# 1952~2018年陕西省夏季温度、降水、风速演变的城郊对比Comparison of the Evolution of Temperature, Precipitation and Wind Speed between City and Suburb in Summer of Shaanxi Province from 1952 to 2018

Abstract: In the process of urban development, the underlying surface of urban areas will have a significant impact on climate change. In this paper, the monthly climatological data of Yulin and Hanzhong stations in Shaanxi Province from 1952 to 2018 were used to analyze the changing trends of air temperature, precipitation and wind speed in urban and suburban areas of Shaanxi Province through Morlet wavelet analysis and sliding t-test. In addition, according to the time series of precipitation in Hanzhong, Morlet wavelet analysis is carried out for the obtained short time series and comparison is made. The results show that compared with Hanzhong, Yulin has lower temperature, less precipitation and higher wind speed. The temperature and wind speed of the two places showed an upward trend, but the precipitation in Hanzhong showed a downward trend, while the precipitation in Yulin showed an upward trend. The change rate of meteorological elements in Hanzhong is more obvious than that in Yulin. The time scales of temperature, precipitation and wind speed are not consistent. From the perspective of time scale, considering the boundary effects, the summer precipitation in Hanzhong has a 5-year cycle, while the summer precipitation in Yulin has no obvious time scale characteristics. The summer temperature in Hanzhong has no obvious time-scale characteristics, while the summer temperature in Yulin has a 2-year cycle, a 5-year cycle and an 8-year cycle. The summer wind speed in Hanzhong and Yulin has no obvious time scale characteristics. In addition, the decomposition of sequences has an impact on the results of wavelet analysis. The period before partial years is not obvious, while the time scale features are obvious after partial years.

1. 引言

Figure 1. Map of Shaanxi Province with Yulin and Hanzhong in red boxes (The image is from http://image.so.com/)

2. 数据和方法

2.1. 数据

2.2. 小波分析

2.2.1. 母小波

Morlet小波为复数小波，包含了实部虚部。表达式如下

$\Psi \left(u\right)=C{\text{e}}^{-i{\omega }_{0}u}\left({\text{e}}^{-\frac{{u}^{2}}{2}}-\sqrt{2}{\text{e}}^{-\frac{{\omega }_{0}^{2}}{4}}{\text{e}}^{-{u}^{2}}\right)$

${\int }_{-\infty }^{+\infty }{|\Psi \left(u\right)|}^{2}du=1$

2.2.2. 子波

${\int }_{-\infty }^{+\infty }\Psi \left(T\right)\text{d}t=0,\Psi \left(T\right)\in {L}^{2}\left(R\right)$

${\Psi }_{a,b}\left(t\right)={|a|}^{-\frac{1}{2}}\Psi \left(\frac{t-b}{a}\right),a,b\in R,a\ne 0$

2.2.3. 小波变换

$\begin{array}{c}{W}_{f}\left(a,b\right)\equiv {\int }_{-\infty }^{+\infty }{f}_{\left(t\right)}{\Psi }_{a,b\left(t\right)}^{\ast }\text{d}t={\int }_{-\infty }^{+\infty }\left[\frac{1}{2\text{π}}{\int }_{-\infty }^{+\infty }{f}_{\left(\omega \right)}{\stackrel{^}{e}}^{i\omega t}\text{d}\omega \right]{|a|}^{-\frac{1}{2}}{\Psi }^{\ast }\left(\frac{t-b}{a}\right)\text{d}t\\ =\frac{1}{2\text{π}}{|a|}^{-\frac{1}{2}}{\int }_{-\infty }^{+\infty }{\stackrel{^}{f}}_{\left(\omega \right)}{\stackrel{^}{\Psi }}_{\left(a\omega \right)}^{\ast }{\text{e}}^{i\omega b}\text{d}\omega \\ =\frac{1}{2\text{π}}{\int }_{-\infty }^{+\infty }{\stackrel{^}{f}}_{\left(\omega \right)}{\stackrel{^}{\Psi }}_{\left(a\omega \right)}^{\ast }\text{d}\omega \end{array}$

2.2.4. 小波功率谱边界效应及边界影响e-折曲线

3. 降水序列趋势分析及小波分析

3.1. 降水序列趋势分析

Figure 2. Time series of summer precipitation from 1952 to 2018. The dotted line represents Hanzhong and the solid line represents Yulin. Blue represents the original sequence, black represents unitary linear fitting sequence, and red represents sliding average sequence

3.2. 降水序列小波分析

Figure 3. Morlet wavelet analysis of Hanzhong summer precipitation sequence from 1952 to 2018. Above: standardized time series of summer precipitation anomaly (solid red line); Middle left: wavelet power spectrum, black dotted line represents e-folded curve of boundary influence; Center right: time average spectrum (solid blue line), dotted red line is 0.05 confidence line; Bottom: 2~8 years average spectrum (solid blue line), dotted red line is 0.05 confidence line

Figure 4. Same as Figure 3, but Morlet wavelet analysis diagram of Yulin summer precipitation sequence

Figure 5. Wavelet analysis diagram of the sequence (length of 50 years) of Hanzhong summer precipitation after decomposition. Left: 1952~2001; middle: 1960~2009; right: 1969~2018

Figure 6. Wavelet analysis diagram of the sequence (length of 50 years) of Hanzhong summer precipitation after decomposition. Left: 195~1973, center: 1974~1995, right: 1997~2018

4. 气温序列趋势分析及小波分析

4.1. 气温序列趋势分析

Figure 7. Time series of summer temperature from 1952 to 2018. The dotted line represents Hanzhong and the solid line represents Yulin. Blue represents the original sequence, black represents unitary linear fitting sequence, and red represents sliding average sequence

4.2. 气温序列小波分析

Figure 8. Morlet wavelet analysis of summer temperature sequence in Hanzhong from 1952 to 2018. Above: standardized time series of summer temperature anomaly (solid red line); Middle left: wavelet power spectrum, black dotted line represents e-folded curve of boundary influence; Center right: time average spectrum (solid blue line), dotted red line is 0.05 confidence line; Bottom: 2~8 years average spectrum (solid blue line), dotted red line is 0.05 confidence line

Figure 9. Same as Figure 8, but Morlet wavelet analysis diagram of Yulin summer temperature sequence

5. 风速序列趋势分析及小波分析

5.1. 风速序列趋势分析

Figure 10. Summer wind speed time series 1952~2018. The dotted line represents Hanzhong and the solid line represents Yulin. Blue represents the original sequence, black represents unitary linear fitting sequence, and red represents sliding average sequence

5.2. 风速序列小波分析

Figure 11. Morlet wavelet analysis of Hanzhong summer wind speed sequence from 1952 to 2018. Above: standardized time series of summer wind speed anomaly (solid red line); Middle left: wavelet power spectrum, black dotted line represents e-folded curve of boundary influence; Center right: time average spectrum (solid blue line), dotted red line is 0.05 confidence line; Bottom: 2~8 years average spectrum (solid blue line), dotted red line is 0.05 confidence line

Figure 12. Same as Figure 11, but Morlet wavelet analysis diagram of Yulin summer wind speed sequence

6. 结论及展望

1) 气象要素平均状态城郊对比来看，汉中降水明显多于榆林，汉中气温高于榆林，汉中风速明显小于榆林；

2) 气象要素变化趋势城郊对比来看，汉中降水有缓慢减小的趋势，而榆林降水呈现缓慢增大的趋势。两地气温均有缓慢上升的趋势，两地风速均有缓慢增大的趋势；

3) 时间尺度城郊对比来看，考虑边界效应，汉中夏季降水为准5年周期，榆林夏季降水没有明显的时间尺度特征。汉中夏季气温没有明显的周期特征，榆林夏季气温为准2年周期、准5年周期和准8年周期。汉中夏季风速以及榆林夏季风速均没有明显的周期特征；

4) 汉中降水序列拆分后进行小波分析的结果表明，部分年份拆分前周期不明显，拆分后出现明显的时间尺度特征。

1) 郊区和城区各仅用一个气象站代替，气象站个数较少，结果可信度存疑；

2) 汉中相对榆林纬度偏南4˚左右，在气温序列分析中，未能剔除纬度的影响。

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