Subseasonal variability of North American wintertime surface air temperature

Abstract

Using observational pentad data of the recent 34 Northern Hemisphere extended winters, subseasonal variability of surface air temperature (SAT) over North America is analyzed. The four leading modes of subseasonal SAT variability, that are identified with an empirical orthogonal function (EOF) analysis, account for about 60% of the total variance. The first (EOF1) and second (EOF2) modes are independent of other modes, and thus are likely controlled by distinct processes. The third (EOF3) and fourth (EOF4) modes, however, tend to have a phase shift to each other in space and time, indicating that part of their variability is related to a common process and represent a propagating pattern over North America. Lagged regression analysis is conducted to identify the precursors of large-scale atmospheric circulation for each mode a few pentads in advance, and to understand the processes that influence the subseasonal SAT variability and the predictability signal sources. EOF1 is found to be closely related to the Pacific-North American (PNA) circulation pattern and at least part of its variability is preceded by the East Asian cold surge. The cold surge leads to low-level convergence and enhanced convection in the tropical central Pacific which in turn induces the PNA. EOF2 tends to oscillate at a period of about 70 days, and is influenced by the low-frequency component of the Madden–Julian Oscillation (MJO). On the other hand, EOF3 and EOF4 are connected to the high-frequency part of the MJO which has a period range of 30–50 days. These findings would help understanding the mechanisms of subseasonal surface air temperature variability in North America and improving weather predictions on a subseasonal time scale.

1 Introduction

The subseasonal time scale refers to that ranging from a week to a season. Subseasonal variations of wintertime near surface air temperature (SAT) have a significant impact on societal and economical activities. For instance, a persistent extreme of cold temperature in Canada is usually associated with health problems, excessive consumption of energy, and increased cost and risk in transportation. However, our understanding of the extratropical wintertime atmospheric subseasonal variability is limited, and we have tremendous difficulties in producing a useful prediction of near surface air temperature beyond about one week.

Extratropical weather is frequently influenced by recurring circulation patterns, usually referred to as weather regimes. Among the dominant circulation patterns are the Pacific-North American pattern (PNA) (e.g., Wallace and Guztler 1981) and North Atlantic Oscillation (NAO; e.g., Barnston and Livezey 1987)/Arctic Oscillation (AO; e.g., Thompson and Wallace 1998). On the interannual time scale, the PNA was observed to be partly connected to the tropical forcing of the El Niño-Southern Oscillation (ENSO) (e.g., Horel and Wallace 1981). This connection is in fact a major skill source for seasonal predictions (e.g., Shukla et al. 2000; Derome et al. 2001). Recent studies suggest that there is possibility of explaining and predicting the interannual variability in the surface NAO/AO (e.g., Riddle et al. 2013; Scaife et al. 2014). On the subseasonal time scale, whether the PNA variability is related to a mechanism other than atmospheric internal dynamics is less clear. The NAO, however, was found to be generated mainly by sources internal to the atmosphere (e.g., Hurrell et al. 2003). Predictions of the PNA and NAO on a subseasonal time scale have limited skill (e.g., Johansson 2007).

Recent studies indicate that the Madden–Julian Oscillation (MJO) has an important impact on the extratropical atmospheric circulation, and thus provides a source of skill to subseasonal weather predictions, particularly during boreal winter. The MJO is a tropical large-scale oscillation that is dominated by periods of 30–70 days and zonal wavenumber one propagating eastward (Madden and Julian 1971, 1994). The MJO tropical convection excites Rossby waves that influence large-scale teleconnection patterns, including the PNA (e.g., Mori and Watanabe 2008) and the NAO (e.g., Lin et al. 2009). The wintertime surface temperature in North America was found to be connected to the MJO (Lin and Brunet 2009; Yao et al. 2011; Rodney et al. 2013; Johnson et al. 2014).

In this study, we identify the dominant patterns of the wintertime subseasonal SAT variability in North America. The atmospheric large-scale circulations associated with the dominant patterns are analyzed. The main objective is to identify precursors that may lead to the subseasonal SAT variability, and study the mechanisms and signal sources. We will analyze how the MJO contributes to the dominant SAT patterns in North America, and what are the other possible mechanisms besides the MJO. These questions are crucial to the subseasonal prediction in North America.

Section 2 describes the data used and the analysis methodology. In Sect. 3 the four leading modes of subseasonal SAT variability in North America are identified through an empirical orthogonal function (EOF) analysis, and their spatial and temporal characteristics are discussed. Sections 4 and 5 analyze the precursor and mechanism for the first and second EOF modes (EOF1 and EOF2), respectively, whereas Sect. 6 discusses the combined phenomenon of the third and forth EOF modes (EOF3 and EOF4). Summary and conclusions follow in Sect. 7.

2 Data and methodology

The daily averaged data of the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) global reanalysis of atmospheric fields (Kalnay et al. 1996) are used in this study. Variables used here include 2-m near surface air temperature (SAT), geopotential height on 500-hPa (Z500), zonal and meridional winds on 200- and 850-hPa, sea level pressure (SLP). To represent the tropical convection, the daily averaged satellite-observed outgoing longwave radiation (OLR) data from the National Oceanic and Atmospheric Administration (NOAA) polar-orbiting series of satellites (Liebmann and Smith 1996) are used. Also analyzed are the pentad data of the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) (Xie and Arkin 1997). These data are provided by the NOAA/OAR/ESRL PSD, Boulder, CO, from their Web site at http://www.cdc.noaa.gov/.

To represent the MJO, the Real-Time Multivariate MJO (RMM) index of Wheeler and Hendon (2004) is used. The daily values of RMM1 and RMM2 are obtained from the Centre for Australian Weather and Climate Research website (http://www.cawcr.gov.au/staff/mwheeler/maproom/RMM/). The RMM1 and RMM2 were calculated by projecting the combined fields of $15^{\circ }\hbox {S--}15^{\circ }\hbox {N}$ meridionally averaged OLR and zonal winds at 850 and 200 hPa onto the two leading empirical orthogonal function (EOF) structures as derived using the same meridionally averaged variables. The time series of RMM1 and RMM2 vary mostly on the intraseasonal time scale, and the associated three-dimensional flow structure captures the MJO variability.

The horizontal resolution for the NCEP/NCAR reanalysis data, the OLR and the CMAP precipitation is $2.5^{\circ } \times 2.5^{\circ }$, except for the 2-m air temperature which is interpolated to this resolution from a Gaussian grid of $192\times 94$. The velocity potential and stream function are derived from the zonal and meridional winds at 200- and 850-hPa. The daily values of the NCEP/NCAR reanalysis, the OLR and the MJO index are averaged for consecutive five days to construct pentad data. The analysis is conducted for the 34 extended winters from 1979/1980 to 2012/2013 except for the CMAP data that end in 2011, where the extended winter is defined to be the 30 pentads starting from the pentad of November 2–6 to March 27–31. The 24th pentad of each extended winter always covers a period from February 25 to March 1, no matter if it is a leap year or not. Thus in the case of a leap year, the data for that “pentad” is actually an average for 6 days.

The seasonal cycle which is the time mean and first two harmonics of the 34-year (32-year for CMAP data) pentad climatology is first removed for each grid point. The mean for each extended winter is then removed in order to eliminate interannual variability. The seasonal cycle and interannual and longer timescale variability have already been removed in the RMM1 and RMM2 data.

3 Leading modes of subseasonal SAT variability

We start by looking at the wintertime climatology of SAT in North America. As can be seen from Fig. 1a, which is the SAT averaged in the extended winter (from November 2 to March 31) of the 34 years, cold air below 0 °C dominates in the high latitude continent and strong meridional temperature gradient exists between 30°N and 40°N. Land-sea contrast of SAT is also obvious. Shown in Fig. 1b is the standard deviation of the pentad-to-pentad variability of SAT. The subseasonal variability of SAT is much stronger over the continent than the ocean. There are two regions of strong subseasonal variability where the standard deviation exceeds 6 °C, one in western Canada to the east of the Canadian Rockies and the other in northeastern Canada.

Fig. 1

a Time average, b standard deviation of pentad-to-pentad variability of SAT during extended winter (NDJFM) for the period of 1979/80 to 2012/13. Contour interval is 4 °C for (a), and 0.5 °C for (b). Contours with negative values are dashed. Areas shaded for (a) are those with SAT colder than −8 °C, for (b) with standard deviation larger than 5 °C

To identify the dominant modes of subseasonal variability of SAT in North America, an empirical orthogonal function (EOF) analysis is performed on the pentad SAT anomaly for the 34 extended winters from 1979/80 to 2012/13. The area used here is 10°–70°N and 150°–40°W. The effect of unequal areas represented by different grid points is taken into account by multiplying the data by the square root of the cosine of the latitude at that grid point. Figure 2 shows the distribution of the four leading EOFs, presented as the linear regression of SAT to the respective principal component (PC) time series. They account for 23, 15, 11 and 10 % of the total variance, respectively. EOF1 and EOF2 are well separated from each other and from the rest EOFs according to the criterion of North et al. (1982). EOF3 and EOF4, however, are not separated from each other, although they are separated from other EOFs. In fact, EOF3 and EOF4 are related to each other in space and time, and they together represent a propagating structure of SAT variability, as will be discussed below.

Fig. 2

The four leading EOFs of SAT represented as regressions of pentad SAT onto the respective principal component (PC). The magnitude corresponds to one standard deviation of the PC. The contour interval is 1 °C. Contours with positive and negative values are in red and blue, respectively. The zero contour is not plotted. The percentage of variance explained by each EOF mode is indicated above each panel

EOF1 is characterized by a monopole spatial structure (Fig. 2a). Over the North American continent this mode has a variability of the same sign, with strong variability over Canada and the north part of the US. A positive (negative) phase of EOF1 corresponds to above (below) normal temperature. The maximum center appears in western Canada to the east of the Rockies. The second mode (EOF2) features a dipole pattern with opposite signs of variability over the northwest and southeast North American continent (Fig. 2b). A positive (negative) EOF2 corresponds to cold (warm) SAT in northwestern Canada and Alaska, and warm (cold) SAT in the central and eastern US. Both EOF3 and EOF4 have multiple anomaly centers along the northeast-southwest direction. A positive EOF3 is associated with positive SAT anomalies in northeastern Canada, and negative SAT in western Canada, whereas a positive EOF4 has positive SAT emerged in the western US, negative SAT over the region stretched from Alaska to the southeastern US, and positive SAT over the northeast corner of Canada. It appears that EOF4 has a spatial phase shift to the northeast comparing to EOF3.

To demonstrate the temporal characteristics of the leading EOFs, power spectra of the principal components of the four leading EOFs (PC1, PC2, PC3 and PC4) are calculated and displayed in Fig. 3. The spectra are illustrated with an area-conserving format in which variance is proportional to area under the curve. As can be seen, all the four leading PCs have a significant part of variance at subseasonal periods (30–90 days). In particular, PC1 has a peak near 50 days, and PC2 around 70 days, statistically significant at the 99 % level. PC4 has a statistically significant peak in the range of 30–50 days. PC3 also has large power spectrum values in the range of 30–50 days, although it does not pass the 99 % level (it passes 95 % level). Both PC3 and PC4 have large power spectrum values in the range of 30–50 days, again indicating that EOF3 and EOF4 are related.

Fig. 3

Power spectra of the principal components (PCs) of the first four EOF modes. The red curve is the red-noise spectrum computed from the lag 1 autocorrelation. The orange curve is the power spectrum of 99 % significance level. Indicated in vertical dashed lines are time preiods of 90, 55 and 30 days

To further analyze the relationship between EOF3 and EOF4, the lag correlation between PC3 and PC4 is calculated and shown in Fig. 4. The correlation peaks when PC4 lags PC3 by two pentads (10 days). The small lag correlation between PC3 and PC4 indicates that they are largely independent. On the other hand, although the correlation of 0.18 is small, it well passes the 0.01 statistical significance level according to a Student t test. Therefore PC3 and PC4 also have a component that is dependent to each other. In doing the Student t test for correlation and regression, as the time series is auto-correlated, the number of degree of freedom and the effective sample size have to be reduced. The effective sample size is estimated as $N' = N (1-r1^2)/(1+r1^2)$ (e.g., Bretherton et al. 1999), where $r1$ is the lag-1 autocorrelation and $N$ the original sample size which is 1,020 in our case. The lag-1 autocorrelation for PCs is around 0.4, thus $N'$ is around 740. Considering the spatial relationship of EOF3 and EOF4 (Fig. 2c, d), this lag correlation indicates that EOF3 and EOF4 represent a northeastward-propagating pattern. Similar lag correlation is calculated between each pair of PC1, PC2, PC3 and PC4. No significant correlation is found other than that between PC3 and PC4. This also confirms that PC1 and PC2 are independent.

Fig. 4

Lag correlations between PC3 and itself (black), and with PC4 (red)

The distinct spatial and temporal structures of EOF1 and EOF2 imply that they may have different physical origins and predictability sources. The dependent component of EOF3 and EOF4, on the other hand, may be associated with a common process. In the next section, we will analyze the large-scale circulation anomalies associated with the four leading modes. Through lead-lag regression analysis, we will identify precursors and predictability sources associated with the four leading modes of subseasonal SAT variability in North America.

4 EOF1

From the last section, it is known that the four leading modes of SAT subseasonal variability in North America together explain about 60 % of the total variance. Here we explore the large-scale atmospheric circulation structure associated with each mode. In particular, we are interested in identifying their precursors a few pentads in advance. This will help to understand the mechanism of the subseasonal SAT variability and the predictability sources.

To study the connection between a leading mode and a large-scale atmospheric field, lagged regressions are calculated between the PC of this mode and the atmospheric field. As we are interested in finding precursors, the regressions when the atmospheric field leads the PC are analyzed.

The first mode (EOF1) is characterized by a monopole structure of SAT variability in North America (Fig. 2a), which accounts for about 23 % of the total variance. It tends to fluctuate at a period of 50 days (Fig. 3). What process and mechanism are responsible for this continental scale subseasonal SAT variability is of great interest.

We first look at the evolution of SAT itself in the Northern Hemisphere. Shown in Fig. 5 are the lagged regression maps of 2-m air temperature anomaly with respect to PC1. The magnitude of SAT corresponds to one standard deviation of PC1. Lag-$n$ indicates that the SAT anomaly leads PC1 by $n$ pentads. Shaded areas represent those where the regression is at a 0.01 significance level according to a Student t test. On the regression map of $\hbox {lag}=-3$ (Fig. 5a), a large area of cold SAT anomaly can be seen over north Asia centered in Siberia, indicating that three pentads before a positive PC1 there is a wide-spread cold temperature anomaly over north Asia. This is a very significant precursor for the leading North American SAT subseasonal variability mode. One pentad later ($\hbox {lag}=-2$; Fig. 5b), the cold SAT anomaly of north Asia intensifies and its extent expands southward, with its front reaching the east coast of China. The cold air continues pushing southeastward. After another pentad ($\hbox {lag}=-1$; Fig. 5c), the center of the cold SAT anomaly is located in the southeast coast of China. This process is reminiscent of a wintertime cold surge in East Asia (e.g., Lau et al. 1983). At the same time, significant SAT anomalies develop downstream, a warm anomaly in the subtropical central Pacific, a cold anomaly near the Bering Strait, and a warm anomaly over the North American continent. On the simultaneous regression map (Fig. 5d), the Asian cold anomaly is almost totally disappeared, with only a hint of cold air along the southeast coast of China. Meanwhile, the Bering Strait cold anomaly and North American warm anomaly intensify significantly.

Fig. 5

Lagged regressions of SAT onto PC1. Lag-$n$ means that the SAT anomaly leads the PC by $n$ pentads. The magnitude corresponds to one standard deviation of the PC. Shaded areas represent those where the regression is statistically significant at a 0.01 level according to a Student t test. Contour interval is 0.2 °C. The zero contour is not plotted, and contours with positive and negative values are in red and blue, respectively

The above discussion implies that the wintertime East Asian cold surge is an important precursor and a contributing factor for the North American subseasonal SAT variability mode EOF1. We will next demonstrate that the cold air movement in East Asia observed in Fig. 5 agrees in different aspects with the cold surge of the East Asian winter monsoon. The strength of Siberian cold air mass and East Asian cold surge largely determine the magnitude of the East Asian winter monsoon. Numerous previous studies have demonstrated that associated with a stronger East Asian winter monsoon are stronger cold surges, stronger Siberian high and increased East Asian subtropical westerly jet (e.g., Lau and Li 1984; Ding and Krishnamurti 1987; Jhun and Lee 2004). Lau et al. (1983) investigated the day-to-day evolution of middlelatitude circulation associated with monsoonal surges during the winter of 1978–1979 and found that the intensification of the East Asian subtropical westerly jet at 200-hPa is also closely related to cold surges on a synoptic time scale. Therefore, we look at the evolutions of sea level pressure and 200-hPa zonal wind anomalies.

Fig. 6

Lagged regressions of sea level pressure (SLP) onto PC1. Contour interval is 0.5 hPa. Shaded areas represent those where the regression is statistically significant at a 0.01 level according to a Student t test. The zero contour is not plotted, and contours with positive and negative values are in red and blue, respectively

The lagged regression maps of sea level pressure (SLP) and 200-hPa zonal wind with respect to PC1 are shown in Figs. 6 and 7, respectively. Three pentads before a positive PC1 (Fig. 6a), a significant above normal SLP anomaly appears over the northern Eurasian continent. One pentad later ($\hbox {lag}=-2$; Fig. 6b), the positive SLP anomaly intensifies over Siberia. After that it penetrates southward (Fig. 6c), and by the time of $\hbox {lag}=0$ the positive SLP anomaly spreads to the subtropical North Pacific. During this process we also observe the enhancement of the Aleutian low, and development of the negative SLP anomaly over North America. Associated with the intensification of the Siberian high, the 200-hPa westerlies accelerate near the jet core and decelerate to its north and south (Fig. 7a, b), a feature very similar to that associated with an enhanced East Asian winter monsoon (e.g., Jhun and Lee 2004; Li and Yang 2010).

Fig. 7

Lagged regressions of 200-hPa zonal wind onto PC1. Contour interval is $0.5\, \hbox {m s}^{-1}$. Contours with negative values are dashed. Shaded areas represent those where the regression is statistically significant at a 0.01 level according to a Student t test

The next question is how the East Asian cold surge influences the EOF1 mode of SAT in North America. A number of previous studies have provided evidence that there is a significant tropical–extratropical interaction associated with the East Asian cold surge. The tropical convection over the maritime continent of Borneo and Indonesia is enhanced following cold surges (e.g., Chang et al. 1979; Lau 1982). In Lau et al. (1983), it was found that the convective activity over the equatorial central Pacific is also enhanced after the cold surge. Here we hypothesize that the enhanced tropical central Pacific convective diabatic heating induces a Rossby wave teleconnection pattern propagating into the North Pacific and North America to influence the SAT variability there.

To demonstrate that this is indeed the case, shown in Fig. 8 are the lagged regression maps of OLR, which is a good representation of tropical convection. As can be seen, there exists a negative OLR anomaly (above normal convection) in the tropical eastern Indian Ocean and the South China Sea when the cold air and high pressure are built up in the Siberian region (Fig. 8a, b), which is consistent with previous studies (e.g., Lau 1982). At $\hbox {lag}=-1$ and $\hbox {lag}=0$, accompanying with the cold surge into the South China Sea and the tropical western Pacific, convection is enhanced over the tropics. In particular there is a strong positive convection (negative OLR anomaly) development in the tropical central Pacific (Fig. 8c, d). The lagged regression maps of precipitation rate (not shown) have almost the same features.

Fig. 8

Lagged regressions of OLR onto PC1. Contour interval is $1\, \hbox {W m}^{-2}$. Shaded areas represent those where the regression is statistically significant at a 0.05 level according to a Student t test. The zero contour is not plotted, and contours with positive and negative values are in red and blue, respectively

As an atmospheric response to the enhanced tropical central Pacific convective diabatic heating, a two-dimensional Rossby wave or teleconnection pattern is usually produced (e.g., Hoskins and Karoly 1981; Jin and Hoskins 1995). The lagged regression maps of 200-hPa streamfunction with respect to PC1 are illustrated in Fig. 9. It is clear that a significant wave train is generated at $\hbox {lag}=-1$ and enhanced at $\hbox {lag}=0$ (Fig. 9c, d). In fact, this wave train bears almost the same distribution as the PNA pattern (e.g., Wallace and Guztler 1981). Similar structure of the atmospheric circulation anomaly can be observed from the lagged regression maps of 500-hPa geopotential height (not shown).

Fig. 9

Lagged regressions of 200-hPa streamfunction onto PC1. Contour interval is $10\times 10^5\, \hbox {m}^{2}\, \hbox {s}^{-1}$. Shaded areas represent those where the regression is statistically significant at a 0.01 level according to a Student t test. The zero contour is not plotted, and contours with positive and negative values are in red and blue, respectively

Also can be noted from Fig. 8 is that the negative OLR anomaly in the tropical Indian Ocean at $\hbox {lag}=-3$ moves slowly eastward. At lag = 0 it merges with the tropical Pacific convection anomaly. This process is reminiscent of the MJO. It is likely that the 50-day spectral peak associated with PC1 (Fig. 3a) is related to the MJO variability.

It thus can be concluded that the EOF1 mode of SAT subseasonal variability in North America is associated with the PNA teleconnection pattern. At least part of its variability is forced by the diabatic heating anomaly in the tropical central Pacific that is associated with low-level convergence originated from the East Asian cold surge.

5 EOF2

The second mode EOF2 has a dipole spatial structure of SAT variability with warm (cold) SAT anomalies in the central and eastern US and cold (warm) SAT anomalies in northwestern Canada and Alaska,

Similar lagged regression analysis is performed as in the last section to identify precursors and possible predictability sources of EOF2. It is found that this mode is closely connected to changes in tropical convections associated with the Madden–Julian Oscillation (MJO). Shown in Fig. 10 are the lagged regression maps of OLR anomaly with respect to PC2. Three pentads before a positive PC2, there are significant tropical convection anomalies in the Indian Ocean and western Pacific region with a dipole structure, i.e., enhanced convection in the eastern Indian Ocean and reduced convection in the tropical western Pacific (Fig. 10a). The negative and positive OLR anomaly centers are located slightly to the south of the equator. This dipole structure of convection anomalies is reminiscent of Phases 2 and 3 of the MJO according to the definition of Wheeler and Hendon (2004). The convection anomalies move eastward with time (Fig. 10b–d). By Lag = 0 the negative OLR is centered near the Maritime continent and the positive OLR is located east of the date line and is weakened.

Fig. 10

Same as Fig. 8, except for regressions onto PC2

Associated with the tropical convection anomalies, the tropical upper divergence anomalies show a feature which also corresponds well to the MJO. Figure 11 illustrates the 200-hPa velocity potential regression with PC2. A wavenumber 1 structure of the velocity potential field in the tropics is clear. A strong enhanced upper divergence is already developed three pentad before PC2. The divergence signal propagates eastward.

Fig. 11

Lagged regressions of 200-hPa velocity potential onto PC2. Contour interval is $1\times 10^5\, \hbox {m}^{2}\, \hbox {s}^{-1}$. Shaded areas represent those where the regression is statistically significant at a 0.01 level according to a Student t test. The zero contour is not plotted, and contours with positive and negative values are in red and blue, respectively

Shown in Fig. 12 is the regression of 200-hPa stream function in the Northern Hemisphere with respect to PC2. It is evident that a wave train develops in the North Pacific starting from $\hbox {Lag}=-2$ and intensifies in Lags −1 and 0. This represents an extratropical response to the tropical diabatic forcing of the MJO and agrees well with previous studies (e.g., Matthews et al. 2004; Kim et al. 2006; Lin et al. 2010). With a linearized global primitive equation model, Lin et al. (2010) demonstrated that a dipole diabatic heating anomaly structure in the tropical Indian Ocean and western Pacific similar to MJO Phases 2 and 3 is very efficient in generating a Rossby wave train that propagates into the extratropical North American region. This wave train is close to being orthogonal to the PNA which is associated with PC1. Therefore, it appears that the tropical convection associated with EOF1 and EOF2 excited orthogonal wave trains.

Fig. 12

Same as Fig. 9, except for regressions onto PC2

The lagged regression of SAT (Fig. 13) indicates that the SAT anomalies develop in the Pacific and North American region, closely associated with the upper circulation. By $\hbox {lag}=0$ which is about two pentads after MJO Phases 2, the North American dipole SAT pattern is fully developed. This MJO and SAT connection agrees well with Lin and Brunet (2009), who documented the influence of the MJO on Canadian wintertime SAT (their Fig. 3f).

Fig. 13

Same as Fig. 5, except for regressions onto PC2

Spectral analysis of PC2 indicates that it tends oscillate at a period of about 70 days (Fig. 3). Then how is it associated with the MJO which was described as a 30–60 day oscillation in early studies (e.g., Madden and Julian 1971, 1994). The period of MJO was found to be broader in boreal winter (30–100 days) than boreal summer (30–50 days) (e.g., Zhang and Dong 2004). Based on satellite observations, Izumo et al. (2010) identified two frequency bands for the MJO during boreal winter that they referred to as the low-frequency (55–100 days) MJO and high-frequency (30–50 days) MJO. In order to confirm that there exist two frequency bands for the MJO, plotted in (Fig. 14) are the power spectra of RMM1 and RMM2 (Wheeler and Hendon 2004) during the 34 extended winters under study. Both RMM1 and RMM2 clearly have two spectrum peaks, one near 70 days and the other near 40 days. It thus can be concluded that PC2 is associated with the low-frequency component of the MJO.

Fig. 14

Same as Fig. 3, except for RMM1 and RMM2

6 EOF3 and EOF4

From Sect. 3, it is known that EOF3 and EOF4 tend to have a phase shift to each other in space and time, indicating that they are related to a common process and they represent a northeastward-propagating pattern over North America.

In order to identify precursors for EOF3 and EOF4 and to find out what process is responsible for them, we analyze the lagged regressions with respect to PC3 and PC4. Illustrated in Fig. 15 is the lagged regression of 500-hPa geopotential height with respect to PC3. Two pentads before PC3, a negative NAO pattern is clear (Fig. 15b). After that at $\hbox {lag}=-1$ (Fig. 15c), the Icelandic positive height anomaly center intensifies and is slightly moved westward. Meanwhile, a wave train appears upstream which seems originated from the tropical central Pacific. The pattern over the North American continent slowly moves eastward, and by lag = 0 a northeast–southwest dipole structure is created. O ne pentad before PC4, a positive height anomaly center emerges near the west coast of the US (not shown).

Fig. 15

Lagged regressions of 500-hPa geopotential height onto PC3. Contour interval is 10 m

From the SAT regression maps (Fig. 16), a precursor for EOF3 can be identified which is a cold anomaly across the north part of the Eurasian continent at the lags from $-3$ to $-1$. This cold anomaly is likely a result of the negative NAO discussed above. Shown in Fig. 17 is the SAT regression maps with respect to PC4. Figure 17b is similar to Fig. 16d, confirming that PC3 and PC4 are related and PC4 lags PC3 by about two pentads.

Fig. 16

Same as Fig. 5, except for regressions onto PC3

Fig. 17

Same as Fig. 5, except for regressions onto PC4

Lin et al. (2009) investigated the relationship between the NAO and the tropical MJO and found that a negative NAO occurs after MJO Phase 7 which corresponds to reduced convection in the eastern Indian Ocean and enhanced convection in the tropical central Pacific. To see if the negative NAO leading EOF3 and EOF4 of the North American subseasonal SAT variability is related to the tropical MJO, we look at the OLR regression maps (Fig. 18). Indeed that three pentads before EOF3, a tropical dipole OLR anomaly is evident which corresponds to MJO Phase 7 with reduced (enhanced) convection in the eastern Indian Ocean (central Pacific). The convection anomalies propagate eastward along the equator. Therefore EOF3 and EOF4 are both related to the tropical convection of the MJO. As a matter of fact, the EOF3 SAT pattern over North America (Fig. 16d) agrees well with the SAT anomaly over Canada two pentads after MJO Phase 7 as observed in Lin and Brunet (2009; their Fig. 3u).

Fig. 18

Same as Fig. 8, except for regressions onto PC4

From the spectral analysis (Fig. 3), it appears that both PC3 and PC4 have a spectral peak in the range of 30–50 days. Therefore the high-frequency MJO is a signal source for EOF3 and EOF4 of the North American subseasonal SAT variability.

7 Summary and conclusion

In this study we have examined the subseasonal variability of North American wintertime surface air temperature (SAT), based on the pentad data of the recent 34 years (1979–2013). The dominant modes of SAT variability are identified using an empirical orthogonal function (EOF) analysis. The four leading modes account for about 60 % of the total variance. Then lagged regression analysis is conducted to identify the precursors of large-scale atmospheric circulation for each mode a few pentads in advance, and to understand the processes that influence the subseasonal SAT variability and the predictability signal sources.

The leading mode (EOF1) represents temperature variability of the same sign over the whole North American continent with strong variability over Canada and the north part of the US. Its principal component (PC1) has a power spectrum peak near 50 days. This mode is found to be related to the Pacific-North American (PNA) circulation pattern. A significant precursor is the East Asian cold surge which occurs about three pentads before a positive phase of EOF1. The cold surge leads to low-level convergence and enhanced convection in the tropical central Pacific which in turn induces a positive PNA pattern.

The second mode (EOF2) is characterized by a dipole structure of SAT anomaly with opposite signs of variability in the northwest and southeast parts of the North American continent. It tends to oscillate at a period of about 70 days. The MJO in boreal winter is composed of two components, i.e., the low-frequency (50–90 days) and high-frequency (30–50 days)components. EOF2 is influenced by the low-frequency component of the MJO. Three pentads before a positive EOF2 (warm in the southeastern and cold in the northwestern North American continent), enhanced convection in the eastern Indian Ocean and reduced convection in the tropical western Pacific are observed, a tropical structure corresponding to MJO Phases 2. Associated with the tropical convection anomalies, a wave train develops in the Pacific and North American region which influences the North American SAT.

The third (EOF3) and forth (EOF4) modes are found to have a phase shift to each other in both space and time, indicating that they are related to the same process. They together represent a northeastward propagating pattern over North America. It is evident that EOF3 and EOF4 are connected to the high-frequency part of the MJO which has a period range of 30–50 days. It should be noted, however, that although statistically significant, the maximum lagged correlation of 0.18 between PC3 and PC4 indicates that both modes have a large part of variance that is independent of each other, and thus have different origins. The atmospheric internal dynamics is likely an important mechanism responsible for part of the variance of each mode.

All the four modes of SAT variability have statistically significant precursors about three pentads in advance. This implies that there is potential for a useful prediction of these modes. The results also indicate that all the four leading SAT modes have a connection to the tropics. For EOF1 the link is indirect, as the precursor starts with the cold surge of the East Asian monsoon. In this case, the tropical central Pacific convection serves as a “bridge” linking the cold surge and the North American SAT variability. EOF2, EOF3 and EOF4 are directly connected to the tropical MJO. The importance of the tropics is thus clear in the subseasonal SAT variability in North America. This implies that the subseasonal prediction would benefit from improved data assimilation, numerical model initialization, and model physics in the tropical regions.

It should be noted that the connections between the dominant modes of North American SAT variability and the precursors are obtained through statistical analysis. The signals are in general weak, although they are statistically significant. It is unclear how practically useful they are as these signals are embedded in relatively strong noises related to atmospheric internal dynamics such as nonlinear interactions. In the extratropical region, it is likely that the atmospheric internal dynamics is the main cause for subseasonal variability, including the PNA and NAO variability. The results of this study indicate that there are other mechanisms in addition to the local internal dynamics that contribute to the North American SAT subseasonal variability.

The findings obtained in this study are based on analysis of observations. Whether or not a state-of-the-art numerical model can simulate the processes is unclear. How the tropical-extratropical interactions that determine the North American SAT subseasonal variability are influenced by the basic climatological state, sea-land distribution and other parameters is also to be understood. Hopefully future numerical modelling and model intercomparison studies would help to better understand the dynamics involved in the subseasonal SAT variability in North America.