Evolution of meteorological factors during 1980–2015 in the Daqing River Basin, North China

Precipitation and temperature data, such as the homogeneity, trend, abrupt change, and periodicity, obtained at 40 meteorological stations in the Daqing River Basin from 1980 to 2015 are analyzed using the Mann–Kendall method, anomaly accumulation, Rescaled range analysis (R/S analysis) and wavelet transform. The regularity of climate change is studied to provide guidelines for the rational utilization of water resources. The results show that the annual precipitation has an insignificant upward trend and suddenly changes in 2007. The precipitation evolution can be divided into three types of periodicity, that is, 22–32, 8–16, and 3–7 year time scales, where the 28 year scale is the first main period of precipitation change. The annual average temperature shows a notable upward trend, with 1992 as the change year. The annual average temperature can be divided into three types of periodicity, that is, the 25–32, 14–20, and 5–10 year time scales, where the 28 year scale is the first main period of temperature change. In conclusion, the climate of the Daqing River Basin gradually turns into humid and hot climate. The results provide valuable reference for the assessment of the effects of climate change, and the management of water resources.


INTRODUCTION
Global warming has proved to be an indubitable fact (Sharma & Goyal ). The increase in the temperature accelerates the hydrological cycle (Tian & Yang ). Precipitation is a considerable part of the hydrological cycle and the main source of surface runoff. Because of climate change, precipitation, that is, the precipitation frequency and intensity has significantly changed due to climate change. This change further aggravates the spatiotemporal difference in the distribution of precipitation, affects the rational utilization and planning of regional water resources, and influences the sustainable socio-economic development (Xu et al. ). Under the current climate change condition, it is particularly important to discuss the long-term effects of the climate change on the meteorological factors on the global and regional scales (Kukal & Irmak ). Previous studies showed that, the changes in air temperature and precipitation present different spatio-temporal trends at regional and global scales (Crowley ; Li et al. ). In addition, regional climate change leads to the increase in the occurrence of natural disasters, such as drought and flood, as a result of the imbalance of water resources (Yang & Lau ).
One of the most crucial elements of the complex hydrological environment is the temperature. A global increase in the temperature has been determined, which varies in space and time. Precipitation plays a prominent part in hydrological processes and is the important contributor to affecting the water balance (Yang et al. ; Dai ; Stocker et al. ). Studies showed that the precipitation increased throughout the 20th century in the whole world (IPCC ) (Solomon et al. ). Global land precipitation increased by approximately 2% over the 20th century (New et al. ). Analogue to the temperature, distinct temporal and spatial changes can be observed in the precipitation. Furthermore, precipitation strongly varies, even on a small scale (Kukal & Irmak ). Therefore, research on precipitation and temperature characteristics has gradually become a hot topic in the fields of meteorology, hydrology, and ecology. Scholars studied the precipitation and temperature on a global scale (Zhang et  average warming and wetting rates of 0.32 C/10 a and 5.82 mm/10 a, respectively, by examining the climate change as well as periodicity and temporal and spatial variability from 1960 to 2016 (Xu et al. ).
There are also more detailed studies, such as using indices to identify climate change, as well as the seasonal research on the trends of temperature and precipitation.
Nine indices were applied to detect the drought and wetness cycle to determine the spatio-temporal precipitation and temperature characteristics in the Pearl River Basin   Figure 2.

Anomaly accumulation method
The anomaly accumulation is a method to judge the change trend directly from the curve. For the hydrological variable Yi with sample length n, the anomaly accumulation value S k at a certain time is expressed as follows: (Jiang et al.

):
where S k is the anomaly accumulation value in the K year, Yi is the observation value in i year, Y is the average value of observation series, n is the length of observation series.
If S k fluctuates around the value of zero, which indicates that there is homogeneity in time series. Then the standard deviation D y is used to correct the scale of S k . The homogeneity test statistic Q is the ratio of the maxi- If the statistic Q exceeds the critical value, it means that the series is not homogeneous. Table 1 shows the critical values of Q at different confidence levels.
The core of this method is that when the data continues to exceed the average value, the anomaly accumulation value increases, and the curve shows an upward trend, otherwise, it shows a downward trend. According to the fluctuation of the curve, we can judge the long-term evolution trend of the time series.

Mann-Kendall method
where n is the number of samples, t is the extent of all ties (equal values), and x j and x k are the sample time series.
A positive statistical Z value indicates that the variable increases, whereas a negative value implies a decline.
When jZj > Z 1À α 2 , the variable has a notable upward or downward trend at the significant level α. The critical value ±Z 1À α 2 can be obtained from the literature.
When the Mann-Kendall is used to detect the mutation of a sequence, one rank is constructed, where rank S k is the cumulative number of values at time i, which is greater than that at time j.
Definition of statistical variables: The parameter UF K is the standardized normal distribution. Given the significance level α, if |UF K | > U α=2 , the sequence notably changes. Subsequently, the time series x is arranged in reverse order and computed according to the following equation: Based on the statistical sequence UF K and UB K , the change of the time series x and abrupt change point and area can be determined. If UF K is above 0, the sequence has an upward trend; if it is below 0, the sequence has a downward trend. If the critical straight line is exceeded, the trend is significant. If there is an intersection between UF K and UB K between the critical lines, the time corresponding to the intersection is the time at which the abrupt change starts.

Rescaled range analysis (R/S analysis)
The R/S analysis method is also widely used in testing the hydrological series trend. The Hurst index (0 < H < 1), for different H, means that the sequence has different trends.
When H is 0.5, the sequence is absolutely independent, that is, it is a random process. When 0 < H < 0.5, it means that the future trend is opposite to that of the past (i.e., anti-persistent). The smaller H is, the stronger is the anti-persistence. When H > 0.5, it means that the future trend is identical to that of the past (i.e., persistent). The greater H is, the stronger is the persistence (Wang et al. ).

Wavelet analysis
Wavelet analysis is an efficient tool to study the multi-scale, where a is the parameter of scale, b is the parameter of position, and t is the time. For any signal f(t), the wavelet transformation is realized by the convolution of a wavelet scaling and translation set: where Ã represents the conjugation and W f (a, b) denotes the wavelet coefficients. Therefore, the concept of frequency is replaced by the scale on a given scale, which describes the variation of a signal f(t).
The wavelet variance is widely used to obtain the main period of the time series. It is the square of the wavelet transform coefficient that integrates b in the time-domain and can be expressed as follows: The choice of the wavelet function hinges on the specific signal. The Morlet wavelet function is often used in the fields of climate and hydrology. Its definition is as follows: where w 0 is the dimensionless frequency. When w 0 ¼ 6, the wavelet scale and Fourier period are equal. The wavelet spectrum can be used to detect the significance of the period through the spectral density over a range of timescales; it can be calculated as follows (Araghi et al. ): where N is the data length.

Precipitation homogeneity
The precipitation of the Daqing River Basin from 1980 to 2015 is analyzed using anomaly accumulation to determine if it is uniform. The cumulative value of precipitation is shown in Figure 3. The calculated Q value is 0.319126, and it is less than the critical value, which is 1.12 (99% confidence level). The precipitation is thus uniform.

Precipitation trend
A curve is drawn based on the annual average precipitation of the basin from 1980 to 2015. The linear regression equation and five-year moving average curve are fitted, and the rate of change is calculated (Figure 4). The Figure 4 shows an insignif-    Figure 7), that is, the wet season.
When it is negative, it represents a low flow period (dotted lines), that is, the dry season. Generally speaking, three   Trend of the main period. Based on the trend of the main period shown in Figure 10, the average period and characteristics of the variation on different time scales are analyzed. On the 28 years scale, the average period of precipitation change in the basin is ∼20 years (1980-2000 and 2000-2020), with two cycles of wet and dry change.

Temperature homogeneity
The temperature in the Daqing River Basin is analyzed to determine whether it was uniform or not from 1980 to 2015. The cumulative value is shown in Figure 11. The Q value is 0.320163, and it is less than the critical value, which is 1.12 (99% confidence level), such that the temperature is uniform.

Temperature trend
The annual average value and change rate of temperature is drawn ( Figure 12). The temperature has a significant upward trend. Meanwhile, based on the Mann-Kendall test for temperature, the Z value is 3.0919 and passes the significance test with 99% confidence. This means that we have 99% confidence in the significant trend of the temperature.     (Figures 15 and 16).
Temperature variance. Figure 17 shows three notable peaks,  years (1982-2000 and 2001-2018), with two cycles of cold-warm alternation. On the 18-year scale, the average change period of the temperature is ∼12 years (1981-1993, 1994-2005, and 2006-2017), with three cycles of coldwarm alternation.   climate of the Daqing River Basin gradually changes to a humid and hot climate.

DISCUSSION
In summary, the significant increases in the temperature and precipitation represent the main trend, which intensifies the development of humid and hot climate in the Daqing River Basin. First, the trends of precipitation and temperature in the region are consistent, indicating that the interannual change in the temperature is positively related to the precipitation. Secondly, based on the wavelet analysis, it can be concluded that there is a nested structure on multi- year scales of temperature and precipitation, which shows that the mutual response of the two parameters is prominent. The analysis of history is to better predict the future and actively respond to the various climate changes. These results provide useful information for the climate change assessment and the water resource management. In future research, the runoff data will be collected at hydrological stations to study the trends and periodicity of the region.
More detailed research will be carried out on seasonal or even monthly scales.