1. Introduction
El Niño–Southern Oscillation (ENSO) and anthropogenic climate change trends are the most prominent known sources of predictability for the interannual variability of North American surface temperature and precipitation. ENSO, a quasi-periodic shift in tropical Pacific Ocean sea surface temperature (SST) and atmospheric circulation anomalies, affects global climate patterns through atmospheric teleconnections. In a nutshell, anomalous tropical Pacific SST drives anomalous precipitation and upper-level divergence, thus forcing atmospheric Rossby wave propagation, communicating the tropical ENSO signal to higher latitudes, and modulating extratropical temperature and precipitation variability (Horel and Wallace 1981; Ropelewski and Halpert 1986, 1987; Yang and DelSole 2012).
Most prior studies of ENSO teleconnection impacts have focused on shifts in monthly or seasonal means, especially where near-surface temperature is concerned (Halpert and Ropelewski 1992; Kiladis and Diaz 1989; Trenberth and Caron 2000; Yang and DelSole 2012; Infanti and Kirtman 2016). However, some studies have identified ENSO-induced changes in the seasonal probability distribution function (PDF) of daily temperature, including shifts and reduced intraseasonal variance in winter over much of North America during El Niño compared to La Niña (Smith and Sardeshmukh 2000). Shifts in the variability have implications for heat waves, cold snaps, and other high-impact events and can be more important than changes in the mean (Katz and Brown 1992). More incentive for understanding shifts in the variability of daily temperature is provided by earlier studies that have found specific changes in extreme indices, including in the extreme tails of the distribution (Gershunov 1998; Gershunov and Barnett 1998; Higgins et al. 2002), significant negative correlations between ENSO and warm waves in the southern tier of North America in reanalysis data (Westby et al. 2013), and the ENSO dependence of day-to-day winter temperature swings, investigated by Yang et al. (2022).
While it is sometimes sufficient to assume that ENSO teleconnection impacts are linear, with El Niño and La Niña driving temperature shifts of equal magnitude and opposite sign, several studies have noted asymmetries in the teleconnection impacts. Wolter et al. (1999) found that extreme warm winters in the Pacific Northwest were associated with El Niño, with no corresponding impact in La Niña winters. Examining El Niño and La Niña 2-m temperature composites for North America in observations and global climate model experiments, Hoerling et al. (1997, 2001) and Zhang et al. (2011, 2014) identified a zonally oriented linear component and a meridionally oriented nonlinear component, especially for stronger ENSO events. Other studies have examined the asymmetric influence of ENSO on intraseasonal temperature extremes (Arblaster and Alexander 2012; Kenyon and Hegerl 2008; Alexander et al. 2009). Lopez and Kirtman (2019) described an extratropical La Niña streamfunction response that resembles a negative Pacific–North American (PNA) pattern, i.e., with a primarily zonal orientation, and an El Niño response that is more meridionally oriented, and Wu and Hsieh (2004) found El Niño and La Niña were associated with asymmetric 200-hPa geopotential height patterns over North America. Global climate prediction models have been found to produce overly linear teleconnection responses to ENSO that differ from the asymmetric observed patterns and result in forecast errors (Kim et al. 2021; Sutton et al. 2024).
Anthropogenic climate change is a further confounding factor for understanding the variability and predictability of daily temperature. Attributable to increased carbon dioxide and emissions of other greenhouse gases, climate change is increasing seasonal and longer-term average temperatures over nearly the entire globe (Eyring et al. 2021). Along with trend-related changes in the mean, shifts in temperature variability have also been suggested, although conclusions have varied based on analysis approaches, including the use of monthly mean or otherwise aggregated data (Hansen et al. 2012). Differences in trend-related changes in extreme daily minimum and maximum temperature indices were found in Alexander et al. (2006); the authors remark that such asymmetry “hints at potential changes in the shape and/or scale of the distribution of temperature observations.” Rhines et al. (2017) examined daily temperature trends for 1979–2014 across percentiles in a quantile regression framework and found a decreasing trend in the range of the 5th–95th percentiles, that is, decreasing intraseasonal variance, across much of the contiguous United States in winter. Blackport et al. (2021) attributed such decreasing intraseasonal variance to increased anthropogenic greenhouse gas concentrations. These studies note that the impact of trends on intraseasonal variability versus that of climate variability such as ENSO is unresolved.
Drawing these threads together, here we seek to understand the effects of El Niño, La Niña, and trends on the PDF of winter daily temperature for North America in a manner that builds upon and extends previous work. A limitation of previous studies is that they have not examined trends and ENSO teleconnections in a single framework. In this study, we adopt a regression-based approach that includes both ENSO and trends and thus has the potential to disentangle trends and ENSO variability, especially in the longer period (1960–2022) examined here. Previous regression-based studies have typically used symmetric regression models (e.g., Yang and DelSole 2012). We include asymmetric ENSO responses via piecewise linear regression (Draper and Smith 1998). This approach has advantages over composite analysis which has been shown to give biased results and underestimate asymmetry (Frankignoul and Kwon 2022). Previous work using quantile regression has focused on the spatially resolved behavior of extreme quantiles (Rhines et al. 2017) or has approximated quantile changes by changes in distribution moments (e.g., mean and variance) that depend on the assumed underlying distribution (McKinnon et al. 2016). Here, we fit quantile regression coefficients to Legendre polynomials whose leading coefficients correspond exactly to changes in the median and interquartile range and do not depend on the underlying distribution. This approach also has the potential to diagnose ENSO- and trend-related changes to the distribution underlying observed changes in extreme temperatures. Together, these advances provide a more detailed and nuanced representation of the modulation of North American wintertime daily temperature by ENSO and trends.
The paper is organized as follows. Section 2 includes details about the daily 2-m temperature observations, piecewise regression, quantile regression, the Legendre polynomial approach used to summarize the regression coefficients, and statistical significance testing. Results for two regions of North America and in map format are in section 3, with a summary and discussion in section 4.
2. Data and methods
a. Observation data
Daily 2-m temperature data were obtained from the Berkeley Earth Surface Temperature (BEST) website. The BEST daily temperature data are interpolated from station data to the equal-area grid via kriging (Rohde and Hausfather 2020); we use the 1960–2022 data on their original equal-area grid (approximately 180 km × 180 km). Daily temperature anomalies are computed with respect to the daily climatology of the full period. To understand if removing the daily climatology sufficiently removed the seasonality, we examined the distributions of the quantiles (described in section 2c) and found no strong evidence of seasonality (not shown).
December–February (DJF) values of the Niño-3.4 index use the Extended Reconstructed Sea Surface Temperature, version 5 (ERSST.v5), ocean surface temperature dataset (Huang et al. 2017), obtained from the International Research Institute for Climate and Society (IRI) Data Library. ERSST.v5 is a monthly, global observation record with several quality control measures and bias corrections (Huang et al. 2017). The DJF Niño-3.4 index is the anomaly of ERSST.v5 monthly values for December–February averaged over the Niño-3.4 region of 190°–240°E, 5°S–5°N. For the purpose of this study, the 1960–2022 mean is removed to create the index (i.e., no correction for trend is applied). To support this choice, we tested whether DJF Niño-3.4, 1960–2022, has a statistically significant trend in time. First, we tested for a linear trend, finding that the 95% confidence interval for the trend coefficient by bootstrap resampling is [−0.11, 0.16] degrees Celsius per decade. Second, we tested for a quadratic trend, and the 95% confidence intervals for the two coefficients are [−0.31, 0.69] per decade (linear) and [−0.11, 0.054] per decade (quadratic). The lack of statistically significant trends is consistent with the results of L’Heureux et al. (2024), who examined linear trends in Niño-3.4 (all seasons) in three observational datasets over the period 1950–2022.
DJF 200-hPa geopotential height data from the ERA5 reanalysis were obtained from the Copernicus Climate Change Service website; monthly data were aggregated to seasonal.
b. Piecewise regression
c. Quantile regression
We use two methods for estimating quantile regression coefficients. In the first, the p quantile of each DJF season is computed (63 values, 1960–2022) and goes on the left-hand side of Eq. (3). The regression coefficients on the right-hand side are computed with OLS using DJF values of the predictors. The closed-form linear algebra expression for the OLS estimate makes for efficient calculation at many locations and quantile levels. In the second method, the quantile regression coefficients are computed by optimizing asymmetric absolute loss (AAL, also called check loss). For each quantile, optimizing AAL uses all the available daily data, which is 5686 values (number of days in DJF 1960–2022). The AAL estimate is computed iteratively and is computationally more expensive than the OLS estimate. In both methods, the quantile regression is computed for the 17 quantiles ranging from 0.1 to 0.9 by an increment of 0.05.
This study assumes a linear warming trend. Previous work using quantile regression to model the distribution of daily temperature over North America in future climate simulations used a smooth spline to model the warming signal (Haugen et al. 2018, 2019). To test the assumption of a linear trend during the observed period, we examined residuals of the median regression (q = 0.5) that uses piecewise linear Niño-3.4 and a linear trend for the two regions discussed in section 3 (not shown) and found no evidence for time dependence in the residuals. Refitting the regression model with quadratic and cubic polynomial representations of the time trend had little impact on the ENSO coefficients.
d. Legendre polynomials
Examination and analysis of regression coefficients for each of the 17 quantiles are cumbersome, especially when the analysis is performed at many locations. For quantile regression coefficients that vary smoothly with quantile level p, a curve fitting approach is an effective means of summarizing the structure of the coefficients and smoothing sampling variability. For instance, fitting the coefficients by a third-order polynomial in p replaces the 17 regression coefficients with 4 polynomial coefficients, a considerable simplification. McKinnon et al. (2016) used Legendre polynomials to represent quantile trend coefficients and found that they were nearly as efficient in compressing the coefficients as principal component analysis (PCA) while having the advantage of being data-independent.
The first four Legendre polynomials are orthogonal on the interval −1 ≤ x ≤ 1 and are 1, x,
The first four Legendre polynomials Pn(x) plotted as a function of p = (x + 1)/2.
Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0569.1
The first Legendre polynomial is a constant, and its coefficient indicates a shift of the distribution. However, the relation between higher-order Legendre polynomials and distribution moments (variance, skewness, and kurtosis) depends on the base distribution and is less straightforward (Rhines et al. 2017; Falasca et al. 2023). To avoid this issue, we describe changes in the temperature distribution using quantile-based measures instead of moments. The measures, where qp is the p quantile of the distribution, are as follows:
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Median = q1/2
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Interquartile range (IQR) = q3/4 − q1/4
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Bowley’s skewness (b-skew; Kenney 1954) =
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Moors kurtosis (m-kurtosis; Moors 1988) =
The Legendre polynomial coefficients Pn for n = 0, 1, 2, and 3 can be interpreted in terms of these four measures: P0 is a shift of the distribution by one unit and only changes the median. The coefficient P1 increases IQR by one unit and does not change the median, b-skew, or m-kurtosis. The coefficient P2 shifts the median q0.5 to the left by 0.5 units and shifts q0.25 and q0.75 to the left by 0.125, which leaves the IQR unchanged. Consequently, P2 increases b-skew by 0.75/IQR, and the m-kurtosis is unchanged. The coefficient P3 leaves the median unchanged and decreases the IQR. If b-skew was zero, it remains zero. The coefficient P3 increases the numerator of m-kurtosis by 17/32 ∼ 0.53 and reduces the denominator (IQR) by 0.875. Together, these mean that P3 tends to increase m-kurtosis. In summary, P0 and P1 increase the median and IQR of the distribution by one unit, respectively, regardless of the underlying distribution, while P2 and P3 primarily increase the b-skew and m-kurtosis, respectively, and depend on the underlying distribution.
e. Significance testing
We determine the statistical significance of regression coefficients using 1000 bootstrap samples. Block bootstrap sampling by year is used in the case of the AAL estimates to account for intraseasonal serial correlation. In the case of regression and correlation maps, we account for multiple testing using the Benjamini and Hochberg (1995) procedure (see section 13.4 of DelSole and Tippett 2022). The p values from the map are sorted from smallest to largest and compared to the sequence γ/S, 2γ/S, 3γ/S, …γ, where S is the number of land grid points (here, S = 770) and γ is the specified false discovery rate (FDR), here 10%. The null hypothesis is rejected for p values that are smaller than the comparison sequence. We report the number of map points NFDR that pass the FDR test and their maximum p value pFDR.
3. Results
We first illustrate the linear [Eq. (1)] and piecewise linear [Eq. (2)] models using the detrended median anomalies of the observed DJF daily 2-m temperature, 1960–2022, averaged over two approximately 10° × 10° latitude/longitude boxes centered at 51°N, 106°E (“north box”) and at 34°N, 100°E (“south box”) (Fig. 2 and Table 1). These two locations are chosen as illustrations based on known, different El Niño and La Niña temperature teleconnection impacts (e.g., Kiladis and Diaz 1989; Ropelewski and Halpert 1986; Grotjahn et al. 2016). To focus on the ENSO response in this illustration, we removed trends from both the predictors and the predictand. We do this because the ENSO regression coefficients computed with the detrended data match exactly those computed using a regression with a time trend [i.e., Eq. (3) or its linear equivalent]. This equivalence is a consequence of the Frisch–Waugh–Lovell theorem (see also section 9.7 in DelSole and Tippett 2022).
Niño-3.4 and median DJF temperature (blue dots) averaged over the 10° × 10° boxes centered at (a) 51°N, 106°E (north) and (b) 34°N, 100°E (south) along with linear (orange) and piecewise linear (green) fits. (c) The Map showing the location of the boxes and average DJF temperature (colors; °C).
Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0569.1
Summary of regression coefficients (statistically significant at the 5% level in bold) and significance values for Fig. 2.
First, we note that the linear association with ENSO is statistically significant for both the north and south boxes, with p values of 0.004 and 0.026, respectively. However, a significant asymmetry in both locations is revealed by the piecewise models, which separate the responses to warm and cool ENSO conditions. In the north box, the positive response to warm ENSO conditions is stronger than that suggested by the symmetric model, while the response to cool ENSO conditions is not significant. In the south box, the positive response to cool ENSO conditions is stronger than that suggested by the symmetric model, and the response of median 2-m temperature to warm ENSO is not significant. The differing responses to warm and cool ENSO conditions in the two boxes support treating the two conditions as separate predictors by using piecewise regression.
Next, we apply the quantile regression methodology to the same two boxes. The quantiles of DJF daily 2-m temperature anomalies, from 0.1 to 0.9, with an increment of 0.05 (17 quantiles total) are fit using positive Niño-3.4, negative Niño-3.4, and the trend [Eq. (3); Fig. 3]. Each vertical column of dots in the two panels shows the 17 quantiles for 1 year; blue dots indicate quantiles 0.1–0.45, while red dots indicate quantiles 0.55–0.9. Lines, following the same color scheme, indicate the OLS quantile regression fits.
Quantiles of DJF daily 2-m temperature anomalies 1960–2022 averaged over the 10° × 10° box centered at (a) 51°N, 106°E (“north box”) and (b) 34°N, 10°E (“south box”). The 17 quantiles range from 0.1 to 0.9 by 0.05, with the 0.9 quantile indicated by the darkest red dots and the 0.1 quantile by the darkest blue dots. Lines (same color scheme) indicate the OLS quantiles regression fit. The Niño-3.4 index is shown offset (not to scale) for reference.
Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0569.1
A gradual upward trend is noticeable in both north and south boxes. No trend in the range of percentile values is readily apparent in either box. Regarding the north box (Fig. 3a), when the quantiles are compared to the DJF Niño-3.4 index (gray lines in both boxes, not to scale), we find a sharp upward shift of the lowest quantiles and a more subdued downward shift of the high quantiles during warm ENSO conditions, especially noticeable in the strong El Niño winters of 1972–73, 1982–83, 1997–98, and 2015–16. These responses represent warmer conditions and a reduced spread of daily temperatures during warm ENSO conditions. There is no apparent shift of the quantiles during cool ENSO conditions.
The south box (Fig. 3b) exhibits different behavior during warm ENSO conditions, with an upward shift in the lower quantiles and a downward shift in the upper quantiles, representing a contraction of the PDF. More difficult to discern is an overall upward shift during cool ENSO conditions—this and the other qualitative features in Fig. 3 will be made precise using quantile regression coefficients and their projection onto Legendre polynomials next.
The quantile regression coefficients for the three explanatory variables and the 17 quantiles show the nearly uniform effect of the trend across the quantiles in both boxes (Figs. 4a,b, green), indicating a daily temperature distribution that is shifting to the right (warmer) with time, without a clear indication of reduced variability. There is a somewhat stronger trend-related warming in the north than the south, and the warming is slightly stronger for lower quantiles than upper in the south box. ENSO regression coefficients (Figs. 4a,b, blue and red) are mostly consistent with the median DJF temperature analysis (Fig. 2), with only the Niño-3.4 > 0 coefficients being statistically significant in the north box and only the Niño-3.4 < 0 coefficients being statistically significant in the south box. The statistically insignificant ENSO coefficients mostly have the opposite sign as their significant counterparts, further evidence of asymmetry and again consistent with the median DJF temperature analysis. Also, in both boxes, ENSO regression coefficients (Figs. 4a,b, blue and red) are larger for lower quantiles than upper. Of practical interest for computation, we note little difference between the quantile regression coefficients estimated by OLS (dots) and those estimated by AAL (squares) both in terms of their values and their statistical significance. Our preference is to proceed with the OLS estimates because of their substantially lower computational cost. We also note that Legendre polynomial fits of the coefficients serve to smooth quantile-to-quantile variations in the coefficients.
DJF 1960–2022 daily 2-m temperature from Berkeley Earth. (top) Quantile regression coefficients for the three explanatory variables (in legend) and 17 quantiles from 0.1 to 0.9 by 0.05 for (a) the north box and (b) the south box. The units of the ENSO coefficients are degrees Celsius per degree Celsius of Niño-3.4, and the units of the trend are degrees Celsius per decade. Dots indicate OLS estimates, and squares mean AAL estimates. Filled dots and squares mean statistically significant at the 5% level. Dark gray lines are third-order Legendre polynomial fits to the AAL estimates, and light gray are fits to the OLS estimates. (middle) Legendre polynomial coefficients (OLS estimates) for (c) the north box and (d) the south box; 95% confidence intervals by bootstrapping the OLS estimates; filled dots indicate statistically significantly different from zero. (bottom) Regression-fit quantile values for the distribution of daily DJF 2-m temperature anomalies for Niño-3.4 = 1.5 (warm; red), 0 (neutral; green), and −1.5 (cool; blue) for the (e) north box and (f) south box using Legendre polynomial fits to the OLS estimates, no Legendre polynomial fit to the intercept, and time = 2022.
Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0569.1
In the north region, daily temperature shifts to the right (warms) more for lower quantiles than upper quantiles during positive ENSO conditions (Fig. 4a, red), reflecting the shift to the right and spread reduction noted in Fig. 3 (left). The quantile regression coefficients in Figs. 4a and 4b for p = 0.5 match the piecewise ones in Table 1. These effects are summarized by the Legendre coefficients (Fig. 4c): P0, showing the shift, is positive for Niño-3.4 > 0, while P1, the interquartile range, is negative for the same condition. Also of note in Fig. 4c is an increase in P3 during positive ENSO conditions which may reflect the decrease in IQR and inverse dependence of m-kurtosis on IQR. Warming during negative ENSO conditions is evident for below-median quantiles (Fig. 4a, blue; negative coefficients that multiply negative Niño-3.4 index values), but bootstrapping of the OLS estimates indicates this is not statistically significant at the 5% level.
In the south region during warm ENSO conditions (Fig. 4b, red), quantiles lower than approximately 0.7 warm (positive coefficients) while the top quantiles cool (negative coefficients), reducing the spread of the PDF. This is also indicated by the negative P1 Legendre coefficient (Fig. 4d). Uniformly negative coefficients for cool ENSO (Fig. 4b, blue) illustrate a warming shift of the PDF, summarized by P0 (Fig. 4d, blue). To understand if the results could be biased by seasonality remaining in the quantiles, we added seasonality to our AAL analysis (not shown) and found very little difference in the ENSO coefficients.
A further illustration of the above-described impacts on the distribution of daily temperature is provided in Figs. 4e and 4f which shows the regression-fit values of the quantiles themselves of the distribution of daily DJF 2-m temperature anomalies for Niño-3.4 = 1.5, Niño-3.4 = −1.5, and non-ENSO conditions (Niño-3.4 = 0). The rightward shift and steeper slope of the red line reflect the warmer median and reduced IQR of daily 2-m temperature in the north box during El Niño (Fig. 4e), compared to La Niña and non-ENSO. The rightward shift of the blue line and increased slope of the red line in Fig. 4f show the warmer median during La Niña and reduced spread during El Niño, when compared to non-ENSO (Fig. 4f).
Mapping of the four Legendre coefficients for the three predictors shows the differing shifts of the temperature distributions for warm and cool ENSO conditions (Fig. 5). El Niño warms much of the northeast and interior of the continent and shifts the PDF to the left (cools) some of Mexico. We note the extent of the El Niño–related reduced IQR discussed above in both the north and south boxes, as well as a small region of reduced skewness in south-central Canada, a region that is largely missed by our two boxes. Another region that is not considered in the box analysis is Alaska, which has a strong cooling effect from La Niña but no significant shifts in the higher-order coefficients or from El Niño. The trend impact, a positive shift of the PDF, is evident over the entire continent, an unsurprising finding. The lack of any statistically significant change in IQR (i.e., Legendre coefficient P1) anywhere except possibly the northern margins of the continent, is interesting, however, and differs from the findings of earlier studies, though it is consistent with the box analyses.
Maps of quantile regression coefficients expressed in terms of Legendre polynomial coefficients and their associated distribution moments for DJF daily temperature 1960–2022. Black dots indicate regression coefficients that are statistically significantly different from zero with the FDR of 10%; NFDR passes the FDR test with a maximum p value of pFDR. In the second row, the sign of the coefficients has been reversed so that colors indicate the same impacts as the first row.
Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0569.1
To check that the Legendre polynomials are effective in representing the quantile dependence of the coefficients across the full domain, we first performed PCA of the coefficients of each predictor as in McKinnon et al. (2016). The first component is approximately a uniform shift with slightly higher values at lower quantiles (not shown) and explains substantially more variance than the subsequent components (Table 2). Since PCA optimally explains variance, the leading Legendre polynomial explains less variance than the leading EOF, though the advantage of the EOFs is modest. Differences between the variance explained by subsequent EOFs and Legendre polynomials are small, and the variance explained by the first four Legendre polynomials is nearly the same as that for the first four EOFs. Unlike EOFs, which are orthogonal both spatially and as a function of quantile, the variance explained by the Legendre polynomials does not add exactly because their spatial patterns are not orthogonal.
Explained variance for the North American domain by the EOFs of the quantile regression coefficients (top) and Legendre polynomials (bottom).
The above analysis shows that concurrent ENSO state and trend provide statistically significant information about the DJF distribution of daily temperature over North America, mostly about shifts and changes in spread. A natural question with clear implications for long-range prediction is what fraction of the variability is explained by these predictors in combination. The correlation between the regression-fitted distribution shift and the observed distribution shift is around 0.5 over most of the continent with the lowest values over Quebec (and provinces to the east) and in the west of the Cascades and Sierra Nevada ranges (Fig. 6a). Correlation between regression-fitted changes in IQR (P1) is more limited in spatial extent and corresponds mostly where warm ENSO conditions are associated with a reduction in IQR (Fig. 6b). The piecewise linear model results in somewhat higher correlations than the linear model (Figs. 6a,b vs Figs. 6c,d).
Maps of the correlation (left) between fit and observed shifts (Legendre polynomial coefficient 1) and (right) between fit and observed variance (Legendre polynomial coefficient 2). Black dots indicate statistical significance at the 10% FDR. (top) Piecewise regression. (bottom) Regular (symmetric) regression.
Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0569.1
4. Discussion
We have investigated the shifts in the PDF of daily temperature during winter (DJF) over North America, contingent on ENSO and trends, using daily observed 2-m temperature, 1960–2022. We assume a piecewise linear relationship with ENSO and treat cool and warm ENSO conditions as separate predictors. This assumption is substantial, and we examine it in detail by first examining the piecewise regression between detrended DJF median temperature and Niño-3.4 index for two regions in North America, one in south-central Canada and one in the southern Plains. Warm ENSO conditions have a significant warming effect in the north box, while cool ENSO is related to warming in the south box. The opposite phases, cool ENSO in the north and warm ENSO in the south, both show very slight warming, but these relationships are not significant. Our results generally agree with those from ENSO composite analyses of earlier studies (e.g., Hoerling et al. 1997; Zhang et al. 2014; Lopez and Kirtman 2019). Those studies suggest the origins of ENSO teleconnection asymmetry lie in the inherent asymmetry of ENSO forcing over the tropical Pacific, with different heating and upper-level divergence patterns associated with El Niño and La Niña.
Having demonstrated that a regression approach treating warm and cool ENSO as separate predictors is appropriate, we next assessed the full quantile regression with both ENSO conditions and the trend. Four quantile-based measures are used: the median, the IQR, skew, and kurtosis. We found rightward shifts in the median in the north box during warm ENSO and the south box during cool ENSO (expected based on the above analysis) and a rightward shift in the median from the trend in both locations. Warm ENSO is associated with a contraction of the IQR in both north and south, while no significant impact was found for cool ENSO. Also, our results show the greatest upward shift in the lowest (coldest) percentiles, with a more moderate impact on high percentiles. This effect was noted in Gershunov (1998) and Gershunov and Barnett (1998), with implications for predictability discussed therein.
When we extended this analysis to the continental scale, using Legendre polynomials to reduce the large number of coefficients to a manageable 4 × 3, the three predictors were found to have the strongest relationship to shifts in the median. Only warm ENSO conditions were found to cause significant changes in the IQR, showing a contraction (reduced variability) across much of North America. Smith and Sardeshmukh (2000), comparing El Niño and La Niña composites of intraseasonal variance of winter daily temperature over 1959–98, found a similar result of reduced variance in El Niño winters, with more upward shift in the lower percentile.
We did not find a widespread statistically significant contraction of the IQR due to the trend, a different outcome from Blackport et al. (2021). Rhines et al. (2017) found spatially widespread contraction in the distribution of daily minimum and maximum temperatures (their Figs. 3e,f) but without indication of their statistical significance. Some possible reasons for the difference are the longer period used here, differing measures of spread, spatial resolution, and not accounting for ENSO-forced variability. These latter papers, along with Schneider et al. (2015), suggest that reduced IQR can be attributed to a weaker meridional temperature gradient (i.e., Arctic amplification) leading to weaker cold advection. While we did not find this trend-related decreased variance, the contraction in IQR that we observed during warm ENSO conditions could be similarly linked to El Niño–related warming in the north and decreased meridional temperature gradient. Another related possibility is that, in the absence of strong ENSO forcing, the role of subseasonal variability is increased.
Uncovering the mechanics of these noted shifts in the PDF is largely out of the scope of the current study, but we explore the asymmetries in the shift of mean DJF 200-hPa geopotential height (z200), 1960–2022, from ERA5 (Hersbach et al. 2020) in Fig. 7, via the same method as 2-m temperature [Eq. (3)]. We note asymmetries for cool and warm ENSO conditions, with warm ENSO leading to the strongest shift in z200 (Fig. 7d), similar to that in 2-m temperature, and a general correspondence between the location of ridges and troughs and areas of warming and cooling, respectively. Finally, we note that it is likely that the ENSO- and trend-dependent behavior of daily minimum and maximum 2-m temperature would differ from the patterns found in daily mean temperature (e.g., Becker 2023) and is another potential research avenue.
(a)–(c) Maps of quantile regression coefficient P0, representing the shift in the median, for DJF 1960–2022 2-m temperature (as in Fig. 4, repeated for reference). Red indicates warmer shift and blue indicates cooler. (d)–(f) Quantile regression coefficient P0 for DJF 1960–2022 200-hPa geopotential height (z200) from ERA5. Red indicates higher heights and blue indicates lower. Black dots indicate regression coefficients that are statistically significantly different from zero with the FDR of 10%. The sign of regression coefficients in (b) and (e), for Niño-3.4 < 0, has been reversed for consistent coloring.
Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0569.1
Acknowledgments.
We are grateful to our three anonymous reviewers, whose careful comments improved our manuscripts. Emily Becker was partially supported by NSF Award 2223262.
Data availability statement.
We obtained the data used in this analysis from the following locations, which all are freely available: the Berkeley Earth Surface Temperature daily 2-m temperature: https://berkeleyearth.org/data/; ERSST.v5 sea surface temperature: https://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCEI/.ERSST/.version5/; and ERA5 200 hPa-geopotential height: https://www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-v5. Python codes used in this study are available upon request from the authors.
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