Multi-scale update on precipitation characteristics at Jinan, East China

Extreme precipitation triggered by climate change is a hot issue of global concern. This study investigates changes in temporal trends of precipitation at Jinan City, Shandong Province over the last six decades. It first constructs a long series of measured daily precipitation data (1951–2017) and then exploits the relative variability, Mann–Kendall, and rescaled range analysis (R/S analysis) methods to update precipitation characteristics. Results indicate that: (1) annual precipitation varies over 116%, with 74.1% of total precipitation concentrated from June to September, especially for heavy rains and storm days; (2) at the 95% confidence level, the annual rainfall does not increase significantly (U1⁄4 1.15), but there is a significant upward trend in the spring (U1⁄4 2.08), whereas there is no significant downward trend in the fall (U1⁄4 1.03); (3) precipitation sequence mutates in 1990, consistent with spring precipitation series, while there are two to four mutations in summer, autumn, and winter. The above results will provide the theoretical basis and data support for the rational development of water resources in Jinan; meanwhile, studying the law of precipitation changes in Jinan City has important practical significance for flood disaster prevention.


INTRODUCTION
Mastering the dynamic changes of climatic variables such as rainfall and evaporation, as well as the effects of induced disasters, is essential for improving disaster resilience (Roozbeh et al. ). Rainfall is an important factor affecting regional water resources and the eco-economic environment. Abnormal changes in rainfall will lead to droughts and floods  (Zhang ). In order to understand and predict future changes in precipitation, it is essential to formulate long-term adaptation and mitigation measures to deal with climate change (Homsi et al. ).
In recent years, the precipitation mutations and their trends have become research hotspots. Many previous studies revealed that in Brazil, the annual rainfall is evenly distributed, with the northern region having the largest rainfall in summer (Rao et al. ). Guerreiro et al. () studied the variation characteristics of rainfall sequences in the three major Iberian watersheds. Xu & Zhang () analyzed the trend of precipitation characteristics in the Yellow River Basin using 50-year precipitation data and found that the annual precipitation showed a downward trend. According to the dataset of 12 meteorological stations across the Yellow Sea western coast during 1951-2011, Wang et al.
() utilized several methods (e.g., linear regression, Mann-Kendall test) to analyze the trend of extreme precipitation events, and the results verify that in the past few decades, rainfall has become more concentrated and precipitation intensity has increased. Mo et al. () analyzed the precipitation data of the Mayor of Guilin and revealed that the monthly rainfall has a relatively large variability and is unstable; the rainfall shows a downward trend in spring and autumn, and an upward trend in summer and winter.
Using the rainfall data of Wuzhishan City for the past 60 years, Duan et al. (a, b) found that the spatial variation of rainfall and the annual rainfall generally showed a significant increasing trend.
The rainfall variation characteristics have obvious regional features, and there are many methods of analysis used to study the characteristics of precipitation time series changes, including commonly used methods such as linear fitting, linear regression evaluation, relative variability, moving average, Mann-Kendall non-parametric test, etc.
These methods mainly focus on analysis and the current trend of rainfall change, of which, rescaled range analysis (R/S analysis) is mainly used to judge the future change trend; Mann-Kendall mainly analyzes the variation characteristics of precipitation sequences (Hurst et al. ; Danesh et al. ; Wang et al. ; Muthoni et al. ).
Jinan has suffered from severe water shortages for a long time. Since the summer of 2014, Jinan has faced many water shortage problems, such as the continuous decrease in precipitation, the lack of spring water spurt, and the insufficient storage capacity of major reservoirs (Chang et al. ). Meanwhile, the research on precipitation has mainly focused on the rainfall characteristics in the southern mountainous areas, the rainfall characteristics during flood season, and the cause of storm flood disasters. However, based on the long series of data, there are few studies on the characteristics of interannual and annual precipitation in Jinan urban areas (Cao & Lou ). Therefore, this paper mainly uses the R/S analysis method and Mann-Kendall non-parametric test method to analyze the variation characteristics of precipitation in Jinan City, and then verify its relative variability. At present, extreme rainfall events have caused severe disasters in Jinan City. The results of this paper will help Jinan to deal with the uncertainties of rainfall and flood warning management brought about by climate change. In the paper, after the Introduction, the Material and methods are presented. Results and discussion follow and, finally, a summary and the major conclusions are provided.

Study area
Jinan is the capital city of Shandong Province, with the terrain high in the south and low in the north. The urban area is located in the northern part of low hills, on the micro-sloping plains, and the alluvial plains of the Yellow River. The area is located in a warm temperate continental monsoon climate zone with an annual average temperature of 14.7 C and average annual precipitation of 671.1 mm. The summer is warm and rainy, and the winter is cold and dry with less snow. It is dry, rainless, and windy in spring and autumn.

Data collection
In order to better reflect the rainfall change trend in Jinan urban area, we comprehensively consider the representativeness, reliability, and integrity of rainfall data, as well as the long-term and consistency of data length sequence.

Mann-Kendall non-parametric test
The Mann-Kendall non-parametric test mainly analyzes the changing trend of the precipitation series, and further quantitatively judges the overall trend of the series (Burn & Elnur ). It belongs to the non-parametric statistical method and has been recommended by the World Meteorological Organization. For hydrometeorological data with nonnormal distribution, the Mann-Kendall rank correlation test has more outstanding applicability and is often used to detect the frequency trend of precipitation and drought under the influence of extreme climate. For the precipitation sequence x 1 , x 2 , . . . , x n , n is the length of the precipitation series, P i is the number of occurrences of where t is the statistics of Mann-Kendall non-parametric test, Var(t) is the series sample variance, U is the rank correlation coefficient with statistical significance at a ¼ 0:05 level, then U a=2 ¼ ±1:96, when U > 0, the precipitation change shows an upward trend, else downward; when jUj > U a=2 the hypothesis test shows that the sequence change trend is significant, else not significant.
The Mann-Kendall method can analyze the significance of changes in each stage of the sequence, and extract the time, frequency, and significance of the mutation (Duan et al. a, b). In the mutation test, y 1 , y 2 …, y n are the data values in original time series, m i is the number of y i > y j (1 j i n), the statistic S k is calculated by using: Assuming that the original sequences are randomly independent, the mean and variance of S k are: The standard normal test statistic S k is computed as: According to the reverse order of the time seriesy:y n , y nÀ1 , . . . , y 1 , repeat the above steps, calculate the curve of the statistic UB, take a ¼ 0.05, draw the curve of the two statistics UF and UB, and two lines of ±U a/2 on the same graph, the intersection of the two curves UF and UB in the confidence interval is determined as the mutation point, and the time corresponding to the intersection point is the time to start the mutation. Whether UF exceeds the critical value is a sign to determine whether the trend change is significant, that is, if |UF| > 1.96, the changing trend is significant.
R/S analysis R/S analysis is a method for processing time series, mainly identifying the dynamic trend of time series; this method can not only distinguish a random sequence from a nonrandom sequence but also perform a search for the longterm memory process of linear systems. The Hurst index is particularly robust, has a wide range of uses for all time series, and has few assumptions about the system being studied. The basic principle is as follows: {x(t)} is the time series, t ¼ 1, 2, . . ., and for any positive integer τ ! 1, the mean sequence is as follows: Cumulative dispersion X(t, τ): A dimensionless ratio R/S is used to rescale R. After verification, the result satisfies the following formula: where H is the Hurst index.

Stability and volatility characteristics
Many previous studies have proved that linear fitting can reflect the trend of annual precipitation over time very clearly and intuitively. Figure  In the four periods of 1956-1961, 1967-1973, 1980-1993, and 2011-2017 remaining 25 years, including 14 years of annual precipitation increasing but annual precipitation days decreasing; that is, in the past 67 years, about 14 years of precipitation increased but the precipitation days decreased, accounting for 20.9% (14/67), which meant that precipitation in about one-fifth of these years was more concentrated, especially after the 1990s. Therefore, the above indicated that the concentration and the volatility of precipitation were more significant (Figure 3).

Long-term trend and mutation characteristics
Using Mann-Kendall and linear regression to analyze the trend and mutation of annual precipitation in Jinan urban area, Figure 4 shows the statistical result of annual precipitation by the Mann-Kendall non-parametric test.
Combined with the linear regression trend of Figures 2 and 3, the linear fitting slope and relative variability of annual precipitation are both greater than zero, and the linear fitting slope of the relative change of annual precipitation was less than the annual precipitation. This indicated that in the past 67 years, the annual precipitation and its relative variability in urban areas shows a growth pattern, while the relative variability of annual precipitation was not as significant as annual precipitation, and the interannual fluctuations in precipitation exhibited an increase but the trend was not significant. At the 95% significance level, the Mann-Kendall statistic U ¼ 1.15 of the annual precipitation series, which indicated that the annual precipitation in Jinan urban area showed an upward trend, consistent with the above-mentioned linear regression, but the upward trend was not significant. Figure 4 shows that the curves of UF and UB intersect in 1990 and 1992, indicating that the annual precipitation series in Jinan began to change in 1990, and the annual precipitation trend also changed from a decline to an upward trend.

Future change characteristics
The R/S analysis method is mainly to analyze whether the past changes of the annual precipitation series have the same characteristics as the future changes, and further explore the future precipitation variation trends in Jinan.
The Hurst index of the annual precipitation series is calculated by R/S analysis, H ¼ 0.79 > 0.5. The future precipitation sequence is not a stochastic process, and the future trend is positively correlated with the current trend, that is, the trend has a positive persistence.   1962 and 1992 in summer, 1961, 1981, 1990, and 2005 in autumn, and 1960, 1986, and 1996 in winter.

Seasonal precipitation variation characteristics
Quarterly prediction of future changes. Figure

Monthly precipitation variation characteristics
The monthly rainfall and its percentage, the standard deviation, the deviation coefficient, the maximum, the minimum, and the extreme ratio of Jinan City from 1951 to 2017 are shown in Table 2. The maximum precipitation occurred in July, with a mean of 201.1 mm and a maximum of 506.9 mm (1962). The precipitation in January and  December accounted for only 1%, and the minimum precipitation of 0 mm appeared in many years; for example, it appears six times in January (1952,1954,1976,1978,1995,2005) and twice in December (1967December ( , 1999. The precipitation during the flood season (June-September) accounts for 74.1% of the whole year. During the period from January to March and December, the maximum precipitation reached 30 mm. Large-scale heavy rainfall may occur from April to May and October to November, but the number of occurrences is small and uneven. The deviation coefficient of the non-flood season is greater than that of the flood season, which is 1.2 in January and 0.51 in July. Therefore, the precipitation is large and concentrated in the flood season, but small and scattered in the non-flood season.

Daily precipitation variation characteristics
The variation characteristics of daily precipitation. Table 3 shows the precipitation classifications prescribed by the China Meteorological Administration. Figure    the number of moderate rain days with daily rainfall of 10-25 mm is not large, the rainfall accounts for 25.66%; the days with daily rainfall below 10 mm account for 81.54% of the total rainfall days, while the rainfall accounts for only 22.14%. In Jinan City, the total days of rainstorms, heavy rainstorms, and torrential rain that had the greatest impact on urban flooding were 163, accounting for 2.26% of total precipitation days.
Characteristics of heavy rain and rainstorm.
(1) Analysis of stability and volatility results: Figure 1953-1956, 1961-1964, 1971-1974, 1995-1998, and 2003-2005, with periodic characteristics for three consecutive years. For years with precipitation greater than 50 mm (rainstorm), the minimum is 0 days, that appeared in 1955, 1968, 1970, and 1986, respectively. Precipitation greater than 50 mm mainly occurred in 1961-1964, 1991-1994, and 2003-2005, similarly with periodic characteristics for three consecutive years.   (2) Long-term trend and mutation characteristics: Figure 9 also reveals that the linear fitting trend of precipitation days with precipitation more than 25 and 50 mm exhibited an increase, but was not significant. At the 95% significance level, the Mann-Kendall statistic U of the precipitation days with precipitation greater than 25 and 50 mm was 1.04 and 1.47, respectively, with no significant upward trend, which is consistent with the linear fitting results. Combined with Figure 10 (1) The precipitation varies greatly from year to year. The relative change in annual precipitation ranges from À52% to 64%, while the precipitation days are À24% to 45%. In the past 14 years, precipitation has increased, but the precipitation days have decreased, indicating that the precipitation concentration is stronger and more volatile, with abundance and drying regularity of six to nine years. The annual precipitation of Mann-Kendall statistic U ¼ 1.15 (significance level at a ¼ 0.05) represents no significant increase in annual precipitation. The UF and UB curves intersected in 1990, indicating that the annual precipitation sequence began to mutate in 1990, causing precipitation to change from falling to rising. The Hurst index of the annual precipitation series is 0.79, indicating that the future precipitation pattern is the same as the current situation, and its trend and positive persistence are not significantly increased.
(2) The annual precipitation is unevenly distributed, with significant differences in summer and winter, and slightly different in spring and autumn, but less precipitation in spring, mainly due to the influence of the dry continental air mass in the north. From June to September, the precipitation in the flood season accounted for 74.10% of the annual precipitation, with the largest proportion in July and August, and the smallest in January and December. The Mann-Kendall statistic U for spring rainfall was 2.08, showing a significant upward trend.
The increase in summer and winter is not significant, while autumn shows an insignificant downward trend.
The spring mutation time was in 1990, and the summer, autumn, and winter seasons were highly volatile, with two to four mutations. The Hurst index of the four seasonal precipitation series is greater than 0, indicating that the future trend is consistent with the interannual trend.
(3) The days with light rain, heavy rain, and above accounted for 81.54% and 6.91% of the total rainfall days, respectively, while the difference in the ratio of the rainfall to the total rainfall was relatively large, 22.14% and 52.20%, respectively; the precipitation days of heavy rain and rainstorm all showed strong volatility and difference, with an inconspicuous upward trend.
The paper analyzes Jinan's precipitation changes in detail, but it lacks in-depth attribution exploration and sensitivity analysis on important influence factors, and therefore we will conduct in-depth analysis and research in the future.