Abstract

The interannual variability of wintertime North American surface temperature extremes and its generation and maintenance are analyzed in this study. The leading mode of the temperature extreme anomalies, revealed by empirical orthogonal function (EOF) analyses of December–February mean temperature extreme indices over North America, is characterized by an anomalous center of action over western-central Canada. In association with the leading mode of temperature extreme variability, the large-scale atmospheric circulation features an anomalous Pacific–North American (PNA)-like pattern from the preceding fall to winter, which has important implications for seasonal prediction of North American temperature extremes. A positive PNA pattern leads to more warm and fewer cold extremes over western-central Canada. The anomalous circulation over the PNA sector drives thermal advection that contributes to temperature anomalies over North America, as well as a Pacific decadal oscillation (PDO)-like sea surface temperature (SST) anomaly pattern in the midlatitude North Pacific. The PNA-like circulation anomaly tends to be supported by SST warming in the tropical central-eastern Pacific and a positive synoptic-scale eddy vorticity forcing feedback on the large-scale circulation over the PNA sector. The leading extreme mode–associated atmospheric circulation patterns obtained from the observational and reanalysis data, together with the anomalous SST and synoptic eddy activities, are reasonably well simulated in most CMIP5 models and in the multimodel mean. For most models considered, the simulated patterns of atmospheric circulation, SST, and synoptic eddy activities have lower spatial variances than the corresponding observational and reanalysis patterns over the PNA sector, especially over the North Pacific.

1. Introduction

Climatic extremes have substantially influenced human and natural systems and have been extensively investigated in the past two decades (e.g., Meehl and Tebaldi 2004; Wallace et al. 2014; Palmer 2014; van Oldenborgh et al. 2015; Sillmann et al. 2017). The observational Hadley Centre extreme dataset (HadEX; Alexander et al. 2006) and its updated version HadEX2 (Donat et al. 2013), developed by an expert team on climate change detection and indices, have provided the most comprehensive global gridded dataset of temperature and precipitation extremes supporting climate extreme studies. Most of the extreme indices identified in the HadEX/HadEX2 dataset describe moderate climate extremes with reoccurrence times of a year or shorter (Zhang et al. 2011; Sillmann et al. 2013a). Probably due to their robustness and straightforward calculation and interpolation, the extreme indices have been widely used in exploring the climate extreme variability and trend, in detection and attribution studies, and in climate model evaluation and future climate projections (e.g., Donat et al. 2013, 2016; Sillmann et al. 2013a,b, and references therein).

In addition to characterizing the variability and projected changes of climate extremes, physical attribution studies involving extreme events have been widely conducted. In particular, studies indicate that changes in temperature extremes can be attributed to large-scale atmospheric circulation anomalies (e.g., Meehl and Tebaldi 2004; Horton et al. 2015; Grotjahn et al. 2016; Sung et al. 2019), teleconnections (e.g., Thompson and Wallace 2001; Wettstein and Mearns 2002; Quadrelli and Wallace 2004; Harnik et al. 2016; Yu et al. 2018), regional- and global-scale dynamical and thermodynamic changes (e.g., Campbell and Vonder Haar 1997; Durre and Wallace 2001; Dole et al. 2011; Loikith and Broccoli 2012; Barnes 2013; Krueger et al. 2015; Horton et al. 2015; Hong et al. 2018; Tamarin-Brodsky et al. 2019), and external forcings (e.g., Min et al. 2011; Morak et al. 2013; Stott et al. 2016; Lu et al. 2016; Sillmann et al. 2017). The temperature extreme anomaly has also been found to be associated with synoptic-scale wave activities, such as cyclone/anticyclone tracks and blocking activity (e.g., Favre and Gershunov 2006; Wang et al. 2006; Chang et al. 2016; Sillmann et al. 2017). High-frequency wave activity is usually quantified by the variability of sea level pressure and geopotential fields at the synoptic-scale (such as 2–6 or 2–8 days) time range (e.g., Wallace and Gutzler 1981; Blackmon et al. 1984; Ulbrich et al. 2009). The standard deviation of the synoptic-scale quantity, termed the storm track, represents the combined intensities and frequencies of cyclone and anticyclone activities (e.g., Blackmon et al. 1977; Lee et al. 2012).

The purpose of this study is to further document the interannual variability of wintertime North American temperature extremes and explore its formation and maintenance mechanisms. Unlike many previous studies that investigated temperature extremes over some specified regions, we characterize extreme variability by means of an empirical orthogonal function analysis, the principal mode of variability that captures as much as possible of the variance of temperature extremes over the entire North American domain. We analyze large-scale circulation anomalies in association with the leading temperature extreme mode, which contribute to temperature anomalies through thermal advection in the lower troposphere. The generation and maintenance of the preferred atmospheric pattern is further examined by analyzing the anomalies of sea surface temperature (SST) and of the synoptic-scale eddy activity and its forcing feedback on the large-scale circulation. We explore the anomalies associated with the leading extreme variability mode using the observational and reanalysis data, and evaluate these features simulated in the global climate models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5) of the World Climate Research Programme (WCRP).

The rest of the paper is organized as follows: The observational and reanalysis datasets, climate model outputs, and analysis methods are described in section 2. Section 3 presents the interannual variability of wintertime warm and cold extremes, using observed extreme indices. Section 4 explores the large-scale atmospheric circulation and thermal advection anomalies in association with the leading temperature extreme mode, based on the observational and reanalysis data, together with the anomalies of SSTs and synoptic eddy activities. Section 5 assesses the leading mode–associated circulation anomalies in CMIP5 historical simulations. A summary and discussion are given in section 6.

2. Data and methodology

a. Observational and reanalysis datasets and climate model simulations

The observed North American surface temperature extremes analyzed in this study are the December–February (DJF) mean extreme indices from the HadEX2 dataset (Donat et al. 2013) on 3.75° × 2.5° (longitude–latitude) grids. The indices employed consist of warm extremes with the percentage of time when the daily maximum or minimum temperature is greater than its 90th percentile, termed warm days (TX90p) or warm nights (TN90p), respectively, and cold extremes with the percentage of time at which daily maximum or minimum temperature is less than its 10th percentile, termed cold days (TX10p) or cold nights (TN10p), respectively. The percentile-based threshold indices are derived using 1961–90 as the base period and based on a 5-day moving window, as well as applying a bootstrap resampling procedure to avoid inhomogeneity in these indices at the boundaries between the base and out-of-base periods (Zhang et al. 2005). In this analysis, we use the indices over the period 1951–2010. Years refer to the January dates throughout this study. The atmospheric fields used were extracted from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (hereafter, NCEP; Kalnay et al. 1996), including daily temperature, geopotential, and horizontal wind velocities in the troposphere, and sea level pressure (SLP). These variables are on standard 2.5° × 2.5° grids. In addition, we use monthly sea surface temperature data from the Met Office Hadley Centre, version 1 (HadISST1.1; Rayner et al. 2003), for the same 60 years. The SST data are also interpolated to 2.5° × 2.5° grids.

The climate indices employed were mainly downloaded from the Climate Prediction Center (CPC) website (http://www.cpc.ncep.noaa.gov/data/indices), including the monthly Pacific–North American pattern (PNA; Wallace and Gutzler 1981), tropical–Northern Hemisphere pattern (TNH; Mo and Livezey 1986), North Atlantic Oscillation (NAO; e.g., Hurrell et al. 2003), Arctic Oscillation (AO; Thompson and Wallace 1998), Pacific decadal oscillation (PDO; Mantua et al. 1997), and Niño-3.4 [the SST anomaly averaged over the region 5°S–5°N, 120°–70°W, which represents the tropical El Niño–Southern Oscillation (ENSO) variability] indices. The extratropical Asian–Bering–North American (ABNA) teleconnection index (Yu et al. 2016) was computed using the NCEP reanalysis data. Specifically, the index was constructed by a linear combination of the three regionally averaged 500-hPa geopotential anomalies over the ABNA centers of action, based on the normalized DJF mean geopotential field after linearly removing the PNA pattern contribution.

The climate model output was extracted from the CMIP5 multimodel archive of climate simulations (https://esgf-node.llnl.gov/search/cmip5). The 24 models considered, for which all the variables required are available, are ACCESS1.0, BCC_CSM1.1, BCC_CSM1.1(m), CanESM2, CCSM4, CMCC-CM, CNRM-CM5, CSIRO Mk3.6.0, EC-EARTH, FGOALS-s2, GFDL-ESM2M, HadGEM2-CC, HadGEM2-ES, INM-CM4, IPSL-CM5A-LR, IPSL-CM5A-MR, MIROC4H, MIROC5, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, MRI-CGCM3, and NorESM1-M. Descriptions of the climate model configurations can be found on the above website and are documented in Taylor et al. (2012). In this study, we use the historical simulation that incorporates the anthropogenic and natural forcings from the observed atmospheric composition changes in the twentieth century and the early twenty-first century until 2005. We analyze the 55-yr period from 1951 to 2005 and use only one member run (“r1i1p1”) for each model. As in the observations, the modeled extreme indices were calculated using 1961–90 as the base period. The temperature extremes considered also include warm days, warm nights, cold days, and cold nights on 3.75° × 2.5° (longitude–latitude) grids. The atmospheric and oceanic fields employed involve monthly geopotential at 500-hPa and SST, and daily SLP. These variables are interpolated to 2.5° × 2.5° grids.

b. Analysis methods

All analyses are based on DJF seasonal means of the variables considered, originally from monthly, daily, and derived bandpass-filtered data. Synoptic-scale fluctuations are obtained by applying a Butterworth bandpass filter to retain components within 2–8 days (Murakami 1979). An empirical orthogonal function (EOF) analysis is performed to characterize the dominant mode of interannual variability of North American temperature extreme indices. Regression and correlation analyses are then employed to quantify the relationship between variables of interest and the principal component (PC) corresponding to the dominant EOF mode of temperature extremes. The statistical significance level of a correlation is assessed using Student’s t test, assuming one degree of freedom (DOF) per year. The t test is also employed to assess whether a linear trend is statistically significant (e.g., von Storch and Zwiers 1999).

The multimodel quantity estimate is obtained by pooling the statistics of individual models. Since the same amount of data is employed in each case, the multimodel mean statistics are the ensemble average of the 24 model results. The relative agreement of individual model-based anomalous patterns with the NCEP reanalysis result is illustrated using a modified Taylor diagram termed a Boer–Lambert–Taylor (BLT) diagram (Boer and Lambert 2001). A BLT diagram displays the pattern correlation, the ratio of modeled to reanalysis variance, and the relative mean-square difference between model and NCEP quantities.

Storm-track (ST) activity is defined as the root-mean-squares of the 2–8-day bandpass-filtered geopotential at 300-hPa (ST300) and the filtered SLP (STSLP), following previous studies (e.g., Blackmon et al. 1977; Chang et al. 2002; Lee et al. 2012). The anomalous horizontal temperature advection Fadv can be expressed as

 
Fadv=VT¯=u T¯xυ T¯y,
(1)

where V(u, υ) denotes the anomalous horizontal wind velocity, including zonal and meridional components, and T¯ is the DJF climatological mean temperature. The synoptic-scale eddy vorticity forcing Fυ, which contributes to the geopotential tendency, takes the form

 
Fυ=f2(Vζ¯),
(2)

where f is the Coriolis parameter, ζ is the relative vorticity, and V is the horizontal wind velocity. The prime denotes the 2–8-day filtered fluctuation, and the bar represents the DJF mean.

3. Interannual variability of winter temperature extremes

a. Climatological mean and interannual variance

Figure 1 shows the DJF mean and interannual variance of warm days (TX90p), warm nights (TN90p), cool days (TX10p), and cool nights (TN10p) indices over North America. Broadly similar patterns of the climatological mean and interannual variance are seen between warm days and warm nights and between cold days and cold nights. As described in section 2, 1961–90 is used as the base period to estimate the extreme thresholds. Thus, the mean for the whole period of data (1951–2010) analyzed here is different from 10%. The difference may be affected by factors including (i) differences between the climate in 1961–90 and the rest of the dataset; (ii) daily temperature variability, in which regions of high daily temperature variability tend to have a larger bias; and (iii) the way the indices are computed, which may affect the bias level (e.g., Zhang et al. 2005). Nevertheless, the temperature extreme mean and variance calculated over the 60 winters resemble those obtained over the 31 winters from 1979 to 2010 (Yu et al. 2018), indicating the robustness of the results.

Fig. 1.

(top) DJF means (interval 0.8%) and (bottom) variances [interval (5.0%)2] of surface temperature extremes over North America. The percentages of warm days (TX90p), warm nights (TN90p), cold days (TX10p), and cold nights (TN10p) are shown from left to right.

Fig. 1.

(top) DJF means (interval 0.8%) and (bottom) variances [interval (5.0%)2] of surface temperature extremes over North America. The percentages of warm days (TX90p), warm nights (TN90p), cold days (TX10p), and cold nights (TN10p) are shown from left to right.

Warm days and warm nights exhibit high mean values over central-eastern Canada, in particular the Canadian Shield centered over Hudson Bay and the central-eastern parts of Mexico (Fig. 1, top row), with differences mainly in amplitude of the action centers. TX90p is dominated by high variances over Alaska, most of the Canadian Arctic Archipelago, Canadian prairies, and Colorado Plateau. The variance of TN90p bears resemblance to that of TX90p, especially in the northern portions of North America. However, its variance is weaker over the Colorado Plateau than its TX90p counterpart (Fig. 1, bottom row), probably due to topographic influences. Cold days and cold nights show high mean values in the western-central parts of North America, especially the western-central parts of south Canada and the northwestern United States. The high variance regions of TX10p and TN10p are also apparent in western Canada and the northwestern United States, as well as some of the Canadian Arctic Archipelago.

b. Dominant modes of interannual variability

The principal mode of the North American temperature extreme variability is identified by the EOF analyses of DJF mean and area-weighted extreme indices over the land grids within (20°–80°N, 170°–50°W). A close resemblance is seen in the first EOF modes of the TX90p and TN90p anomalies, including the spatial structure and amplitude of the anomalies, as is in the leading EOFs of the TX10p and TN10p anomalies. Hence, Fig. 2 presents the leading mode of combined EOF (EOF1) of the warm TX90p and TN90p anomalies (left), by pooling the TX90p and TN90p anomalies in an EOF analysis, and of the cold TX10p and TN10p anomalies (right). EOF1 accounts for 30.7% (42.1%) of the total interannual warm (cold) extreme variance and is well separated from subsequent EOFs as per the criterion of North et al. (1982).

Fig. 2.

Leading mode of combined EOF of DJF mean (left) warm days and warm nights and (right) cold days and cold nights. Contour interval is 1.0%. Percentage of the mode in explaining the interannual variance is given in the upper-right corner.

Fig. 2.

Leading mode of combined EOF of DJF mean (left) warm days and warm nights and (right) cold days and cold nights. Contour interval is 1.0%. Percentage of the mode in explaining the interannual variance is given in the upper-right corner.

EOF1 of the warm extreme anomalies tends to be dominated by a large anomaly over the domain of interest, with the center of action located over the Canadian Prairies, accompanied by a weak anomaly of opposite sign over Mexico and the southeastern United States. By contrast, EOF1 of the cold extreme anomalies reveals a large anomaly with the same sign over the whole domain, with the action center over western Canada. The two EOF1 patterns exhibit broadly similar features, with differences mainly in the location of the center of action. For demonstration purposes, a positive (negative) sign is used for EOF1 of the TX90p and TN90p (TX10p and TN10p) anomalies, so that an increase of warm extreme corresponds to a decrease of cold extreme. The action center of EOF1 is also collocated with the dominant variance center as seen in the corresponding variance pattern (Fig. 1). In addition, the two EOF1 patterns bear resemblance to EOF1 of the DJF mean surface air temperature T2m anomalies over North America (not shown, but see, e.g., Fig. 6 of Yu and Zhang 2015). It is interesting to note that the anomalous center of action in EOF1 of T2m anomalies is somehow situated between the action centers of the EOF1 patterns of the warm and cold extreme anomalies.

The corresponding principal components (PC1s) for TX90p and TN90p are pretty similar as would be expected, as are the PC1s for TX10p and TN10p. Thus in this analysis, we use the mean of PC1 series for warm (cold) days and nights as an index, termed T90 (T10), to represent the leading warm (cold) extreme variability over North America (thick black curves in Fig. 3). The correlation coefficients between the identified extreme index and the individual PC1 series exceed 0.98 for both warm and cold extremes (Table 1). Hence, the temperature extreme pattern in association with the index we defined (not shown) is nearly identical to the EOF pattern shown in Fig. 2. T90 and T10 are also correlated to each other (correlation r = 0.65), statistically significant at the 1% level (Table 1 and Fig. 3). This implies that an enhancement of warm extremes tends to be accompanied by a reduction of cold extremes over North America (Fig. 2). In addition, T90 and T10 reveal increasing trends over 1951–2010, with a trend of 0.22 decade−1 for both series (gray lines in Fig. 3). This suggests that the warm extremes have had a tendency to increase and the cold extremes have tended to decrease (Fig. 2) over the past several decades. However, the significance level α of the linear trends is not high, with α = 14.6% for T90 and α = 14.8% for T10. The two extreme indices are dominated by interannual variability.

Fig. 3.

(left) Time series of the average of the principal components associated with combined EOF of warm days and warm nights over North America (T90; thick black), its linear trend (gray), and the PNA (red) and PDO (green) indices. (right) As in the left panel, but where the black and gray curves indicate the average of the principal components associated with combined EOF of cold days and cold nights (T10) and its linear trend, respectively.

Fig. 3.

(left) Time series of the average of the principal components associated with combined EOF of warm days and warm nights over North America (T90; thick black), its linear trend (gray), and the PNA (red) and PDO (green) indices. (right) As in the left panel, but where the black and gray curves indicate the average of the principal components associated with combined EOF of cold days and cold nights (T10) and its linear trend, respectively.

Table 1.

Correlation coefficients between the leading principal components of surface temperature extreme anomalies and various climate indices over the period from 1951 to 2010. Assuming one degree of freedom per winter, the correlation at the 5% (1%) significance level is about 0.26 (0.33) for 60 DJFs.

Correlation coefficients between the leading principal components of surface temperature extreme anomalies and various climate indices over the period from 1951 to 2010. Assuming one degree of freedom per winter, the correlation at the 5% (1%) significance level is about 0.26 (0.33) for 60 DJFs.
Correlation coefficients between the leading principal components of surface temperature extreme anomalies and various climate indices over the period from 1951 to 2010. Assuming one degree of freedom per winter, the correlation at the 5% (1%) significance level is about 0.26 (0.33) for 60 DJFs.

4. Generation and maintenance of temperature extreme variability

To aid in understanding the formation and maintenance of temperature extreme anomalies, we analyze the anomalies of large-scale atmospheric circulation and its induced temperature advection in association with the leading temperature extreme modes. We also examine the anomalies of sea surface temperatures and synoptic-scale eddy activities to help understand the maintenance of the preferred pattern of atmospheric variability.

a. Anomalous large-scale atmospheric circulation and temperature advection

First, we calculate the correlations between the extreme indices we defined and several climate indices that are related to North American temperature anomalies as demonstrated in previous studies (e.g., Trenberth et al. 1998; Higgins et al. 2002; Yu et al. 2018). Table 1 lists the correlation coefficients between the time series of T90, T10, and various atmospheric and oceanic indices over the 60 DJFs from 1951 to 2010. T90 is highly correlated with the PNA index, with a correlation coefficient r = 0.74, significant at the 1% level. This indicates that the T90 and PNA series have about 55% variance in common. This relationship is also apparent in the DJF 500-hPa geopotential (Φ500) anomalies regressed upon the T90 index (Fig. 5, bottom left), which exhibits the prominent centers of action of the PNA pattern (Wallace and Gutzler 1981). In addition, most of the extreme values in the T90 series are well corresponding to the extremes in the PNA index (Fig. 3), indicating that the significant correlation between them is not due to a few extreme events. The relationship between the PNA and T90 series also stays steady over the 60 winters, as obtained from a 31-yr running correlation analysis between the two series (not shown). T90 is insignificantly correlated with the NAO, AO, TNH, and ABNA indices at the 5% level (Table 1). Thus, the T90 variability is mainly associated with a PNA-like atmospheric circulation anomaly. Similar results are obtained from the relations between the T10 index and the climate indices considered (Table 1 and Figs. 3 and 5), except for relatively high correlation between the T10 and ABNA indices (r = 0.35). In addition, the main relationships between T90 (T10) and the atmospheric and oceanic indices, as obtained from Table 1, remain the same after removing the linear trend associated with each time series (not shown).

To explore whether the PNA-like pattern has persistent relations with the temperature extreme variability, we further analyze the lead–lag relationship by shifting 3-month mean PNA indices relevant to the T90 and T10 indices in DJF. Figure 4 shows the lead–lag correlations between T90 (T10) and the mean PNA indices from June–August [JAS(−1)] to the following February–April [FMA(0)]. Here “−1” denotes the preceding year and “0” represents the simultaneous year. The correlations between T90 and the PNA indices increase from the preceding summer and become statistically significant at the 5% level from October to December [OND(−1)] (Fig. 4, left). The correlation coefficients continue to increase, reach the maximum from December to February [D(−1)JF(0) or DJF] when the two indices occur simultaneously, and decrease subsequently. In association with the warm T90 index, the Φ500 anomalies over the centers of action of the PNA pattern are not significantly different from zero before OND(−1), become pronounced in OND(−1), reach their highest values in D(−1)JF(0) (Fig. 5, left column), and diminish subsequently (not shown). This suggests that in association with the wintertime warm extreme variability over North America, there exists a pronounced PNA-like pattern from the preceding fall to winter, with a leading time of about two months. The atmospheric circulation anomalies in association with the cold T10 index (Fig. 5, right column) are generally similar to the T90 counterparts, with differences mainly in the amplitude of the anomalies. The T10-associated Φ500 anomalies are slightly weaker over North America than the T90-related anomalies.

Fig. 4.

(left) Lead–lag correlations between the T90 index in DJF and the PNA (red), PDO (green), and Niño 3.4 (blue) indices from JAS(−1) to FMA(0). (right) As in the left panel, but for the correlations with the T10 index. The dashed gray line is the 95% confidence level of correlation. The vertical line indicates the time DJF when the simultaneous correlations between the extreme index and the atmospheric and oceanic indices are shown.

Fig. 4.

(left) Lead–lag correlations between the T90 index in DJF and the PNA (red), PDO (green), and Niño 3.4 (blue) indices from JAS(−1) to FMA(0). (right) As in the left panel, but for the correlations with the T10 index. The dashed gray line is the 95% confidence level of correlation. The vertical line indicates the time DJF when the simultaneous correlations between the extreme index and the atmospheric and oceanic indices are shown.

Fig. 5.

The Φ500 anomalies (contour interval 60.0 m2 s−2) regressed upon the (left) T90 and (right) T10 indices in DJF. Results of anomalies in (top) ASO, (middle) OND, and (bottom) DJF are shown. The zero line is highlighted in bold. The positive (negative) anomalies that are significantly different from zero at the 5% level are red (cyan) shaded.

Fig. 5.

The Φ500 anomalies (contour interval 60.0 m2 s−2) regressed upon the (left) T90 and (right) T10 indices in DJF. Results of anomalies in (top) ASO, (middle) OND, and (bottom) DJF are shown. The zero line is highlighted in bold. The positive (negative) anomalies that are significantly different from zero at the 5% level are red (cyan) shaded.

The anomalous PNA-like pattern induces the exchange of mid–high-latitude air over North America, implying temperature advection contributes to the temperature anomalies. Figure 6 shows the anomalies of horizontal winds and temperature advection Fadv at 850 hPa in OND(−1) and DJF regressed upon the T90 and T10 indices. Accompanying the circulation anomalies described above, pronounced wind anomalies are seen in the lower troposphere. In particular, there are anomalous southern-southwestern winds over the west coast of Canada, westerly wind anomalies over the Canadian prairies, and north wind anomalies in the central parts of North America. The wind anomalies are apparent in OND(−1) and are clearly evident in DJF. The anomalous winds induce warm advection over western Canada (Fig. 6), in particular the Canadian prairies, which collocates with the action centers of warm extreme increase and cold extreme decrease (Fig. 2). Meanwhile, the anomalous north winds and associated cold temperature advection tend to dampen warm anomalies over the southern parts of North America, especially the central-eastern United States, which collocates with the warm extreme decrease and weak cold extreme variation (cf. Fig. 6 with Fig. 2). The collocation between the thermal advection and active temperature anomalies suggests that the anomalous PNA-like circulation and its associated temperature advection in the lower troposphere contribute to temperature extreme variability over North America. Broadly similar results are seen in the T90 and T10-associated anomalies.

Fig. 6.

Anomalies of 850-hPa horizontal temperature advection (shading and contour interval 0.3°C day−1) and winds (arrows; m s−1 with a scale shown in top-left panel; anomalies less than 0.1 m s−1 in both directions are omitted) regressed upon the (left) T90 and (right) T10 indices in DJF. Results of temperature advection and wind anomalies in (top) OND and (bottom) DJF are shown.

Fig. 6.

Anomalies of 850-hPa horizontal temperature advection (shading and contour interval 0.3°C day−1) and winds (arrows; m s−1 with a scale shown in top-left panel; anomalies less than 0.1 m s−1 in both directions are omitted) regressed upon the (left) T90 and (right) T10 indices in DJF. Results of temperature advection and wind anomalies in (top) OND and (bottom) DJF are shown.

b. Anomalous SST

The leading extreme variability is associated with pronounced SST anomalies in the tropical and extratropical Pacific. As listed in Table 1, T90 significantly correlates with the PDO index in DJF, most likely because of the close relationship between the PNA and the PDO indices (r = 0.73 in DJF). The lag correlations between the T90 index and the shifted 3-month mean PDO indices also bear resemblance to the corresponding correlations between T90 and the PNA indices (Fig. 4, left). However, the highest correlation appears between the T90 index in D(−1)JF(0) and the PDO index in JFM(0). This differs from the highest correlation between the T90 and PNA indices, which occurs simultaneously in D(−1)JF(0). The T90-PDO relationship tends to appear slightly after the T90-PNA relation. This is likely due to the PNA forcing influence on the PDO as will be discussed below. In fact, the correlation between the PNA index and its one month lagged PDO series is 0.76, slightly higher than the simultaneous correlation between the two indices. In addition, the correlations between the T90 index and the shifted Niño-3.4 indices are slightly higher than 0.26, the 5% significant level, starting from summer, reaching the maximum in August–October (ASO)(−1), decreasing subsequently, and becoming insignificant in JFM(0) (Fig. 4, left). The evolution of these relationships is also evident between the T10 index and the shifted PDO/Niño-3.4 indices (Fig. 4, right).

Figure 7 further displays the anomalies of 3-month averaged SST and 1000-hPa winds regressed upon the T90 and T10 indices in DJF. In association with the T90 index, significant SST anomalies appear in the tropical central-eastern Pacific in summer [ASO(−1)] and sustain in fall and winter (Fig. 7, left). The SST anomalies over the tropical central-eastern Pacific diminish and are insignificantly correlated with T90 in JFM(0) (not shown). The pronounced SST anomalies in the tropical central-eastern Pacific tend to force the PNA-like atmospheric pattern, as investigated extensively in previous studies (e.g., Horel and Wallace 1981; Shukla and Wallace 1983; Trenberth et al. 1998). In addition, SST depicts a PDO-like structure (Mantua et al. 1997) with widespread SST variations over the Pacific basin clearly from OND(−1). In particular, SST reveals comparable anomalies in amplitude, changing from positive in the tropical central-eastern Pacific to negative in the North Pacific midlatitudes. Pronounced surface wind anomalies corresponding to the PNA-like pattern in the North Pacific are found to be well collocated with the action center of the SST anomalies. This suggests that the anomalous circulation largely drives the SST anomalies in the midlatitude North Pacific, as demonstrated in previous studies (e.g., Wallace et al. 1990; Kushnir et al. 2002). Overall, the T90-associated SST anomalies, especially SST warming in the tropical central-eastern Pacific and the PDO-like pattern over the Pacific basin, favor the occurrence of the PNA-like atmospheric circulation.

Fig. 7.

Anomalies of SST (contour interval 0.1°C) and 1000-hPa wind (arrows; m s−1 with a scale shown at the lower right; anomalies less than 0.1 m s−1 in both directions are omitted) regressed upon the (left) T90 and (right) T10 indices in DJF. Results of SST and wind anomalies in (top) ASO, (middle) OND, and (bottom) DJF are shown. The zero line is highlighted in bold. The positive (negative) SST anomalies that are significantly different from zero at the 5% level are red (cyan) shaded.

Fig. 7.

Anomalies of SST (contour interval 0.1°C) and 1000-hPa wind (arrows; m s−1 with a scale shown at the lower right; anomalies less than 0.1 m s−1 in both directions are omitted) regressed upon the (left) T90 and (right) T10 indices in DJF. Results of SST and wind anomalies in (top) ASO, (middle) OND, and (bottom) DJF are shown. The zero line is highlighted in bold. The positive (negative) SST anomalies that are significantly different from zero at the 5% level are red (cyan) shaded.

The SST anomalies associated with the T10 index (Fig. 7, right) are generally similar to their T90 counterparts. Nevertheless, in association with the T10 index, the significant SST anomaly area is relatively broader in the tropical Pacific than that related to the T90 index. Significant SST anomalies are also seen in the subtropical North Atlantic, presumably due to the interannual SST relationship between the tropical Pacific and subtropical North Atlantic (e.g., Ham et al. 2013; Ham and Kug 2015).

It is worth noting that the SST anomalies in association with the T90 (T10) index that are significantly different from zero at the 5% level are color shaded in Fig. 7. Most of the SST anomalies in the tropical central-eastern Pacific are not significant at the 1% level, whereas the SST anomalies in the North Pacific are still significant at the 1% level (not shown). This is consistent with the relatively low correlation between the T90 (T10) and Niño-3.4 indices and high correlation between the T90 (T10) and PDO indices, as shown in Table 1 and Fig. 4. In addition, previous studies indicated that the PDO-like SST pattern is associated with variations of the intensity and spatial distribution of zonal jet in the North Pacific basin (e.g., Newman et al. 2016), which may further contribute to the temperature extreme variability over North America. The influence of tropical Pacific SST anomalies, including the tropical ENSO variability, on North American climate could also be significantly modified by the PDO variability (e.g., Gershunov and Barnett 1998; Yu and Zwiers 2007). Potential influences of SST anomalies in the North Pacific and Atlantic Ocean, as well as their physical influence processes, on North American temperature extremes remain to be explored.

c. Anomalous synoptic-scale eddy activity

The storm-track climatology exhibits high activities in the midlatitudes of the North Pacific and North Atlantic, particularly the elongated 2–8-day bandpass-filtered Φ300 variance maxima over the western oceans (Fig. 8, contours), as documented in previous studies (e.g., Wallace et al. 1988; Chang et al. 2002; Lee et al. 2012). In association with the T90 index, ST300 features an activity increase situated south and downstream of the climatological Pacific ST300 peak, accompanied by an activity decrease over the North Pacific. The general decrease to the north of the climatological ST300 and increase to its south implies a southward and downstream shift of ST300 activity over the North Pacific. Over North America, ST300 tends to be dominated by activity reductions along the western seaboard of North America and the western United States, accompanied by activity enhancements over most of Canada, with the action center around Hudson Bay (Fig. 8, left, shading). The anomalous pattern can be seen in OND(−1) and DJF. Yet modest differences exist, in particular, weak ST300 activity decreases over the eastern United States in OND(−1) but over eastern Canada in DJF. The T10-associated ST300 anomalies bear resemblance to the T90-related counterparts, with slight differences mainly in amplitude of the anomalies (Fig. 8, right).

Fig. 8.

Anomalies of ST300 (shading; m2 s−2) regressed upon (left) T90 and (right) T10 indices in DJF, superimposed on the ST300 climatology (contours; interval 50.0 m2 s−2; contours less than 600.0 m2 s−2 are omitted). Results in (top) OND and (bottom) DJF are shown.

Fig. 8.

Anomalies of ST300 (shading; m2 s−2) regressed upon (left) T90 and (right) T10 indices in DJF, superimposed on the ST300 climatology (contours; interval 50.0 m2 s−2; contours less than 600.0 m2 s−2 are omitted). Results in (top) OND and (bottom) DJF are shown.

The anomalous storm-track pattern is closely related to the SST and atmospheric circulation anomalies described above. The occurrence of the tropical SST warming in conjunction with the southward and downstream shift of ST300 activity over the North Pacific (cf. Fig. 8 with Fig. 7) is consistent with previous studies, which suggested that the Pacific storm track shifts equatorward and downstream during El Niño winters (e.g., Trenberth and Hurrell 1994; Straus and Shukla 1997). The occurrence of the PNA-like circulation anomaly together with the ST300 activity decrease along the west coast of North America (cf. Fig. 8 with Fig. 5) has also been found in Lau (1988) and Lin and Derome (1997), which investigated the relationship between changes in the low-frequency circulation pattern and storm-track variability.

In general, midlatitude cyclogenesis occurs because of baroclinic instability with strong meridional temperature gradients (e.g., Peixoto and Oort 1992). Anomalies of transient eddy fluxes of heat and momentum are the ultimate mechanisms generating the transients that compose storm tracks. Comparing the structure of anomalous extreme temperatures and storm-track activities (Figs. 2 and 8), it is apparent that the ST300 activity reductions along the western seaboard of North America and the western United States can be attributed to a positive meridional temperature gradient, which is opposite to the climatological mean. By contrast, the ST300 activity enhancement over the Canadian Shield is attributed to a negative meridional temperature gradient there.

On the other hand, storm-track activity may feed back on the large-scale atmospheric circulation. It is well recognized that synoptic-scale vorticity forcing is crucial in reinforcing the anomalous circulation in the upper troposphere (e.g., Lau 1988; Held et al. 1989; Trenberth and Hurrell 1994; Branstator 1995; Kug and Jin 2009). Here we examine the feedback of synoptic-scale eddies on the upper-tropospheric circulation in association with North American extreme variability. Figure 9 displays the anomalies of geopotential and synoptic eddy vorticity forcing Fυ at 300 hPa regressed upon the T90 and T10 indices. In association with the extreme indices, similar circulation structure is apparent at 300 and 500 hPa (cf. contours in Fig. 9 with Fig. 5), indicating an equivalent barotropic anomaly structure in the troposphere. At 300 hPa, the dominant cyclonic circulation forcing (Fig. 9, shading) is seen around the Aleutian low, which coincides well with the negative geopotential anomalies there (Fig. 9, contours). By contrast, anticyclonic forcings are apparent over the subtropical North Pacific and North America, especially southern Canada and the United States, which collocate with positive geopotential anomalies. Similar features are observed in OND(−1) and DJF in association with the T90 and T10 indices, with slight differences mainly in amplitude of the anomalies. Thus, the coincidence of the cyclonic (anticyclonic) vorticity forcing with negative (positive) geopotential anomalies over the PNA sector suggests that synoptic-scale eddies systematically reinforce and aid in maintaining the PNA-like circulation anomaly.

Fig. 9.

Anomalies of Φ300 (contours; interval 100.0 m2 s−2) and Fυ300 (shading; 2.0 × 10−4 m2 s−3) regressed upon the (left) T90 and (right) T10 indices in DJF. The zero line of Φ300 is highlighted in bold. Results in (top) OND and (bottom) DJF are shown.

Fig. 9.

Anomalies of Φ300 (contours; interval 100.0 m2 s−2) and Fυ300 (shading; 2.0 × 10−4 m2 s−3) regressed upon the (left) T90 and (right) T10 indices in DJF. The zero line of Φ300 is highlighted in bold. Results in (top) OND and (bottom) DJF are shown.

5. The leading extreme mode–associated circulation anomalies in CMIP5 simulations

To facilitate a quantitative comparison between CMIP5 model simulations and the observation and reanalysis-based results, we project the CMIP5 simulated temperature extreme indices onto the observed leading extreme patterns (Fig. 2) for each model. The correlations between the projected TX90p and TN90p (TX10p and TN10p) series over the 55 DJFs from 1951 to 2005 are high, exceeding 0.91 (0.95) for the 24 models. Hence, as in the above analysis, we use the mean of projected series for warm (cold) days and nights as the modeled index to represent the modeled leading warm T90 (cold T10) extreme variability for each model. The correlation coefficients between the projected T90 and T10 indices exceed 0.61, significant at the 1% level, for all models considered. We then examine the atmospheric circulation anomalies associated with the leading extreme variability, as well as the anomalies of SST and storm-track activities, in the CMIP5 simulations and compare them with the observation and reanalysis results as described above.

a. Anomalous atmospheric circulation

The Φ500 anomalies in association with the T90 and T10 indices over the 55 years from 1951 to 2005 (not shown), based on the NCEP reanalysis, are nearly identical to those obtained over the 60 years from 1951 to 2010 (Fig. 5), indicating the robustness of the anomalous circulation patterns. Figure 10 shows the multimodel mean of the Φ500 anomalies in OND(−1) and DJF regressed upon the T90 and T10 indices over the 55 years, obtained by averaging the individual model results. There is good agreement between the multimodel mean and reanalyzed Φ500 anomalies (cf. Fig. 10 with Fig. 5). The PNA-like atmospheric pattern is apparent in OND(−1) and clearly evident in DJF in the multimodel mean. The pattern correlations between the multimodel mean and NCEP are 0.70 and 0.91 for OND(−1) and DJF Φ500 anomalies in association with the T90 index, respectively, over the PNA sector (the domain shown in Fig. 10). This indicates that the multimodel ensemble mean and the reanalysis Φ500 share about 83% of the pattern variance in DJF. Nevertheless, the multimodel ensemble mean circulation anomalies are weaker over the Aleutian low region in both OND(−1) and DJF compared to the corresponding reanalysis anomalies but are comparable over North America. Similar results are obtained from the Φ500 anomalies in association with the T10 index (Fig. 10).

Fig. 10.

Multimodel means of Φ500 anomalies (contour interval 60.0 m2 s−2) regressed upon the (left) T90 and (right) T10 indices in DJF. The zero line is highlighted in bold. Results of anomalies in (top) OND and (bottom) DJF are shown.

Fig. 10.

Multimodel means of Φ500 anomalies (contour interval 60.0 m2 s−2) regressed upon the (left) T90 and (right) T10 indices in DJF. The zero line is highlighted in bold. Results of anomalies in (top) OND and (bottom) DJF are shown.

The relative agreement of individual model-based Φ500 anomaly patterns with the NCEP reanalysis result is further investigated using the BLT diagram in Fig. 11. In association with the T90 (T10) index, pattern correlations over the PNA sector for Φ500 in DJF range from 0.76 to 0.92 (from 0.73 to 0.93), except one model with a low pattern correlation of 0.53, with a mean value of 0.91 (0.92) over the 24 models (Fig. 11, bottom panels). The multimodel mean is better than most individual models in this sense. Meanwhile, most models have lower spatial variances compared to NCEP as is seen from the ratio of variances for the simulated and the reanalysis Φ500 anomalies (the green numbers and dashed circles in Fig. 11), although a few models have values slightly higher than one (i.e., 100%). This suggests that the models’ Φ500 anomaly patterns are generally flatter than the reanalysis pattern over the PNA sector. The geographical distributions of the Φ500 anomalies for the 24 models indicate that the differences among individual models are mainly seen over the Aleutian low area (not shown). In addition, the mean-square difference between model- and reanalysis-based patterns (the blue numbers and solid circles in Fig. 11) indicates that the mean model value is lower than most model values. Overall, the leading extreme mode–associated atmospheric circulation patterns in DJF are reasonably well simulated in most CMIP5 models, although most models underestimate the Φ500 anomalies over the Aleutian low region.

Fig. 11.

BLT diagrams displaying the pattern correlation, the ratio of the modeled to NCEP variance, and the relative mean-square difference between model and NCEP anomalies of Φ500 regressed upon the (left) T90 and (right) T10 indices in DJF. Results of Φ500 anomalies in (top) OND and (bottom) DJF are shown. The mean model result is also presented.

Fig. 11.

BLT diagrams displaying the pattern correlation, the ratio of the modeled to NCEP variance, and the relative mean-square difference between model and NCEP anomalies of Φ500 regressed upon the (left) T90 and (right) T10 indices in DJF. Results of Φ500 anomalies in (top) OND and (bottom) DJF are shown. The mean model result is also presented.

The pattern correlations for the Φ500 anomalies in OND(−1) are lower than those in DJF (Fig. 11). The multimodel mean correlation between the simulated and reanalyzed patterns in OND(−1) is 0.70 (0.85) in association with the T90 (T10) index, accompanied by wide spreads of pattern correlation and variance values.

b. Anomalous SST

Figure 12 displays the multimodel mean of the SST anomalies in DJF associated with the leading extreme mode, and the corresponding BLT diagram illustrating the agreement of individual model-based SST anomaly patterns with the observed result. In association with the leading extreme variability, the multimodel mean SST anomalies reveal a SST warming in the tropical central-eastern Pacific, as well as a PDO-like anomaly pattern over the Pacific basin with comparable anomalies in amplitude and opposite anomalies in sign between the tropical Pacific and the North Pacific midlatitudes (Fig. 12, top panels). The multimodel mean SST pattern bears resemblance to that seen in the observation (Fig. 7), with a pattern correlation of 0.67 (0.71) between them for the T90 (T10)-associated SST anomalies within the region (30°S–60°N, 120°E–30°W) shown in Fig. 12.

Fig. 12.

(top) Multimodel means of SST anomalies (contour interval 0.1°C) regressed upon the (left) T90 and (right) T10 indices in DJF. The zero line is highlighted in bold. (bottom) BLT diagrams illustrating the pattern correlation, the ratio of the modeled to the observed variance, and the relative mean-square difference between model and observed anomalies of SST in DJF regressed upon the (left) T90 and (right) T10 indices.

Fig. 12.

(top) Multimodel means of SST anomalies (contour interval 0.1°C) regressed upon the (left) T90 and (right) T10 indices in DJF. The zero line is highlighted in bold. (bottom) BLT diagrams illustrating the pattern correlation, the ratio of the modeled to the observed variance, and the relative mean-square difference between model and observed anomalies of SST in DJF regressed upon the (left) T90 and (right) T10 indices.

Pattern correlations between the individual models and the observations range from 0.24 to 0.73 (from 0.22 to 0.82) for the SST anomalies associated with the T90 (T10) index (Fig. 12, bottom panels). The geographical distributions of the SST anomalies for the individual models indicate that the pattern of SST warming in the tropical central-eastern Pacific and a PDO-like structure over the Pacific basin are seen in most models. However, values of the SST anomalies differ considerably in various models, especially in the midlatitude North Pacific (not shown). In addition, most models have lower spatial variances than the observations, as is seen from the ratio of variances for the simulated and observed SST anomalies. Overall, most models capture the SST warming structure in the tropical central-eastern Pacific that favors the occurrence of the PNA-like atmospheric pattern, but do not capture the spatial variance of the SST anomalies very well.

c. Anomalous storm-track activity

Figure 13 shows the NCEP and multimodel mean results of STSLP anomalies in DJF regressed upon the leading extreme modes. Here the storm track is represented by the root-mean-square of the 2–8-day filtered sea level pressure, the daily data we have for the CMIP5 models. In association with the leading extreme variability, the reanalysis-based STSLP exhibits activity decrease along the west coast of North America and the United States, accompanied by activity increase over the Canadian Shield (Fig. 13, top panels). STSLP also depicts a southward and downstream shift of the storm-track activity over the North Pacific. The STSLP anomalies over North America well correspond to the anomalous meridional temperature gradients there, as discussed above in section 4c. In addition, the STSLP anomaly pattern is broadly similar to that of ST300 (Fig. 8), with differences mainly in the southern United States and parts of the North Atlantic.

Fig. 13.

STSLP anomalies (shading; hPa) regressed upon (left) T90 and (right) T10 indices in DJF, superimposed on the STSLP climatology (contours; interval 0.5 hPa; contours less than 4.0 hPa are omitted), for (top) NCEP and (bottom) the multimodel mean.

Fig. 13.

STSLP anomalies (shading; hPa) regressed upon (left) T90 and (right) T10 indices in DJF, superimposed on the STSLP climatology (contours; interval 0.5 hPa; contours less than 4.0 hPa are omitted), for (top) NCEP and (bottom) the multimodel mean.

The multimodel mean STSLP anomalies (Fig. 13, bottom panels) generally resemble the reanalysis result although values are considerably weaker, especially in the North Pacific. There are also notable differences between the multimodel mean and the reanalysis over the North Atlantic mid–high latitudes for the T90-associated STSLP anomalies and over the Canadian Shield for the T10-associated anomalies. The pattern correlation between the multimodel mean and the reanalysis is 0.72 (0.83) over the PNA sector for the STSLP anomalies in association with the T90 (T10) index.

Figure 14 further evaluates the agreement of individual model-based STSLP anomaly patterns with the reanalysis pattern over the PNA sector. Pattern correlations show a broad range from 0.28 to 0.68 (from 0.23 to 0.76) for the STSLP patterns in association with the T90 (T10) index. The pattern correlation between the multimodel mean and the reanalysis is higher than those between the individual models and the reanalysis, suggesting that the mean model is the best model measured in this sense. The multimodel mean is also the best in terms of the mean-square difference between the model and reanalysis-based anomaly patterns, although this is not the case in measuring the ratio of variances for the model and reanalysis patterns. The smooth pattern of the multimodel mean STSLP (Fig. 13) has a lower spatial variance value than the reanalysis, as illustrated in the ratio of variances for model and reanalysis anomalies (Fig. 14). This feature is also seen for most models, although several models have values slightly higher than the reanalysis.

Fig. 14.

BLT diagrams displaying the pattern correlation, the ratio of the modeled to NCEP variance, and the relative mean-square difference between model and NCEP anomalies of STSLP in DJF regressed upon the (left) T90 and (right) T10 indices. The mean model result is also presented.

Fig. 14.

BLT diagrams displaying the pattern correlation, the ratio of the modeled to NCEP variance, and the relative mean-square difference between model and NCEP anomalies of STSLP in DJF regressed upon the (left) T90 and (right) T10 indices. The mean model result is also presented.

6. Summary and discussion

Based on the observational and NCEP reanalysis data, we study the wintertime interannual variability of North American warm and cold temperature extremes and its formation and maintenance. The principal mode of the temperature extreme variability is identified by EOF analyses of DJF mean extreme indices over North America. We analyze large-scale atmospheric circulation anomalies associated with the leading extreme variability mode, which contribute to the temperature anomalies through thermal advection. We also examine the anomalies of SST and synoptic-scale eddy activities to help understand the maintenance of the preferred atmospheric anomaly pattern. In addition, we evaluate the CMIP5 simulated anomalies of the atmospheric circulation and its maintenance associated with extreme variability, with respect to the observational and reanalysis results. The main findings from this study can be summarized as follows:

  1. The leading mode of the warm extreme TX90p and TN90p (cold extreme TX10p and TN10p) indices in winter is dominated by a large anomaly over North America, with the center of action over the Canadian Prairies (western Canada). An enhancement of the warm extreme mode tends to be accompanied by a reduction of the cold extreme mode, as well as an enhancement of the leading mode of the mean surface temperature anomalies over North America. In addition, the warm extreme mode has tended to increase and the cold extreme mode has tended to decrease over the past several decades.

  2. In association with the leading temperature extreme variability, there appears to be a pronounced PNA-like atmospheric circulation anomaly from the preceding fall to winter. The strong and persistent connection between the PNA index and the North American temperature extreme variability has important implications for seasonal prediction of North American temperature extremes. The anomalous circulation induces the exchange of mid–high-latitude air resulting in anomalous thermal advection, which contributes to the temperature anomalies over North America. The PNA-like circulation anomaly is supported by SST warming in the tropical central-eastern Pacific, as well as a positive dynamical feedback of synoptic-scale eddy activities on the large-scale circulation over the PNA sector.

  3. The leading extreme mode–associated wintertime atmospheric circulation anomalies, together with the anomalous patterns of SST and synoptic eddy activities, are reasonably well simulated in most CMIP5 models considered as well as in the multimodel mean. The PNA-like pattern in the preceding fall is also captured in the multimodel mean, but with wide spreads of pattern correlations and spatial variances over the PNA sector in the individual models. In addition, most models do not capture the spatial variance of the SST anomalies very well. The anomalous storm-track activity is generally weaker in the model simulations than the reanalysis, especially over the North Pacific. The mean model is better than most models in measuring the correlation and the mean-square difference between model- and reanalysis-based anomaly patterns.

The leading mode of the interannual warm and cold extreme anomalies over North America and its associated large-scale circulation anomalies are investigated in this study. The subsequent EOF modes (e.g., Fig. A1 in the  appendix), each accounting for less than 20% of the interannual variance, also play roles in explaining the extreme anomalies and may be related to various atmospheric teleconnections. In addition, regional-scale dynamical and thermodynamical anomalies, such as local vertical motions and adiabatic processes, would lead to surface temperature and temperature extreme anomalies directly through the variation of the surface energy balance. These are several issues remaining to be explored.

Acknowledgments

We are indebted to Dr. Xuebin Zhang for helpful discussion on the topic, Tommy Jang and Joshua Lau for assistance in data processing, Yang Feng for help with graphing, and Megan Hartwell for polishing the manuscript. We thank the anonymous reviewers for their constructive suggestions and comments, which helped to improve the study. Data used in this study are described in section 2.

APPENDIX

EOF2 and EOF3 of Temperature Extreme Anomalies

Figure A1 shows the second and third modes of combined EOF of DJF mean warm days and warm nights and cold days and cold nights.

Fig. A1.

As in Fig. 2, but for the (top) second and (bottom) third modes of combined EOF of DJF mean (left) warm days and warm nights and (right) cold days and cold nights.

Fig. A1.

As in Fig. 2, but for the (top) second and (bottom) third modes of combined EOF of DJF mean (left) warm days and warm nights and (right) cold days and cold nights.

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