Study of the Lower Stratospheric Temperature over the Arabian Peninsula

: Given the current concerns about climate change, particularly, the stratospheric temperature effect on climatic surface temperature, it is of fundamental importance to investigate the impact of the lower stratospheric temperature on regional climate. This paper examines the lower stratospheric temperature (LST) at 50 hPa in the winter season and its relation to the surface air temperature (ST) over the Arabian Peninsula in the period 1951–2016. Generally, LST had an insigniﬁcant decreasing trend over the entire period, with a relatively high standard deviation of 1.3 ◦ C. According to the coefﬁcient of variability (COV), the ﬂuctuation in the LST from year to year is relatively high, especially in the last reference period (1981–2010). An insigniﬁcant increasing (0.05 ◦ C per year) trend through the period between 1951 and 1992 was observed, while an insigniﬁcant decreasing ( − 0.05 ◦ C per year) trend was observed during the second period of 1993–2016. From the spectral analysis, the periodicity cycles of LST time series at periods of about 2.2, 2.54, and 13.2 years with respect to the 95% signiﬁcance conﬁdence level were found. LST may be inﬂuenced by quasi-biennial oscillation and the sunspot cycle. A strong relationship was found between LST and ST over the Arabian Peninsula.


Introduction
Recently, researchers have become aware of the importance of stratospheric temperature in the climate system. Study of the stratospheric temperature is one of the important components of global climate change. Studies of [1,2] reveal that changes in the tropospheric temperature and/or changes in the stratospheric temperature provide insights into their effects on these mechanisms, which induce climate change [3,4]. Based on satellite data in the 1990s, the mean annual lower and middle stratospheric temperatures decreased [5]. In addition, based on observed data from satellite and radiosondes, it was found that, globally, the troposphere has warmed and the stratosphere has cooled since the mid-20th century [6]. Manabe and Strickler; Simmons et al. [7,8] found that tropospheric warming and stratospheric cooling are affected by increasing stratospheric water vapor. Variations in temperature within the stratosphere are important for estimating trends [9] and changes in stratospheric ozone [4,[10][11][12]. These studies concluded that, as a global mean, the upper stratosphere and lower mesosphere cooled at a rate of at least 2 K/decade between 1980 and 2000, and the lower stratosphere cooled at approximately half to one K per decade while the cooling rate of the mid-stratosphere was approximately 0.5 K/decade. Over a similar period, the magnitude of mean

Methodology
Regression method with least squares [32] was used to derive a linear trend and evaluate the temperature variations in climate change. Regarding the data of the lower stratospheric temperature time series (Figure 2), one can find that the temperature was gradually increased until the beginning of the 1990s, then decreased to the end of the period. Therefore, for the trend analysis of the wintertime stratospheric temperature over Arabian Peninsula, the entire analysis period  was divided into two phases: the first half is from 1951 to 1992 and the second from 1993 to 2016. Correlation and principal component analysis can be used to access teleconnection patterns [33]. These methods, which possess both advantages and disadvantages, are broadly applied in climate research. The correlation method is the most straightforward of these methods [34]. Many natural physical systems are characterized by lead-lag relationships and play a crucial role in the study of the correlation between time series [35]. Cross-correlation of lead-lag is often used to explore physical mechanisms that could participate in the Arabian Peninsula's temperature changes. Average value change could be expressed as the coefficient of variations (COV), as COV = , where is the average value and is the reference period standard deviation. The COV was used to evaluate the stability of the temperature regime at lower stratospheric temperature (LST). Moreover, the COV is an indicator of the reliability of the average. The average is less reliable when the COV is high, but more reliable when the COV is low. Also, changes in COV show a change in the mean value. It is worth noting that the best spectral explanation and the best autocorrelation explanation are closely linked to Fourier transform [36]. Broersen; Priestley [36,37] provided the foundation for calculation of the LST time series power spectrum. Markov red noise theory and χ2-tests were used for testing the statistical confidence of power spectra [38].

Methodology
Regression method with least squares [32] was used to derive a linear trend and evaluate the temperature variations in climate change. Regarding the data of the lower stratospheric temperature time series (Figure 2), one can find that the temperature was gradually increased until the beginning of the 1990s, then decreased to the end of the period. Therefore, for the trend analysis of the wintertime stratospheric temperature over Arabian Peninsula, the entire analysis period (1951-2016) was divided into two phases: the first half is from 1951 to 1992 and the second from 1993 to 2016. Correlation and principal component analysis can be used to access teleconnection patterns [33]. These methods, which possess both advantages and disadvantages, are broadly applied in climate research. The correlation method is the most straightforward of these methods [34]. Many natural physical systems are characterized by lead-lag relationships and play a crucial role in the study of the correlation between time series [35]. Cross-correlation of lead-lag is often used to explore physical mechanisms that could participate in the Arabian Peninsula's temperature changes. Average value change could be expressed as the coefficient of variations (COV), as COV = Y − Y re f SD re f , where Y re f is the average value and SD re f is the reference period standard deviation. The COV was used to evaluate the stability of the temperature regime at lower stratospheric temperature (LST). Moreover, the COV is an indicator of the reliability of the average. The average is less reliable when the COV is high, but more reliable when the COV is low. Also, changes in COV show a change in the mean value. It is worth noting that the best spectral explanation and the best autocorrelation explanation are closely linked to Fourier transform [36]. Broersen; Priestley [36,37] provided the foundation for calculation of the LST time series power spectrum. Markov red noise theory and χ 2 -tests were used for testing the statistical confidence of power spectra [38].

Trend Analysis
In wintertime, averages of the lower stratospheric temperature at 50 hPa (LST) were calculated and plotted for the period 1951-2016 ( Figure 2). The mean LST value was −65.42 °C for the entire period, but the variation of LST was unclear for any specific year. The time series of the LST in the period 1951-2016 is displayed in Figure 2, accompanied by the findings of the linear trend analysis. In general, an insignificant decreasing trend (−0.01 °C) of the winter LST during the whole period (1951-2016) was found, with a comparatively large standard deviation of 1.3 °C. This cooling over 66 years could not well-described as a linear trend, due to the increased cooling since 1993. As stated in Section 2 of this study, the total period of analysis was categorized into two phases: the first one between 1951 and 1992, and the second one between 1993 and 2016. Accurate examination showed that the LST has increased during the first phase but decreased in the second one. An insignificant increasing trend ( = 0.21), at a rate of 0.05 °C per year with a standard deviation value of 1.34 °C, was found for the first phase, whereas the time series exhibited an insignificant decreasing trend ( = 0.12) at −0.05 °C per year in the second phase, with a standard deviation of 1.0 °C. This finding is a clear demonstration of the phase selection effect on the trend evaluations, as discussed in [39]. Over the Arabian Peninsula, the warmest years of the LST (Figure 2) were 1992 and 1982, which may have been influenced by eruptions of Mount Pinatubo and El Chichon, respectively. The results align or support analyses conducted in the past, including [4,40]. The 1982 El Chichon and 1992 Mt. Pinatubo influenced the northern hemisphere's stratospheric temperature [5]. The lower stratosphere warmed, while the area close to the surface cooled after the Pinatubo eruption caused changes in atmospheric circulation [41].
For more insight on the dynamics of temperature variability, one can compare the lower stratospheric temperatures in the Arabian Peninsula with those in other areas. Therefore, the

Trend Analysis
In wintertime, averages of the lower stratospheric temperature at 50 hPa (LST) were calculated and plotted for the period 1951-2016 ( Figure 2). The mean LST value was −65.42 • C for the entire period, but the variation of LST was unclear for any specific year. The time series of the LST in the period 1951-2016 is displayed in Figure 2, accompanied by the findings of the linear trend analysis. In general, an insignificant decreasing trend (−0.01 • C) of the winter LST during the whole period (1951-2016) was found, with a comparatively large standard deviation of 1.3 • C. This cooling over 66 years could not well-described as a linear trend, due to the increased cooling since 1993. As stated in Section 2 of this study, the total period of analysis was categorized into two phases: the first one between 1951 and 1992, and the second one between 1993 and 2016. Accurate examination showed that the LST has increased during the first phase but decreased in the second one. An insignificant increasing trend (R 2 = 0.21), at a rate of 0.05 • C per year with a standard deviation value of 1.34 • C, was found for the first phase, whereas the time series exhibited an insignificant decreasing trend (R 2 = 0.12) at −0.05 • C per year in the second phase, with a standard deviation of 1.0 • C. This finding is a clear demonstration of the phase selection effect on the trend evaluations, as discussed in [39]. Over the Arabian Peninsula, the warmest years of the LST (Figure 2) were 1992 and 1982, which may have been influenced by eruptions of Mount Pinatubo and El Chichon, respectively. The results align or support analyses conducted in the past, including [4,40]. The 1982 El Chichon and 1992 Mt. Pinatubo influenced the northern hemisphere's stratospheric temperature [5]. The lower stratosphere warmed, while the area close to the surface cooled after the Pinatubo eruption caused changes in atmospheric circulation [41].
For more insight on the dynamics of temperature variability, one can compare the lower stratospheric temperatures in the Arabian Peninsula with those in other areas. Therefore, the correlation coefficient between the Arabian Peninsula LST time series and the Northern Hemisphere  (Table 1). A strong positive relationship (99% significance level) between the Arabian Peninsula LST time series and tropical LST, subtropical LST, and mid-latitude LST regions was found (Table 1). However, a strong negative relationship (99% significance level) between the Arabian Peninsula LST and polar regions was observed (Table 1). Moreover, there was no relationship between the Northern Hemisphere LST time series and the Arabian Peninsula LST (Table 1). Salby and Callaghan [42] showed the inverse relationship between high and low latitudes of the stratospheric temperature, and that relationship was accompanied by a similar reversal trend of ozone [43]. The behavior of subtropical and mid-latitude lower stratospheric temperature time series was the same as in the tropics [4].

Periodogram Analysis
The power spectrum of the LST time series was computed using the autocorrelation spectral analysis method [36,37], and tested using Markov red noise theory and χ 2 -tests [38]. The linear graphs of LST highlight the persistent alternating periods between the anomalies. Through the analysis of periodic behavior, a spectral analysis of the variance of these time series can provide more detailed information. Figure 3 clearly demonstrates peaks at periods of about 2.2, 2.54, and 13.2 years, which are significant at the 95% confidence level. From the spectral analysis, one can suppose that LST was described by non-periodic behavior. In this study, some explanations of the periodicities stated above are presented.
This study has shown that the quasi-biennial oscillation may affect LST. The findings of [44] showed that the quasi-biennial oscillation normally operates with a periodicity of 26 to 30 months. In addition, [45] found that the periodicity of the quasi-biennial oscillation was approximately 28 months in the lower stratosphere. Anstey et al. [46] argued that the periodicity of the quasi-biennial oscillation varies from approximately 22 to 36 months. The periodicity of the quasi-biennial oscillation averages approximately 28 months [29], but is known to have interannual variations of several months, [45]; however, the quasi-biennial oscillation could be affected by solar cycles [47] and by the propagating planetary waves into the stratosphere [13]. Figure 4 illustrates the distribution pattern of the quasi-biennial oscillation and LST time series. Also, cross-correlation coefficient lead-lag between two time series is represented in Figure 4. From this Figure, it is easily observed that significant cross-correlations (0.27) at the 95% level are spotted at lag 1 of the quasi-biennial oscillation. Therefore, the LST may be affected by previous quasi-biennial oscillations. graphs of LST highlight the persistent alternating periods between the anomalies. Through the analysis of periodic behavior, a spectral analysis of the variance of these time series can provide more detailed information. Figure 3 clearly demonstrates peaks at periods of about 2.2, 2.54, and 13.2 years, which are significant at the 95% confidence level. From the spectral analysis, one can suppose that LST was described by non-periodic behavior. In this study, some explanations of the periodicities stated above are presented.   This study has shown that the quasi-biennial oscillation may affect LST. The findings of [44] showed that the quasi-biennial oscillation normally operates with a periodicity of 26 to 30 months. In addition, [45] found that the periodicity of the quasi-biennial oscillation was approximately 28 months in the lower stratosphere. Anstey et al. [46] argued that the periodicity of the quasi-biennial oscillation varies from approximately 22 to 36 months. The periodicity of the quasi-biennial oscillation averages approximately 28 months [29], but is known to have interannual variations of several months, [45]; however, the quasi-biennial oscillation could be affected by solar cycles [47] and by the propagating planetary waves into the stratosphere [13]. Figure 4 illustrates the distribution pattern of the quasi-biennial oscillation and LST time series. Also, cross-correlation coefficient leadlag between two time series is represented in Figure 4. From this Figure, it is easily observed that significant cross-correlations (0.27) at the 95% level are spotted at lag 1 of the quasi-biennial oscillation. Therefore, the LST may be affected by previous quasi-biennial oscillations. Kuai et al.;Haigh [48,49] found that the sunspot cycle is a significant contributor to stratospheric variability. The length of the solar cycle has varied between 9 and 13 years [50]. Between two solar minima, the sunspot cycle's interval may be as short as 9 years and up to 14 years (https://scied.ucar.edu/sunspot-cycle). Figure 5 shows the time series of the sunspot number and LST. It is obvious from this figure that the cross-correlation coefficient between sunspot number and LST is 0.27 at zero lag; therefore, the number of sunspots may affect the LST in the winter season. Crooks and Gray [21] found the same results when studying the effects of the sunspot cycle and quasibiennial oscillation on the polar vortex.   [48,49] found that the sunspot cycle is a significant contributor to stratospheric variability. The length of the solar cycle has varied between 9 and 13 years [50]. Between two solar minima, the sunspot cycle's interval may be as short as 9 years and up to 14 years (https: //scied.ucar.edu/sunspot-cycle). Figure 5 shows the time series of the sunspot number and LST. It is obvious from this figure that the cross-correlation coefficient between sunspot number and LST is 0.27 at zero lag; therefore, the number of sunspots may affect the LST in the winter season. Crooks and Gray [21] found the same results when studying the effects of the sunspot cycle and quasi-biennial oscillation on the polar vortex.

Relationship between the Lower Stratospheric and Tropospheric Temperature over the Arabian Peninsula
Many researchers, such as [51,52], have studied the relationship between the stratospheric and tropospheric temperature. They concluded that stratospheric processes are important in organizing the weather and climate systems of Earth. In addition, [53] found that stratospheric disturbances can affect the surface, and may represent an essential part of the mean zonal tropospheric response [54][55][56]. Moreover, during the winter season, stratosphere-troposphere connections display a strong coupling [57,58]. In this section, the relationship between LST and ST over the Arabian Peninsula is examined. Cross-correlation lead-lag is critical for exploration of physical mechanisms that could contribute to the relationship between LST and ST over the Arabian Peninsula. Figure 6 indicates that the maximum correlation coefficient between LST and ST was observed at zero lag (r = −0.50). This finding suggests that ST is linked to LST in this region.

Relationship between the Lower Stratospheric and Tropospheric Temperature over the Arabian Peninsula
Many researchers, such as [51,52], have studied the relationship between the stratospheric and tropospheric temperature. They concluded that stratospheric processes are important in organizing the weather and climate systems of Earth. In addition, [53] found that stratospheric disturbances can affect the surface, and may represent an essential part of the mean zonal tropospheric response [54][55][56]. Moreover, during the winter season, stratosphere-troposphere connections display a strong coupling [57,58]. In this section, the relationship between LST and ST over the Arabian Peninsula is examined. Cross-correlation lead-lag is critical for exploration of physical mechanisms that could contribute to the relationship between LST and ST over the Arabian Peninsula. Figure 6 indicates that the maximum correlation coefficient between LST and ST was observed at zero lag (r = −0.50). This finding suggests that ST is linked to LST in this region.
Climate 2019, 7, x FOR PEER REVIEW 7 of 12 Figure 5. The distribution pattern of the sunspot number and LST time series. The CC represents the correlation coefficient at zero lag, which is significant at the 95% confidence level.

Relationship between the Lower Stratospheric and Tropospheric Temperature over the Arabian Peninsula
Many researchers, such as [51,52], have studied the relationship between the stratospheric and tropospheric temperature. They concluded that stratospheric processes are important in organizing the weather and climate systems of Earth. In addition, [53] found that stratospheric disturbances can affect the surface, and may represent an essential part of the mean zonal tropospheric response [54][55][56]. Moreover, during the winter season, stratosphere-troposphere connections display a strong coupling [57,58]. In this section, the relationship between LST and ST over the Arabian Peninsula is examined. Cross-correlation lead-lag is critical for exploration of physical mechanisms that could contribute to the relationship between LST and ST over the Arabian Peninsula. Figure 6 indicates that the maximum correlation coefficient between LST and ST was observed at zero lag (r = −0.50). This finding suggests that ST is linked to LST in this region. Domeisen; Angell [59,60] showed coupling between the troposphere and the stratosphere on extreme weather and climate incidences. On a global average, since 1979, the temperature at the surface was warmer when compared to the troposphere, and the troposphere was warmer than the stratosphere [61][62][63][64]. Also, globally, the observed tropospheric temperature since 1958 has warmed and the stratosphere has cooled, in general, at a rate of 0.1 • C per decade [65][66][67][68][69] notwithstanding in the tropics and subtropics, where warming was spatially variable and most significant [70,71]. Based on global observations, the ST has warmed since the late 1950s, whereas cooling of the stratosphere has been an ongoing process since 1979 [2]. This is attributed to the important role of greenhouse gases in cooling the stratosphere and warming the troposphere [2, 10,72,73]. Troposphere-stratosphere conjunctions characterized by this association exist through all timescales, from weekly variations [74] to long-term climate change [75][76][77][78]. In the extremely cold winters of 1962 and 1963 all across Europe, that recurred in the years 2009-2010, the recorded low values of the North Atlantic Oscillation were due to the strong easterly phase of quasi-biennial oscillation [79,80].

Conclusions
This study examines the lower stratospheric temperature (LST) and the relationship between surface air temperature and lower stratospheric temperature over the Arabian Peninsula. In 1982 and 1992, the maximum LST was observed, which could be related to volcanic eruptions. Numerous studies, such as [81][82][83], demonstrate the influence of volcanic eruptions on the temperatures of the lower stratosphere and Earth's surface. These studies found that lower stratospheric warming and surface cooling occurred after a volcanic eruption. According to the linear trend, an insignificant downward cooling (−0.01 • C/year) through the period between 1951 and 2016 was found. The time series of the LST over the entire period was divided into two phases: the first one was from 1951 to 1992 and the second one was from 1993 to 2016. In the period between 1951 and 1992, there was an insignificant increasing linear trend (0.05 • C/year) in the LST, whereas in the period between 1993 and 2016, there was an insignificant decreasing linear trend (−0.05 • C/year). From the coefficient of variability (COV) method, the average value of the LST tends to increase. The mean values through the reference periods (1961-1990, 1971-2000, and 1981-2010) were more dependable due to the low value of the COV (−0.43, −0.42, and −0.01, respectively). Power spectrum analysis of LST time series and periodic behavior revealed peaks at 2.2, 2.54, and 13.2 years (significant at the 95% confidence level). Consequently, the quasi-biennial oscillation (2.2 and 2.54 years) and sunspots (13.2 years) may affect the LST. Correlation analysis was used to determine the relationship between the temperature of lower stratosphere and troposphere. A remarkably inverse relationship (r = −0.50; 99% confidence level) between LST and ST was found in the Arabian Peninsula during the winter season. Lead-lag cross-correlation was used to investigate the physical mechanisms between time series [35]. Lead-lag cross correlations between LST and the ST demonstrate that the correlation coefficient is −0.50 at zero lag. Many previous studies, e.g., [51,[53][54][55][56][57], have pointed out that the stratosphere and troposphere were related to each other in wintertime. According to [2], stratospheric cooling in association with surface temperature warming is due to the role of greenhouse gases.