPa streamfunction pattern (Fig. 1a). When the MVP is negative, this combination of an anticyclonically breaking trough with enhanced convection is consistent with a tropical moisture plume and the formation of an atmospheric river (McGuirk et al. 1987; Ralph et al. 2011).
b. Impacts over North America
Figure 2 shows the 850-hPa temperature and 500-hPa geopotential height anomalies for each RMM phase with a 6–10-day lag. The RMM typically passes through one phase in 7 days, so the lag is analogous to shifting the composites by one phase. Taking that shift into account, Fig. 2 is consistent with the zero-lag composites from Zhou et al. (2012). RMM phases 2–6 lead to warm anomalies over central and eastern North America, while phases 7, 8, and 1 lead to cold anomalies.
Composite anomalies of 850-hPa temperature (shading) and 500-hPa geopotential height (contoured every 30 m) averaged 6–10 days after the RMM ≥ 1.0 in a given phase. Only temperature anomalies that are 95% significant are shaded. The numbers in the top right denote how many events were used in each composite.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-13-00118.1
Figure 3 subdivides the aforementioned composite analyses using the MVP index with the same lag. The numbers in the top right of each panel indicate how many events fall into that combination of the MVP and the RMM. An event is simply defined as any set of consecutive composite dates. While the distribution of events between negative, neutral, and positive MVP varies between RMM phases, it remains broad enough to be a useful discriminator. This contrasts with NOAA/CPC's PNA, which has a stronger phase relationship with the MJO (Higgins and Mo 1997; Mori and Watanabe 2008; Riddle et al. 2013).
As in Fig. 2, but subdivided by days when (left) MVP ≤ −0.75, (middle) −0.75 < MVP < +0.75, and (right) MVP ≥ +0.75.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-13-00118.1
The North American temperature anomalies following each RMM phase change with the phase of the MVP (Fig. 3). For example, the warm signals over eastern North America in RMM phases 2 and 5 only occur when the MVP is negative. This behavior is consistent the MVP's 200-hPa streamfunction EOF (Fig. 1a), which contains a ridge over the eastern United States when it is negative. Conversely, the cold signals in RMM phases 8, 1, and 2 occur almost exclusively when the MVP is positive, which would be associated with a 200-hPa trough. Only RMM phases 3, 4, and 7 have significant temperature anomalies larger than 2°C when the MVP is neutral, suggesting that these anomalies are associated with a different teleconnection pattern. The MVP can therefore be a useful discriminator of which MJO events may influence North American temperatures and which may not. Similar plots using the NOAA/CPC's PNA index failed to replicate these patterns (not shown).
c. Global patterns
Figure 4 uses global composite analyses to explore different MVP states during RMM phase 5. OLR anomalies (shading) are used as proxies for convective heating, whereas the 200-hPa total zonal wind (black contours) and streamfunction (red and blue contours) illustrate the extratropical patterns. To first order, the tropical convection shows a similar pattern in each panel with enhanced convection near the Maritime Continent and suppressed convection over the Indian Ocean. These patterns are consistent with previous composites for RMM phase 5 (Wheeler and Hendon 2004; Waliser et al. 2009). The largest differences occur over the central North Pacific and the tropical Atlantic. When the MVP is negative, enhanced convection is collocated with the troughs in the 200-hPa wave train. The trough–ridge couplet over the Pacific is also associated with a retraction of the Pacific jet (Jaffe et al. 2011). Such a retraction allows an equatorward flux of wave energy (Kiladis 1998), which could explain the anticyclonic wave breaking in the streamfunction anomalies. These features are weaker when the MVP is neutral and absent when it is positive, resulting in progressively more zonal extension of the jet.
Composite OLR anomalies (shading), total 200-hPa zonal winds (black contour at 50 m s−1), and 200-hPa streamfunction anomalies (red and blue contours every 5 × 106 m2 s−1) for RMM Phase 5 when (a) MVP ≥ +0.75, (b) −0.75 < MVP < +0.75, and (c) MVP ≤ −0.75. Only OLR anomalies that are 95% significant are shaded. The numbers in the top right denote how many events were used in each composite.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-13-00118.1
Figure 5 provides composite analyses for RMM phase 8. In this phase, the tropical convection is distinctly different for the various phases of the MVP. The negative MVP composite (Fig. 5c) is most similar to the canonical MJO response. Convection is strongly enhanced near the date line in the South Pacific convergence zone, whereas a broad area of suppressed convection is present to the west. The neutral MVP (Fig. 5b) composite presents a similar pattern, albeit weaker in amplitude. During the positive MVP phase (Fig. 5a), convection is less organized with a wavenumber 2 pattern. Recalling Fig. 3, however, this disorganized convection during the positive MVP is associated with the largest temperature anomalies over North America. In contrast, the well-organized MJO observed with the negative MVP has virtually no influence on those temperatures.
As in Fig. 4, but for RMM phase 8.
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-13-00118.1
The larger North American temperature response for the positive MVP in RMM phase 8 is in part a response to the zonal extension of the Pacific jet (Fig. 5c). That extension leads to cyclonic wave breaking along the extratropical waveguide and ridge amplification over western North America (Martius et al. 2007; Moore et al. 2010). The North American temperatures seem to be more sensitive to these changes in the extratropical waveguide than to the changes in the MJO's core convective forcing.
Figures 4 and 5 identify differences in convection over the Pacific for each phase of the MVP. These differences could be related to changes in the low-frequency background associated with El Niño–Southern Oscillation (ENSO), which also affects North American temperatures (Ropelewski and Halpert 1996). Figure 6 shows the number of events when the MVP is positive (red) or negative (blue) during RMM phase 5 (Fig. 6a) or phase 8 (Fig. 6b), and the correlation values between the number of RMM/MVP events and the Niño-3.4 index (Fig. 6c).
Events per year when the MVP ≥ +0.75 (red) or MVP ≤ −0.75 (blue, shown as negative) during December–February during RMM (a) phase 5 or (b) phase 8. (c) Mean Niño-3.4 index averaged December–February. Years on abscissa denote the year in January (e.g., December 1979–February 1980 is listed as 1980). Correlations with Niño-3.4 are shown on the right in (a) and (b).
Citation: Monthly Weather Review 141, 11; 10.1175/MWR-D-13-00118.1
The strongest El Niño (1982/83, 1997/98) and La Niña (1988/89, 1999/2000) events (Fig. 6c) are not clearly evident in terms of MVP events for either phase of the MJO (Figs. 6a,b). The coincidence of negative MVP and RMM phase 5 (Fig. 6a, blue) is more common during La Niña years, as evidenced by the −0.18 correlation. However, this correlation is not significant at the 90% confidence level, and virtually no correlation is seen for days with positive MVP (red).
ENSO plays a larger role in the RMM–MVP relationship during phase 8 (Fig. 6b). The MVP is more likely to be positive in RMM phase 8 during La Niña (−0.31), whereas it is more likely to be negative during El Niño (+0.44). Both correlations are significant at the 90% confidence level. These relationships are consistent with the changes in OLR found near the date line in Fig. 5. La Niña also favors cyclonic wave breaking similar to that in Fig. 5a, whereas El Niño is more conducive to anticyclonic breaking (Shapiro et al. 2001). Roundy et al. (2010) found that a trough over eastern North America was strongest in RMM phase 8 during El Niño. In this study, however, that trough is strongest when the MVP is positive (Fig. 5a), which is correlated with La Niña. Further research is needed to investigate these differences.
4. Summary and discussion
In an effort to understand which MJO events affect North American temperatures and which do not, this study developed a new index: the multivariate PNA (MVP). The MVP is the first combined EOF of 20–100-day filtered OLR, 850-hPa streamfunction, and 200-hPa streamfunction. This EOF is then projected onto unfiltered data to produce a principal component time series that can be extended in near–real time. The resulting MVP index should be useful for anticipating the influence of the MJO in each RMM phase on North American weather patterns (Fig. 3).
The MVP EOF pattern represents a form of the PNA, but the results in Fig. 3 could not be replicated with the NOAA/CPC PNA index. The MVP's waveguide is shifted 5°–10° southward, which places a circulation center close to the latitude of the Pacific jet. Perhaps because of this shift, the two indices have different relationships with North American temperatures. The PNA has a stronger association with northwestern Canada, while the MVP has a greater influence over the eastern United States (not shown).
Another distinction is that the RMM and the PNA covary more than the RMM and the MVP. The PNA is likely to be positive during RMM phases 8/1 and negative during phases 4/5 (Higgins and Mo 1997; Mori and Watanabe 2008; Riddle et al. 2013). The northward shift in the circulation pattern between the NOAA/CPC PNA index relative to the MVP is associated with a stronger circulation anomaly to the south of the jet and concomitant zonal wind anomalies near the equator. The RMM index is largely influenced by such anomalies (Straub 2013), so they suggest a natural connection between the two indices. The southward shift in the circulation pattern between the MVP index relative to the NOAA/CPC PNA index is associated with a weaker circulation anomaly to the south of the jet. The southward shift may indicate a stronger relationship between the MJO and the extratropical circulation, which suggests the MVP may be a better discriminator of the MJO's impact on temperatures over eastern North America during those phases.
Large differences exist among the temperature patterns generated for each RMM–MVP combination (Fig. 3). These differences could be related to combinations of 1) variability in convective forcing from the Eastern Hemisphere, 2) variability in forcing from the central North Pacific, and 3) variability in the Pacific jet and its associated wave breaking (Figs. 4 and 5). The latter two are closely related: convection near Hawaii can be enhanced by equatorward propagation of anticyclonically breaking Rossby waves (Kiladis 1998), but the convection can also enhance those waves (Ralph et al. 2011).
For RMM phase 5, the changes in convective forcing from the Eastern Hemisphere are subtle (Fig. 4), which suggests that the tropical and extratropical differences over the central North Pacific are likely more important. RMM phase 8, on the other hand, exhibits much larger variations in convection in the Eastern Hemisphere between phases of the MVP (Fig. 5). The RMM phase 8 convection is robust during the positive phase of the MVP (Fig. 5a), even though it has little impact on North American temperatures (Fig. 3). Meanwhile, the disorganized convection during the negative MVP is associated with larger North American cold anomalies. This dichotomy reinforces the hypothesis that variations in the Pacific jet and its associated wave breaking significantly modulate the MJO's impacts over North America.
This short study opens numerous avenues for future research:
What is the role of convectively coupled Kelvin waves in generating the convective anomalies near Hawaii (Straub and Kiladis 2003; Ralph et al. 2011)?
This study only compared two forms of the PNA: the MVP and the NOAA/CPC PNA index. Could additional insight be gained from exploring related indices developed by Johnson and Feldstein (2010) and Riddle et al. (2013)?
Can interactions among the MJO and other teleconnections explain the North American temperature anomalies in RMM phases 3, 4, and 7?
Numerical models have shown increasing skill in predicting the MJO (Seo et al. 2009; Weaver et al. 2011). Could numerical forecasts of the MVP extend the range of the relationships observed here?
Acknowledgments
This work benefited from discussions with Klaus Weickmann and Ed Berry. The OLR and reanalysis data were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, from their website at http://www.esrl.noaa.gov/psd/. The RMM index was obtained from Matt Wheeler of the Australian Bureau of Meteorology (http://cawcr.gov.au/staff/mwheeler/maproom/RMM/). Schreck received support for this research from the NOAA/Climate Data Record (CDR) Program through the Cooperative Institute for Climate and Satellites–North Carolina (CICS-NC).
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