1 Introduction

Surface air temperature is an important climatic parameter, and its variability severely affects hydrological processes and the environment. Understanding and being able to predict its spatial and temporal variability both at the local and global scales is a challenging task (Shi and Xu 2008; Moral 2009; Xu et al. 2010; Ceppi et al. 2012). The Intergovernmental Panel on Climate Change (IPCC)’s 4th Assessment Report (AR4) reported 0.74 °C (range 0.56 to 0.92 °C) increment in global mean air temperature over the past 100 years (1906–2005). Degaetano and Allen (2002) analyzed the extreme temperature trends across the United States and found a significant increase in extreme temperature (both maximum and minimum) over the 1950–96 periods, particularly at urban sites. Wang et al. (2009) found warming temperature trends of surface air temperature (mean) during the winter (DJF), spring (MAM), and early summer (JJA) along with a modest countrywide cooling trend in late summer and autumn (SON). Trenberth et al. (2007) concluded that the Southeastern United States is one of the few regions of the Earth showing a cooling trend during the twentieth century. Portmann et al. (2009) added that this cooling trend is strongest in the late spring–early summer period. However, Wang et al. (2009) found a countrywide cooling trend in the late summer and autumn. Robinson et al. (2002) showed that annually-averaged air temperatures in the southern Great Plains have decreased during 1988–1997 from those of 1951–1980. In the very recent study of Rogers (2013), it show similar findings with previous researchers that the portions of the Southern and Southeastern United States are experiencing downward air temperature trends in all the seasons from 1895–2007. Extremely warm or freezing temperatures can cause harm to any crops. Schlenker and Roberts (2009) analyzed the yielding temperature for three main crops (such as corn, soybeans, and cotton) in the US soil. They have found the yield temperatures up to 29 ° C for corn, 30 ° C for soybeans, and 32 ° C for cotton but temperatures above these thresholds temperatures are very harmful.

Global and continental level of climatic analysis have been very useful to understand the large scale phenomena of change, but these are less useful for local to regional scale of planning (Shi and Xu 2008; Brekke et al. 2009). A change in climate that may occur at a global scale may not reflect changes that may occur at regional scales (Trajkovic and Kolakovic 2009; Martinez et al. 2012). Thus, it is imperative to analyze climate variability on a local scale, especially in regions that exhibit complex weather patterns, e.g., North Carolina. Long-term temperature trend analyses in a smaller scale utilizing the various statistical methods have been studied in many areas of the world. Such as, for the state of Florida, Martinez et al. (2012) evaluated the significance and magnitude of annual, seasonal, and monthly trends in precipitation, mean temperature, maximum temperature, minimum temperature, and temperature range using the nonparametric Mann-Kendall test and Sen’s slope, respectively for the time periods 1895–2009 and 1970–2009. Karaburun et al. (2011) used the Mann-Kendall test and Sen’s method to study the annual, seasonal and monthly mean, minimum, and maximum temperatures for eight meteorological stations in Istanbul from the 1975 to 2006 period. ElNesr et al. (2010) investigated temperature changes for Saudi Arabia using 29 meteorological stations based on nonparametric Mann-Kendall-tau coefficient and Sen’s slope estimator.

There have been very few published works analyzing the climatic variable patterns over North Carolina. Boyles and Raman (2003) detected seasonal and annual precipitation and temperature trends in North Carolina during the period of 1949–1998. They found the temperatures during the 1950s were the warmest in 50 years. But the last 10 years were warmer than average. They also found that the difference between the maximum and minimum temperatures was decreasing over the 50-year study period.

This study focused on understanding the long-term trends (magnitude and direction) in surface air temperature (mean, maximum, and minimum) in North Carolina. It used daily data of 60 years (1950–2009) from the 249 meteorological stations uniformly distributed across the state (1station per 548 km2). The Mann-Kendall (MK) nonparametric test was applied to detect the significant trend. The Theil-Sen approach (TSA) was applied to quantify the trend magnitude. The Sequential Mann-Kendall (SQMK) was also applied for abrupt temporal change point detection. It is expected that the findings of this study will add to the understanding of regional temperature variability over the last several decades in North Carolina.

2 Materials and methods

2.1 Study area

The state of North Carolina is located in the Southeastern United States (75° 30′–84° 15′ W, 34°–36° 21′ N) (Fig. 1). The study covered an area of approximately 136,399 km2. There are a total of 100 counties and the population is nearly 9.5 million (approx.) in 2010 (U.S. Census Bureau 2010). North Carolina has three diverse topographic zones from mountainous region in the west to a coastal region in the east. The western part of the state comprises 40 % of the area, and piedmont zone comprises about 20 %. The land slopes upward as we move from the eastern piedmont plateau to the western part containing the southern Appalachian Mountains (Great Smokey Mountains and Blue Ridge). The three regions of North Carolina that included the mountain, piedmont, and coastal, have 89, 82, and 78 meteorological stations, respectively as shown in Fig. 1.

Fig. 1
figure 1

Regional distribution and geographical position of the 249 meteorological stations in North Carolina

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Topographic features that range from 46 m from the eastern coastal area to the western mountain area of 1,829 m height makes North Carolina one of the most complex climates in the United States (Boyles and Raman 2003; Robinson 2005). The average temperature of North Carolina varies more than −6.7 °C (20 °F) from the lower coast to the highest elevations in all the season of the year. Average annual temperature on the southern part of the lower coast is nearly as high as that of interior northern Florida, while the average on the summit of Mount Mitchell (2,037 m, is the highest peak of the Appalachian Mountains and the highest peak in the eastern United States) is lower than that of Buffalo, NY (State climate office of North Carolina 2013). Southwestern North Carolina is the rainiest in the eastern United States, receiving 2,286 mm of rainfall annually because southerly winds are forced upward in passing over the mountain barrier whereas less than 80 km from this region to the north, in the valley of the French Broad river, surrounded by mountain ranges on all sides, is the driest point south of Virginia and east of the Mississippi river (State climate office of North Carolina 2013). These altitude variation features and anomalous precipitation in some portion across North Carolina produces zonal temperature trend variations.

2.2 Data

Maximum and minimum temperatures from the 249 stations across North Carolina were analyzed for the period of 1950–2009. The data were obtained from the United States Department of Agriculture-Agriculture Research Service (USDA-ARS) USDA-ARS 2012) which were originally facilitated by the National Oceanic and Atmospheric Administration (NOAA)’s Cooperative Observer network (COOP) and Weather-Bureau-Army-Navy (WBAN) stations.

Daily values were averaged to obtain seasonal and annual temperatures for each of the 249 stations. Mean temperature was calculated by averaging daily maximum and minimum temperature. Seasons were defined as follows: Winter (January, February, March); Spring (April, May, June); Summer (July, August, September); and Autumn (October, November, December). This is consistent with the work of Boyles and Raman (2003) for North Carolina.

The methods and techniques for detecting and correcting non-homogeneities in the climate data series have been investigated by many researchers (Peterson et al. 1998; Costa and Soares 2009; Tabari et al. 2011). In this study, both the double-mass curve analysis (Tabari and Hosseinzadeh Talaee 2011) and autocorrelation analysis were applied to the temperature time series of each station. Double-mass curve analysis is a graphical method for checking consistency of a hydrological or meteorological record. It is considered to be an essential tool before taking it for the further analysis. Inconsistencies in hydrological or meteorological data recording may occur due to various reasons, such as: instrumentation, changes in observation procedures, or changes in gauge location or surrounding conditions (Peterson et al. 1998, Tabari et al. 2011). Finally, spatial maps of trend analyses were developed using surface interpolation techniques within the ArcGIS framework.

2.3 Trend analysis methods

Past studies have used various statistical methods for significant trend analysis, trend magnitude, and change point detection analysis of hydrometeorological variables (e.g., Boyles and Raman 2003; Río et al. 2011; Tabari and Hosseinzadeh Talaee 2011; Tabari et al. 2011; Martinez et al. 2012; Jha and Singh 2013; Sonali and Nagesh 2013; Chang and Sayemuzzaman 2014). Tests for the detection of trends in hydrometeorological time series can be classified as parametric and nonparametric methods. Parametric trend tests require data to be independent and normally distributed, while nonparametric trend tests require only that the data be independent (Huth 1999). Critical reviews of studies have revealed that nonparametric methods have the advantage and reliability over parametric methods (Zhang et al. 2008; Sonali and Nagesh 2013). The brief descriptions of the three nonparametric statistical methods employed in this study are provided below.

2.3.1 Mann-Kendall (MK) trend test

The MK statistical test has been frequently used to quantify the significance of trends in hydrometeorological time series (Douglas et al. 2000; Yue et al. 2002; Partal and Kahya 2006; Tabari and Hosseinzadeh Talaee 2011; Tabari et al. 2011; Martinez et al. 2012; Gocic and Trajkovic 2013; Sayemuzzaman and Jha 2014). Original work was done by Mann (1945) and after that Kendall (1975) derived the test statistic distribution. The MK test statistic S (Mann 1945; Kendall 1975) is calculated as

$$ S={\displaystyle \sum_{i=1}^{n-1}{\displaystyle \sum_{j=i+1}^n sgn\left({x}_j-{x}_i\right)}} $$
(1)

In Eq. (1), n is the number of data points, x i and x j are the data values in time series i and j (j > i), respectively and in Eq. (2), sgn (x j  − x i ) is the sign function as

$$ \mathrm{sgn}\left({x}_j-{x}_i\right)=\left\{\begin{array}{c}\hfill +1, if\left({x}_j-{x}_i\right)>0\hfill \\ {}\hfill 0, if\left({x}_j-{x}_i\right)=0\hfill \\ {}\hfill -1, if\left({x}_j-{x}_i\right)<0\hfill \end{array}\right. $$
(2)

The variance is computed as

$$ V(S)=\frac{n\left(n-1\right)\left(2n+5\right)-{\displaystyle {\sum}_{k=1}^m{t}_{k\kern0.5em }\left({t}_k-1\right)\left(2{t}_k+5\right)}}{18} $$
(3)

In Eq. 3, n is the number of data points, m is the number of tied groups and t k denotes the number of ties of extent k. A tied group is a set of sample data having the same value. In cases where the sample size n > 10, the standard normal test statistic Z S is computed using Eq. (4):

$$ {Z}_{\mathrm{S}}=\left\{\begin{array}{cc}\hfill \frac{S-1}{\sqrt{V(S)}},\hfill & \hfill if\;S>0\hfill \\ {}0,\hfill & \hfill if\;S=0\hfill \\ {}\hfill \frac{S+1}{\sqrt{V(S)}},\hfill & \hfill if\;S<0\hfill \end{array}\right. $$
(4)

Positive values of Z S indicate increasing trends while negative Z S values show decreasing trends. Testing trends is done at the specific α significance level. When |Z S| > \( {Z}_{1-\frac{\alpha }{2}} \), the null hypothesis is rejected and a significant trend exists in the time series. \( {Z}_{1-\frac{\alpha }{2}} \) is obtained from the standard normal distribution table. In this analysis, we applied the MK test to detect if a trend in the temperature time series was statistically significant at significance levels α = 0.01 (or 99 % confidence intervals) and α = 0.05 (or 95 % confidence intervals) were used. At the 5 and 1 % significance level, the null hypothesis of no trend is rejected if |Z S| > 1.96 and |Z S| > 2.576, respectively.

2.3.2 Theil-Sen approach (TSA)

The MK test does not provide an estimate of the magnitude of the trend. For this purpose in this study, a nonparametric method referred to as the Theil-Sen approach (TSA) was used. TSA was originally described by Theil (1950) and Sen (1968). This approach provides a more robust slope estimate than the least-squares method because it is insensitive to outliers or extreme values and competes well against simple least squares even for normally distributed data in the time series (Hirsch et al. 1982; Jianqing and Qiwei 2003). The TSA is also known as Sen slope estimator. Sen’s slope estimator has been widely used by the researchers for the trend magnitude prediction in hydro-meteorological time series (Partal and Kahya 2006; ElNesr et al. 2010; Tabari et al. 2011; Martinez et al. 2012; Gocic and Trajkovic 2013; Sayemuzzaman and Jha 2014). This study used the magnitude of the trend, with the following steps:

  1. (i)

    The interval between time series data points should be equally spaced.

  2. (ii)

    Data should be sorted in ascending order according to time, then the following formula was applied to calculate Sen’s slope (Q k):

    $$ {Q}_{\mathrm{k}}=\frac{x_j-{x}_i}{j-i}\mathrm{for}\;k=1,\dots ..,N, $$
    (5)

    In Eq. (5), X j and X i are the data values at times j and i (j > i), respectively.

  3. (iii)

    In the Sen’s vector matrix members of size \( N=\frac{n\left(n-1\right)}{2}, \) where n is the number of time periods. The total N values of Q k are ranked from smallest to largest and the median of slope or Sen’s slope estimator is computed as:

    $$ {Q}_{\mathrm{med}}=\left\{\begin{array}{cc}\hfill {Q}_{\raisebox{1ex}{$\left[N+1\right]$}\!\left/ \!\raisebox{-1ex}{$2$}\right.},\hfill & \hfill \mathrm{If}\;N\;\mathrm{is}\;\mathrm{odd}\hfill \\ {}\hfill \frac{Q_{\left[\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right]}+{Q}_{\left[\raisebox{1ex}{$N+2$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right]}}{2},\hfill & \hfill \mathrm{if}\;N\;\mathrm{is}\;\mathrm{even}\hfill \end{array}\right. $$
    (6)

    Q med sign reflects data trend direction, while its value indicates the steepness of the trend.

2.3.3 Serial correlation effect

The MK test requires time series to be serially independent. Von Storch and Navarra (1995) suggested to pre-whiten the time series data before applying the MK test to remove serial correlation from the data sets. Serial correlation was tested prior to the application of MK test and TSA. The steps were adopted in the sample data (X 1, X 2,………, X n) are following:

  1. 1.

    The lag-1 serial coefficient (r 1) of sample data X i, originally derived by Salas et al. (1980) but several recent researchers have been utilizing the same equation (Xu et al. 2010; Gocic and Trajkovic 2013) to compute (r 1). It can be computed by

    $$ {r}_1=\frac{\frac{1}{n-1}{\displaystyle {\sum}_{i=1}^{n-1}\left({x}_{\mathrm{i}}-E\left({x}_{\mathrm{i}}\right)\right)\cdot \left({x}_{\mathrm{i}+1}-E\left({x}_{\mathrm{i}}\right)\right)}}{\frac{1}{n}{\displaystyle {\sum}_{i=1}^n{\left({x}_{\mathrm{i}}-E\left({x}_{\mathrm{i}}\right)\right)}^2}} $$
    (7)
    $$ E\left({x}_{\mathrm{i}}\right)=\frac{1}{n}{\displaystyle \sum_{i=1}^n{x}_{\mathrm{i}}} $$
    (8)

    Where E(x i) is the mean of sample data and n is the number of observations in the data.

  2. 2.

    According to Salas et al. (1980) and several recent researchers (Mohsin and Gough 2010; Gocic and Trajkovic 2013) have used the following equation for testing the time series data sets of serial correlation.

    $$ \frac{-1-1.645\ \sqrt{n}-2}{n-1}\le {r}_1\le \frac{-1+1.645\sqrt{n}-2}{n-1} $$
    (9)

    If r 1 falls inside the above interval, then the time series data sets are independent observations. In cases where r 1 is outside the above interval, the data are serially correlated.

  3. 3.

    If time series data sets are independent, then the MK test and the TSA can be applied to original values of the time series.

  4. 4.

    If time series data sets are serially correlated, then the ‘Pre-whitened’ time series may be obtained as (x 2 − r 1 x 1, x 3 − r 1 x 2,… … … … … …, x n  − r 1 x n − 1) (Partal and Kahya 2006; Gocic and Trajkovic 2013).

2.3.4 Sequential Mann-Kendall (SQMK) change point analysis

In a long-term trend analysis, beginning of trend year, trend changes over time, and abrupt trend detection analysis are very important. For this purposes, SQMK test are widely used by researchers (Partal and Kahya 2006; Mohsin and Gough 2010; Tabari et al. 2011). SQMK is a sequential progressive (u (t)) and backward (u’ (t)) analyses of the MK test. If the two series are crossing each other, the year of crossing exhibit the year of trend change (Tabari et al. 2011). If the two series crosses and diverge to each other for a longer period of time, beginning diverge year exhibit the abrupt trend change (Mohsin and Gough 2010). Its sequential behavior fluctuates close to the zero level. The application of SQMK test has the following four steps in sequence:

  1. 1.

    At each comparison, the number of cases x i  > x j is counted and indicated by n i . Where x i  (i = 1, 2, … …, n) and x j (j = 1, ….., i − 1) are the sequential values in a series.

  2. 2.

    The test statistic t i of SQMK test is calculated by Eq. (10)

    $$ {t}_i={\displaystyle {\sum}_i{n}_i} $$
    (10)
  3. 3.

    The mean and variance of the test statistic are calculated using Eqs. (11) and (12), respectively.

    $$ E(t)=\frac{n\left(n-1\right)}{4} $$
    (11)
    $$ \mathrm{Var}\left({t}_i\right)=\frac{i\left(i-1\right)\left(2i+5\right)}{72} $$
    (12)
  4. 4.

    Sequential progressive value can be calculated in Eq. (13)

    $$ u(t)=\frac{t_i-E(t)}{\sqrt{\mathrm{Var}\left({t}_i\right)}} $$
    (13)

    Similarly, sequential backward (u’ (t)) analysis of the MK test is calculated starting from the end of the time series data.

3 Results and discussion

The observed data used in this study comes from a dense network (1 per 548 sq. km). Finer resolution is expected to produce better trend analyses results. A previous attempt by Boyles and Raman (2003) had station density of 1 per 2,393 km2. We used Matlab R2012b to generate the algorithm of three different nonparametric methods. Arc-GIS10.0 tool was used to create the surface interpolation and other necessary maps.

3.1 MK trend test analysis

Figure 2 shows the results of the nonparametric Mann-Kendall test. Higher percentages of positive (increasing) and negative (decreasing) trends were detected in T min and T max data series, respectively. For T min trends in spring, summer, autumn, winter, and annual, 56, 84, 83, 58, and 73 % of the stations were found to have increasing trends, respectively. Similarly for T max trends in respective seasons, 81, 77, 46, 59, and 74 % of the stations were found to have decreasing trends. T min exhibits higher warming trends in summer and autumn than winter and spring. However, T max shows higher cooling trends in spring and summer than winter and autumn. From the above analysis, it is obvious that T min trends are increasing and T max trends are decreasing within the analysis period of 1950–2009. This implies that the differences between the maximum and minimum temperatures are decreasing. Boyles and Raman (2003) found a decrease in differences of maximum and minimum temperatures for the period of 1949–1998. Similar analysis of T mean shows increasing trends in all seasons except spring (Fig. 2).

Fig. 2
figure 2

The percentage of stations with positive and negative trends by the MK trend test for the average annual and seasonal T max, T min, T mean series in the period of 1950–2009

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Further analyses were conducted to identify the stations with significant trend. Figure 3 shows the percentages of stations with significant temperature trend (level of confidence ≥ 95 %). Percentages of stations with significant positive trends in T min during spring, summer, autumn, winter, and on annual basis were found to be 20, 35, 30, 0, and 19, respectively. Similarly, 29, 16 and 13 % of stations were found to have significant negative trends in T max for spring, summer, and annual average, respectively. In T mean data series analysis, it appears that the summer and autumn are getting warmer and spring is getting cooler.

Fig. 3
figure 3

The percentage of stations with significant (confidence level ≥ 95 %) positive and negative trends by the MK trend test for average annual and seasonal T max, T min, T mean series in the period of 1950–2009

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The spatial distribution of the annual and seasonal T min trend test results of 249 stations by the MK method are presented in Fig. 4. The map shows the location of gauging stations with both positive and negative trends. A 99 and 95 % confidence level positive trends stations were seen in the westernmost part of the mountain zone of North Carolina in all seasons and annual analysis. Statewide positive trends stations were detected in the summer season. In the winter season, significant negative trends and several positive trends stations were detected in the mid-piedmont and mountain zone area. Most of the coastal zone stations are showing positive trends in all seasons and annual analysis.

Fig. 4
figure 4

Spatial distribution of MK statistics of annual and seasonal T min series

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In Fig. 5, annual, spring, and summer scale, 99 and 95 % confidence level negative trends stations were shown statewide except several positive trends stations. In winter, insignificant positive–negative trends were detected statewide except several significant trends found in the southern piedmont and mountain zone. In the autumn season, 99 and 95 % confidence level positive trends were found in most of the stations in the coastal zone.

Fig. 5
figure 5

Spatial distribution of MK statistics of annual and seasonal T max series

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3.2 Minimum temperature (T min)

Moderate positive slopes were found in almost all seasons and on annual basis in the furthest eastern part of North Carolina which is shown in Fig. 6. This finding is in slight disagreement with the Boyles and Raman (2003) study where some portion of the eastern part was found to have decreasing trends. The entire eastern part shows an increasing trend of minimum temperature except for the spring season, which shows a slightly decreasing trend for some of eastern North Carolina. In the western and southern part of the piedmont zone, moderate negative trends were found in all the seasons and on annual basis. In winter and spring season, the southwest part exhibits slight positive trend; however, in the same region, more positive temperature trend was found in summer, autumn, and on an annual basis. Overall, five maps in Fig. 6 show the increasing trend over the period of 1950–2009. In the case of winter season T min, Boyles and Raman (2003) reported positive slope in the southern mountain, similar to the findings of this study presented here; however, reported negative slopes in the southern coastal plain are found to be in disagreement. We found that in winter, T min temperature trend ranged from −0.06 °C/year to +0.07 °C/year. In spring season, T min shows decreasing trend in most places except the eastern coastal part with increasing trend. This finding is similar to the finding earlier attempted by Boyles and Raman (2003) who found decreasing trend in spring in the southern coastal part. In spring, T min temperature ranged from −0.05 °C/year to +0.05 °C/year, while in summer, it gives distinct positive trend allover (Fig. 6) except a few locations in the southern coast, eastern piedmont, and some part of the mountain zone. These findings support Boyles and Raman (2003) results unlike the dominating positive slopes features in the piedmont zone. Similarly, T min temperature trend ranged from −0.05 °C/year to +0.06 °C/year in summer and from −0.04 °C/year to +0.07 °C/year in autumn. Widespread positive trend in the coastal zone and all over North Carolina is clearly evident in Fig. 6. However, the eastern piedmont and southern coastal zones are demonstrating the positive trend, similar to the patterns in other three seasons.

Fig. 6
figure 6

Minimum temperature (T min) trends for winter, spring, summer, autumn, and yearly average

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3.3 Maximum temperature (T max)

In spring, summer, and on annual average, T max is decreasing over most of the piedmont and mountain area (Fig. 7). Increasing T max pattern was found in the southern coastal area in all four seasons and on annual basis. These trends are opposite to the trends of T min for each respective region. Boyles and Raman (2003) has also concluded the same pattern. However, the previous research found the zero slopes for most of the coastal plain and southern mountains which we found nonzero and increasing trends. It can be observed from Fig. 7 that for the summer and spring season, the trend in T max is negative throughout North Carolina except some parts of the southern and eastern coast, western piedmont, southern mountain T max trend ranged from −0.12 °C/year to +0.03 °C/year in summer, −0.11 °C/year to +0.04 °C/year in spring, −0.11 °C/year to +0.05 °C/year in winter, and from −0.12 °C/year to +0.04 °C in autumn. On annual average analysis, T max trend varied from −0.11 °C/year to +0.035 °C/year. Lowest value of T max trend in summer and autumn season is −0.12 °C/year, which is the highest decreasing trend considering all (T max -T min) of the four seasons and on annual average analysis. On the other hand, highest value of T min trend in autumn is 0.07 °C/year, which is the highest increasing trend.

Fig. 7
figure 7

Maximum temperature (T max) trends for winter, spring, summer, autumn, and yearly average

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3.4 Regional temperature trend

Out of the 249 meteorological stations, three regions of North Carolina, mountain, piedmont, and coastal zone have 89, 82, and 78 stations, respectively. Daily average temperatures recorded at all stations on a region were averaged and categorized as regional temperature of that region for regional temperature trend analysis.

Table 1 shows the TSA output for trend magnitude and MK trend test value (Z value) of regional average annual and seasonal T max and T min, data series for the period of 1950–2009. Trends are presented for the statistically significant at the 99 % and 95 % confidence levels (presented in underline-bold and bold character, respectively, in the table). Four seasons and annual average of T max were showing negative trends for three regions except for mountain and piedmont of autumn season, which was showing positive trends. Higher positive trend was found in the piedmont region in spring (−0.0144 °C/year) and summer (−0.0107 °C/year) season. T min was showing positive trends for all three regions in four seasons and yearly average analysis. Higher warming trend was found in the coastal region in autumn (+0.0194 °C/year) and summer (+0.0136 °C/year) season and the mountain region in autumn (+0.0138 °C/year) season. In all four seasons, the coastal region has higher warming trends in T min series.

Table 1 Results of the MK Statistics (Z value) and TSA (slope-value) for three regions (mountain, piedmont, and coastal zone) of North Carolina in annual and seasonal timescale of T min and T max data series over the period 1950–2009
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3.5 Change point detection analysis

Based on the Sequential Mann-Kendall (SQMK) test, the graphical analysis of the forward (u(t)) and backward (u’(t)) curves of annual and seasonal T max and T min data series in the mountain, piedmont, and coastal regions were analyzed to identify the beginning year of change. Analysis of SQMK results was shown in Table 2. Increasing and decreasing trends are represented by (+) and (−), respectively; each region is characterized by a year which reflects the initiation of a positive or a negative trend. Due to the lack of space, the regions which exhibited the higher positive and negative trends result shown in Table 1, SQMK test results only on those regions were shown graphically in Figs. 8 and 9.

Table 2 Approximate year of beginning of the positive and/or negative trend according to the SQMK test for three regions (mountain, piedmont, and coastal zone) of North Carolina in annual and seasonal timescale over the period of 1950–2009
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Fig. 8
figure 8

Graphical representation of the forward, u(t) and the backward, u’(t) series of the Sequential Mann-Kendall (SQMK) test for coastal zone of seasonal average of T min data series in the period of 1950–2009

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Fig. 9
figure 9

Graphical representation of the forward, u(t) and the backward, u’(t) series of the Sequential Mann-Kendall (SQMK) test for mountain, piedmont, and coastal zone of seasonal average of T max data series in the period of 1950–2009

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Regional average of seasonal T min trend in the coastal zone was found to have the highest warming trends when compared with the other two zones (Table 1). Figure 8, graphical result for the coastal zone, showed that the observed warming trend in winter, spring, summer, and autumn seasons had begun approximately in 1990, 1980, 1975, and 1970, respectively. Summer season of T min data series was showing significant positive trend and in 2009 the test results reaches almost three, which crosses the 99 % confidence level value of 2.58. After 1985, there was increasing T min trend detected till 2009 in summer. Winter T min was warming in the last two decades without very sharp cooling nature. Autumn season has warming and cooling nature of T min; since 1970 it has started increasing trend and in 2009 the trend crosses the value 1.96 (limit for 95 % confidence level).

Regional average of all four seasons of increasing T max trends was inconsistent among the three regions (Table 1). Thus, SQMK test results of the winter (mountain), spring (piedmont), summer (mountain), and autumn (piedmont) seasons were chosen for the graphical analysis. The SQMK test (Fig. 9) detected T max decreasing trends in all regions, which started from 1956, 1956, and 1985 in spring (piedmont), summer (mountain), and autumn (piedmont) seasons, respectively. Increasing and decreasing trends were found in winter (mountain) of T max data series. There is a huge decrement of T max trend of summer season in the mountain zone that happened from 1957 to 1968, and then it slightly increases till 2009. For spring season in the piedmont zone, huge cooling trends of T max existed from 1957 to 1975, and then it slightly increases till 2009. Analysis of the full range of figures with the approximate year of beginning of the positive and negative trend according to the SQMK was shown in Table 2. In winter T max, three regions were showing decreasing and increasing trends in 1975 and in 1990, respectively. In Table 2, “N” for some stations denotes that there is no significant trend for the periods. Warming winter temperature trends across North Carolina was detected in the last two decades.

3.6 Comparison of surface air temperature (SAT) with North Atlantic Oscillation (NAO) index

NAO is the key indicator of the climate variability occurring in the northern hemisphere (Hurrell 1996). NAO positive (negative) phase is associated with a stronger (weaker) north–south pressure gradient between the subtropical high and the Icelandic low. Positive NAO indices are associated with warmer temperatures over the eastern United States (Hurrell 1995). NAO monthly data sets are collected from the Climate Prediction Center/National Oceanic and Atmospheric Administration (CPC 2013). Monthly data were averaged to generate the annual and seasonal data series.

Correlation-coefficient (r) of 10-year moving average, between mean SAT and NAO index in seasonal and monthly timescale over North Carolina was calculated and presented in Table 3. Moving correlation method is widely used by researchers for analyses of possible variations in the relationships between two climate time series (e.g., Slonosky et al. 2001; Gershunov et al. 2001).

Table 3 Coefficient of Correlation (r) in 10 year moving average, between mean temperature and NAO index in seasonal and monthly time scale in North Carolina
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Polyakova et al. (2006) analyzed the changing relationship between the NAO and key North Atlantic climate parameters (SAT, sea surface temperature (SST), and sea level pressure (SLP)) in their study. Since the r value in winter season was the highest (Table 3), a separate chart was constructed to observe the phase behavior between the winters mean SAT and NAO index (Fig. 10). Two time periods, 1960 ∼ 1976 and 1986 ∼ 1995, were found to have similar phase with the winter SAT and NAO index. r values of 0.76 (at 99.9 % confidence level) and 0.61 (at 95 % confidence level) were found on the time periods 1960 ∼ 1976 and 1986 ∼ 1995, respectively. This study attempted to link the relational pattern between mean SAT and NAO indices across North Carolina; however, the complex understanding of the linkages is very primitive and needs further research.

Fig. 10
figure 10

Graphical representations of 10-year moving average of winter mean SAT (surface air temperature) and NAO index

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4 Summary and conclusions

This study investigated maximum and minimum temperatures for the seasonal and annual trends by analyzing 249 data points in North Carolina for the period of 1950–2009. Statistical methods used were the nonparametric Mann-Kendall (MK) test for significant trend detection, the Theil-Sen approach (TSA) for the magnitude of the trend, and the Sequential Mann-Kendall (SQMK) test for the change point detection. Prior to the trend analysis, pre-whitening technique was applied to eliminate the effect of lag-1 serial correlation in the temperature data series.

A consistent increasing trend was detected in minimum temperature in most of North Carolina in annual and seasonal analysis, especially in summer and autumn, over the study period. On the contrary, consistent decreasing trend was found in maximum temperature on an annual basis and in seasonal analysis with distinct trend in summer and spring However, annual and seasonal analysis of MK test in 5 % and less significance level (95 % and more confidence level) represent that the mean temperature trends were increasing. About 20 and 15 percentages of stations were found to have the significant warming mean temperature trends in autumn and summer, respectively. The magnitude of the highest warming trend in minimum temperature and the highest cooling trend in maximum temperature is +0.073 °C/year in autumn season and −0.12 °C/year in summer season, respectively. Due to the diverse topographic nature in North Carolina from west to east, regional (mountain, piedmont and coastal) annual and seasonal scale average temperature were also analyzed in this study. Coastal zone exhibited highest warming mean temperature trend whereas Mountain zone’s mean temperature showed decreasing trend than other zones. The SQMK test results indicated that the significant increasing trends in minimum temperature data and decreasing trend in maximum temperature data began in general around after 1970 and after 1960, respectively in most of the stations.

The trend identified in the mean surface air temperature (SAT) was compared with North Atlantic Oscillation (NAO) with 10-year moving average values. Two time periods, 1960 ∼ 1976 and 1986 ∼ 1995, were found to have similar phase with the winter SAT and NAO index. This study attempted to link the relational pattern between mean SAT and NAO indices across North Carolina; however, the complex understanding of the linkages is very primitive and needs further research.