Chun-xia ZOU*, Xiang-dong SHEN, Hong-yun LI, Xia-zi LI, Zhang-jun LI

1. College of Water Conservancy and Civil Engineering, Inner Mongolia Agricultural University, Hohhot 010018, P. R. China

2. College of Ecology and Environmental Science, Inner Mongolia Agricultural University, Hohhot 010018, P. R. China

3. Inner Mongolia Weather Bureau, Hohhot 010051, P. R. China

Wavelet analysis of spring climate characteristics in arid aeolian area of agro-pastoral ecotone in China

Chun-xia ZOU*1, Xiang-dong SHEN1, Hong-yun LI1, Xia-zi LI2,3, Zhang-jun LI3

1. College of Water Conservancy and Civil Engineering, Inner Mongolia Agricultural University, Hohhot 010018, P. R. China

2. College of Ecology and Environmental Science, Inner Mongolia Agricultural University, Hohhot 010018, P. R. China

3. Inner Mongolia Weather Bureau, Hohhot 010051, P. R. China

The unique regional climate characteristics are among the main reasons for the frequent wind-sand activity in arid and cold areas in the agro-pastoral ecotone in Inner Mongolia, China. This paper focuses on the time series of temperature and precipitation in spring when sandstorms often occur in the area. Based on meteorological data for a 46-year period from 1959 to 2004, multi-scale variations and abrupt changes in temperature and precipitation were analyzed with the Mexican hat function (MHF) wavelet method, showing the multi-scale variation characteristics of temperature and precipitation, as well as the periods and change points at different time scales. The relationship between temperature and precipitation was obtained using the wavelet analysis method. Obvious staggered features of the variations of spring temperature and precipitation were observed in this agro-pastoral ecotone. The strongest oscillation periods of spring temperature variations were 1 and 22 years, while for precipitation, the strongest oscillation periods of variations were 2, 8, and 22 years. In addition, lower spring temperature corresponded to lower precipitation, whereas higher temperature yielded higher precipitation rate.

spring temperature; spring precipitation; climate characteristics; MHF wavelet method; arid aeolian area; agro-pastoral ecotone

1 Introduction

Wind erosion has become one of the constraints of local economic development in the arid aeolian area of the agro-pastoral ecotone in Inner Mongolia, China. Many scholars have conducted research on wind erosion, including the distribution rule of wind erosion, through field and laboratory experiments (Zang et al. 2003; Chen et al. 2007; Sun et al. 2007; Zou et al. 2010). However, wind erosion is a complicated process influenced by many factors, such as climate, which has been shown to be the internal driving force of soil erosion (Zhu et al. 2008). Climate-driven wind erosivity has a strong relationship with sandstorm days (Zouet al. 2011) in the agro-pastoral ecotone. According to studies on the temporal and spatial distribution characteristics of atmospheric dust fall in Beijing, China, the spring dust fall is related to the spring climate (Tang et al. 2011). Skidmore (1994) proposed that temperature and precipitation are the main meteorological factors that affect wind erosion. Therefore, investigation of the climate characteristics is necessary to understand the causes of regional soil erosion by wind.

The wavelet transform analysis method has been widely used in the study of climate characteristics of different areas to investigate the meteorological variations of variables such as precipitation and temperature. It can help to obtain the relationship between temperature and precipitation, based on a study of the climate characteristics for a period of nearly 100 years in Beijing (Xie et al. 2000). The variation of annual precipitation in the Da’an area in Jinlin Province from 1959 to 2007 was studied based on the Morlet wavelet by Lu et al. (2010), while Ye et al. (2004) studied the characteristics of spring precipitation in the Loess Plateau area, Inner Mongolia, and Shan-Gan-Ning district using the wavelet analysis method. Yang et al. (2009) studied the characteristics of temperature change in spring. Partal and Kü?ük (2006) used a discrete wavelet transform to determine possible trends in the time series of total annual precipitation. The different complexity distributions of precipitation processes of the Chien River Basin (a sub-basin of the Minjiang Basin) in two periods (from 1952 to 1980 and from 1981 to 2009) were examined using the fractal method, based on the continuous wavelet transform (Luan et al. 2011). Mishra et al. (2011) used power laws and wavelet transforms to perform wet and dry spell analyses of precipitation generated by a global climate model. Most of these studies focused on the climate change and reasons. The climate characteristic plays an important role in arid aeolian areas.

The agro-pastoral ecotone in Inner Mongolia, China, is classified as an arid and semi-arid region, where sandstorms occur frequently in spring due to its varied temperature, lack of and non-uniform precipitation, sparse vegetation, and poor ecological environment. This study intended to investigate the characteristics of the spring climate as the main determinant of sandstorm activity and soil erosion, including the laws of air temperature and precipitation variations in the agro-pastoral ecotone in Inner Mongolia.

2 Description of research area

The research area is located at Siziwang (SZW) Banner (41°33′N, 111°38′E) with an elevation of 1 490.7 m above sea level, in the central part of an agro-pastoral ecotone in northern China. The 48-year mean annual precipitation from 1958 to 2006 is less than 315 mm, and the precipitation is concentrated in summer and fall, from June to October. The wind is much stronger in spring than at the other time of a year, with a mean speed of up to 4.8 m/s. Dust storms and sandstorms occur frequently during this period, accounting for 49% and 75.6% of the total in a year, respectively. In recent years, large amounts of tillage have beenremoved at increasing rates, and the area has become one of the poorest in Inner Mongolia in terms of the environment, ecosystem, and economy.

3 Data and methods

3.1 Data

All meteorological data of air temperature and precipitation from 1959 to 2004 in April were collected from the Inner Mongolia Weather Bureau and the SZW Banner weather station.

3.2 Wavelet analysis

Wavelet analysis is a mathematical method that provides a time-scale view of a time series, expressing a process in terms of averages and changes of averages over successively large scales. This also implies that the wavelet transform is a natural tool for investigating the scaling relationships inherent in many spatial and temporal processes, which have been expressed in terms of frequency and time coefficients (Fu 2006). The wavelet transform can be regarded as a mathematical microscope, for which the position and magnification correspond to the two coefficients.

The Mexican hat function (MHF) is particularly well-conditioned for time-based study, and is expressed as

whereg(t) is a mother wavelet, andtis a variable.

Ifg(a,b,t) is a mother wavelet composed of a time seriesf(t) and series parametersaandb, the wavelet transform coefficient is a convolution off(t) andg(a,b,t), and is defined as follows:

whereais a scale or frequency factor,bis the time factor, andTg(a,b) is the wavelet transform coefficient.

The discrete form is

where Δtis the sampling interval,iis the serial number, andnis the number of sampling points.

Thus, the result of the wavelet transform can be obtained by combining Eqs. (1) and (3).

Moreover, the variance of the MHF wavelet can be written as

4 Results and discussion

4.1 Multi-scale variations and abrupt features of spring air temperature

Four transition stages of the average spring air temperature were observed in SZW Banner using original data and the octic polynomial curve in Fig. 1: (1) a relatively cold period from the late 1950s to the early 1960s, (2) a relatively warm period in the mid-1960s, (3) a relatively cold period from the late 1960s to the early 1990s, and (4) a relatively and increasingly warm period from the mid-1990s to the mid-2000s. The average temperature was the lowest in the early 1960s, and the spring air temperature has risen each year since the mid-1990s.

Fig. 1 Variation of average spring temperature anomaly

In this study, a sample length of up to 23 years was used. The series was extended forward and backward to the length of the sample before the wavelet transform of the series. After the transform, the extended part was abandoned. Figs. 2(a) and 2(b) show the wavelet transform of the anomalous monthly average air temperature in spring from 1959 to 2004. The strength of the signal is illustrated by the values of the wavelet transform coefficient in Fig. 2, positive values showing a stronger signal, negative values showing a weaker signal, and zero corresponding to an abrupt change point, similarly hereinafter.

As shown in Fig. 2(a), the upper portion is relatively sparse, corresponding to a large-scale wave period (low frequency), and the lower part is relatively dense with high frequency. The distribution of the variables with different-scale periods is not uniform; that is to say, since 1959, the wave period of the monthly average spring temperature has varied. The centers of the strongest waves were located in the mid-1960s to early 1970s, the late 1970s, the early 1980s, the mid-1990s, the late 1990s, and the early 2000s, and the corresponding periods were 1 to 2, 3 to 5, 1 to 2, 1 to 2, 1 to 2, and 13 to 16 years, respectively.

The structure of spring air temperature was different at another scale. The small-scale warm-cold variation was nested in a large-scale variation. Abrupt change points can be diagnosed by the continuous wavelet transform coefficients, and their characteristics can be examined at different scales.

For the 15- to 23-year scale, the mean temperature in spring mainly experiencedalternations of cold and warm at two large time scales: a colder period before 1989 and a warmer one after 1989, with an abrupt change point in 1989. For the smaller-scale period, the climate fluctuation was more complex. For example, for the 3- to 5-year time scale, six transition stages of temperature were observed: a colder period before 1964, a warmer period from 1964 to 1975, a colder period from 1976 to 1982, a warmer period from 1983 to 1988, a colder period from 1989 to 1996, and a warmer period after 1996. The abrupt change points were 1964, 1976, 1983, 1989, and 1996. It appears that if the time scale is smaller, the climate fluctuation becomes more complex. It can be seen from the open contour shown in Fig. 2(a) that the air temperature tended to become higher at large time scales.

Fig. 2 Wavelet transform of mean spring temperature anomaly

Fig. 3 shows that the strongest wave periods of spring air temperature were 1 and 22 years over the whole time scale, illustrating notable characteristics of inter-annual and inter-decadal temperature variations according to the MHF wavelet variance.

Fig. 3 MHF wavelet variance of mean spring temperature

4.2 Multi-scale variations and abrupt features of spring precipitation

The spring precipitation series in SZW Banner and the octic polynomial curve are shown in Fig. 4. Six stages of change occurred from 1959 to 2004. Precipitation was relatively scarce in the early 1960s, the whole of the 1970s, and from the late 1980s to the mid-1990s, and relatively abundant in the late 1960s, the early and mid-1980s, and the late 1990s to 2004.

Fig. 4 Variation of percent of spring precipitation anomaly

For further multi-time scale analysis of spring precipitation, the length of the data was extended forward and backward, and the maximum period of the wave was set to be about half of the data length, that is, 23 years. The distribution of periodic variations of the spring precipitation at different time scales was different in this time domain (Fig. 5(a)).

Fig. 5 Wavelet transform of percent of spring precipitation anomaly

Oscillating periods have varied at different time scales since 1959. The strongest centers of oscillation were in the mid-1960s, the mid- to late 1970s, the early to mid-1980s, the early1990s, the late 1990s, and the early to mid-2000s, with periods of 2 to 3, 1 to 2, 2 to 3, 1 to 2, 1 to 2, and 6 to 9 years, respectively. That is, for cycles of about 1 to 2 years, the strongest oscillation occurred in the mid- and late 1970s and the early and late 1990s. The mid-1960s, as well as the early and mid-1980s, fits the cycle of 2 to 3 years, while the early and mid-2000s fit the 6-to-9-year cycle. The strong local feature in the time-frequency domain indicates a signal distribution in different-scale periods.

The variation of the spring precipitation was obvious in terms of years and decades, displaying two alternations: scarce before 1989 and abundant after 1989, with a 15- to 23-year time scale. The year 1989 was a catastrophe point. Complicated alternations were observed at smaller time scales. For example, at a time scale of 3 to 5 years, four alternations between the scarce and the abundant, i.e., the periods before 1962, from 1962 to 1968, from 1969 to 1996, and after 1997, were observed. At this scale, 1962, 1969, and 1997 were the catastrophe points. Smaller time scales tended to show more complicated alternations.

According to the MHF wavelet variance analysis shown in Fig. 6, the strongest oscillations of the spring precipitation were 2, 8, and 22 years, with obvious inter-annual and inter-decadal characteristics observed during the entire time domain.

Fig. 6 MHF wavelet variance of spring precipitation

4.3 Relationship between air temperature and precipitation

Over the whole time domain, the wavelet coefficient is in-phase (Figs. 2(a) and 5(a)). The variation of precipitation in spring in SZW Banner corresponds to the variation of temperature: lower temperature results in less precipitation, whereas higher temperature yields higher precipitation rate.

The detailed variations of wavelet coefficients for both air temperature and precipitation at different time scales are shown in Fig. 7. The spring precipitation-temperature relationship shows drier-colder and warmer-wetter characteristics at a 20-year time scale, which is in-phase. For the 2-year time scale, the phase difference is intricate in various periods. For example, the phases in the early and mid-1970s, the mid- and late 1980s, and the mid-1990s were in contrast to the periods before the 1970s and after the mid-1990s.

5 Conclusions

Fig. 7 Variation trends of mean spring air temperature and precipitation at different time scales

(1) The spring air temperature exhibits obvious staggered features. At the time scale of 15 to 23 years, two variations are observed: it is colder before 1989 and warmer afterwards. For smaller-scale periods, the variation is more complicated. Over the whole time domain, the strongest oscillation is observed at 1 and 22 years, indicating notable inter-annual and inter-decadal characteristics. The air temperature is higher at larger time scales, which can be seen from the open contour shown in the wavelet transform figures.

(2) The obvious staggered feature of precipitation is similar to that of air temperature. For the time scale of 15 to 23 years, two variations are observed: it is drier before 1989 and wetter after 1989. For smaller-scale periods, the variation is more complicated. Over the whole time domain, the strongest oscillations are observed at 2, 8, and 22 years, indicating notable inter-annual and inter-decadal characteristics. For both small and large time scales, precipitation is high, and even higher levels are expected in the future.

(3) The precipitation-temperature relationship shows drier-colder and wetter-warmer characteristics, which contribute to the trend of wind erosion climatic erosivity. Therefore, the soil erosion by wind is serious due to the climate characteristics in the dry and cold area of the agro-pastoral ecotone in Inner Mongolia, China.

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(Edited by Yun-li YU)

This work was supported by the National Natural Science Foundation of China (Grant No. 100262001), the Advanced University Science Foundation of Inner Mongolia (Grant No. NJzy08044), and the Ph. D. Foundation of Inner Mongolia Agricultural University (Grant No. BJ07-27).

*Corresponding author (e-mail:anna-zcx@163.com)

Received Sep. 28, 2011; accepted Apr. 7, 2012