Spatial and temporal variation characteristics and frequency analysis of extreme precipitation from 1959 to 2017: A case study of the Longtan watershed, southwest China

According to current global climate projections, the average global mean surface temperature increase of approximately 0.65–1.06 °C from 1880 to 2012 caused warming temperatures and more frequent extreme events (IPCC et al. 2013). Sudden and variable extreme climate events represented by extreme precipitation and climate change impact at regional and global scales lead to many serious natural disasters, such as floods and droughts (Arnell & Gosling 2016; Akter et al. 2018; Davarpanah et al. 2021), which pose a great threat to all aspects of human society, including production, life and ecology (Karagiannidis et al. 2012). In the context of global warming, due to the complex topographic conditions in the southwestern region of China and the influence of monsoonal circulation, there is a greater risk of experiencing extreme precipitation, which can cause catastrophic damage to agricultural production. Therefore, further research on the characteristics of extreme precipitation changes should be carried out.

The study of extreme precipitation can be done mainly from two perspectives: extreme precipitation index and frequency analysis. In recent years, scholars have achieved many results in studying the spatial and temporal characteristics of extreme precipitation using extreme precipitation indicators. Lupikasza et al. (2011) selected eight extreme precipitation indices for the study and found that the increasing trend of extreme precipitation dominates in the central-eastern part of Germany, while the opposite is true for the southern part of Poland, where a clear spatial divergence in the spatial and temporal variation of extreme precipitation is observed. The global extreme precipitation characteristics were studied by calculating and analyzing 10 extreme precipitation indices, and the results showed a global trend of increasing extreme precipitation in general since the 20th century, with the opposite trend in local areas of Asia (Alexander et al. 2006). In China, Shi et al. (2018) used daily precipitation data from 344 meteorological stations and selected 10 indices to study the spatial and temporal variation of extreme precipitation in eastern China. Eleven extreme indicators were applied to the study of extreme climate in relation to altitude in southwestern China, and it was found that more precipitation occurred at higher altitudes, but the increase of extreme precipitation events mainly occurred at lower altitudes (Li et al. 2012).

Besides, several probability distribution models and preferred methods have been used to study extreme precipitation frequency analysis. Forestieri et al. (2018) conducted a regional frequency analysis of extreme rainfall in Sicily (Italy) using three distributions. The regional parameters of these distributions were estimated using L-moments and considering a hierarchical approach. The results highlighted that for the lower return periods, all distributions showed the same accuracy while for higher return periods the LN3 distribution provided the best result. The five popular probability distributions (generalized extreme value (GEV), Generalized Logistic, Weibull, Gamma and Log-Normal) were compared by Anderson–Darling (A–D) and Kolmogorov–Smirnov test methods. It was found that the GEV represents the primary distribution pattern for the study area (Benyahya et al. 2014); in China, the probability plot method (P–P plot), quantitative plot method (Q–Q plot), K–S test and A–D test were also used to select the most appropriate distribution, and it was found that the GPD distribution model performed better than the GEV distribution model (Mo et al. 2019). Feng et al. (2014) performed regional frequency analysis based on the L-moment method, and the results of the goodness-of-fit measure indicated that Pearson type III (PE3) and GEV distributions were more suitable for the HeiHe River basin. Besides, many comprehensive studies have been carried out at regional or national scales, such as in America (Sveinsson et al. 2002), Korea (Park et al. 2001) and Norway (Hailegeorgis et al. 2013).

In summary, previous studies on extreme precipitation have yielded certain results, but the following problems remain to be solved: (1) There are differences in the applicability of different probability distribution functions to the study of extreme precipitation frequency analysis in different regions, and the method for selecting the optimal distribution model has not been unified: (2) Fewer studies have been conducted to analyze the frequency of extreme precipitation in watersheds in the karst region of southwest China. Therefore, the Longtan watershed, which is located at the junction of Guangxi, Yunnan and Guizhou and has the representative characteristics of the karst area, was selected for this study, with a view to providing a scientific basis for coping with climate change and disaster prevention in the Longtan watershed.

The Longtan watershed is located at the junction of Yunnan, Guizhou and Guangxi provinces, ranging from 23 °11′ to 27 °01′N, 102 °14′ to 107 °32′E, covering a drainage area of 98,500 km² (Figure 1). The Longtan watershed is located at the junction of low and middle latitudes, which is combined with the complex topography of karst development and more rock forests. Due to the influence of topography, climate and geographical location, the Longtan watershed is prone to flooding rainstorms in the rainy season and persistent droughts in the non-rainy season, with significant spatial differences, which adversely affect the water forecast, joint scheduling and operational safety of water conservancy projects. In addition, most of the agricultural production in the watershed relies only on natural precipitation as a source of moisture, which is sensitive to changes in precipitation. Sudden and variable extreme precipitation poses a large disaster risk to agricultural production. Therefore, it is necessary to strengthen the study of extreme precipitation in the region.

Daily precipitation data, which are the basis for the analysis of extreme precipitation indices, were provided by the China Meteorological Administration (http://data.cma.cn/wa). The data consisted of historical daily precipitation observations covering 1959–2017 from 15 meteorological stations in and adjacent to the watershed. The missing data for individual years at meteorological stations were interpolated based on correlations from similar stations. The meteorological station distribution and information are shown in Figure 1.

Based on the extreme precipitation indices proposed by the highly recognized Expert Team on Climate Change Detection and Indices (ETCCDI), seven extreme precipitation indices were finally selected from the core indices (Gebrechorkos et al. 2019), in which the definitions can be found from the website (http://etccdi.pacificclimate.org/indices_def.shtml). Based on the properties of these extreme indices, the seven indices can be further classified into three categories, namely, duration indices (continuous drought index (CDD), consecutive wet days (CWD)), intensity indices (maximum 1-day precipitation amount (RX1D), maximum consecutive 5-day precipitation amount (RX5D), precipitation on very wet days (R95p) and simple daily intensity index (SDII)) and frequency indices (R50 mm) (Table 1). Precipitation data from 15 meteorological stations were quality controlled using RClimDex software (obtained from http://etccdi.pacificclimate.org/software.shtml), which was also used to calculate the seven extreme precipitation indices selected for this paper at annual timescales. (Zhang et al. 2005). The average extreme precipitation indices were calculated as the arithmetic mean of the values from these 15 stations.

For cases where the trend of the hydrological series is very obvious, the process line and other methods are often used to make an intuitive judgment, but for those where the judgment is more difficult or not reliable enough, the method of statistical tests is usually resorted to. The Mann–Kendall, Spearman, and linear trend regression statistical tests were used to analyze the trend of each index. The critical value method and the P-value method were used to determine the significance of the change trend.

For the analysis of mutation time, the preceding step is referenced to the inverse series, and another curve, ⁠, is obtained; the intersection of the two curves is defined as a mutation time.

The empirical orthogonal function (abbreviated as EOF) can separate the spatial distribution structure and time-series variation of meteorological elemental variable fields (Small & Islam 2006; Sun et al. 2012). The calculation is as follows:

• (1)

  The data are processed in the form of anomaly to obtain the data matrix ⁠, where m denotes the number of sites and n the number of years.

• (2)

  The covariance matrix is obtained by calculating the cross product of X and ⁠.

• (3)

  The characteristic root (⁠⁠) and the characteristic vector of are calculated.

• (4)

  EOF onto the original matrix to calculate the time coefficient PC corresponding to the spatial eigenvector is projected.

• (5)
  The variance contribution rate of characteristic vector, the formula is calculated as follows:

  

  (6)

If satisfies ⁠, the modes corresponding to the two eigenvalues are independent and valuable signals. The error range is calculated by checking the characteristic roots in turn. If the error range of two adjacent characteristic roots overlaps, the significant difference between the two characteristic roots is not significant. Finally, the eigenvalues of the significant characteristic roots of each index were interpolated using the ARCGIS spatial interpolation technique with the ordinary Kriging spatial interpolation method to draw the maps.

In this study, nine probability distribution models (Gamma, Gamma (3P), Pareto, GEV, Log-Gamma, Log-Logistic, Log-Normal, Weibulll (3P) and Weibulll) were used to fit RX1D, RX5D and R95p series. In general, the more parameters are, the greater the flexibility is, so it is more suitable for data. However, the more parameters, the more difficult parameter estimation should be. There are different methods to estimate the parameters of each distribution, including the method-of-moments, L-moments and the maximum likelihood estimation (MLE). In this study, the maximum likelihood method, which was most commonly used to estimate the parameters of statistical distributions, was chosen.

Table 2 shows the results of significance tests for the trends in the seven extreme precipitation indices, of which only the trend in CWD was significant. Figure 2 shows the linear trend of mean annual values of each index, and in general, all seven indices showed relatively small fluctuations. CWD showed a significant decreasing trend with a linear trend of −0.2 day/decade. CDD showed a non-significant increasing trend with a linear trend of 0.5 day/decade. The trends of intensity indices (i.e., RX1D, RX5D, R95p, SDII) were not significant, with linear trends of 0.97 mm/decade, −0.45 mm/decade, 4.04 mm/decade and 0.1 mm/(day·decade), respectively. Among them, the RX5D showed a decreasing trend, while the RX1D, R95p and SDII showed an increasing trend. Besides, a non-significant increasing trend in the frequency index R50 mm was detected, with a linear trend of 0.045 day/decade.

The mutation test results are given in Figure 3, where the curve was the statistics obtained when calculating the sequence time series which further characterized the variation of the extreme precipitation index in different years. CDD showed a general upward trend between 1959 and 2017, with a fluctuating decline before the 1980s and an increase beginning after the 1980s. The decreasing trend of CWD was very stable, exceeding the critical line of significant level after 2009, and the decreasing trend was significant. RX1D fluctuated greatly in the 1960s and 1970s, with a downward–upward–downward trend, and began to show an upward trend after the 1990s. RX5D was relatively volatile until 1975, with a flat trend after the 1980s. R95p was fluctuating in the 1960s and 1970s, with a downward and then upward trend, a little change after the 1970s, and relatively pronounced fluctuations around 2000. SDII trends fluctuated widely, with increasing trends around the 1970s and after the 2000s, and flat changes in the 1980s. R50 mm (heavy precipitation days) fluctuated considerably in the 1960s, falling and then rising, with a flat trend after the 1980s.

Temporal variation characteristics indicated that only the number of CWD in the Longtan watershed showed a significant decreasing trend from 1959 to 2017, while the trends of the remaining indices were not significant. The results of the M–K trend test further showed that the trend of CWD decrease was more significant after 2009. CDD, RX1D and SDII indices were more volatile. At the same time, it was found that CWD showed a significant decreasing trend, but CDD showed a non-significant increasing trend in the Longtan watershed in the past 59 years, reflecting a trend of drought in the watershed as a whole. However, R95, Rx1d, SDII and R50 mm showed a non-significant increasing trend, indicating an increasing trend in the frequency and intensity of extreme precipitation. Overall, the results of this study and the previous results showed reduced but more concentrated precipitation in southwest China (Liu & Xu 2016; Wang et al. 2019; Sun et al. 2021).

Due to the large uncertainty of the possible mutation years for each extreme precipitation index, the paper first used the M–K mutation test to test the mutation points for the seven extreme precipitation indices, and the results are shown in Figure 3. At the same time, the moving t test was used for verification, and the results are shown in Figure 4.

The and curves of the CDD sequence were found to have intersection at the critical line in 1974–1976, while only 1976 is the jump year through verification of the moving t test method. The and curves of RX1D had four intersection points in 1965–1972 and one intersection point around 1983. The moving t tests were done before and after the jump years of the extreme precipitation index RX1D in the Longtan watershed, and the mean value of RX1D showed a significant jump in 1983, so the abrupt change of RX1D may have occurred in 1983. The and curves of CWD, RX5D, R95p, SDII and R50 mm sequences all have multiple intersections between the critical lines; combined with the moving t test, CWD had a mean value of 7.53 before 2002 and a mean value of 6.7 after the jump, which passed the significance level test of ⁠. Therefore, CWD may have mutated in 2002. While no obvious mutation site was found in RX5D and R95p, R50 mm had probably mutated in 2013, and SDII had probably mutated twice in 1994 and 2013.

Overall, none of the results of the M–K mutation tests could determine the specific mutation year, and combined with the moving t test to verify other indices, some mutation sites were identified, but the mean jumps were small and no significant mutation sites were identified. In general, the abrupt changes in the extreme precipitation index occurred mainly in the 1980s, 1990s and 2010s, and the trend of abrupt changes was not significant, and these results remain largely consistent with previous studies (Yang et al. 2015; Wang et al. 2019). To a certain extent, it reflected that the Longtan watershed was facing the risk of increased rainfall and flooding along with the increased risk of drought, and there was a need to improve the response capacity of urban and rural areas to extreme rainfall and flooding events.

Variance contribution rate (⁠⁠), cumulative variance contribution rate (⁠⁠) and North test results (⁠⁠) of the first four decomposition eigenvectors of each extreme precipitation index were calculated, and the results showed that the first and second modes of CDD, RX1D, RX5D and SDII, and the first modes of CWD, R50 mm and R95p passed the North test and were the significant modes.

The EOF decomposed a significant characteristic vector can reflect the spatial distribution structure of each extreme precipitation index, which represents different spatial variation characteristics. Figure 5 shows the spatial distribution of the duration indices (CDD, CWD) and the time coefficient (principal components), and the variance contributions of CDD (V1) and (V2) are 40.8 and 16.0%, respectively. The CDD (V1) had positive components in most areas, except for a small combination of locations in Guangxi, Guizhou and Yunnan, which were negative areas, showing the variation of partial-whole reverse phase. The centers of high values of CDD (V1) occurred in the southwestern and central parts of the watershed. The distribution of CDD(V2) showed significant spatial differences, with the inverse sign in the southwest and the northeast, showing the variation of the southwest–northeast reverse phase, with the positive high-value area in the northeast mainly near the Wangmo station and the negative high-value area in the southwest mainly near the Luxi station. The variance contribution of CWD (V1) was 26.6%, showing the consistent variation in the whole region with all positive values and a high-value area in the southwest.

Combined with the time coefficient analysis, CDD (V1) corresponding to CDD (PC1) showed the variation of partial-whole reverse phase with positive values in most areas and negative values in small areas, when the value of CDD (PC1) was positive (negative), CDD was more (less) in most areas of the Longtan watershed and locally less (more). CDD (PC1) had an overall fluctuating upward trend, with an overall upward trend in CDD in most areas of the Longtan watershed and an overall downward trend in a small number of areas. The years 1979 and 1984 were years of drought and low rainfall in most parts of the watershed and localized increased precipitation. The time coefficient was characterized by a clear interannual oscillation variation.

CDD (PC2) reflected the change of ‘southwest–northeast’ inversion, because the corresponding eigenvector CDD (V2) showed a distribution of positive northeast and negative southwest; when the value of PC2 was positive (negative), the CDD in the northeast of the Longtan watershed was more (less) and the southwest was less (more). The fluctuation of CDD (PC2) was relatively flat, and the coefficient value was large and positive only in 2010, indicating that the spatially southwest of the Longtan watershed had more precipitation while the northeast was drier in 2010.

CWD (PC1) reflected consistent changes across the region and were positive, when CWD (PC1) was positive (negative), CWD was high (low) across the region and CWD (PC1) had an overall fluctuating decreasing trend, which indicated an overall decreasing trend of CWD in the Longtan watershed from 1959 to 2017.

Figure 6 shows the spatial distribution of each intensity and frequency index (RX1D, RX5D, R95p, SDII and R50 mm) characteristic vector and the time coefficient (PC). The analysis showed that RX1D (V1), R95p (V1), SDII (V1) and CWD (V1) had the same type of spatial distribution, indicating the consistent variation in the whole region with positive signs. The centers of high values were all found in the northeastern part of the watershed. RX5D (V1), RX1D (V2) and SDII (V2) have the same spatial distribution type as CDD (V2), showing a clear ‘southwest–northeast’ inverse phase distribution, with positive values in the northeast and negative values in the southwest. The spatial distribution types of RX5D (V2), R50 mm (V1) and CDD (V1) were the same, showing the variation of partial-whole reverse phase, with high-value centers occurring in the northeastern and central parts of the watershed.

The analysis of each index significant characteristic vector showed that there were three variation types in the Longtan watershed from 1959 to 2017. Firstly, the characteristic vectors were all positive, such as CWD (V1), RX1D (V1), R95p (V1) and SDII (V1), indicating a consistent variation across the region with a clear distribution of high-value regions. Secondly, the characteristic vector showed a ‘southwest–northeast’ inverse phase distribution, such as RX5D (V1), CDD (V2), RX1D (V2) and SDII (V2), indicating the ‘southwest–northeast’ inverse phase variation, and the high- and low-value areas are clearly distributed. Thirdly, the characteristic vector showed a mixed-type distribution with positive and negative values, such as CDD (V1), RX5D (V2) and R50 mm (V1), indicating the variation of partial-whole reverse phase.

By analyzing the cumulative variance contribution rate (⁠⁠), we could find the first two characteristic vectors of each extreme precipitation index were close to 50%; therefore, these two characteristic vectors could well describe the type of spatial variation of each index in the Longtan watershed from 1959 to 2017. The variance contribution of the first eigenvector of each index was the largest, while the first eigenvector space of a total of four indices (RX1D, R95p, SDII and CWD) showed the consistent variation in the whole region, indicating that the spatial variability of extreme precipitation in the Longtan watershed from 1959 to 2017 was characterized by the most typical region-wide consistent type.

The type showed a consistent distribution of high-value areas of eigenvectors mostly distributed in the northeastern part of the Longtan watershed while combining the variation of temporal coefficients. It was found that the two regions of Guangxi and Guizhou had the highest possibility of extreme precipitation events, while central and Yunnan were the regions where extreme precipitation was less likely to occur. The conclusions above were consistent with those achieved by Ding (2014), Xu et al. (2015) and Liu & Xu (2016). The variation of the CDD also illustrated this point. The high positive value of CDD (V1) was in the southwestern part of the watershed, and the time coefficient was overwhelmingly positive, while the high negative value of CDD (V2) was in the southwestern part of the watershed, and the time coefficient was negative most of the time, indicating that there were more CDD and higher drought risk in central and Yunnan regions.

Table 3 shows the results of the K–S test for the goodness of fit of the nine distribution functions for RX1D at each station, and it was calculated that 100% of the Gamma, Gamma (3P), Log-Logistic, Log-Normal and GEV distribution functions passed the K–S test, and none of the fit results for the Pareto distribution passed the significance test. The bold numbers in the table indicate the minimum statistics, and most of the D values of the GEV distribution were smaller than the statistics of the other models. The mean value of each distribution model was also calculated for each of the 15 sites, and the GEV model has the smallest mean value. This implied that the GEV distribution function was more suitable for the RX1D index. Meanwhile, the optimal distributions for different stations of the three extreme precipitation indices were statistically, and it was obvious that the GEV distribution was a better distribution for different indices. The evaluation of the goodness of fit for all indices was comprehensive, and the GEV distribution function had the best fit for the extreme precipitation indices in the Longtan watershed and was highly applicable.

Precipitation was calculated for RX1D, RX5D and R95p indices at 5-, 20- and 50-year return period levels for 15 meteorological stations using the optimal distribution model. Figure 7 shows the spatial distribution of three extreme precipitation indices at different return period levels.

The spatial and temporal characteristics of extreme precipitation in southwest China had been studied extensively, but the frequency analysis of extreme precipitation was lacking. The innovation of this study was to select a representative karst area watershed in southwest China as the object to study the frequency distribution of extreme precipitation. To ensure the reasonableness of the study results, a total of nine probability distribution models were selected to be fitted and model preferences were made, and the GEV model was found to be optimally applicable in the Longtan watershed. By estimating the 5-, 20-, and 50-year return period levels of the selected indices, it could be found that the distribution of the different return periods of the extreme precipitation indices was similar, and most of the extreme precipitation was distributed in the central and northeastern parts of the Longtan watershed, that was, the Guangxi and Guizhou regions. The result of the higher intensity of extreme precipitation in the middle and lower reaches may exacerbate the uneven distribution of water resources in the basin on spatial and temporal scales. The analysis results will provide scientific basis and technical support for the local government to prevent extreme rainfall.

There are still some problems waiting to be solved in further study. The Longtan watershed has a problem of relatively few sites, and subsequent studies may combine satellite inversion data of slightly shorter years or climate model data downscaled (e.g., ERA5, CMIP5-6) after site calibration to obtain better spatially representative data for analysis. Because the physical mechanism of the phenomenon of extreme precipitation mutations is still unclear, the methods of mutation detection are not very mature, and various detection methods have their inherent advantages and disadvantages, so more methods should be used for mutation testing, while choosing the appropriate significance level and determining a more accurate mutation time. In addition, for a linear and smooth spatio-temporal series, the variance and mean values remain statistically stable as the length of time changes, and the spatial eigenvalues decomposed by the EOF method have high accuracy. However, the variance and mean values of the time series are constantly changing due to the non-linearity and non-smoothness of the spatio-temporal series caused by human activities and climate change. It is possible to cause interference to the accuracy of the geospatial modalities decomposed by the EOF method. The study of extreme precipitation in this paper is based on historical rainfall data, and in order to obtain more representative results, we should further explore the causes of extreme precipitation by combining the characteristics of climate change and human activities. At the same time, corresponding future change prediction and risk assessment studies can be conducted to provide local governments with more scientific references for water resource planning and disaster prevention.

Warming climate and human activities have a great influence on the frequency and intensity of extreme precipitation events. Exploring the variation pattern of extreme rainfall based on precipitation data is the key to disaster prevention and mitigation, designing hydraulic projects, and achieving sustainable development and utilization of water resources. The main framework of this paper was to analyze and calculate extreme precipitation indicators and conduct a study on the frequency distribution of extreme precipitation. The main conclusions were as follows:

• (1)

  The characteristics of temporal changes showed that the overall change of each extreme precipitation index in the Longtan watershed in the past 59 years was not significant, CWD in the duration index had a decreasing trend, CDD had an increasing trend, while the intensity index and frequency index almost all had an increasing trend, indicating that the watershed was generally becoming drier, but the precipitation was more concentrated and the possibility of extreme precipitation has become greater.

• (2)

  Through EOF analysis, the spatial variation characteristics of each extreme precipitation index were mainly of three types, namely, region-wide consistent, southwest–northeast inverse, and interphase mixed, among which the region-wide consistent type was the most typical, and the representative indices include intensity index RX1D, R95p, SDII and persistence index CWD, but the difference in the distribution between the high-value area in the northeast and the low-value area in the southwest was obvious. By analyzing the time coefficients, the increasing trend of extreme precipitation occurring in Guangxi and Guizhou areas, which were located in the high-value area, was larger. In contrast, Yunnan was in the low-value area, and the precipitation conditions were poorer compared with those in Guangxi and Guizhou areas and at the same time, combining with the time coefficient analysis of each eigenvector of CDD, an increasing trend of CDD was detected, so the risk of drought in the Yunnan area in the basin was higher.

• (3)

  From the results of the K–S test, it could be seen that the GEV distribution was the optimal distribution function applicable to RX1D, RX5D and R95p indices. By comparing the precipitation for the 5-, 20-, and 50-year return periods, it could be found that the precipitation distribution of each extreme precipitation index was similar for different return periods, and most of the extreme precipitation was distributed in the northeastern part of the study area containing Guangxi and Guizhou regions.

This study was funded by the National Natural Science Foundation of China (Nos. 51969004 and 51979038), the Guangxi Natural Science Foundation of China (2017GXNSFAA198361), and the Innovation Project of Guangxi Graduate Education (YCBZ2019022).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.