1 Introduction

Precipitation is one of the most important climate elements directly affecting the availability of water resources (Randall et al. 2007). Recently, it has been suggested that one of the most noticeable consequences of global atmospheric warming is water cycle modification, with precipitation being a key point in the process (Luis et al. 2011). Temporal and spatial variability of precipitation around the world is receiving increasing attention, for the information about changing patterns of precipitation is the starting point for accurate assessment of water resources, flood and drought control, understanding climate change, and efficient water management (Wang et al. 2011). At present, several precipitation-related indices (e.g., extreme precipitation indices, precipitation concentration index, rainfall erosivity, and standard precipitation index) are widely used by many researchers to investigate the changing patterns of precipitation.

Precipitation extremes exert a huge impact on human beings, and it is of vital importance to study the regular pattern of meteorological and hydrological factors. Extreme hydrological events related to precipitation and streamflow can cause large losses of human life and exponentially increasing costs associated with them (Karl and Easterling 1999). With significant global warming, some extreme precipitation events will become more and more frequent and much effort has been made to detect and analyze the trend in the occurrence of extreme events which happened in the past decades. Many studies have shown that the changes in extreme precipitation indices around the globe exhibited strong regional-scale variability. In China, much work has been done on extreme precipitation.

Precipitation concentration is represented not only by the percentages of annual total precipitation on several rainy days but also by the time and degree of concentration of the total precipitation within a year. Higher precipitation concentration has the potential to cause floods and droughts, which is expected to exert considerable pressure on water resources. Different indices have been used for this purpose, and among these, two types of precipitation concentration index were widely applied. The first kind of precipitation concentration index (Oliver 1980) represents the degree to which annual total precipitation is distributed over 12 months, while the second kind of precipitation concentration index (Martin-Vide 2004) is used to evaluate the contribution of the days of greatest rainfall to the total amount.

Rainfall erosivity is a numerical description of the potential of rainfall to erode soil and is one of the key input parameters for USLE (RUSLE) modeling (Lee and Heo 2011). The rainfall erosivity (R factor) is traditionally determined by calculating the average annual sum of the product of a storm’s kinetic energy E and its maximum 30-min intensity I 30, known as the EI30 (Wischmeier and Smith 1978). Accurate estimation of rainfall erosivity requires subhourly rainfall records, which are rarely available with good spatial and temporal coverage. Consequently, there have been many attempts to predict rainfall erosivity from data of annual precipitation, monthly precipitation, and daily precipitation. In China, the simplified rainfall erosivity model developed by Zhang et al. (2002) has been most widely used (Xin et al. 2011; Huang et al. 2013a).

The standard precipitation index (SPI) developed by Mckee et al. (1993) was widely used to reveal meteorological drought and was proven to be a useful tool in the estimation of the intensity and duration of drought events. Conceptually, the SPI is the number of standard deviations by which the precipitation values recorded for a particular location would differ from the mean over certain periods (Paltineanu et al. 2009). Positive SPI values represent higher than median precipitation; negative values indicate less than median precipitation (Bordi and Sutera 2001). The main advantage of the SPI is that it represents the same probability of drought occurrence irrespective of season, location, or climate. In China, the SPI has been applied for accessing spatial and temporal variation of dryness/wetness in some important regions, since it is simple and commonly used, taking only rainfall into account.

Located in central south China, Hunan is an important agricultural province with abundant natural resources, which plays a key role in the sustainable development of the economy and ecology of this region. Hunan Province is a major producer of grain in China, which is the fifth largest producer of the 31 provinces. In particular, Hunan is the largest producer of rice and ramie, the second largest producer of tea, and the third largest producer of oranges. However, frequent droughts and floods in this province have hindered its economic development and resulted in severe environmental problems. In addition, Hunan is also one of the provinces with serious soil erosion in south China (He 2000). Thus, the study of precipitation changes in this province is increasingly being paid more and more attention. However, most trend-related studies about precipitation focused on annual and seasonal precipitation (Zhang et al. 2008, 2009a). Therefore, the key objectives of this study are to systematically investigate long-term trends of precipitation indices in both space and time using historical observed daily precipitation from 1961 to 2010. Such a study may provide a valuable database for the management and planning of water resources under the backdrop of globe warming in Hunan Province.

2 Study region and data

2.1 Study region

Located to the mid-lower reaches of the Yangtze River, Hunan Province (109° E–115° E, 24° N–31° N) is an inland province including 14 municipalities with a total area of 211,800 km2, which is 2.21 % of the total land area of China. Hunan Province is a mountainous region with an elevation descending from south to north that varies from 2,000 to 12 m. The annual rainfall is from 1,300 to 1,600 mm, and the annual average temperature is 16–18 °C. Hunan Province has a dense hydrological network that can be divided into five main components: the Dongting Lake Region, the Xiang River basin, the Zi River basin, the Yuan River basin, and the Li River basin. Dongting Lake, which is located in northern Hunan Province, is the second largest freshwater lake in China. Hunan is one of the Chinese provinces that frequently suffer from severe flooding and drought disasters. Affected by the monsoon circulation and complex topography, the temporal and spatial distribution of precipitation is uneven, with 69 % of the annual precipitation concentrating in April–September.

2.2 Data

There are a total of 97 meteorological stations in Hunan Province. On the basis of record length, 86 stations with over 50-year records were selected as candidate stations. The raw data sets of daily precipitation amounts for the period 1961–2010 at the 86 candidate stations were collected from the National Meteorological Information Center of China. We used the RclimDex software package (http://cccma.seos.uvic.ca/ETCCDMI), to “clean up” the daily precipitation data. The process of “cleaning up” included (1) identifying errors in the precipitation data, such as precipitation value below 0 mm; (2) searching for outliers, where we choose 3 standard deviations as the threshold for a finer quality control of the data; (3) using the generalized data plot in RclimDex to visually inspect the data to further identify outliers and a variety of other problems that may cause error or bias in analyzing changes in the seasonal cycle or variance of the data; and (4) using RHtestsV3 (Wang and Yang 2010) to detect artificial shifts that could exist in a time series. After rejecting 11 stations with inhomogeneous series, 75 stations were finally selected in this study. The locations of the 75 stations are plotted in Fig. 1.

Fig. 1
figure 1

Meteorological stations used in this study and location of Hunan Province, China

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3 Methodology

In this study, the spatial and temporal changing patterns of extreme precipitation indices, precipitation concentration indices, and rainfall erosivity in Hunan Province during 1961–2010 are analyzed by the Mann–Kendall test at the scale of individual stations and region. Spatial and temporal variation of dryness/wetness has been assessed by means of the SPI, and the principal component analysis (PCA) is applied to the SPI series. The detailed principles of calculating indices and methods are described in the following text.

3.1 Calculation of precipitation indices

3.1.1 Extreme precipitation indices

The ETCCDI defined 27 core extreme indices based on daily temperature and precipitation amount. Exact definitions of all the indices are available from the ETCCDI website. In this study, only the extreme indices derived from daily precipitation were analyzed. Altogether, nine extreme indices are chosen from the 27 climate indices (Table 1). An R-based program, RClimDexV3 developed at the Climate Research Branch of the Meteorological Service of Canada and available from the ETCCDI Web site (http://cccma.seos.uvic.ca/ETCCDMI), is applied to calculate these nine extreme indices.

Table 1 Definitions of the extreme precipitation indices
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3.1.2 Precipitation concentration index

In this paper, two types of precipitation concentration index were used to explore the changing features of precipitation concentration in Hunan Province. To distinguish the two indices, the precipitation concentration index invented by Oliver (1980) was defined as PCI1, and the precipitation concentration index invented by Martin-Vide (2004) was defined as PCI2.

PCI1

PCI1, a statistical index, was proposed as an indicator of monthly rainfall heterogeneity (Oliver 1980). It was calculated according to Eq. (1):

$$ PCI1=\frac{{\displaystyle \sum_{i=1}^{12}{P_i}^2}}{{\left({\displaystyle \sum_{i=1}^{12}{P}_i}\right)}^2}\times 100 $$
(1)

where P i is the monthly precipitation in month i. According to the proposed formula, the lowest theoretical value of PCI1 is 8.3, indicating the perfect uniformity in precipitation distribution (i.e., that same amount of precipitation occurs in each month). Oliver (1980) suggested that PCI1 values of <10, 11–15, 16–20, and >20 represent the uniform precipitation distribution (i.e., low precipitation concentration), moderate precipitation concentration, irregular precipitation distribution (i.e., high precipitation concentration), and strong irregular precipitation distribution (i.e., very high precipitation concentration), respectively.

PCI2

PCI2, a statistical index, was proposed to assess the contribution of the days with the greatest rainfall to the total amount (Martin-Vide 2004). It was developed in accordance with the fact that the distribution of precipitation frequencies is generally adjustable with negative exponential distributions (Wang et al. 2013). Martin-Vide (2004) introduces the computational procedure as follows: (1) The precipitation class limits are classified based on suitable class interval (1 mm was chosen as the class interval in this article); (2) the number of rainy days range falling into each class is counted, and the associated amount of precipitation is computed (in this paper, a rainy day is defined when daily precipitation is ≥1 mm); (3) the cumulative summation of output items in step (2) is calculated; (4) following step (3), an exponential curve X (accumulated percentages of days) versus Y (accumulated percentages of precipitation) is derived and can be expressed as Y = aXexp(bX), where a and b are the regression coefficients estimated by the least-squares method. The area S enclosed by the bisector of the quadrant and the polygonal line provides a measure of concentration. The Gini concentration index 2S/10,000 is used as a concentration measure (Martin-Vide 2004). The precipitation concentration assembles the Gini coefficient, which is the area circled by the perfect distribution (45°) line and the Lorenz curve (the Lorenz curve is described by the model Y = aXexp(bX).

3.1.3 Rainfall erosivity

In this study, the rainfall erosivity was calculated using the simple method developed by Zhang et al. (2002). This method obtains annual, seasonal, and monthly rainfall erosivity using aggradations of the half-month rainfall erosivity, which is estimated based on daily rainfall data. The method uses the following function:

$$ {M}_i=\alpha {\displaystyle \sum_{j=1}^k\left({D}_j\right)}\beta $$
(2)

where M i is the half-month rainfall erosivity (megajoules-millimeter per square hectometer per hour per year) and D j is the effective rainfall for day j in 1.5 months. D j is equal to the actual rainfall if the actual rainfall is larger than the threshold value of 12 mm, which is the standard for China’s erosive rainfall. Otherwise, D j is equal to zero. The term k is the number of days in the half-month. The terms α and β are the undetermined parameters and computed as follows:

$$ \beta =0.8363+\frac{18.114}{{\overline{P}}_{\mathrm{d}12}}+\frac{24.455}{{\overline{P}}_{\mathrm{y}12}} $$
(3)
$$ \alpha =21.486{\beta}^{-7.1891} $$
(4)

where P d12 is the average daily rainfall larger than 12 mm and P y12 is the yearly average rainfall for days with rainfall larger than 12 mm.

3.1.4 SPI

The SPI was computed by including the long-term monthly precipitation data at a given period (McKee et al. 1993). After fitting a Gamma distribution and transforming it to a normal distribution by an equal probability transformation, the SPI is computed as the precipitation anomaly of the transformed data, divided by the standard deviation of the transformed data (Bordi et al. 2004a). Based on the calculated SPI, the intensities of dry and wet events are classified as displayed in Table 2. The SPI can track dry/wet events on different time scales, i.e., 1, 3, 6, 12, and 24 months, and is flexible with respect to the period chosen. Among users, there is a general consensus about the fact that the SPI on shorter time scales (i.e., 3 or 6 months) describes drought events affecting agricultural practices, while on the relatively longer ones (i.e., 12 or 24 months), it is more suitable for water resources management purposes (Raziei et al. 2009). A time scale of 24 months has been proven as a suitable time scale, which can capture the low-frequency variability avoiding an explicit annual cycle (Bordi et al. 2004b). Therefore, we focus on the results of the calculated SPI concerning the 24-month time scale (i.e., SPI-24).

Table 2 The standardized precipitation index (SPI) categories based on the initial classification of SPI values
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3.2 Mann–Kendall test

The Mann–Kendall (M–K) trend test, which is highly commended for general use by the World Meteorological Organization, was used to characterize the trends for several precipitation-related indices and to test their significance. The rank-based M–K method is a nonparametric method, commonly used to assess the significance of monotonic trends of the climate data.

In the M–K trend test, the null hypothesis, H 0, is that the data in a time series {X i, i = 1, 2,…, n} are independent and identically distributed random variables and the hypothesis, H 1, is that there is a trend in the series. Statistic parameter, S 0, is defined as follows:

$$ {S}_0={\displaystyle \sum_{i=1}^{n-1}{\displaystyle \sum_{j=i+1}^n\operatorname{sgn}\left({x}_j-{x}_i\right)}} $$
(5)

where n is the length of the series (n > 40), k = 1, 2,…, n − 1, j = 2, 3,…, n, and

$$ \operatorname{sgn}\left({x}_j-{x}_i\right)=\left\{\begin{array}{l}+1,{x}_j>{x}_i\\ {}0,{x}_j={x}_i\\ {}-1,{x}_j<{x}_i\end{array}\right. $$
(6)

It has been proven that when n ≥ 8, S 0 follows approximately the normal distribution with 0 mean and the variance (assuming no tied groups) as follows:

$$ \mathrm{Var}\left({S}_0\right)=\frac{n\left(n-1\right)\left(2n+5\right)}{18} $$
(7)

Standardized statistic Z can be calculated as follows:

$$ Z=\left\{\begin{array}{l}\frac{S_0-1}{\sqrt{\mathrm{Var}\left({S}_0\right)}},{S}_0>0\\ {}0,{S}_0=0\\ {}\frac{S_0+1}{\sqrt{\mathrm{Var}\left({S}_0\right)}},{S}_0<0\end{array}\right. $$
(8)

A positive value of Z indicates an increasing trend, and a negative value of Z indicates a decreasing trend, while a zero value of Z indicates no trend. At the 10 % significance level, the null hypothesis of no trend is rejected if |Z| > 1.645. To eliminate the effect of serial correlation on M–K results, the “pre-whitened” technique is used to remove effects of serial correlation before M–K analysis (Huang et al. 2013a).

In M–K test, another very useful index is the Sen slope, which is the magnitude of the monotonic change and is given as follows:

$$ \mathrm{slope}=\mathrm{Median}\left(\frac{x_j-{x}_i}{j-i}\right),\forall i<j,\kern0.5em 1<i<j<n $$
(9)

In this function, the estimator Sen slope is the median over all combination of record pairs for the whole data.

3.3 Principal components analysis

The PCA is a popularly used method to identify patterns in climatic data and to highlight their similarities and differences (Santos et al. 2010). It is basically a data reduction method, which explains the correlation among several new uncorrelated variables in terms of a small number of underlying factors without extreme loss of information. The new (uncorrelated) variables are called principal components (or principal component scores) and consist of linear combinations of the original variables. In this study, the original SPI series at each meteorological station are X i,1, X i,2,…, X i,k , where k is the number (75) of the stations and i represents the time length of the SPI series at each station (576 for SPI-24). The principal components are produced for the same time period by using linear combinations according to the following equation:

$$ \left[\begin{array}{l}{X}_{i,1}\\ {}{X}_{i,2}\\ {}\vdots \\ {}{X}_{i,k}\end{array}\right]\bullet \left[\begin{array}{cccc}\hfill {a}_{11}\hfill & \hfill {a}_{12}\hfill & \hfill \cdots \hfill & \hfill {a}_{1k}\hfill \\ {}\hfill {a}_{21}\hfill & \hfill {a}_{22}\hfill & \hfill \cdots \hfill & \hfill {a}_{2k}\hfill \\ {}\hfill \vdots \hfill & \hfill \vdots \hfill & \hfill \cdots \hfill & \hfill \vdots \hfill \\ {}\hfill {a}_{k1}\hfill & \hfill {a}_{k2}\hfill & \hfill \cdots \hfill & \hfill {a}_{kk}\hfill \end{array}\right]=\left[\begin{array}{l}{Y}_{i,1}\\ {}{Y}_{i,2}\\ {}\vdots \\ {}{Y}_{i,k}\end{array}\right] $$
(10)

where Y values are the orthogonal and new linearly uncorrelated variables which explain most of the total variance. The coefficients of the linear combinations are called “loadings” and represent correlation between the original data and the corresponding principal component scores (PCS) time series. In order to find more localized spatial patterns of variability, a rotation of the principal components with the Varimax procedure is applied. The procedure simplifies the spatial patterns by isolating regions with similar temporal variations and has been proven to be the most common orthogonal method to improve the creation of regions of maximum correlation between the variables and the components (Bordi et al. 2004a, b; Raziei et al. 2009).

3.4 Continuous wavelet transform analysis

The continuous wavelet transform (CWT) technique, as a tool for analyzing localized variations of power within a time series, was applied. Through CWT analysis, the hydrological series are decomposed into time–frequency space to determine both the dominant modes of variability and how those modes vary in time. The concept and procedure of the wavelet method can be found at http://paos.colorado.edu/research/wavelets/. Recently, the wavelet transform has been widely applied in the fields of climatic changes and hydrological changes.

4 Results and discussions

4.1 Trends of extreme precipitation indices during 1961–2010

In this study, nine extreme indices were calculated for the 75 meteorological stations in Hunan Province. The Mann–Kendall test was used to test any trend in these indices. The results of trends for annual extreme precipitation indices series at each station in Hunan Province during 1961–2010 are given in Table 3. In a majority of cases, most precipitation indices suggest that both the amount and the intensity of precipitation are increasing. For example, all the stations have increasing trends in mean precipitation amount on a wet day (SDII). For annual total precipitation in wet days (PRCPTOT), annual maximum 1-day precipitation (RX1day), annual maximum 5-day precipitation (RX5day), maximum number of consecutive dry days (CDD), heavy precipitation days (R10mm), rainstorm days (R50mm), and very wet day precipitation (R95pTOT), the proportion of stations with positive trends for these indices is 78.7, 82.7, 76.0, 69.3, 52.0, 81.3, and 86.7 %, respectively, and the proportion of stations with negative trends for these indices is 21.3, 14.7, 21.3, 26.7, 40.0, 12.0, and 6.7 %, respectively. Differing from other indices, 73.3 % of stations display decreasing trends in consecutive wet days (CWD). Thus, there is a tendency towards positive trends dominating, consistent with the intensification of the hydrological cycle in Hunan. Figure 2 gives the spatial distribution of trends in extreme precipitation indices. Strong trends can be mainly found for SDII, RX1day, R95pTOT, and CWD. For SDII, the significant upward trends are mainly found in the southern and central areas of Hunan Province (Fig. 2b). The 15 stations with significant increasing trends for RX1day are located in west and south Hunan (Fig. 2c). Similarly, the 14 stations in west and south Hunan show significant increasing trends for R95pTOT (Fig. 2i). As for CWD, the 13 stations showing significant degreasing trends are mainly found in north and central Hunan (Fig. 2f). Besides, the regional trends for extreme precipitation indices are listed in Table 4. For Hunan as a whole, the trend in PRCPTOT is weak and nonsignificant, and shows an increase (7.64 mm/decade), consistent with other precipitation indices. Six other regional indices also show increasing trends: SDII, RX1day, RX5day, CDD, R50mm, and R95pTOT, although only SDII shows a statistically significant increasing trend (0.23 mm/decade). The regional trend for CWD and R10mm is −0.14 and −0.08 days/decade, respectively. Compared with the other studies, the extreme precipitation indices have large variations in Hunan (Table 4).

Table 3 Number of stations with significant positive (SP), insignificant positive (ISP), significant negative (SN), insignificant negative (ISN), and no change (NC) trends for extreme precipitation indices used in this study
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Fig. 2
figure 2

Spatial distribution for trends of nine extreme precipitation indices during 1961–2010 (if the trend is significant at the 10 % significance level, then a ring is placed around the plus or minus symbols)

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Table 4 Regional trends of extreme precipitation indices form this study and other works
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Precipitation changes in the Yangtze River basin are controlled mainly by the East Asian Monsoons. The summer circulation over East Asia shows a strengthening trend of the continental high over Eurasia and a weakening trend of the western Pacific subtropical high (Wang and Zhou 2005). The northeasterly wind tendency over central east China is weakening the southwesterly summer monsoon in the region, limiting the northward extension of summer monsoon and causing longer stay of Meiyu front (quasi-stationary fronts with heavy rainfall systems elongated mainly from the east–northeast to west–southwest orientation over East Asia from late spring to mid-summer) in the Yangtze River basin (Huang et al. 2013a). As a result, the extreme precipitation increased in the middle-lower reaches of the Yangtze River. Changes in precipitation extremes are likely to have greater immediate impact on human society than changes in mean rainfall amount. Detection of trends in extreme precipitation indices may have important implications for flood risk/control in Hunan Province. The research results of this paper indicate that increasing flood may risk Hunan Province. The positive changes in annual maximum 1-day precipitation, annual maximum 5-day precipitation, very wet day precipitation and rainstorm days may result in higher variability of flood risk. It should be mentioned here that Hunan is heavily populated, economically developed, and a risk-prone region. Therefore, the effective measures should be taken to reduce huge damage due to extreme climatic events in Hunan.

4.2 Spatial and temporal variability of PCI during 1961–2010

Temporal distribution of precipitation throughout the year has been studied by the precipitation concentration index (PCI1). Figure 3a shows the spatial distribution of the PCI1 values, calculated from the rainfall data set of each individual year and averaging over the observation years. These values range from a minimum value of 11.8 to a maximum value of 14.0. As described by Oliver (1980), PCI values below 10 indicate a uniform monthly rainfall distribution throughout the year, whereas values from 11 to 20 denote seasonality in rainfall distribution (Coscarelli and Caloiero 2012). Nevertheless, the precipitation concentration in Hunan denotes a seasonality of the pluviometric distribution. In normal year, summer monsoon starts to influence the Yangtze River basin in April retreating in October, and the precipitation in the mid-lower Yangtze River basin is concentrated during summer season, which makes up about half of the annual total (Gemmer et al. 2008; Huang et al. 2013a). This may cause the seasonality of precipitation concentration in Hunan Province. Also, the PCI1 distribution is not uniform over the whole territory. The seasonality is more marked in the northwest of this province, with peak values in the Li River basin. The results emerging from the application of the Mann–Kendall test to the yearly PCI1 values of each station are shown in Table 5. More than half of stations display increasing trends in PCI1, of which seven stations have significant trends. From a spatial perspective, those stations showing significant increasing trends are mainly observed in south Hunan (Fig. 3b). The regional changing pattern of PCI1 in Hunan presents an insignificant positive trend (Table 6), accompanying with a week tendency towards a greater seasonal rainfall distribution during the year. This tendency is well confirmed by the other study results obtained by applying the linear regression model to the seasonal precipitation. Zhang et al. (2008) estimated a significant positive trend for summer and winter precipitation, and the concomitant insignificant negative trend for the spring and autumn rainfall. Since in Hunan rainy season is from April to September, the positive trend estimated for summer precipitation, and the concomitant negative trend obtained for the spring and autumn precipitation, can determine a more inhomogeneous distribution of precipitation during the year. The inhomogeneous rainfall distribution is unfavorable not only for water resource but also for agricultural production. Thus, the upward trend found for seasonality in rainfall distribution should be attached importance.

Fig. 3
figure 3

Spatial distribution for annual average values and trends of PCI1 during 1961–2010 (if the trend is significant at the 10 % significance level, then a ring is placed around the plus or minus symbols)

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Table 5 Number of stations with significant positive (SP), insignificant positive (ISP), significant negative (SN), insignificant negative (ISN), and no change (NC) trends for precipitation concentration indices used in this study
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Table 6 The Mann–Kendall test for precipitation concentration indices over Hunan
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The precipitation concentration index (PCI2) is suitable to investigate the contribution of precipitation extremes of certain time durations. According to Zhang et al. (2009b), the PCI2 has been calculated based on yearly precipitation series, meaning that one PCI2 for 1 year and then detect the possible trends of PCI2 for each station. Spatial patterns of average PCI2 and associated trends are all presented. The map of spatial distribution of PCI2 (Fig. 4a) shows that there is a large spatial variability for the precipitation concentration in Hunan Province. An obvious progression gradient can be found from the centre of Hunan to the peripheral area, especially from the middle region to the northwest region. From a spatial perspective, the highest precipitation concentrations (PCI2 values are up to 0.577) are mainly found in northwest Hunan. On the contrary, the larger areas of central Hunan Province are dominated by lowest precipitation concentrations (PCI2 values are between 0.540 and 0.548). Table 5 also summarizes the results showing the numbers of stations which present different trends of PCI2 series. The overall impression for PCI2 trends during the past decades is that a dominance of positive trends is observed in this province, especially the 16 stations in west and east Hunan, which are characterized by significant increasing trends (Fig. 4b). The results emerging from the application of the M–K test to the yearly PCI2 series on scale of entire province are very clear, and the PCI2 over Hunan presents a significant positive trend with the 10 % significance level (Table 6). Increasing PCI2 in Hunan Province during the past 50 years would enhance the percentage of rain contributed by a few very rainy days. The changing patterns of extreme precipitation indices shown in Table 4 corroborate this conclusion, which can partly explain the increasing frequency of floods across Hunan.

Fig. 4
figure 4

Spatial distribution for annual average values and trends of PCI2 during 1961–2010 (if the trend is significant at the 10 % significance level, then a ring is placed around the plus or minus symbols)

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4.3 Spatial and temporal variability of rainfall erosivity during 1961–2010

Rainfall erosivity, considering rainfall amount and intensity, is an important parameter for soil erosion risk assessment under future land use and climate change (Meusburger et al. 2012). The estimation of rainfall erosivity may contribute to a better prediction of soil erosion and sediment delivery. In this study, the annual rainfall erosivity was calculated using the method of Zhang et al. (2002). It can be found from Table 7 that the annual rainfall erosivity for Hunan varies between 5,109.1 and 10,409 MJ mm hm−2 h−1 a−1, and their mean value is 7,285.2 MJ mm hm−2 h−1 a−1 with a very high standard deviation (STD), thereby indicating that the rainfall erosivity varies spatially across the region. According to the research results of Huang et al. (2013b) in the Yangtze River basin, we define the region with an annual average rainfall erosivity of ≤4,000 MJ mm hm−2 h−1 a−1 as the region characterized by a low rainfall erosivity and the region with an annual average rainfall erosivity of ≥7,000 MJ mm hm−2 h−1 a−1 as the region dominated by high rainfall erosivity. Annual average rainfall erosivity ranging between 4,000 and 7,000 MJ mm hm−2 h−1 a−1 is classified as medium rainfall erosivity. Based on this classification, Fig. 5a shows that medium rainfall erosivity is mainly detected in middle Hunan, while other areas of this province are characterized as high rainfall erosivity. The results of the M–K test for the annual rainfall erosivity series at each station in Hunan Province during 1961–2010 are given in Table 8, and Fig. 5b shows the spatial distribution of trends. It can be observed from Fig. 5b that most of this province is dominated by increasing trends in annual erosivity. However, the increasing trends are statistically significant in only 6 out of the 75 stations. These phenomena are in good agreement with the annual precipitation trends detected in the study of Zhang et al. (2009b), which indicate that the temporal variation of annual precipitation may be the proximate cause of the changes in annual rainfall erosivity. Water resources and soil erosion are the very important environmental concerns in Hunan Province. Being affected by the abundant rainfall, man-made destructions of natural environment, and complex characteristics of landform, the area of soil and water loss in Hunan is making up 19.07 % of total acreage. Soil erosion rate may be expected to change in response to change in climate for various reasons, the most of direct was the change in the erosive power of rainfall (Nearing et al. 2004). Disturbingly, the increasing changes in rainfall erosivity may aggregate soil erosion in this province.

Table 7 Statistical characteristics of annual average rainfall erosivity (megajoules-millimeter per square hectometer per hour per are) for each station in Hunan Province during 1961–2010
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Fig. 5
figure 5

Spatial distribution for annual average values and trends of annual rainfall erosivity during 1961–2010 (if the trend is significant at the 10 % significance level, then a ring is placed around the plus or minus symbols)

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Table 8 Number of stations with significant positive (SP), insignificant positive (ISP), significant negative (SN), insignificant negative (ISN), and no change (NC) trends for annual rainfall erosivity
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4.4 Spatial and temporal variability of the SPI during 1961–2010

On the basis of 50 years of monthly precipitation in the 75 meteorological stations, 75 series of standardized precipitation indices were obtained for large time scale. The PCA was applied to the time series of the SPI at 24 months (SPI-24) at each station in Hunan Province. Observing the results from the PCA and taking into account the variance explained by each rotated principle component, three main patterns (R-loading 1, R-loading 2, and R-loading 3) were identified (Table 9). These three patterns explain more than 70 % of the total variance in the original SPI series. The spatial pattern of the three principle component series was characterized by mapping the values of the factorial matrix. As previously mentioned, for a given time scale, this matrix contains the correlations between each component and the SPI-24 series at the 75 stations. For that purpose, the inverse distance weighted (IDW), a spatial interpolation method available in ArcGIS 9.3 was utilized. In this way, three different and spatially well-defined regions with different temporal evolution of droughts were identified (Fig. 6). As illustrated in Fig. 6a, the first component explains 28.64 % of the total variance and has higher values in the south of this province (Fig. 6a). Nevertheless, it is overwhelming that the first R-loading of SPI-24 is mainly a representative for drought evolution in the most of south Hunan. The second component, R-loading 2, explains 26.00 % of the total variance for SPI-24, and represents mainly the drought evolution of middle areas (Fig. 6b). It can be found from Fig. 6c that the north Hunan is attributed to the third component (R-loading 3, 15.41 % of the total variance). Overall, the aforementioned patterns are clearly spatially distributed and do not overlap. These regional patterns in precipitation are likely to be associated with the complex topography and spatial configuration of large-scale circulation systems in Hunan.

Table 9 Percentages of variance explained by the principal components for the SPI on 24-month time scale in Hunan Province
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Fig. 6
figure 6

a–c First three rotated loading patterns (R-loading) of the principal components of the SPI on 24-month time scale in Hunan Province and d–f time series of the corresponding rotated principle components scores (PCS) during the study periods (red line denotes the fitting linear trend)

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Meanwhile, to better illustrate temporal variability of dryness/wetness for subregions, the corresponding rotated PCS are investigated. In Fig. 6, the temporal variability of PCS is also shown, and their trends are detected using a linear regression model. The three time series of PCS display multiyear fluctuations, and it is expected that remarkably dry or wet events in different magnitudes have occurred in different years. Figure 6d, e shows that both the PCS-1 and PCS-2 are characterized by long-term positive linear trends (PCS-1: R 2 = 0.036, p < 0.001; PCS-2: R 2 = 0.013, p < 0.001) during the past 50 years. Obviously, the wet tendency prevails in central and south Hunan. This was also confirmed by other studies (Zhang et al. 2009b), which found increasing trends of wet conditions associated with strengthening precipitation in central and south Hunan. In contrast, the third score (PCS-3) in Fig. 6f exhibits a long-term negative linear trend (R 2 = 0.028, p < 0.001). This means that most of north Hunan is dominated by dry tendency. It should be pointed that north Hunan is the important commodity grain base of China, while this region is also assessed as the seriously sensitive areas of agricultural drought. The rapid development of economy, explosion of city population, and serious soil erosion have intensified the water shortage in the northern area, resulting in many severe environmental and ecological problems. More worryingly, the dry tendency detected in this paper may bring in a great negative impact on agricultural production and water resource of this region. Furthermore, the CWT technique was applied on PCS to detect the periodicity of dryness/wetness. It can be observed from Fig. 7 that a 4–8-year periodical feature is noticeable in each SPI series over the province. Similar periodical features are also identified with a dominant cycle of about 4–5 and 7–8 years for the annual frequency of occurrence of precipitation events in the Yangtze River basin (Becker et al. 2008). In summary, the PCA seems to well localize in space three distinct subregions characterized by different dryness/wetness patterns. Thus, for an efficient water resources management under the backdrop of climate change and in planning measures for mitigating the adverse impacts of future drought occurrences, these subregions should be independently considered.

Fig. 7
figure 7

Wavelet power spectrum of the time series of PCS. The 5 % significance level against red noise is shown as thick black contours. The cone of influence (COI) where edge effects might distort the picture is shown as the U-shaped curves

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Finally, some further investigations were made in this study based on the SPI categories of Table 2. The temporal evolution of the percentage of stations affected by different dry/wet events of varying intensity is shown in Fig. 8. The extremely wet events that affected a higher proportion of stations occurred in the 1990s and 2000s, but usually, not more than 10–40 % of the total stations were affected in either decade (Fig. 8d). This observation indicates that flood intensity can be highly diverse spatially, and extremely wet events can be recorded in some stations, while in other sectors, it may have a severe or moderate intensity. Similarly, the numbers of stations affected by severe and moderate wet events are larger after 1990s (Fig. 8e, f). On the contrary, the proportions of stations affected by different drought intensities have descended after 1990s (Fig. 8a–c). These results further indicate that Hunan Province is dominated by wet tendency, and the flood hazards may become increasingly serious. This was also confirmed by other study on the mid-lower Yangtze River basin (Gemmer et al. 2008), which found increasing trends of wet conditions associated with enhanced precipitation since 1990. Moisture flux plays a key role in changes of drought and wet conditions. The decreasing meridional geopotential height from west to east along the Yangtze River basin caused more moisture propagation from the west to the east parts, which may benefit more precipitation in the middle and lower Yangtze River basin (Zhang et al. 2010). As we know, the changes of drought and wet conditions have great efforts on agricultural production. In this case, the agriculture activities in Hunan should be well organized based on the new phenomenon in the changing climate.

Fig. 8
figure 8

Temporal evolution of the percentage of stations affected by different dry/wet events

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5 Conclusions

In this study, the spatial and temporal characteristics of changes in several precipitation-related indices 1961–2010 in Hunan Province were explored. The main findings are summarized as follows:

  1. 1.

    Among several extreme precipitation indices, strong trends could be observed for SDII, RX1day, R95pTOT, and CWD. It could be found that all the stations in Hunan had experienced a positive trend for SDII indices; 29 out of the 75 stations showed significant positive trends, most of which are located in the southern and central areas. Also, 15 and 14 stations showed positive significant trends for RX1day and R95pTOT, respectively, and these stations were mainly located in the scatted area of west and south Hunan. Decreasing trends for CWD were observed in most areas of Hunan; 13 out of the 75 stations showed significant negative trends, and these stations were located in the central and northern areas of Hunan.

  2. 2.

    Two precipitation concentration indices were studied in this paper. For monthly rainfall heterogeneity, all the stations had moderate precipitation concentrations, and more than half of the stations were characterized by an insignificant upward trend in precipitation concentration. When it comes to the contribution of the days of greatest rainfall to the total amount, higher precipitation concentration was mainly observed in the scatted areas of northwest Hunan, and most of Hunan was characterized by an insignificant upward trend in precipitation concentration.

  3. 3.

    The annual average rainfall erosivity in Hunan Province was distributed unevenly, with a minimum of 5,109.1 MJ mm hm−2 h−1 a−1 at Chenbu station and a maximum of 10,409 MJ mm hm−2 h−1 a−1 at Anhua station. From the M–K test, the annual rainfall erosivity presented upward trends in most of the stations. However, only 6 out of the 75 stations were significant at the significance level of 10 %.

  4. 4.

    Dryness/wetness patterns were assessed through the SPI series computed on 24-month time scales, and their variability was analyzed by applying the PCA to the index time series. In terms of the first three loadings, spatial division was conducted into three subregions with different climatic variabilities: a remarkable wet tendency prevails in the central and southern areas, while the northern areas are dominated by a remarkable dry tendency. Furthermore, the wavelet transform analysis shows clearly that the dryness/wetness is subjected to 4–8-year cycles among different sub-regions from 1961 to 2010.