Spatial and temporal variation of precipitation characteristics in the semiarid region of Xi ’ an, northwest China

Precipitation variations mostly affect the water resource planning in semi-arid regions of northwest China. The objective of this study is to quantitatively explore the spatial and temporal variations of precipitation in different time scales in Xi ’ an city area. The Mann – Kendall test and wavelet analysis methods were applied to analyze the precipitation variability. In terms of temporal variation of precipitation, the results indicated that the annual precipitation exhibited a signi ﬁ cant decreasing trend during 1951 – 2018. Except for summer precipitation representing a slightly increasing trend, the other seasonal precipitations had a similar decreasing trend to annual precipitation throughout 1951 – 2018. The monthly precipitation had different change trends, showing the precipitation from June to September could account for 58.4% of the total annual precipitation. In addition, it was clear that annual precipitation had a signi ﬁ cant periodic change, with the periods of 6, 13, 19, and 27 years. For the spatial variation of precipitation during 1961 – 2018, the results showed that annual and seasonal precipitation exhibited obvious spatial differences, indicating an increasing spatial trend from north to south. Thus, understanding the precipitation variation in Xi ’ an city can provide a theoretical foundation of future water resources management for other cities in semi-arid regions of northwest China.


GRAPHICAL ABSTRACT INTRODUCTION
Precipitation is the essential element to explore hydrological processes (Emmanuel et al. ), showing significant variability in terms of frequency, duration, intensity, and trend to identify its driving potential of extreme events to affect socioeconomic conditions to evaluate the spatial and temporal variation of precipitation (Sharma et al. ).
Meanwhile, the identification of the periodic variability of precipitation is of most importance for rainfall modeling and forecasting (Sang et al. ). Thus, it is necessary to explore quantitatively precipitation variation characteristics in urban areas. In recent years, the periodicity, spatial and For instance, China's sponge city development policy was put forward to solve many urban waterlogging issues which are due to frequent extreme precipitation events (Ding et al. ; Ma et al. ). In all, it is important to systematically evaluate the spatial and temporal variations of precipitation to help us upgrade the understanding of precipitation variability.
Xi'an city was not only the site of four of the world's ancient civilizations, but is also a large industrial city and a typical megacity in the semi-arid region in northwest China (Wang et al. ). Precipitation variation is potentially challenging the sustainable utilization of water resources in the semi-arid region of Xi'an. Meanwhile, with the rapid development of urbanization, the spatial and temporal variation of rainfall distribution has become uneven and significant in Xi'an (Chen et al. ). In addition, urban waterlogging has become an increasingly serious natural hazard under the changing environment in Xi'an city in recent years, while it has been affected by the factor of precipitation change (Wang et al. ).
Therefore, quantitative analysis of the spatial and temporal variation of precipitation distribution can provide a good For instance, Chen et al. () carried out the assessment of precipitation variations for the Guanzhong Plain (includes Xi'an) with an April-June gridded precipitation dataset for the period 1800-2009, which revealed that a gridded precipitation dataset can be better used to analyze the precipitation distribution, but it just focused on changes in monthly precipitation of Xi'an city. As mentioned above, there was still the need to investigate the spatial variation of precipitation with the gridded precipitation data in the semi-arid region of Xi'an, northwest China.
Moreover, choosing the appropriate method is of great importance to explore the spatial and temporal variation of precipitation. The statistical and graphical methods can be effectively used to detect long-term time series responses to various disturbances (Zhang et al. ). The Mann-Kendall test method is an important nonparametric statistical method widely used to detect the changing trend In addition, ArcGIS, as a leading GIS (geographic information system) software platform, has been successfully applied to analyze and visualize gridded datasets in climatological and meteorological studies (Xu et al. ). Thus, it can provide a better understanding of precipitation spatial visualization with the gridded precipitation data based on ArcGIS. The above-mentioned analysis methods can provide a better advantage for the precipitation variations' exploration in this work. Therefore, the aim of this study is to quantitatively investigate the spatial and temporal variations of precipitation based on the employed methods in Xi'an city. The entire urban region scale was selected in this work. It will provide a guide for managing regional water resources effectively and improving the capability for urban inundation disaster prevention and mitigation. The remainder of the paper is organized as follows. Details of the study area are described in the section below. This is followed by a section providing a description of the data resources and methods, including the linear analysis, Mann-Kendall test, and wavelet analysis method. Analysis results of the spatial and temporal variation of precipitation are presented in the next section, which also provides a detailed discussion about this work.
Lastly, brief conclusions of this paper are drawn in the final section.

STUDY AREA
Xi'an city is located in the hinterland of Shaanxi province in northwest China, the ninth National Central City in China. It is an important node city of the Belt and Road Initiative with an urbanization rate of 74.01% (Hu et al. ). As shown in Figure 1, the urban area lies between 107 30 0 and 110 E and between 33 30 0 and 35 N, covering a total area of approximately 1.1 × 10 4 km 2 , and its southern and eastern parts are the Qinling Mountains and the Loess Plateau in the north.
The terrain gradually rises from west to east, north to south, and the river flows from southeast to northwest. The urban climate is characterized by sub-humid warm temperate continental monsoon with four distinct seasons and abundant rainfall. The annual precipitation has a remarkable seasonal variability affected by the continental monsoon in Xi'an city (Bai & Wang ). The average annual precipitation in Xi'an city is 522.4 to 719.5 mm, with roughly 60% of it concentrated in the four months from July to October with an obvious seasonal change (Hu et al. ). In the past ten years, the duration of rainstorm and heavy rain has shown an increased trend, and thus the short-term heavy rainfall causes serious urban water-logging events with high frequency occurrence in Xi'an city (Wei et al. ). Hence, Xi'an city was selected as the case study to analyze the precipitation variations in this paper.

Data
The monthly precipitation from Xi'an meteorological station during 1951-2008 was obtained from the National Climate Center of China Meteorological Administration (CMA) (http://data.cma.cn/). This station was used to collect data from 1951 to 2008 as the national station. The location of the Xi'an meteorological station is shown in Figure 1. Therefore, the seasonal precipitation data and annual precipitation data were obtained from the monthly precipitation data. In order to better examine precipitation change, maintain data continuity and long-time data acquisition, it is necessary to add the numbers of annual precipitation and monthly precipitation time series data. The annual and monthly precipitation  Additionally, the dataset of gridded monthly precipitation in China (Version 2.0) (http://data.cma.cn/data/cdcdetail/ dataCode/SURF_CLI_CHN_PRE_MON_GRID_0.5.html) was adopted in this study. The gridded monthly precipitation dataset with a resolution of 0.5 × 0.5 from 1961 to 2018 within Xi'an city was released by the CMA. Meanwhile, the gridded seasonal and annual precipitation data were obtained from the gridded monthly precipitation.
Each grid cell contained monthly precipitation data in these grid cells' region. The above-mentioned collected precipitation data were strictly controlled by CMA and SPBS without missing any values.

Method
In this study, we applied the Mann-Kendall test method to analyze the trends of annual, seasonal, and monthly precipitation in Xi'an city during 1951-2018, and it was also used to identify the abrupt change year of the precipitation.
Then, spatial distribution of precipitation was explored in different time scales based on the spatial analysis and interpolation of ArcGIS. In addition, the wavelet analysis method was applied to better examine the periodicity of precipitation. Linear regression and Durbin-Watson (DW) test were employed to carry out linear trend analysis and check data autocorrelation, respectively.

Linear regression and Durbin-Watson test
In order to test autocorrelation of precipitation data, the DW test method can be used to check data autocorrelation in this work. Moreover, linear regression was applied to analyze trend change of variables. The general form of the linear regression equation is as follows (Yin ): where Y represents response variable, Y is annual precipitation data in this work; ω represents the frequency; β 0 represents the constant term, β represents the linear regression coefficient vector; X represents the independent variable, X is year in this work; ε represents a random error.
The linear regression coefficient is less than zero and greater than zero, indicating the precipitation data series decreasing and increasing linear trend. The DW test method is the most famous test for series autocorrelation (Yin 202 where d represents number of observations; e i , e i-1 represents residual of observations.

The Mann-Kendall test method
The Mann-Kendall test method was used to examine the nonlinear trend of precipitation in different time scales, and abrupt change year of precipitation in Xi'an city. ( (4) where the statistic S obeys the normal distribution with a mean of zero; x i and x j are two sequential data values of the variable; n is the length of the data series; and Z is the test statistic value. (2) Mann-Kendall change-point test analysis: The Mann-Kendall test method was also applied to examine the abrupt change-point time. Thus, the calculation process was: where UF is the forward statistic sequence; and UB is the backward sequence with a reversed series of data.
In the case of UF >0 and UF <0, it shows that the time series present an increasing trend and decreasing trend,  (12): where W f (a, b) represents the wavelet coefficient; a is the scale factor, reflecting the periodic scale of wavelet; b is the time factor; i represents the imaginary number; c is a constant.
In addition, the Morlet wavelet in CWT was applied to detect the periodicity of precipitation in this study. The reason is that the Morlet wavelet has the clear advantage where s represents the wavelet scale; ω represents the frequency; H(ω) represents the Heaviside step function; ω 0 represents the non-dimensional frequency. After

RESULTS AND DISCUSSION
This section described the temporal and spatial variation trends of precipitation in different time scales, and explores the abrupt change and periodicity change.
Variation trends and abrupt change analysis of precipitation in Xi'an city Variation trends of precipitation  Table 1 and Figure 2. The highest annual precipitation was 2.89 times higher than the lowest annual precipitation. Table 1 shows   Mann-Kendall trend test analysis in the next section. The average seasonal precipitation was presented in descending order of precipitation value, as summer precipitation (234.19 mm), autumn precipitation (184.06 mm), spring precipitation (128.34 mm), and winter precipitation (23.14 mm) (Table 2). However, seasonal precipitation variation was more significant than that of annual precipitation (the smallest C v of 21%). In addition, the coefficient of variance of the winter precipitation (C v is 63%) is larger than that of the other seasonal precipitations and annual precipitation (Table 2). This indicated that the data sequence of winter precipitation was more significant with a high discrete degree from 1951 to 2018, as shown in Table 2. This phenomenon was possibly because the temporal distribution of precipitation was uneven, and may be affected by climate change.     At the regional scale, the highest average annual precipitation in the southwest was higher than that of the other regions. While the precipitation was less in the western and northern regions, the higher precipitation was in the eastern and southern regions of Xi'an urban area, suggesting that the Qinling Mountains region in the eastern and southern regions had the higher precipitation. In addition, the spatial distribution patterns of the average seasonal precipitation were similar to those of the average annual precipitation (Figure 9), showing that the spatial distributions of the average seasonal precipitation increased from the north to the south. Compared to the spatial distribution of the average precipitation in spring, autumn, and winter, there was a significant distribution difference in average summer precipitation (Figure 9(b)). In addition, it was obvious that both the average annual and seasonal precipitation in the eastern and western wings of the urban southern region were quite different. Figure 10 shows the distribution of trends of the average annual precipitation during different periods in Xi'an city.    (a) 1961-1969 (b) 1970-1979 (c) 1980-1989 (d) 1990-1999 (e) 1951-1954, 1963-1972, 1982-1989, 1999-2007, and 2017-2018, indicat-ing high annual precipitation for these periods in the entire area. Meanwhile, the low annual precipitation periods with negative wavelet coefficient values were 1955-1962, 1973-1981, 1990-1998, and 2008-2016, suggesting

Comparison with previous studies
The spatial and temporal variation of precipitation is a crucial issue related to water resource management and planning in Xi'an city. In this study, we have shown a detailed assessment of the temporal variation trend in annual, seasonal, and monthly precipitation. It showed a decreasing trend in annual precipitation, with the regression   Therefore, it is important to further examine spatial and temporal variations of precipitation at the urban regional scale.

CONCLUSIONS
Based on the long-term measured precipitation data , this study investigated the spatial and temporal vari- • The spatial distributions of annual precipitation and seasonal precipitation were investigated in Xi'an city, indicating the regional precipitation had significant spatial variation characteristics. The spatial distribution of the seasonal precipitation was similar to the annual precipitation during 1961-2018, showing a spatial trend of increasing precipitation gradient from north to south, and the highest precipitation was mainly concentrated in the southwest region. Similarly, the precipitation for six separate periods exhibited the same spatial variation trend.
In summary, the obvious temporal variations and spatial distribution characteristics of precipitation in Xi'an city were discussed in this work. The results from this study will help to achieve better comprehensive understanding of the precipitation variations in Xi'an city, and can provide guidance for future water resource management and planning, and water resources optimal allocation under changing climate in other cities in semi-arid regions.
Meanwhile, this study could also provide basic references for investigating the spatial and temporal variations in other urban regions in China. In addition to the above-mentioned results, the effect of climate change and human activity on precipitation also requires further investigation in future research.