Research On the Multiscale Characteristics of the Early Spring Temperature and Response To Climate Indices Over the Past 179 Years in the Qinling Mountains

Examination of the periodic differences in temperature in the Qinling Mountains at different time scales is highly important in research on the long-term evolution of the regional climate system and ecological environment. Based on February-April temperature data from 1835 to 2013 obtained at 27 weather stations in the Qinling Mountains reconstructed through tree rings, the multiscale characteristics of the early spring temperature time series on the southern and northern slopes of the Qinling Mountains and the response to climate signals were analyzed. The results indicate that the early spring temperature in the Qinling Mountains exhibits signicant periodic characteristics on multiple time scales. Reconstruction at the different time scales reveals that the interannual scale change in the temperature variation on the northern slope of the Qinling Mountains plays a decisive role. The temperature on the northern slope exhibits a higher amplitude at the interannual and interdecadal scales than does that on the southern slope, and temporal differences occur at the quasi-century scale. The temperature achieves the strongest correlation with the original Atlantic Multidecadal Oscillation (AMO) sequence during the entire study period. In addition, the different time scales reveal that there exists a signicant response relationship between the temperature at the interannual scale and the May sea temperature in the NINO3.4 area, which lags by one year. At the different time scales and various time ranges, the Qinling early spring temperature responds differently to the climate signals, which is an important factor leading to a lower correlation during the entire study period.


Introduction
The Qinling Mountains, as an important north-south geographic boundary in China, are extremely sensitive to climate change. Therefore, this region has become a typical area for climate change research.  (Yan and Zheng 2001). The growth rate on the northern slope was higher than that on the southern slope, and the annual average temperature difference between the northern and southern slopes was gradually reduced. Over the past 122 years, the Qinling Mountains attained a signi cant correlation with the sea temperature in the tropical western Paci c and other regions (Tian et al. 2011). Previous studies have provided information and a reference to further examine the temporal change trend of the temperature in the Qinling Mountains. However, existing work has mainly focused on the application of traditional statistical methods in temperature change studies, such as linear tting and moving average methods, to calculate temperature warming trends at a constant rate (Ji et al. 2014). However, in terms of time series, the temperature not only exhibits a single linear change or multiple linear changes but also exhibits a complex process involving nonlinear and nonstationary states, including quasiperiodic changes on varying time scales. The multiscale temperature oscillation in long-term series re ects the periodic changes within the climate system, and different periodic changes can re ect cold and warm periods of climate change at multiple scales, which has implications for the study of long-term climate system trends and global warming mitigation. Therefore, it remains important to investigate the periodic changes in the Qinling temperature at different time scales.
In the early spring, winter snow melts in the Qinling Mountains and plants germinate. The temperature uctuations during this period directly affect vegetation growth in the region, and vegetation changes in turn affect regional climate changes and natural disasters caused by variations. Therefore, studying the multiscale periodic change in the early spring temperature is highly important for the prediction of the temporal evolution trend of plant growth and prevention of the formation of regional climate disasters.
Previous studies have indicated that multiscale climate signals, such as the El Niño/Southern Oscillation  . In addition, the Qinling regional climate exhibits a good response to ENSO and other indices (Ma et al. 2001), but the different climate signals characteristically experience periodic changes on multiple scales. There is less concern regarding the differences in the temperature response to global climate signal changes at the various time scales.
In this paper, temperature data obtained at 27 meteorological stations in the Qinling area from February-April 1835 to 2013 reconstructed via the tree-ring width chronology method are employed to conduct multiscale analysis of the 179-year early spring temperature time series pertaining to the southern and northern slopes of Qinling to reveal the multiscale regional changes in temperature against the background of global warming. We analyze the correlation between the temperature and a variety of climate signals on different time scales to study the possible responses of cyclical temperature changes within the context of multiscale global climate changes, explore the nature of regional cyclical temperature changes in depth, and further provide a reference for regional climate prediction.

Overview of the study area and data sources
The Qinling Mountains (32°40′N-34°35′N, 105°30′E-111°3′E) comprise the boundary between the north and south and between the subtropical and warm temperate zones in China, and these mountains further contain sensitive ecological environments ( Figure. 1). Over the past 60 years, the temperature trend rate on the northern slope of the Qinling Mountains was 0.24℃/10 a, and the temperature trend rate on the southern slope reached 0.15℃/10 a (Zhang et al. 2018).
The temperature data analyzed in this paper include the average temperature at 27 meteorological stations in the Qinling area from February-April 1835 to 2013 reconstructed from 32 tree-ring width chronology data (Hou et al. 2017). The data are established with a linear regression equation, and the data reliability is tested with the one-by-one elimination method. The correlation coe cients of the data retrieved from each meteorological station are all above 0.4, the complex correlation coe cient and reliability value of the F test both reach 0.99, and the error reduction value approaches 0.3. The reliability values, such as the sign test and product average, are above 0.99. The test results con rm that the reconstruction results are accurate and reliable.
The seven climate signals selected in this paper to study the multiscale response to the Qinling temperature include regional ocean temperatures or large-scale atmospheric circulation phenomena under long-term series, and all these climate signals exhibit periodic changes at different scales.
Monthly average data of these 7 climate signals are acquired from the o cial website of the National Oceanic and Atmospheric Administration (NOAA) (http//www.noaa.gov) ( Table 1).  (Wei 1999). This method inherits the advantages of the EMD adaptability, addresses the problem of unclear modal separation and extracts climate change signals more truthfully and reliably. This method rst adds quali ed white noise to the original signal, continuously deepens the signal intensity for cyclic testing and thereafter computes the overall average value to cancel the added white noise. The result is then applied as the nal intrinsic mode function (IMF) component of EEMD: In equation (1) The time-dependent intrinsic correlation (TDIC) method is a correlation analysis method based on the EEMD method proposed by Chen et al (Chen et al. 2010). This method is suitable to evaluate the relationship between two sets of sequences at different time scales. TDIC analysis rst compares the two sets of IMFs decomposed via EEMD and selects those IMFs with similar average periods among the sets of sequences for internal correlation analysis. In the analysis process, the minimum sliding window size for comparison should be clari ed, and Student-t test should be performed to verify whether there occurs a signi cant correlation between the two sets of IMF sequences. In the nal established TDIC correlation matrix, the abscissa indicates the time, the ordinate indicates the size of the sliding window, and the part that fails the signi cance test is shown in the gure (Adrsh 2017). Compared to the traditional correlation analysis method, the advantage of this method is that local correlation between any two data columns can be analyzed to re ect the differences in the correlation between the data during the different periods. In addition, this method calculates the IMF correlation after EEMD application, so it is more suitable to study the correlation of nonlinear and nonstationary time series, which is di cult to accomplish in traditional correlation analysis.
Multiscale temperature reconstruction further explores the change trend of the temperature at the different time scales. This paper adds IMF components at the different time scales to obtain the overall temperature change trend on a given scale. Interannual scale changes are determined by adding IMF components that re ect the interannual period. The decadal scale is obtained by adding IMF components re ecting the interdecadal period. Larger-scale periodic oscillations are obtained by adding IMF components with a scale larger than the decadal period and the trend term RES.

Results And Analysis
3.1 Trend characteristics of the temperature changes According to Figure 2, over the past 179 years, the temperature tendency rate in the Qinling Mountains reaches 0.013℃/10 a on the northern slope and 0.010℃/10 a on the southern slope, and the increase rate on the northern slope is slightly higher than that on the southern slope. The temperature anomaly indicates that the temperature uctuation range on the northern slope is generally larger than that on the southern slope. Except for a large difference in individual years, the temperature on both the southern and northern slopes exhibits a nonlinear and nonsteady increase trend, and the temperature experiences a uctuation process of increase -decrease -increase -decrease -increase -increase. Since the beginning of this century, there has occurred a notable increase in the number of years with an average temperature 0.5°C higher than the average temperature during the study period, which indicates that the probability of extreme temperature events in the Qinling Mountains has considerably increased. Traditional linear trend analysis cannot re ect the true conditions of the temperature uctuations during the study period. Therefore, a nonlinear research method different from traditional methods should be adopted when studying temperature change in this area.

Multiscale changes in the temperature
With the use of MATLAB2014a software as the platform, the signal-to-noise ratio between the white noise-disturbed and original signals reaches 0.2, and the number of samples is 100. During the 179-year study period, the average temperature on the southern and northern slopes of the Qinling Mountains from February to April is multiscaled based on the EEMD method, and 5 IMF components and trend item RES are obtained for both the northern and southern slopes. The eigenmode components of temperature decomposition on the northern slope are denoted as IMFn, and those on the southern slope are denoted as IMFs. These two sets of IMF components in turn re ect the multiscale changes in temperature from a high frequency to a low frequency on the southern and northern slopes of the Qinling Mountains from February to April ( Figure. 3). The change in the amplitude indicates the strength of the cycle, which is the result of the joint action of internal movement and external factors of the climate system (Xue et al. 2013). The residual trend item RES re ects the overall trend over time of the temperature changes during the study period. Figure 3 shows that the early spring temperature in the Qinling Mountains exhibits periodic oscillations at the various time scales, such as interannual, interdecadal, and quasi-century oscillations. On an interannual scale, the northern and southern slopes attain average periods of quasi 3 a (IMFn1 and IMFs1), quasi 7 a (IMFn2), and quasi 8 a (IMFs2). The cyclical temperature changes on the northern and southern slopes are roughly the same at the interannual scale, but the beginning and ending years and the amplitudes of the changes are different.
At the interdecadal scale, the temperature on the northern slope experiences periodic uctuations of quasi 17 a (IMFn3) and 43 a (IMFn4), while the temperature on the southern slope experiences periodic uctuations of quasi 19 a (IMFs3) and 37 a (IMFs4). The cycles on the northern and southern slopes are not very different, but the amplitudes are dissimilar. The 1859-1880 and 1925-1963 periods on the northern slope belong to the strong IMFn3 period. The trend for the southern slope is relatively at, and the amplitude is signi cantly lower than the average amplitude from 1894-1924, which is the weaker IMFs3 period. The amplitude of IMFn3 on the northern slope is generally higher than that on the southern slope. Except for the period from the 1940s to the 1990s, the amplitude of IMFn4 on the northern slope is slightly lower than that of IMFs4 during the rest of the period. The difference in amplitude indicates that the temperature on the northern slope at the quasi-18-19 a scale is more cyclical, while that on the southern slope at the quasi-37-43 a scale is more cyclical.
On a quasi-century scale, the periods of IMFs5 and IMFn5 are similar. Except for the large uctuations in the temperature cycle and amplitude on the southern slope from 1839-1871 and 1902-1950, the temperature change periods and amplitudes on the southern and northern slopes are similar during the remainder of the period. The trend items RESn and RESs reveal that over the past 179 years, the temperatures on the northern and southern slopes exhibit a nearly linear but actually nonlinear risinggentle -rising trend.

Reconstructing the multiscale characteristics of the air temperature
This paper reconstructs the interannual, interdecadal, and quasi-century scale periodic changes in the temperature in the Qinling Mountains ( Figure. 4). Among these changes, the interannual temperature change is obtained by adding the rst and second IMF components, the interdecadal scale temperature change is determined by adding the 3rd and 4th IMF components, and the quasi-century scale temperature change is obtained by adding the 5th IMF component and the RES trend term.
According to Figures 2 and 4, the reconstructed interannual scale change trend can describe the uctuation state of the original temperature sequence during the study period. The interdecadal change fully re ects the variation in the original temperature anomaly during the different periods of the climate patterns, and the quasi-century scale changes explain the general trend of the temperature changes during the study period. On an interannual scale, the temperature amplitude on the northern slope is generally higher than that on the southern slope. However, since the late 1990s, the interannual scale amplitude on the southern slope is higher than that on the northern slope. At the interdecadal scale, the amplitude on the northern slope is higher than that on the southern slope during the entire study period, and the temperature on the southern slope changes slowly. On a quasi-century scale, before 1940, the amplitude on the northern slope was higher than that on the southern slope, and the temperature change on the northern slope was more severe than that on the southern slope. After 1940, the temperature amplitude on the southern slope was higher than that on the northern slope, and the uctuations intensi ed.
At the interannual and interdecadal scales, the amplitude of the temperature on the northern slope of the Qinling Mountains is generally higher than that on the southern slope. The possible reason is that the Qinling Mountains are located in the tail region of the East Asian monsoon. Hence, the northern slope area is more greatly affected by the alternation between the East Asian and northwest monsoons and the complex changes in global climate circulation. The northern slope is shaded by the Qinling Mountains, the underlying surface, including vegetation, topography and other factors, is more sensitive to climate changes, and vegetation growth imposes a more obvious modulating effect on the temperature. The northern slope exhibits a large temperature difference between the morning and evening and between the months. In the months with su cient heat, the climate change is similar to that on the southern slope, but the difference is obvious in the other months. Due to many factors, the temperature amplitude on the northern slope of the Qinling Mountains is higher than that on the southern slope. Qinling Mountains has been rising over the past 50 years, which is mainly re ected at the interdecadal and quasi-century scales. The temperature growth rate on the northern slope is higher than that on the southern slope, which is mainly manifested in the dramatic changes in temperature on the northern slope on an interdecadal scale ( Table 2).
The variance contribution rate constitutes the basis to evaluate the degree of in uence of the frequency and amplitude of each component on the overall characteristics of the original temperature series . Table 3 provides the variance contribution rate of the air temperature components (IMFn and IMFs) on the southern and northern slopes of the Qinling Mountains after decomposition and calculates the correlation coe cient with the original air temperature series. The contribution rate to the interannual variance on the northern slope is 47%, the decadal variance contribution rate is 31.64%, and the quasicentury scale variance contribution rate is 21.36%. The sum of the contribution rates to the interannual variance on the southern slope is 52%, the sum of the decadal variance contribution rates is 21.22%, and the sum of the quasi-century scale variance contribution rates is 26.78%. Both the southern and northern slopes reveal the most signi cant temperature changes at the interannual scale. The difference is that the decadal contribution on the northern slope exceeds the quasi-century scale contribution, while the quasicentury scale contribution on the southern slope is greater than the decadal contribution.
Through the signi cance test, it is found that except for IMFn2 on the northern slope of the Qinling Mountains, which falls on the 0.05 con dence line, the other components occur above the 0.05 con dence line, and the signi cance test is passed. Each component on the southern slope passes the signi cance test and is signi cantly higher than that on the northern slope ( Figure. 5). The test results correspond to the variance contribution rate and correlation coe cient of the original series.   (Table 4), which indicates a better synchronization trend. The insigni cant quasi-century scale correlation with the average temperature in China over the past 100 years may be attributed to the short temperature series over the past 100 years and the fewer quasi-century scale uctuations, which re ects the changes above the quasi-century scale. In contrast, since the 1950s, the warming trend thereafter is similar to that of the other series. Figure 6 shows the comparison results of the reconstructed Qinling area temperature in this paper to the three sets of temperature series at the interdecadal and quasi-century scales. On an interdecadal scale, several series reveal similar uctuation trends. On a quasi-century scale, the temperature trend in the Qinling region decomposed in this paper attains the highest correlation with the temperature uctuation trend in central Qinling from May to July, indicating that the periodicity of the temperature in the Qinling region from February to April is representative for the study of the periodicity of the temperature in the region during other periods. Since 1950, the quasi-century-scale uctuation trends of the four series are almost the same, revealing a trend of falling rst and then rising. This trend has been con rmed by many scholars (  The multiscale temperature oscillation in the Qinling Mountains not only re ects the nonlinear feedback within the climate system but also re ects the periodic evolution of the climate system under external forcing. To identify the response of the Qinling Mountain temperature to ocean oscillations and atmospheric circulation at different time scales based on the periodic changes in the early spring temperature and to provide a basis for the prediction of regional climate evolution, this paper selects seven climate signals to study the response of the multiscale periodic changes in the early spring temperature in the Qinling Mountains to global climate change (     temperature are negatively correlated with the global average early spring temperature or an important in uencing factor causing these two components to be uncorrelated during the entire study period. This further indicates that the Qinling early spring temperature exhibits a unique change cycle at this scale. Although the Qinling early spring temperature and the Niño 3.  Overall, as shown in Figure 7, compared to the other climate signals (such as NAO, SOI, NP, and PDO), AMO achieves a closer relationship with the changes in the Qinling early spring temperature. Moreover, this relationship is re ected at the different time scales, which is consistent with the conclusion that the relationship between AMO and the temperature in China is stronger than that with the other climate signals, as reported by Wang et al. . This stable relationship between these two variables may be one of the main in uencing factors of the multiscale change in the early spring temperature in Qinling. There are many possible reasons for the mechanism by which AMO affects the temperature. Tung et al. proposed that the multidecadal temperature oscillation is a change mode re ected by AMO that affects the internal changes in the climate system (Ka-Kit and Zhou 2013). Lu et al.
acknowledged that AMO affects the multidecadal changes in the climate of the Eurasian continent by causing a feedback mechanism of the atmosphere and ocean in the western Paci c (Lu et al. 2006). In addition, studies have found that most areas in China experience a warm winter when the AMO phenomenon occurs in the positive (warm) phase (Qu et al. 2006). This conclusion has also been con rmed by different scientists. The interdecadal variation in AMO and the East Asian monsoon still yields an obvious modulation effect. When AMO occurs in the positive phase, the East Asian summer monsoon will increase, the winter monsoon will weaken, and the cold phase will be reversed (Li et al. 2009). Therefore, the change in AMO at the interdecadal scale may be an important factor leading to the increase in the early spring temperature in the Qinling area. Table 7 demonstrates that at the different time scales, the relationship between AMO and the Qinling early spring temperature is not unique. These two variables are positively correlated on certain scales and negatively correlated on other scales. During the entire study period, the correlation between the original temperature series and the AMO index was lower than that with the decomposed components. It may be that the positive correlation on certain scales may be offset by the negative correlation at the other scales. Alternatively, within the same IMF, the positive correlation during certain periods may be offset by the negative correlation during other periods. Figure 7 shows that the phase changes of the air temperature and AMO at the different time scales are the same during certain periods but are the opposite during the other periods. For example, IMF2 exhibits the opposite phase of the temperature and AMO from 1940-1970, and IMF5 exhibits the same phase from 1920-1958. Figure 7 shows that there occurs an alternating phenomenon in the correlation between the air temperature and AMO for each IMF component. To analyze the relationship between these two variables, it is necessary to conduct a dynamic correlation analysis of the region.
Traditional correlation analysis indicates that the longer the time span is, the more unstable factors occur, and the temperature and climate signals experience nonlinear changes, which makes it di cult to accurately characterize the correlation. To quantify the relationship between these two aspects locally, dynamic correlation analysis should be carried out (Rodó et al. 2006;Scafetta N 2014). When performing dynamic correlation analysis to study the relationship between two time series with multiscale features, it is necessary to perform local correlation analysis by selecting an appropriate sliding window.
TDIC analysis is performed between the IMFs components of the two time series with a similar periodicity, and a TDIC analysis chart is generated by adaptively selecting the sliding window size (to ensure the stability of the sliding window, rather than the stability of the entire time domain). The rst four IMF components with a clear signi cance were selected with the TDIC method to analyze the correlation between AMO and air temperature ( Figure. 8). The abscissa in the gure represents the year, and the ordinate represents the size of the sliding window for these two data columns. Figure 8 shows that AMO attains a correlation with alternating positive and negative air temperatures in the IMF1 component, and a signi cant negative correlation is obtained from 1940-1975, while the IMF2 component achieves no signi cant correlation in most years. Except for the two ends of the sliding window, the IMF3 and IMF4 components are signi cantly positively correlated throughout the entire study period. AMO and the temperature also attain a signi cant correlation at the quasi 3 a scale, but this correlation varies over time, which leads to a lower correlation during the entire study period. The reason for this reversal is currently unclear. This may be attributed to the many years of lead-lag correlation between the temperature and climate signals and the complexity of the internal interaction between the ocean and the atmosphere.
The terrain of the Qinling Mountains is complex, and the temperature response to the AMO climate signal may be different in the various regions. Figure 9 shows the spatial correlation between the temperature and AMO at various scales. Mountains attains a higher amplitude than that on the southern slope at the interannual and interdecadal scales most of the time. On a quasi-century scale, the amplitude is higher than that on the southern slope before 1940, and vice versa thereafter. Over the past 50 years, the increase in the early spring temperature on the northern slope of the Qinling Mountains was larger than that on the southern slope, mainly due to interdecadal temperature uctuations.
The early spring temperature in the Qinling Mountains responds differently to the climate signals at the different time scales and various time ranges. There exists a signi cant correlation between the temperature and AMO during the same period and a signi cant correlation with SOI in May and with Niño 3.4, NP, and NAO in December, lagging one year. On an interannual scale, the temperature attains the most signi cant response to the May SST in the Niño 3.4 area. At the interdecadal scale, the response is the strongest for AMO. At the quasi-century scale, the responses of the various climate signals are signi cant, and the correlation is generally higher than that at the interannual and interdecadal scales.
The early spring temperature in the Qinling Mountains achieves a stronger synchronization with global climate change on a larger scale. The weaker correlation between the temperature and AMO at the interannual scale is attributed to the different correlations during the various periods, and the positive and negative correlations cancel each other during the entire study period. In terms of spatial changes, these two aspects reveal that the larger the scale, the wider the response range is, and there are differences between the different altitudes.
In addition, it should be noted that since the temperature data selected in this paper comprise an average sequence from February to April, although the sequence is related to the trend of annual average temperature changes, there are certain differences. Hence, the data cannot represent continuous temperature changes. Therefore, the possible lead-lag correlations between the temperature and climate signals at the different time scales, such as the monthly or interdecadal time scales, were not analyzed. Finally, since the long-term temperature and climate signals are reconstructed from proxy data, there exists a certain error, which may also be one of the factors that cause the correlation between these two variables to be insigni cant, which should be further veri ed with more comprehensive data. Figure 1 Distribution of the meteorological stations and tree-ring sampling sites in the Qinling Area