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  • View in gallery

    PDF distributions for (a) Charlotte and (b) Fort Lauderdale of winter daily Tmax (a1, a2, b1, b2) and Tmin (a3, a4, b3, b4) separated by ENSO phase (a1, a3, b1, b3) and AO phase (a2, a4, b2, b4). Solid black lines correspond to the warm regimes (either La Niña or AO+) and solid gray lines correspond to the cold regimes (either El Niño or AO−). Dashed lines indicate the respective expected value.

  • View in gallery

    Statistical moments of (a) Tmax and (b) Tmin during neutral years. Mean, standard deviation, skewness, and excess kurtosis in subpanels 1–4, respectively. Horizontal color bar applies to the skewness and excess kurtosis (subpanels 3,4).

  • View in gallery

    Relationship between the Tmin and Tmax (top) standard deviation, (middle) skewness, and (bottom) kurtosis for the neutral state defined based on (left) ENSO and (right) AO. Stations in Florida are represented by red circles.

  • View in gallery

    Difference between the means, standard deviations, skewnesses, and kurtoses (subpanels 1–4, respectively) of (a) Tmax of La Niña, (b) Tmax of El Niño, (c) Tmin of La Niña, and (d) Tmin of El Niño vs neutral years. Small color bars apply to the mean (subpanel 1); the large color bar applies to the standard deviation, skewness, and excess kurtosis (subpanels 2–4).

  • View in gallery

    As in Fig. 4 but for (a) AO+, (b) AO−, (c) AO+, and (d) AO− vs neutral years.

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Quantifying the Non-Gaussianity of Wintertime Daily Maximum and Minimum Temperatures in the Southeast

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  • 1 Center for Ocean–Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida
  • | 2 Center for Ocean–Atmospheric Prediction Studies, and Department of Earth, Ocean and Atmosphere Science, The Florida State University, Tallahassee, Florida
  • | 3 Center for Ocean–Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida
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Abstract

In this paper the statistics of daily maximum and minimum surface air temperature at weather stations in the southeast United States are examined as a function of the El Niño–Southern Oscillation (ENSO) and Arctic Oscillation (AO) phase. A limited number of studies address how the ENSO and/or AO affect U.S. daily—as opposed to monthly or seasonal—temperature averages. The details of the effect of the ENSO or AO on the higher-order statistics for wintertime daily minimum and maximum temperatures have not been clearly documented.

Quality-controlled daily observations collected from 1960 to 2009 from 272 National Weather Service Cooperative Observing Network stations throughout Florida, Georgia, Alabama, and South and North Carolina are used to calculate the first four statistical moments of minimum and maximum daily temperature distributions. It is found that, over the U.S. Southeast, winter minimum temperatures have higher variability than maximum temperatures and La Niña winters have greater variability of both minimum and maximum temperatures. With the exception of the Florida peninsula, minimum temperatures are positively skewed, while maximum temperatures are negatively skewed. Stations in peninsular Florida exhibit negative skewness for both maximum and minimum temperatures. During the relatively warmer winters associated with either a La Niña or AO+, negative skewnesses are exacerbated and positive skewnesses are reduced. To a lesser extent, the converse is true of the El Niño and AO−. The ENSO and AO are also shown to have a statistically significant effect on the change in kurtosis of daily maximum and minimum temperatures throughout the domain.

Corresponding author address: Lydia Stefanova, Center for Ocean–Atmospheric Prediction Studies, The Florida State University, 2035 E. Paul Dirac Dr., Tallahassee, FL 32306. E-mail: lstefanova@fsu.edu

Abstract

In this paper the statistics of daily maximum and minimum surface air temperature at weather stations in the southeast United States are examined as a function of the El Niño–Southern Oscillation (ENSO) and Arctic Oscillation (AO) phase. A limited number of studies address how the ENSO and/or AO affect U.S. daily—as opposed to monthly or seasonal—temperature averages. The details of the effect of the ENSO or AO on the higher-order statistics for wintertime daily minimum and maximum temperatures have not been clearly documented.

Quality-controlled daily observations collected from 1960 to 2009 from 272 National Weather Service Cooperative Observing Network stations throughout Florida, Georgia, Alabama, and South and North Carolina are used to calculate the first four statistical moments of minimum and maximum daily temperature distributions. It is found that, over the U.S. Southeast, winter minimum temperatures have higher variability than maximum temperatures and La Niña winters have greater variability of both minimum and maximum temperatures. With the exception of the Florida peninsula, minimum temperatures are positively skewed, while maximum temperatures are negatively skewed. Stations in peninsular Florida exhibit negative skewness for both maximum and minimum temperatures. During the relatively warmer winters associated with either a La Niña or AO+, negative skewnesses are exacerbated and positive skewnesses are reduced. To a lesser extent, the converse is true of the El Niño and AO−. The ENSO and AO are also shown to have a statistically significant effect on the change in kurtosis of daily maximum and minimum temperatures throughout the domain.

Corresponding author address: Lydia Stefanova, Center for Ocean–Atmospheric Prediction Studies, The Florida State University, 2035 E. Paul Dirac Dr., Tallahassee, FL 32306. E-mail: lstefanova@fsu.edu

1. Introduction

Understanding the statistical distribution of daily winter temperature extremes is of practical interest to the human endeavors in ecology, agriculture, and utilities planning. This is particularly true for regions such as the U.S. Southeast where winter hard freezes are a relatively rare and potentially catastrophic occurrence. The winter climate of the Southeast is strongly influenced by the phase of ENSO. During El Niño phase winters, the 300-hPa wind anomalies show an increased southwesterly flow over the Gulf of Mexico (Kennedy et al. 2007) as the tropical/Pacific jet splits over North America, leading to an increased frequency of winter gulf cyclones (Eichler and Higgins 2006). In the Southeast these contribute increased cloudiness (Angell and Korshover 1987; Angell 1990; Park and Leovy 2004) and frequent rains (Gershunov and Barnett 1998) over the region; as a result, the typical El Niño winter weather is wet and cool (Ropelewski and Halpert 1986, 1987; Kiladis and Diaz 1989). During the La Niña phase, the tropical/Pacific jet stream becomes a single zonal jet that is typically shifted northward (Smith et al. 1998). The storm tracks associated with midlatitude cyclones tend to stay north of the U.S. Southeast (Eichler and Higgins 2006), limiting the amount of cold air that reaches the region; as a result, La Niña years are generally warmer and drier in the Southeast (Ropelewski and Halpert 1986, 1987; Kiladis and Diaz 1989). However, variability in the polar jet stream position can result in extreme cold outbreaks with either ENSO phase. In addition to the ENSO phase, winter temperatures in the Southeast are strongly influenced by the Arctic Oscillation (AO)/North Atlantic Oscillation (NAO) and to some extent Pacific–North America (PNA) teleconnections (Higgins et al. 2002; Hagemeyer 2006).

While seasonal averages can be used as a helpful guideline for climate application models, intraseasonal extremes are often a more important factor for practical consequences—a single deep freeze event in south Florida can wreck havoc on the local agriculture (Attaway 1997). Certain agricultural crops, such as citrus and vegetables, grown in portions of the U.S. Southeast during winter and early spring are highly susceptible to damage from freezing temperatures. A series of impact freezes in the 1980s, following a serious freeze in 1977, left the citrus industry in Florida reeling. Approximately one-third of the state’s commercial citrus trees were destroyed and the total monetary loss was in billions of dollars (Miller 1991). Freezing temperatures also have an impact on wildlife, such as the Florida manatee. Mortality rates for manatees tend to have a strong seasonal emphasis in winter. Manatees can die from hypothermia during unusually cold winters, as they are unable to increase heat production by metabolism to counter losses to the environment (O’Shea et al. 1985).

To understand the seasonal-scale risk of experiencing extreme cold/warm winter days, it is important to understand the changes in distributions of daily minimum/maximum temperatures under different large-scale regimes. Do these distributions simply shift to the left or right with ENSO or AO phase change? Atmospheric variable statistics are not strictly Gaussian (e.g., Sura et al. 2005), and daily minimum and maximum temperatures are no exception. A shift in their expected value (warmer during La Niña, colder during El Niño) does not guarantee a corresponding shift for the entire distribution. The current literature is ambiguous about the temperature extremes associated with ENSO phase. Some sources suggest that extreme cold events are more likely with El Niño (which is associated with below-normal winter temperatures) (e.g., Gershunov 1998; Higgins et al. 2002) or that extreme warm events are more likely with La Niña (e.g., Wolter et al. 1999). Others (e.g., Rogers and Rohli 1991; Hansen et al. 1999; Smith and Sardeshmukh 2000) suggest that severe cold outbreaks may be more likely with La Niña.

Normal (Gaussian) distributions are fully described by their mean and standard deviation. For non-Gaussian distributions, higher moments need to be considered as well. The first four moments (mean, standard deviation, skewness, and kurtosis) are generally sufficient to describe most atmospheric variable distributions. Several studies have documented the non-Gaussian nature of surface air temperatures (Toth and Szentimrey 1990; Barnston 1993; Huth et al. 2001; Ryoo et al. 2004; Shen et al. 2011). A handful of studies (Smith and Sardeshmukh 2000; Higgins et al. 2002) have considered the higher (>1) statistical moments of surface temperatures in the United States under different ENSO and AO/NAO conditions. Both studies use gridded data—from the National Centers for Environmental Prediction (NCEP) 2.5° reanalysis (Kalnay et al. 1996) in the case of Smith and Sardeshmukh (2000) and 0.5° Cooperative Observation Program (COOP) station–based gridded dataset (Janoviak et al. 1999) in the case of Higgins et al. (2002)—and examined the response of daily mean surface temperatures to different large-scale climate regime forcing.

While the analysis of gridded data provides useful insights, gridding tends to reduce the variance of observed temperatures (Tencer et al. 2011) and is generally associated with the introduction of biases in their means, especially in winter (De Gaetano and Belcher 2007) and for maximum temperatures (De Gaetano and Belcher 2007; Tencer et al. 2011). The errors introduced by gridding are highly region- and method-dependent (e.g., Shen et al. 2005; DeGaetano and Belcher 2007; Rupp et al. 2010; Tencer et al. 2011; Berrocal et al. 2012) and are a function of station density (Legg 2011). By its implicit smoothing, gridding filters out potentially valuable spatial detail at the local and regional scale that can be gleaned from analysis of ungridded station data, especially near terrain features (Tencer et al. 2011; Legg 2011) and coastal boundaries (De Gaetano and Belcher 2007). In addition, averaging of daily minimum and maximum surface temperatures to obtain the daily average obscures the fact that the daily minimum and maximum surface temperatures often have dissimilar probability distribution function (PDF) shapes (Barnston 1993; Shen et al. 2011) and disparate responses to the large-scale climate regimes. To illustrate this point, we constructed PDFs of daily minimum (Tmin) and maximum surface temperatures (Tmax) for two stations in the Southeast—Charlotte, North Carolina (Fig. 1A), and Fort Lauderdale, Florida (Fig. 1B), under El Niño/La Niña and AO+/AO regimes (see Table 1 and section 2b for the regime definitions). Such separation of Tmin and Tmax makes it possible to appreciate, for example, that the warming of the expected values of the daily means associated with El Niño relative to La Niña is largely attributable to changes in the PDF of Tmax but not Tmin for Charlotte, and to both Tmin and Tmax for Fort Lauderdale. The warming associated with AO+, on the other hand, stems mostly from changes in the Tmin distribution for Fort Lauderdale, but is evenly contributed by Tmin and Tmax for Charlotte. In addition to these shifts of the expected values, distinct deformations of the PDFs are evident as well.

Fig. 1.
Fig. 1.

PDF distributions for (a) Charlotte and (b) Fort Lauderdale of winter daily Tmax (a1, a2, b1, b2) and Tmin (a3, a4, b3, b4) separated by ENSO phase (a1, a3, b1, b3) and AO phase (a2, a4, b2, b4). Solid black lines correspond to the warm regimes (either La Niña or AO+) and solid gray lines correspond to the cold regimes (either El Niño or AO−). Dashed lines indicate the respective expected value.

Citation: Journal of Climate 26, 3; 10.1175/JCLI-D-12-00161.1

Table 1.

Summary of the ENSO and AO phase in January–February for the years 1960–2009. The number within parentheses indicate a year’s rank among the 10 years with the warmest (superscript) and coldest (subscript) January–February.

Table 1.

While it is possible to produce a catalog of all station distributions in different phases of these large-scale oscillations, this approach is impractical for two reasons: the need for a very large number of plots—one for each temperature variable at each station in every climate regime—and the lack of depiction of large-scale patterns of variability across stations. Instead, in this study we summarize the PDFs and describe their geographical variability based on the distribution’s first four statistical moments. We examine station daily minimum (Tmin) and maximum (Tmax) temperatures, as well as the daily average (Tave) and diurnal range (Trange) during different ENSO and AO phases. The data and methodology used for this study are described in section 2. Results and a discussion are presented in section 3, and section 4 provides a summary and concluding remarks.

2. Data and methodology

a. Station temperature data

We use quality controlled digital data from the Summary of the Day dataset (DS3200 and DS3206) supplied by the National Climatic Data Center (NCDC). The daily measurements of maximum and minimum temperature are provided by the National Weather Service’s Cooperative Observation Program (COOP), which has reported these elements for over 100 years. Each dataset contains over 8000 active observing stations, though for the purpose of this study, stations were used from the states of Alabama, Florida, Georgia, North Carolina, and South Carolina.

The observing record at each station from the five selected states is at least from 1960 to 2009, although some stations have data as far back as the early 1900s. For the purposes of this study, we selected only stations reporting since at least 1960. Stations that have more than five consecutive years of missing data were discarded so that each station left met the criteria to use the multiple linear regression technique set forth by Smith (2007) to replace any missing temperature data at the station. In case of missing data for a given station, correlations between the existing time series at this reference station and surrounding stations within a 50-mile radius are computed and stations with correlations greater than 0.6 are retained for use in reconstructing the reference station missing data. The choice of the 0.6 correlation cutoff was made by Smith (2007) as a compromise between the need for high interstation correlation and the need for a sufficient number of surrounding stations to be used in the linear regression procedure. Once the useable surrounding stations have been identified, all data is detrended and the seasonal cycle removed before computing the multiple linear regressions to determine a residual value, which is used to replace the missing value at the reference station, and the trend and seasonal cycle are then reapplied. For the present study, we use the January and February Tmin and Tmax between 1960 and 2009 at all 272 stations in Florida, Georgia, Alabama, North Carolina, and South Carolina that satisfy the criteria above. Note that any potential concerns regarding the effects of station moves, instrumental changes, or land-use changes during the study period are alleviated by the high degree of spatial coherence of our results.

b. Climate regime definitions

The ENSO phase (ENSO neutral, El Niño, or La Niña) is defined based on the Multivariate ENSO Index (MEI) of Wolter and Timlin (1993; http://www.esrl.noaa.gov/psd/enso/mei/mei.html). The January–February MEI averages for each year between 1960 and 2009 were calculated, and the 10 years with the largest positive values were designated as El Niño years; similarly, the 10 years with the largest negative values were designated as La Niña years. The AO phase (AO neutral, AO+, or AO−) is defined based on the Arctic Oscillation index (http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/ao.shtml), and a similar ranking of years was performed to determine the 10 years with the highest positive January–February average AO value and the 10 years with the strongest negative AO values. The ENSO and AO phases for January–February of the years between 1960 and 2009 are summarized in Table 1.

c. Methodology

We opted for selecting exactly 10 yr in each regime (El Niño, La Niña, AO+, and AO−) so as to ensure a sufficient amount of data points in each regime. Most years designated as nonneutral exceed ±1 standard deviation of the relevant index; all of them exceed ±0.85 standard deviations. Owing to the relatively short data record, we are unable to treat the effects of ENSO and AO separately. Undoubtedly, as evident from Table 1, there is a certain degree of overlap between ENSO and AO years. We acknowledge that separate consideration of each regime combination listed in Table 1 would be ideal, had the data record been sufficiently long to populate each cell with a large number of years. However, given this data record limitation, we argue that considering ENSO and AO as independent forcings is justified based on the low correlation between the time series of the two indices (Higgins et al. 2002) and the consequential fact that both El Niño and La Niña years contain a similar number of AO+ (three versus four) or AO− (two versus one) years.

We analyze the first four statistical moments—mean, variance, skewness, and kurtosis—of the wintertime daily air surface temperature variables (maximum, minimum, average, and range) for stations in the U.S. Southeast under different large-scale climate regimes. As a first step, the seasonal cycle is removed from the dataset; that is, climatological values for each date are calculated and subtracted from each data point. Further work is shown in terms of the resulting anomalies.

The statistical moments are defined as follows. The mean of a station variable x is calculated as
eq1
Here R is a given regime (ENSO neutral, El Niño, La Niña, AO neutral, AO+, or AO−), is the number of years in the dataset that fall within the selected regime R, and n is the number of days between 1 January and 28 February (i.e., 58). The corresponding standard deviation is given by
eq2
Variance, the second statistical moment, is defined as the square of the standard deviation. In the remainder of the text, for simplicity, we discuss the standard deviation instead of the variance.
Skewness is a measure of the asymmetry of the distribution. It is defined as
eq3
For a Gaussian variable, is zero. Negative (positive) describes a distribution for which the left (right) tail is longer than the right (left) and whose mean value is smaller (larger) than its median value.
Kurtosis is a measure of the sharpness of the distribution. It is defined as
eq4
For a Gaussian variable is 3. Excess kurtosis is defined as . Negative (positive) excess kurtosis describes a distribution that is flatter (sharper) than the normal distribution and whose tails are lighter (heavier).

d. Error and significance estimation

To correctly quantify the non-Gaussianity of temperature data we also need to specify the statistical errors we expect in our skewness and kurtosis estimates. The exact standard errors [remember that approximately 68%/95%/99% of close-to-Gaussian data can be found between ±1/2/3 standard errors (SE)] of skewness and kurtosis depend on their underlying distribution but can be approximated for weakly non-Gaussian data as and , respectively, where is the effective number of independent observations (e.g., Brooks and Carruthers 1953). It has been shown (e.g., Perron and Sura 2013) that the formulas for and are good approximations even for strongly non-Gaussian data. The standard error estimates for the mean and standard deviation can be related to the standard deviation magnitude using the expressions and .

As we are mainly interested in the non-Gaussian statistics of the temperature data, let us estimate the expected standard errors for skewness and kurtosis. For the present observational analysis we used 50 years of data (1960–2009). Therefore, the entire wintertime (January–February) record consists of, neglecting 29 February of leap years, 50 × 59 = 2950 days. As our climate regime definition uses the 10 yr with the highest/lowest ENSO and AO indices, we have 590 days in each distinct ENSO and AO climate state. Of course, the neutral states contain the remaining 30 years with 1770 days. If we now make the realistic assumption that surface air temperature has a decorrelation time scale of about 3 days all over the southeastern United States (Barnston 1993), we can estimate the number of independent observations in the ENSO and AO climate regimes as (the total number of days in each regime, 590, divided by the decorrelation time scale of 3 days). In the neutral state there are (the total number of days in the neutral condition, 1770, divided by the decorrelation time scale) independent records. Thus, the standard errors of skewness and kurtosis in each climate regime are and , respectively. The standard errors in the neutral phases, due to the larger number of independent observations, are somewhat smaller, namely, and . As we are also interested in the skewness and kurtosis differences between ENSO/AO regimes and neutral phases, we use the Gauss propagation of uncertainty law to estimate the standard errors of the differences:

In light of the following presentation and discussion of skewness and kurtosis maps, the error estimates mean that most of the non-Gaussian skewness structures presented in this paper (regimes and regime differences) are significant at the 95% level because the amplitudes of almost all large-scale skewness features fall outside the ±2 SE range. Most of the kurtosis patterns are also significant at the 95% level, yet there are situations (i.e., variables and regions) where the significance level goes down to 68% (±1 SE). Therefore, overall we can be confident that the results shown here are not statistical artifacts but represent tangible physical phenomena.

3. Results and discussion

a. Neutral years

In neutral years (for brevity, in this section, these are defined with respect to ENSO; results for neutral years defined with respect to AO are nearly identical), the expected values of the distributions of the anomalies of Tmax and Tmin (Figs. 2a1,b1) and Trange and Tave (not shown) are all close to zero, indicating that it is unlikely that ENSO-neutral years are biased by the presence of an AO signal, despite the relatively larger number of AO− years in the ENSO-neutral regime (see Table 1). Temperature standard deviations (Figs. 2a2,b2) generally decrease southward and are smallest in the Florida peninsula (hereafter FP), with the exception of Tmin, whose standard deviation increases westward and is relatively uniform in the north–south direction, although it is somewhat smaller in the southernmost parts of the FP. The geographic distribution of skewness varies among the different temperature variables. Maximum temperatures have a left (negative) skewness that increases southward, reaching the largest negative values in the FP (Fig. 2a3). In contrast, minimum temperatures are positively skewed in the non-FP (NFP) part of the domain and negatively skewed in FP (Fig. 2b3). The diurnal temperature range is weakly negatively skewed outside of FP and weakly positively skewed in the FP (not shown). The daily mean temperature has negligible skewness with the exception of the FP where it has pronounced negative skewness (not shown). The geographic distribution of excess kurtosis also varies among the four temperature variables. For Tmax (Fig. 2a4) and Trange (not shown) the excess kurtosis is increasingly negative to the north outside of the FP but with some positive values in the southern portion of the FP. The excess kurtosis of Tmin (Fig. 2b4) and Tave (not shown) is negative, with the largest values found in the Big Bend region of Florida.

Fig. 2.
Fig. 2.

Statistical moments of (a) Tmax and (b) Tmin during neutral years. Mean, standard deviation, skewness, and excess kurtosis in subpanels 1–4, respectively. Horizontal color bar applies to the skewness and excess kurtosis (subpanels 3,4).

Citation: Journal of Climate 26, 3; 10.1175/JCLI-D-12-00161.1

The physical mechanisms responsible for the climatological structure of temperature first four statistical moments are quite complex and mostly beyond the scope of this study. Relevant considerations should include the climatological frequency of cloud-free skies, which increases southward (Winsberg 2003), the much stronger impact of sea surface temperature in the FP (ibid.), and the climatological frequency and intensity of cold and warm fronts throughout the region. Cold frontal passage frequency generally decreases southward to the FP (hence the larger temperature variances to the north); however, since fronts decelerate in their penetration southward and frequently become stationary (Hardy and Henderson 2003), the duration of frontal-passage-related weather increases southward (DiMego et al. 1976). It takes a very strong—and thus infrequent—arctic front to penetrate all the way to the FP, bringing very low humidities and extremely cold temperatures (Winsberg 2003) to the area (hence the increasingly negative skewness to the south). The diurnal temperature range is positively correlated with the frequency of cloudiness, precipitation, and humidity (Karl et al. 1987; Leathers et al. 1998); consequently, the largest diurnal temperature ranges are found in the FP (Leathers et al. 1998).

Scatter diagrams (Fig. 3) provide a summary of the differences in distribution shapes of Tmin and Tmax under neutral conditions. Whether the latter are defined on the basis of ENSO or AO makes little difference (cf. the left and right columns of Fig. 3), which illustrates the relative robustness of the results. With the exception of Florida stations (red circles), the standard deviations of minimum and maximum temperatures are of comparable magnitudes, skewnesses are of comparable (and small, <0.5) magnitudes but of opposing sign (negative for Tmax, positive for Tmin), and the kurtoses are generally smaller for Tmax. For the Florida stations, on the other hand, the standard deviation of Tmin is larger than that of Tmax, both Tmin and Tmax are negatively skewed with the left (negative) skewness of Tmin stronger than that of Tmax, and the kurtosis of Tmax is larger than that of Tmin.

Fig. 3.
Fig. 3.

Relationship between the Tmin and Tmax (top) standard deviation, (middle) skewness, and (bottom) kurtosis for the neutral state defined based on (left) ENSO and (right) AO. Stations in Florida are represented by red circles.

Citation: Journal of Climate 26, 3; 10.1175/JCLI-D-12-00161.1

b. ENSO phase

We find that the ENSO phase has different effects on the expected values of Tmax versus Tmin (Figs. 4a1,b1 versus 4c1,d1): both are warmer (relative to the neutral ENSO phase values) in La Niña winters, while El Niño cools Tmax but has a mixed effect on Tmin (generally cooling in FP and warming elsewhere). A likely explanation for this is that during El Niño winters there is an increased number of gulf storms (Eichler and Higgins 2006). The air masses associated with such storms are not particularly cold, but the increase in cloudiness (Angell 1990; Park and Leovy 2004) restricts daytime surface warming; this same cloudiness, however, restricts the nighttime radiative cooling. As a result of the shifts in the distributions of Tmin and Tmax, the diurnal temperature range increases (relative to the neutral ENSO phase values) in La Niña years and decreases in El Niño years, consistent with the relationship of diurnal temperature range and precipitation and cloudiness discussed by Karl et al. (1987) and Leathers et al. (1998). The absolute values of the temperature range change associated with La Niña are smaller than those associated with El Niño. The daily mean temperatures are increased in La Niña winters and decreased in El Niño winters, with the effect’s magnitude being somewhat weaker in the latter.

Fig. 4.
Fig. 4.

Difference between the means, standard deviations, skewnesses, and kurtoses (subpanels 1–4, respectively) of (a) Tmax of La Niña, (b) Tmax of El Niño, (c) Tmin of La Niña, and (d) Tmin of El Niño vs neutral years. Small color bars apply to the mean (subpanel 1); the large color bar applies to the standard deviation, skewness, and excess kurtosis (subpanels 2–4).

Citation: Journal of Climate 26, 3; 10.1175/JCLI-D-12-00161.1

The standard deviation of Tmax and Tmin (Figs. 4a2,b2,c2,d2) and Tave (not shown) is increased in La Niña years and reduced in El Niño years for the northern portions of the domain with the amplitude of the response being stronger during El Niño. Interestingly, both El Niño and La Niña years see a reduction of standard deviation for these variables over the FP. The diurnal temperature range standard deviation is not affected by the ENSO phase in any systematic way.

The magnitude of negative skewness for Tmax is reduced in FP in El Niño years and increased in much of the domain in La Niña years (Figs. 4a3,b3). For Tmin (Figs. 4c3,d3) the results are similar, except that the La Niña effect is more confined to the FP. This is also reflected in the daily averages. The skewness of the diurnal temperature range does not respond to the ENSO phase in any systematic way (not shown).

The north–south gradient of the kurtosis of Tmax in neutral years is exacerbated in La Niña years and reduced in El Niño years (Figs. 4a4,b4). The distribution of Tmin is sharpened in the northern parts of the domain (to the point of becoming sharper than Gaussian) during El Niño years (Figs. 4c4,d4). The Tmin kurtosis is also increased in the FP during La Niña years and decreased in El Niño years. The kurtosis of Trange is generally reduced in El Niño years and is not systematically affected in La Niña years (not shown). In La Niña years, the behavior of Tave kurtosis is similar to that of Tmin, while in El Niño years it is similar to that of Tmax. In terms of absolute values, El Niño affects the kurtoses of Tmin and Tave more than La Niña does.

c. AO phase

The expected values of Tmax, Tmin (Figs. 5a1,b1,c1,d1), Trange, and Tave (not shown) are increased in AO+ and decreased in AO−, the latter with the exception of Trange, which does not have a uniform response to AO−. The standard deviations of Tmax, Tmin (Figs. 5b2,c2), and Tave are decreased in AO+ and increased in AO− (with the exception of the FP where the standard deviation of Tmin is decreased in both cases). The standard deviation of Trange does not have a uniform response to the AO phase. The skewness anomaly of Tmax (Figs. 5a3,b3) and Tave is negative during AO+ and positive during AO−; for Tmin (Figs. 5c3,d3) and Trange, the effect of AO phase on skewness is minimal. The Tmax kurtosis (Fig. 5a4) is increased in much of the domain and especially in Florida during AO+. During AO− (Fig. 5b4), stations farther north exhibit increased kurtosis, while those in the FP have flattened distributions. The sharpening of distributions outside Florida and flattening in the FP during AO−, as well as the sharpening of distributions in the FP, are also seen in Tmin (Figs. 5c4, d4), Trange, and Tave.

Fig. 5.
Fig. 5.

As in Fig. 4 but for (a) AO+, (b) AO−, (c) AO+, and (d) AO− vs neutral years.

Citation: Journal of Climate 26, 3; 10.1175/JCLI-D-12-00161.1

d. Discussion

The warmest winters on record are frequently—but not always—associated with either a positive AO phase or with La Niña [see the years superscripts in Table 1, indicating the ranking of the 10 warmest and coldest January–February years between 1960 and 2009 for the U.S. Southeast, based on data from the NCDC (http://www7.ncdc.noaa.gov/CDO/cdo)]. Similarly, the coldest years are frequently—but not always—associated with a negative AO phase or with El Niño (subscripts in Table 1). Still, 40% of the extreme warm/cold years occur during years that are neutral with respect to both AO and ENSO.

Our results indicate that the ENSO effect on average temperatures is primarily manifested through shifts in the expected values of the daily temperature maxima. The spatial distribution of the expected value shifts is strongly reminiscent of the precipitation anomaly distribution associated with La Niña/El Niño phases, suggesting that the driving mechanism behind the Tmax response is the corresponding decrease/increase of cloudiness that suppresses/promotes daytime radiative warming of the surface temperatures. Daily minimum temperatures are affected to a lesser degree, suggesting that the El Niño–related increase in cloudiness promotes the suppression of nighttime radiational cooling that partially compensates for the cooling of daytime temperatures. In contrast, the AO effect on average temperatures is manifested through evenly matched shifts in both minimum and maximum temperatures. This can be explained by the fact that changes in the AO phase, unlike changes in the ENSO phase, are directly related to the frequency of high-latitude frontal systems penetrating into the Southeast. The surface temperature changes brought about by such systems are associated with the advection into the area of very cold air instead of with cloudiness-dominated radiative effects. It should be noted, however, that, despite the much stronger AO (compared to ENSO) signal in the surface temperatures in the Southeast, it is of lesser practical consequence because the predictability of AO, unlike that of ENSO, is limited.

In addition to shifts in the expected values of the daily minimum and maximum surface temperatures, our study demonstrates that there are statistically significant large-scale changes in the higher moments of the temperature distributions that may affect the likelihood of experiencing extreme cold outbreaks. For example, in southern Alabama and the FP, La Niña winters (which are, on average, warmer than neutral) manifest increased standard deviation, increased negative skewness, and increased kurtosis of daily maximum temperatures. Increased negative skewness and increased kurtosis are seen in the warm regimes (AO+ and La Niña) for both Tmin and Tmax in the FP. These increases translate into thicker and longer left tails of the distributions and, therefore, into a relatively high likelihood of experiencing temperatures significantly colder than the expected (warm) value (see Figs. 1b1,b3 for a visual illustration). The use of station (as opposed to gridded) data in the present study makes it possible to fully appreciate the statistically significant specific behavior of peninsular Florida’s temperatures compared to the remainder of the Southeast.

4. Summary

Our analysis confirms that the distributions of winter daily maximum and minimum temperature anomalies are distinctly non-Gaussian. The shapes of their distributions have coherent spatial structures, with pronounced north–south gradients. At most stations, the PDFs of Tmin and Tmax have distinctly different shapes. The effects of ENSO and AO on daily minimum/maximum temperatures go beyond mere shifts in the means—also influencing the distribution shape in a disparate, spatially coherent, and statistically significant manner. The spatial distribution of the first four statistical moments for Tmin and Tmax, as well as a gross summary of the sign of their changes under ENSO or AO regime conditions, is summarized in Table 2.

Table 2.

Summary of the first four statistical moments of daily maximum and minimum surface air temperatures for the Southeast in January–February in neutral years, and deviations from neutral years during ENSO and AO phases. A+ − indicates a positive negative valued change in the given regime relative to neutral-year values. Whenever a sign appears by itself, it applies to both Florida (FP) and non-Florida (NFP). If only one of FP/NFP is mentioned, the change in the remaining region is negligible.

Table 2.

In the warm regimes (La Niña and AO+) compared to neutral, a larger effect is seen in the expected values of Tmax than of Tmin; magnitudes are similar between the La Niña and AO+ responses. With the exception of the FP, the standard deviation of both Tmin and Tmax increases in La Niña, and decreases in AO+ years. In both La Niña and AO+ years Tmax is more negatively skewed than in neutral years over most of the domain; the skewness of Tmin is unchanged except in south Florida. Distributions of Tmax are sharpened for most of the domain in AO+ years and for Florida and the Gulf Coast in La Niña years. The Tmin distributions are sharpened in south Florida for both warm regimes.

In the cold regimes (El Niño and AO−) compared to neutral, cool anomalies are seen in the expected values of Tmax for El Niño and cold anomalies in both Tmax and Tmin for AO−. With the exception of Florida, the standard deviation is strongly decreased in El Niño years and slightly increased in AO− years. El Niño reduces the negative skewness of Tmin and Tmax in Florida; AO− increases the positive skewness of Tmax in south Florida.

Let us end this paper with several thoughts on potential utilizations and future research. The documented values of the first four statistical moments at individual stations within each regime have the potential to be used in practical applications, such as the generation of synthetic data for agricultural crop yields or risk assessment models. To that end, future work is needed to develop a simple relationship between the distribution statistical moments and threshold exceedance probabilities. How could that be done? It is possible to relate the first four statistical moments of a variable’s distribution to the probability of exceedance of any chosen threshold values given some simple assumptions. For example, Sura and Sardeshmuhk (2008) and Sardeshmukh and Sura (2009) developed a general stochastic model (i.e., a null hypothesis) for the non-Gaussian statistics of weather and climate variability that has been verified for various atmospheric and oceanic variables (Sura 2011).

In addition, if changes in the higher moments indeed alter the likelihoods of winter temperature extremes, the accurate representation of these moments should be an important consideration in the interpretation of climate and climate change modeling studies. A consequent question to follow up, therefore, is the extent to which global and regional circulation models (or, for that matter, reanalyses) are indeed capable of accurately representing the higher moments of surface temperature distributions and the changes in such distributions associated with large-scale climate signals. This question is addressed in a forthcoming paper.

Acknowledgments

This work was partially supported by a grant from USDA. PS was also supported through NSF Grant AGS-0903579. The authors thank Dr. J. J. O’Brien and Mr. D. Zierden for useful discussions of the U.S. Southeast climate, and two anonymous reviewers for their constructive comments that helped improve the manuscript.

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