Spatio-temporal Evolution Analysis of Rainfall Erosivity During 1901-2017 in Beijing, China


 Rainfall erosivity is regarded as one of the main factors affected soil erosion. Based on the 117 a monthly precipitation data of Beijing from 1901 to 2017, the temporal and spatial variation characteristics of rainfall erosivity in Beijing were analyzed by using Theil-Sen median analysis (Sen) and the Mann–Kendall (MK) trend test, R/S analysis method, cumulative anomaly method , MK mutation test method, Pettitt test, and wavelet analysis. The results showed that the average annual rainfall erosivity in Beijing ranged from 1080.6 to 6432.78 MJ • mm / (hm2 • h • a), with an average value of 3465.06 MJ • mm / (hm2 • h • a), showing a gradual decrease from southeast to northwest. In the seasonal distribution, 86% of rainfall erosivity was mainly concentrated in summer. In the past 117 years, the annual rainfall erosivity in most areas of Beijing had shown a downward trend, but its future trend also showed an increasing trend, indicating that Beijing, especially the northern part, was facing greater potential pressure of soil erosion. Through the cross validation of various methods, the abrupt change interval of rainfall erosivity in Beijing from 1901 to 2017 was from 1994 to 1997. The change of rainfall erosivity in Beijing has strong oscillation in 32 years and small periodic change in 15 and 7 years. The results will provide decision-making basis for soil erosion control and water/soil conservation planning. Additionally, they will be benefited to ensure the national agricultural and food security.


Introduction 93
Soil erosion is almost one of the most serious natural hazards which can affect 94 other rainfall parameters to compute rainfall erosivity. The above calculation data of 128 rainfall erosivity are mainly from precipitation data of meteorological stations, 129 researchers only use the appropriate interpolation method to obtain complete 130 precipitation data. 131 At present, most of the calculated data of rainfall erosivity mainly comes from 132 meteorological sites with short time series, while with long time series of high 133 resolution remote sensing data to calculate the rainfall erosivity relatively few, the main 134 data used in this paper is the long time series of 1 km high-resolution monthly 135 precipitation data. Compared with the data from meteorological stations, it has a higher 136 spatial resolution and a longer time series, so its accuracy in calculating rainfall 137 erosivity in regions, understanding spatio-temporal variability and determining areas 138 vulnerable to rainfall erosivity will be greatly improved. 139 In China, there are few studies on rainfall erosivity, especially in Northeast and 140 North China. Beijing is located in North China. As the administrative center and 141 economic center of China, the population density of Beijing is comparatively higher 142 than that of other surrounding areas; meanwhile, the social and economic 143 development is rapid. Beijing is mountainous in the northwest and plain in the 144 southeast, with heavy rainfall and serious soil erosion problems; therefore, the rainfall 145 distribution in Beijing is uneven, and the temporal and spatial evolution of rainfall 146 erosivity will also show certain rules. In addition, due to the influence of thermal 147 dynamic factors and other factors, drought and flood disasters occur frequently in 148 Beijing. Accordingly, the study of rainfall erosivity in Beijing from 1901 to 2017 can 149 supply a theoretical reference for the comprehensive protection and management of 150 soil erosion, and then have a profoundly impact on the ecosystem balance of Beijing. 151 The objective of this research was to (i) calculate the rainfall erosivity by using the 152 monthly precipitation data to analyze the spatio-temporal differences and Hurst index 153  (1) 201 where: R-rainfall erosivity index (MJ•mm / (hm 2 •h); I30 -Maximum 30 min 205 rainfall intensity (mm / h), E-total kinetic energy of rainfall (MJ/hm 2 ), ir -breakpoint 206 rainfall intensity (mm / h) in the r period of a rainfall process, which can be divided into 207 n periods, -rainfall in the r period (mm), er-unit rainfall kinetic energy in the r period 208 (MJ / (hm 2 •mm). E '-the total kinetic energy of a day's rainfall (MJ / hm 2 ), which is a 209 part of the total kinetic energy of a rainfall. The coefficient of determination of daily rainfall model and monthly rainfall 219 model was 0.72, and the coefficient of determination of annual rainfall was 0.58. As 220 the monthly rainfall data is used in this paper, the monthly rainfall model was 221 adopted. 222

Theil-Sen median analysis and the Mann-Kendall trend test 223
Theil-Sen median trend analysis (Sen, 1968) linked with the Mann-Kendall test 224 (Mann, 1945;Kendall, 1975) have been widely used to analyze the temporal variation 225 of temporal trends of hydrological data (Qiao et al. 2020). 226 Theil-Sen Median method, also known as Sen Slope estimation method, is a trend 227 calculation method that is used in non-parametric statistics. This method has high 228 computational efficiency and is often used in trend analysis of hydrological elements of 229 long time series data. Mann-Kendall trend test (Huang et al. 2013) is a non-parametric statistical test 234 method, which was first proposed by Mann in 1945 and has been widely used in the rejected, and the time series data show significant trend changes. Z1-α/2 is the value 238 corresponding to the distribution table of the standard normal function at the 239 confidence level Z. When |Z| is greater than 1.65, 1.96, and 2.58, it means that the 240 trend has passed the significance test with reliability of 90%, 95% and 99%, 241 respectively. 242

R/S analysis method 243
The R/S analysis method (Li et  the temperature is changeable, and the daily range is large, so it is easy to have gale 338 and dust weather; in summer, it is hot and rainy, which is the season of thunderstorm, rain, comfortable and pleasant; in winter, it is cold and dry, windy and less snow. The 341 study season is divided into spring (March, April, May), summer (June, July, August), 342 autumn (September, October, November) and winter (December, January, February). 343 It can be known from fig. 4 that the spatio-temporal distribution of rainfall 344 erosivity in different seasons was quite different. 86% of the rainfall erosivity in 345 Beijing was concentrated in summer, ranging from 1992.84 to 4152.47 MJ • mm / 346 (hm 2 • h • a), and its spatial distribution was similar to that of the average rainfall 347 erosivity in Beijing. 348 The range of rainfall erosivity in spring was 124.45 to 424.46 MJ • mm / (hm 2 • 349 h • a), and the rainfall erosivity in the whole province was generally low, including was close to that in spring, but there were differences in spatial distribution. In 354 autumn, the rainfall erosivity in the north and west of Beijing was higher than that in 355 the south. The warm and humid air in the southeast was uplifted by the Yanshan 356 Mountain and Taihang Mountain, and formed a rain-bearing area on the windward 357 slope and a rain-less area on the leeward slope. Therefore, the spatial distribution 358 feature of rainfall erosivity was formed. 359 Compared with other seasons, the value of rainfall erosivity was the lowest in 360 winter. The high value area was located in the urban area, where it can be saw that the 361 urban heat island effect had a certain impact on the rainfall, so the rainfall erosivity 362 was relatively high. Sen, the MK trend test, and Hurst index were adopted to explore temporal 368 evolution of rainfall erosivity. 369

Annual trends of rainfall erosivity 370
The variation trend results of rainfall erosivity in Beijing were displayed in the 371  In the analysis of the change process of rainfall erosive accumulation anomaly 397 curve (Fig. 7), the fluctuating rising stages were as follows : 1907-1917, 1921-1925, 398 1945-1979, 1993-1996, 2015-2017. The fluctuating decreasing stages as follows: 399 1901-1907, 1917-1921, 1925-1945, 1979-1984, 1996-2015. The rest stages show 400 fluctuation state and the trend change was not obvious. Therefore, it can be inferred 401 that 1907, 1917, 1921, 1925, 1945, 1979, 1996, 2015  Beijing, we used wavelet analysis to detect its periodic variation. From the wavelet 432 variance diagram (Fig. 10), it can be found that there were three peaks, which 433  (Table 2). This paper studied the correlation between El Niño/La Niña 449 events and rainfall erosivity in Beijing. In the correlation analysis, the relative 450 changes of annual average rainfall erosivity in Beijing and El Niño/La Niña events 451 were analyzed by comparison. 452 As can be seen from the table below, the average annual rainfall erosivity during 453 El Niño events was 178.09 MJ•mm / (hm 2 •h•a), the average annual rainfall erosivity 454 mm / (hm 2 •h•a), and the erosivity of annual average rainfall was 288.53 MJ•mm / 457 (hm 2 •h•a). The rainfall erosivity in the case of El Niño/La Niña events was greater 458 than that in the case of El Niño events and lower than that in the case of non El 459 Niño/La Niña events. However, in the case of non El Niño/La Niña events, the 460 rainfall erosivity was greater than that in the case of La Niña events and El Niño 461 events. From the numerical variation, it can be summarized that the range of rainfall 462 erosivity between El Niño/La Niña events was no obvious pattern. The influence of 463 cold and hot events formed by El Niño/La Niña events on rainfall and rainfall 464 erosivity in Beijing did not show strong regularity. ENSO and rainfall erosivity in 465 Beijing were not stable. El Niño events did not strictly correspond to high values 466 whereas La Niña event did not strictly correspond to a low value.   The data used in this paper were monthly precipitation grid data with resolution 471 of 1km, and the data used by previous scholars (Xu et   Compared with other static factors, rainfall erosivity can show the potential 496 changes of soil erosion more dynamically (Zhong et al. 2015). Therefore, this paper of rainfall erosion power in Beijing was very unbalanced. Although it has declined in 500 recent years, there are still rising risks in the future. Therefore, we have put forward 501 some suggestions for reducing rainfall erosivity, coping with extreme climate change, 502 weakening soil erosion and improving the quality of living environment. 503 First of all, it is necessary to carry out ecological greening, especially for the 504 densely populated urban areas with relatively high rainfall erosivity and high degree 505 of urbanization. It is necessary to expand the green area and strengthen the 506 construction of sponge city to prevent urban waterlogging. Second, it is necessary to 507 strengthen the slope management to prevent the occurrence of debris flow and 508 landslide in the northern mountainous areas. Then, it is necessary to standardize the 509 development of agriculture, no tillage and so on. 510

Conclusions 511
Beijing is the political and cultural center of China and has a dense population. 512 Extreme rainfall in this area can lead to urban floods, landslides and debris flows in 513 mountainous areas, as well as loss of people's lives and property, so we should attach 514 great importance to it (zhong et al. 2017). As an important factor of soil erosion, the 515 research on rainfall erosivity will provide scientific data support for soil erosion 516 monitoring, soil and water conservation research and comprehensive control in 517 Beijing. Through the study, we draw the following conclusions. 518 (1)The average annual rainfall erosivity ranged from 1080.6 to 6432.78 MJ•mm / 519 (hm 2 •h•a), and the multi-year average rainfall erosivity was 3465.06 MJ•mm / (hm 2 • 520 h•a). The rainfall erosivity fluctuated obviously, the fluctuation range had decreased 521 in recent years, and the rainfall erosivity value had shrunk. 522 (2)The spatial distribution of rainfall erosion in Beijing: the rainfall erosivity in 523 southeast was high, and the rainfall erosion in northwest was low, and it displayed a 524 downward trend from southeast to northwest. 525 (3)From the perspective of seasonal change, the rainfall erosivity of Beijing was 526 concentrated in summer and the smallest mainly occurred in winter, which was 527 related to the rainfall characteristics of Beijing with large and concentrated rainfall 528 and dry and less rain in winter. 529 (4)The trend change of rainfall erosivity in Beijing showed a decreasing trend as a 530 whole. Combined with Hurst index, the rainfall erosivity in Beijing still had the risk 531 of rising, so it should be prevented. 532 (5) Through the cross validation of various methods, the abrupt change interval of 533 rainfall erosivity in Beijing from 1901 to 2017 was from 1994 to 1997. 534 (6) The change of rainfall erosivity in Beijing has strong oscillation in 32 years and 535 small periodic change in 15 and 7 years. 536 (7) The influence that El Niño/La Niña events caused on rainfall and rainfall erosivity 537 in Beijing did not show strict regularity. ENSO and rainfall erosivity in Beijing were 538 not stable. El Niño events did not strictly correspond to high values whereas La Niña 539 event did not strictly correspond to a low value. 540 541 542