# Extreme Precipitation Changes in the Semiarid Region of Xinjiang, Northwest China

Authors: Yanwei Zhang; Quansheng Ge; Minzhe Liu
Journal: Advances in Meteorology
 (2015)

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## Abstract

This study focuses on extreme precipitation changes in Xinjiang Province of Northwest China, which has experienced an increase in climate disasters in recent years. This paper investigates extreme precipitation events in Xinjiang, using 54 stations with daily precipitation records from the period 1961–2008. Different statistical tests and approaches were used to check the significance of trends of single and Xinjiang regionally aggregated precipitation series for intensity and in frequency. There were predominantly positive trends in annual maximum precipitation and a remarkable increment in the frequency of extreme precipitation over certain thresholds (from 10 to 40 mm). Although the series of frequencies exceeding thresholds had positive trends, only a minority were statistically significant. This lack of significance is because of the high variability of extreme precipitation in space and time. Thus, significant trends were evident when we assessed the extreme precipitation indicators of intensity and frequency at the regional level, both in intensity and frequency over thresholds, with a clearer signal in Xinjiang.


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## Body

## 1. Introduction

Extreme precipitation events cause significant damage to agriculture, ecology, and infrastructure, disruption of human activities, injury, and loss of life [1–7]. In recent years, floods have become more frequent in Xinjiang Province of Northwest China, raising the question of whether these were caused by increased frequency of precipitation or changes in land use. Jianfeng et al. [8] found that trends of extremes and annual precipitation in Xinjiang over the last decades were increased frequency. Since annual precipitation there increased during the last decades of the 20th century [2, 3, 9], it is possible that the same could occur with extreme precipitation. With global warming, more intense and frequent extreme precipitation events should be expected at the global scale, as a result of greater atmospheric water content and likely decrease of thermodynamic stability [10]. According to the Intergovernmental Panel on Climate Change [11] assessment report concludes that there was an increase in extreme precipitation in many mid-latitude regions during 1951–2003 over that expected, owing to changes in mean total precipitation. Xinjiang is at mid-latitudes. This implies that the study of extreme precipitation is insufficient and should be adapted to climate projections and trends. Extreme precipitation trends vary with region, increasing in some regions and decreasing in others. This is because warming and water vapor trends have regional differences and because of other factors like frequency and intensity of precipitation. Ding et al. [12] studied summer precipitation trends in the China region, showing that North and Northeast China have had severe and persistent droughts, whereas the Yangtze River Basin and South China have had much more significant extreme rainfall or flood events.As one of the most important irrigated agricultural production areas in China, Xinjiang is characterized by a susceptible ecological environment and serious water shortage. In this context, precipitation changes are crucial in the sustainable ecological environment and regional socioeconomy. Increasing and intensifying weather extremes, particularly those related to precipitation, will enhance the sensitivity of the ecological environment to climate changes. The Xinjiang extreme precipitation field has a generally zonal gradient, from almost 80 mm per day in the northwest to less than 25 mm in areas of the southeast. Flood and drought will potentially increase in frequency and intensity in 21st century Xinjiang, as a result of global warming [13].In this paper, the different statistical tests and approaches are applied to destinations with different extreme precipitation characteristics (intensities and frequencies) and we check the significance of trends of single and regionally aggregated precipitation series in order to identify how and to what extent extreme precipitation change has affected the agriculture, ecology, and infrastructure of Xinjiang, China (Figure1).Figure 1
Regions and observation stations used.


## 2. Data and Methodology

### 2.1. Data Sources

A daily precipitation dataset at 55 stations across Xinjiang during 1961–2008 was provided by the National Climatic Centre of China, China Meteorological Administration. This institution performed quality control of the dataset prior to its release, and homogeneous detection for the dataset has also been done (e.g., [8]). Stations with missing precipitation data of more than one year were excluded from the dataset, and daily precipitation data from 54 meteorological stations were analyzed. Figure 1 shows locations of these stations.The AM (annual maximum) series consists of the most extreme events of each year in a given period. According to the Fisher-Tippett theorem, the asymptotic distribution of a series of sample maxima (AM series) belongs to one of three basic distributions (Frechet, Weibull, and Gumbel), regardless of the original distribution of the observed data. These three families were combined into a single distribution, now known as the generalized extreme value (GEV) distribution [14]. Precipitation data were available as the daily totals. Therefore, we analyzed daily maximum precipitation, which could frequently be distributed over the daily period.


### 2.2. Methodology

The theory of extreme value statistics states that the largest ofm independent observations from a fixed distribution will approach a known distribution as m increases, regardless of the distribution from which the observations came [15]. This is known as the Extremal Types Theorem, analogous to the Central Limit Theorem. The theory and approaches are applicable to the distribution of extreme minima by analyzing the variable X [16].The probability density function (PDF) of a GEV distribution is(1)fx=1β1+κx-ςβ1-1/κ·exp⁡-1+κx-ςβ1/κ,1+κx-ςβ>0.ς,β, and κ are the location, scale, and shape parameters, respectively. The cumulative distribution function (CDF) of a GEV is (2)Fx=exp⁡-1+κx-ςβ1/κ.This CDF can be inverted to yield an explicit formula for the quantile function,(3)F-1p=ς+βκ-ln⁡p-κ-1.Because the moments of the GEV involve the gamma function, estimating GEV parameters using the method of moments is no more convenient than the alternative method of maximum likelihood, which is frequently used in hydrologic applications. Maximum likelihood methods can be easily adapted to include effects of covariates or additional influences [17]. For moderate and large sample sizes, results of the two parameter estimation methods are usually similar. Based on (3), the return period XT can be computed as(4)XT=ς-βκ1--log⁡1-1T-κ,κ≠0,XT=ς-βlog⁡-log⁡1-1T,κ=0.The generalized Pareto distribution (GPD) is essentially a simple primitive distribution model [12], designed specifically to describe probability features of the entire observation dataset, beyond a given critical value (threshold).The distribution function of GPD is(5)Fx=1-1-κx-β1α11/κ,κ>0,β1≤x≤β1+β1κorκ<0,β1≤x<ϖ,(6)Fx=1-1-κx-β1α11/κ,κ=0,where β1 denotes the threshold, α1 the scale parameter, and κ the shape parameter (linear type). If y=x-β1 indicates values of the variable X above threshold β1, we may rewrite the distribution function as F(x). It is seen from (5) that, for κ=0, the GPD can be simplified to a logarithmic distribution [15, 18].From the size of samples with one year as a unit, annual crossing rates above a certain threshold in yearst can be given [18] as(7)λx=λt1-Fx,where λ is a mean of multiyear crossing rates between a given value of an extreme event and threshold β1. Based on (5) and (7), the return period XT can be computed as(8)XT=β1+α1κ1-λT-κ,κ≠0.Based on (6) and (7), the return period XT can be computed as(9)XT=β1+α1ln⁡λT,κ=0,in which λ denotes the yearly mean crossing rate, β1 the given threshold, α1 the scale parameter, and κ the shape parameter (to designate the distribution curve type). Then, the related GPD model and its quantile can be found by obtaining GPD parameters using the given estimation method. In a special case with λ=1, that is, the peaks-over-threshold (POT) crossing rate appearing once per year, we simplify (8)-(9) to (10)XT=β1+α1κ1-T-κ,κ≠0,XT=β1+α1ln⁡T,κ=0.The Poisson probability distribution is(11)Fx=eλ×λxx!,where λ is a positive real number, equivalent to the expected number of occurrences during a given interval.


## 2.1. Data Sources

A daily precipitation dataset at 55 stations across Xinjiang during 1961–2008 was provided by the National Climatic Centre of China, China Meteorological Administration. This institution performed quality control of the dataset prior to its release, and homogeneous detection for the dataset has also been done (e.g., [8]). Stations with missing precipitation data of more than one year were excluded from the dataset, and daily precipitation data from 54 meteorological stations were analyzed. Figure 1 shows locations of these stations.The AM (annual maximum) series consists of the most extreme events of each year in a given period. According to the Fisher-Tippett theorem, the asymptotic distribution of a series of sample maxima (AM series) belongs to one of three basic distributions (Frechet, Weibull, and Gumbel), regardless of the original distribution of the observed data. These three families were combined into a single distribution, now known as the generalized extreme value (GEV) distribution [14]. Precipitation data were available as the daily totals. Therefore, we analyzed daily maximum precipitation, which could frequently be distributed over the daily period.


## 2.2. Methodology

The theory of extreme value statistics states that the largest ofm independent observations from a fixed distribution will approach a known distribution as m increases, regardless of the distribution from which the observations came [15]. This is known as the Extremal Types Theorem, analogous to the Central Limit Theorem. The theory and approaches are applicable to the distribution of extreme minima by analyzing the variable X [16].The probability density function (PDF) of a GEV distribution is(1)fx=1β1+κx-ςβ1-1/κ·exp⁡-1+κx-ςβ1/κ,1+κx-ςβ>0.ς,β, and κ are the location, scale, and shape parameters, respectively. The cumulative distribution function (CDF) of a GEV is (2)Fx=exp⁡-1+κx-ςβ1/κ.This CDF can be inverted to yield an explicit formula for the quantile function,(3)F-1p=ς+βκ-ln⁡p-κ-1.Because the moments of the GEV involve the gamma function, estimating GEV parameters using the method of moments is no more convenient than the alternative method of maximum likelihood, which is frequently used in hydrologic applications. Maximum likelihood methods can be easily adapted to include effects of covariates or additional influences [17]. For moderate and large sample sizes, results of the two parameter estimation methods are usually similar. Based on (3), the return period XT can be computed as(4)XT=ς-βκ1--log⁡1-1T-κ,κ≠0,XT=ς-βlog⁡-log⁡1-1T,κ=0.The generalized Pareto distribution (GPD) is essentially a simple primitive distribution model [12], designed specifically to describe probability features of the entire observation dataset, beyond a given critical value (threshold).The distribution function of GPD is(5)Fx=1-1-κx-β1α11/κ,κ>0,β1≤x≤β1+β1κorκ<0,β1≤x<ϖ,(6)Fx=1-1-κx-β1α11/κ,κ=0,where β1 denotes the threshold, α1 the scale parameter, and κ the shape parameter (linear type). If y=x-β1 indicates values of the variable X above threshold β1, we may rewrite the distribution function as F(x). It is seen from (5) that, for κ=0, the GPD can be simplified to a logarithmic distribution [15, 18].From the size of samples with one year as a unit, annual crossing rates above a certain threshold in yearst can be given [18] as(7)λx=λt1-Fx,where λ is a mean of multiyear crossing rates between a given value of an extreme event and threshold β1. Based on (5) and (7), the return period XT can be computed as(8)XT=β1+α1κ1-λT-κ,κ≠0.Based on (6) and (7), the return period XT can be computed as(9)XT=β1+α1ln⁡λT,κ=0,in which λ denotes the yearly mean crossing rate, β1 the given threshold, α1 the scale parameter, and κ the shape parameter (to designate the distribution curve type). Then, the related GPD model and its quantile can be found by obtaining GPD parameters using the given estimation method. In a special case with λ=1, that is, the peaks-over-threshold (POT) crossing rate appearing once per year, we simplify (8)-(9) to (10)XT=β1+α1κ1-T-κ,κ≠0,XT=β1+α1ln⁡T,κ=0.The Poisson probability distribution is(11)Fx=eλ×λxx!,where λ is a positive real number, equivalent to the expected number of occurrences during a given interval.


## 3. Results

To study trends of extreme precipitation intensities and frequencies during 1961–2008, an ordinary least-squares linear trend analysis of annual maxima was done for the 54 series. The number of series with positive trends exceeds negative ones by a factor of more than two (46 positives and 8 negatives). In addition, the spatial distribution of trend signs shows a clear predominance of positives (Figure2).Figure 2
Change in intensities of annual maximum rainfall events (1961–2008).We also assessed changes in the frequency of extreme precipitation. Extreme events were counted when they exceeded a defined threshold. An analysis of seasonal (excluding summer) and monthly trends was established for different extreme precipitation indices. Next, the ratio between quantities of extreme events was calculated for the last 24-year period of the analysis (1985–2008) and for the first 24-year period (1961–1984). Figure3 shows the frequency ratio for different thresholds. In most of the region, the frequency of extreme events was higher in the second period (ratio greater than 1). For the 10 and 20 mm thresholds, there are large areas with ratios between one and two, with greatest values in the center and west of Xinjiang. For the 30 mm threshold, the ratio reaches its highest values (exceeding 7) in the center of Xinjiang. For the 40 mm threshold, the ratio reaches even higher values in the east of Xinjiang, but most of the region west of Xinjiang has values lower than 1. This preliminary analysis indicates that there were predominantly positive trends in annual maximum precipitation during 1961–2008, as well as a remarkable increment in the frequency of extreme precipitation over different thresholds (10 to 40 mm).Figure 3
Frequencies exceeding indicated thresholds (1985–2008/1961–1984).
(a)
(b)
(c)
(d)


### 3.1. Intensity of Extreme Precipitation

Extreme value theories are widely used in many fields of science (e.g., the insurance industry, financial markets, and natural disaster risk management). Such theory is important, because modeling extreme event distributions is generally associated with a large margin of error. This is because extreme events are by definition rare, and thus very few extreme value data are available to estimate appropriate parameters.The variable of interest here is extreme precipitation intensity. Fits of the precipitation series were performed using the maximum likelihood method. This method can be easily adapted to include effects of covariates or other influences [17]. The method of maximum likelihood is a much better approach to parameter fitting for the three distributions [17]. The principle of this estimation is to adopt the model with greatest likelihood. This method has the great advantage of allowing addition of the fitting of covariables.First, we apply the GEV distribution fit to the 54 series of annual maxima. Model 1 was fit with the location (ς), the scale (β), and the shape (κ) parameters invariant in time, suggesting a stationary series. Then, to identify possible temporal trends, Model 2 was fit with a linear trend for the location parameter μ.Model 1:ς, β, and κ are all constant.Model 2: considerς(t)=μ0+μ1×t. σ and γ are constant.We use probability and Q–Q plots to examine these models. Figure4 shows the probability and Q–Q plots of the series fit according to Model 1. In all series, fits of this quality were observed. To determine which of the two models fits each series better, the likelihood ratio test was applied. The results of this test in the two models show that, in all cases, the series do not have a significant trend at the 95% confidence level for the annual maxima.Figure 4
(a) Probability plot; (b) quantile-quantile plot for Xinjiang, Model 1.
(a)
(b)Although there is a predominantly positive trend (Figure2), the extreme precipitation makes it difficult to find significant trends. As explained by Coles [15], modeling with the maximum value per block wastes other potentially useful information in the extreme value analysis. First, the GPD was fit to each series assuming stationary behavior of the scale and shape parameters (Model 1). Then, to detect the presence of trends in values of precipitation intensity, the GPD was fit assuming temporal variation of the scale parameter (σ) (Model 2). The scale parameter represents the energy of an extreme event, and this may change with time.Model 1:σ and γ are constant.Model 2: considerσ(t)=σ0+σ1×t. γ is constant.Results of the fit according to Model 1 show a quality similar to those observed with the GEV model (Figure5). The likelihood ratio test was also applied, to evaluate which of the two proposed models was the most satisfactory for the available series. Model 2 adjusted better than Model 1, showing a positive trend of intensity. The POT method using the GPD shows that there were significant positive trends in Xinjiang, indicating that significance of extreme precipitation in Xinjiang is sensitive to the method used.Figure 5
Probability plot (a) and quantile-quantile plot (b) for Xinjiang, Model 1.
(a)
(b)


### 3.2. Frequency of Extreme Precipitation

First, to detect trends in extreme precipitation frequency, 1-day precipitation amounts exceeding 10, 20, 30, and 40 mm thresholds were counted. Then, we compared stationary and nonstationary Poisson processes and applied the nonparametrical Mann-Kendall test. We used the Poisson distribution to fit the annual number of 1-day precipitation amounts exceeding the 20 and 30 mm thresholds. These were chosen as representative low and high thresholds, considering that extreme precipitation has a strong east–west gradient in Xinjiang and therefore in many western locations. The chi-square test (χ2) was applied to assess adjustments to the distribution. In the 54 series, 45 fit well for the 20 mm threshold and 41 for the 30 mm threshold. The series fitting the Poisson distribution were also fit to a nonstationary Poisson process, adopting a model with a temporally variable λ parameter [19]:(12)log⁡λt=λ0+λ1×t.We applied the likelihood ratio test to evaluate which of the two models is the better option. Figure6 shows that less than half of the series have significant positive trends. However, the fact that there was a considerable percentage of series with significant trends deserved further analyses, especially at the regional level.Figure 6
Percentage of stations with significant positive trends in frequency exceeding indicated thresholds.We used the Mann-Kendall test [20, 21] to analyze each of the 54 series of annual cases with 1-day extreme precipitation over 10, 20, 30, and 40 mm thresholds. Table 1 shows the number and percentages of series for Xinjiang with positive and negative trends, for each threshold. We find a clear prevalence of positive trends, which for 10 mm thresholds is over 80%. The percentages of extreme precipitation series with significant trends are not higher than 37%. This result is similar to that of the Poisson distribution.Table 1
Number of series with positive (POS) and negative (NEG) trends and respective percentages.
Threshold (mm)
POS
POS %
NEG
NEG %
10
47
87
8
13
20
43
80
11
20
30
40
74
14
36
40
34
63
20
37


### 3.3. Precipitation Frequencies Exceeding Thresholds

Since precipitation in Xinjiang has significant interannual variability [22], this may contribute to reducing the significance of long-term trends when the series are composed of annual values. Therefore, to assess long-term trends, precipitation events exceeding certain thresholds over the entire region (54 stations) were counted for 4-year periods, starting in 1961–1964 and ending in 2005–2008 (Figure 7). The Mann-Kendall test applied to these series shows positive trends, with a 90% level of confidence (Table 2). Then, we compared the trend for different thresholds, that is, the percent increase between endpoints. The extreme precipitation event trend increases with threshold value 20–30% for 10 and 20 mm, about 50% for 30 mm, and almost 100% for 40 mm. The frequency of extreme precipitation events is significant for all thresholds in Xinjiang. Results show that the percent increase in the number of precipitation events over 10 mm during 1961–2008 increased faster than for the other thresholds (Figures 7(a)–7(d)).Table 2
Confidence level of positive trends of the frequency of rainfalls over the indicated thresholds.
Threshold (mm)
Entire region (%)
10
97.5
20
97.5
30
97.5
40
95Figure 7
Frequency of occurrence of extreme precipitation events in Xinjiang exceeding 357 thresholds as follows: (a) 10; (b) 20; (c) 30; (d) 40 mm. Trends indicated in panels are 358 cases/year.
(a)
(b)
(c)
(d)


## 3.1. Intensity of Extreme Precipitation

Extreme value theories are widely used in many fields of science (e.g., the insurance industry, financial markets, and natural disaster risk management). Such theory is important, because modeling extreme event distributions is generally associated with a large margin of error. This is because extreme events are by definition rare, and thus very few extreme value data are available to estimate appropriate parameters.The variable of interest here is extreme precipitation intensity. Fits of the precipitation series were performed using the maximum likelihood method. This method can be easily adapted to include effects of covariates or other influences [17]. The method of maximum likelihood is a much better approach to parameter fitting for the three distributions [17]. The principle of this estimation is to adopt the model with greatest likelihood. This method has the great advantage of allowing addition of the fitting of covariables.First, we apply the GEV distribution fit to the 54 series of annual maxima. Model 1 was fit with the location (ς), the scale (β), and the shape (κ) parameters invariant in time, suggesting a stationary series. Then, to identify possible temporal trends, Model 2 was fit with a linear trend for the location parameter μ.Model 1:ς, β, and κ are all constant.Model 2: considerς(t)=μ0+μ1×t. σ and γ are constant.We use probability and Q–Q plots to examine these models. Figure4 shows the probability and Q–Q plots of the series fit according to Model 1. In all series, fits of this quality were observed. To determine which of the two models fits each series better, the likelihood ratio test was applied. The results of this test in the two models show that, in all cases, the series do not have a significant trend at the 95% confidence level for the annual maxima.Figure 4
(a) Probability plot; (b) quantile-quantile plot for Xinjiang, Model 1.
(a)
(b)Although there is a predominantly positive trend (Figure2), the extreme precipitation makes it difficult to find significant trends. As explained by Coles [15], modeling with the maximum value per block wastes other potentially useful information in the extreme value analysis. First, the GPD was fit to each series assuming stationary behavior of the scale and shape parameters (Model 1). Then, to detect the presence of trends in values of precipitation intensity, the GPD was fit assuming temporal variation of the scale parameter (σ) (Model 2). The scale parameter represents the energy of an extreme event, and this may change with time.Model 1:σ and γ are constant.Model 2: considerσ(t)=σ0+σ1×t. γ is constant.Results of the fit according to Model 1 show a quality similar to those observed with the GEV model (Figure5). The likelihood ratio test was also applied, to evaluate which of the two proposed models was the most satisfactory for the available series. Model 2 adjusted better than Model 1, showing a positive trend of intensity. The POT method using the GPD shows that there were significant positive trends in Xinjiang, indicating that significance of extreme precipitation in Xinjiang is sensitive to the method used.Figure 5
Probability plot (a) and quantile-quantile plot (b) for Xinjiang, Model 1.
(a)
(b)


## 3.2. Frequency of Extreme Precipitation

First, to detect trends in extreme precipitation frequency, 1-day precipitation amounts exceeding 10, 20, 30, and 40 mm thresholds were counted. Then, we compared stationary and nonstationary Poisson processes and applied the nonparametrical Mann-Kendall test. We used the Poisson distribution to fit the annual number of 1-day precipitation amounts exceeding the 20 and 30 mm thresholds. These were chosen as representative low and high thresholds, considering that extreme precipitation has a strong east–west gradient in Xinjiang and therefore in many western locations. The chi-square test (χ2) was applied to assess adjustments to the distribution. In the 54 series, 45 fit well for the 20 mm threshold and 41 for the 30 mm threshold. The series fitting the Poisson distribution were also fit to a nonstationary Poisson process, adopting a model with a temporally variable λ parameter [19]:(12)log⁡λt=λ0+λ1×t.We applied the likelihood ratio test to evaluate which of the two models is the better option. Figure6 shows that less than half of the series have significant positive trends. However, the fact that there was a considerable percentage of series with significant trends deserved further analyses, especially at the regional level.Figure 6
Percentage of stations with significant positive trends in frequency exceeding indicated thresholds.We used the Mann-Kendall test [20, 21] to analyze each of the 54 series of annual cases with 1-day extreme precipitation over 10, 20, 30, and 40 mm thresholds. Table 1 shows the number and percentages of series for Xinjiang with positive and negative trends, for each threshold. We find a clear prevalence of positive trends, which for 10 mm thresholds is over 80%. The percentages of extreme precipitation series with significant trends are not higher than 37%. This result is similar to that of the Poisson distribution.Table 1
Number of series with positive (POS) and negative (NEG) trends and respective percentages.
Threshold (mm)
POS
POS %
NEG
NEG %
10
47
87
8
13
20
43
80
11
20
30
40
74
14
36
40
34
63
20
37


## 3.3. Precipitation Frequencies Exceeding Thresholds

Since precipitation in Xinjiang has significant interannual variability [22], this may contribute to reducing the significance of long-term trends when the series are composed of annual values. Therefore, to assess long-term trends, precipitation events exceeding certain thresholds over the entire region (54 stations) were counted for 4-year periods, starting in 1961–1964 and ending in 2005–2008 (Figure 7). The Mann-Kendall test applied to these series shows positive trends, with a 90% level of confidence (Table 2). Then, we compared the trend for different thresholds, that is, the percent increase between endpoints. The extreme precipitation event trend increases with threshold value 20–30% for 10 and 20 mm, about 50% for 30 mm, and almost 100% for 40 mm. The frequency of extreme precipitation events is significant for all thresholds in Xinjiang. Results show that the percent increase in the number of precipitation events over 10 mm during 1961–2008 increased faster than for the other thresholds (Figures 7(a)–7(d)).Table 2
Confidence level of positive trends of the frequency of rainfalls over the indicated thresholds.
Threshold (mm)
Entire region (%)
10
97.5
20
97.5
30
97.5
40
95Figure 7
Frequency of occurrence of extreme precipitation events in Xinjiang exceeding 357 thresholds as follows: (a) 10; (b) 20; (c) 30; (d) 40 mm. Trends indicated in panels are 358 cases/year.
(a)
(b)
(c)
(d)


## 4. Conclusions

(1)
Changes in the frequency of precipitation events exceeding thresholds from 10 to 40 mm were predominantly positive. These results indicate that extreme precipitation became more frequent and intense during the last several decades in the Xinjiang region.
(2)
The POT methodology using the GPD shows significant positive trends, indicating that significance of the extreme precipitation in Xinjiang is sensitive to the method used.
(3)
Regarding the numbers and percentages of series with positive and negative trends for each threshold, we find a clear prevalence of positive trends, which for low thresholds are over 80%. The percentages of extreme precipitation series with significant trends are not higher than 37%. This result is similar to that of the Poisson distribution.
(4)
Precipitation frequencies exceeding thresholds show that the percent increase of the number of precipitation events over 10 mm during 1961–2008 was faster than for the other thresholds.



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*Source: 645965-2015-05-20.xml*