Spatial and temporal variability of daily precipitation in Haihe River

J. Geogr. Sci. 2010, 20(2): 248-260 DOI: 10.1007/s11442-010-0248-0 © 2010

Science in China Press

Springer-Verlag

Spatial and temporal variability of daily precipitation in Haihe River basin, 1958–2007 CHU Jianting1,2,3, XIA Jun1, XU Chongyu4, LI Lu1,2, WANG Zhonggen1 1. Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China; 2. Graduate University of Chinese Academy of Sciences, Beijing 100039, China; 3. Institute of Physics & Meteorology, University of Hohenheim, Garbenstr. 30, D-70955 Stuttgart, Germany; 4. Department of Geosciences, University of Oslo, P O BOX 1047 Blindern, N-0316 Oslo, Norway

Abstract: The seasonal variability and spatial distribution of precipitation are the main cause of flood and drought events. The study of spatial distribution and temporal trend of precipitation in river basins has been paid more and more attention. However, in China, the precipitation data are measured by weather stations (WS) of China Meteorological Administration and hydrological rain gauges (RG) of national and local hydrology bureau. The WS data usually have long record with fewer stations, while the RG data usually have short record with more stations. The consistency and correlation of these two data sets have not been well understood. In this paper, the precipitation data from 30 weather stations for 1958–2007 and 248 rain gauges for 1995–2004 in the Haihe River basin are examined and compared using linear regression, 5-year moving average, Mann-Kendall trend analysis, Kolmogorov-Smirnov test, Z test and F test methods. The results show that the annual precipitation from both WS and RG records are normally distributed with minor difference in the mean value and variance. It is statistically feasible to extend the precipitation of RG by WS data sets. Using the extended precipitation data, the detailed spatial distribution of the annual and seasonal precipitation amounts as well as their temporal trends are calculated and mapped. The various distribution maps produced in the study show that for the whole basin the precipitation of 1958–2007 has been decreasing except for spring season. The decline trend is significant in summer, and this trend is stronger after the 1980s. The annual and seasonal precipitation amounts and changing trends are different in different regions and seasons. The precipitation is decreasing from south to north, from coastal zone to inland area. Keywords: climate change; spatial and temporal variability of precipitation; Mann-Kendall method; Kolmogorov-Smirnov test; Z test; F test; Haihe River basin

1

Introduction

With the global warming, the local hydrological pattern will change, or has been changing. Received: 2009-08-18 Accepted: 2009-10-12 Foundation: National Basic Research Program of China, No.2010CB428406; The Key Knowledge Innovation Project of the CAS, No.KZCX2-YW-126; Key Project of National Natural Science Foundation of China, No.40730632 Author: Chu Jianting, Ph.D, specialized in climate change, land surface processes and water resources research * Corresponding author: Xia Jun, Professor, E-mail: [email protected]

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CHU Jianting et al.: Spatial and temporal variability of daily precipitation in Haihe River basin, 1958–2007

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One of the import aspects of this change is the spatial and temporal variability of precipitation. In addition, the abnormal seasonal variability and uneven spatial-temporal distribution of precipitation are often the direct reasons for the extreme flood and draught events. In China, spatial-temporal variability of precipitation in watershed scale, as well as the impact of precipitation on runoff, has been paid more and more attention. The research results from Zhang et al. (2009b) and Ren (2007) show that great differences exist in the temporal trend & spatial distribution of precipitation over different river basins in China. Zheng (2001) studied the temperature, precipitation and runoff of the Yellow River basin for 1951–1998. The results showed that the discharge in the Yellow River basin has been decreasing continuously since the 1950s, however, this is not true as for precipitation; violent human activity is one of the main reasons for the decrease of discharge. Jiang (2005) analyzed the reasons for the discharge decrease in the Tarim River basin and pointed out that the precipitation in the 1970s is less than in the 1960s, while tends to increase after the 1970s. Zhang et al. (2008b) analyzed the spatial-temporal trend of extreme precipitation in the Yangtze River basin, and they found that the variability of extreme precipitation is milder before the 1970s, while has obvious increasing or decreasing trend after the 1970s depending on the regions and seasons; the wet days decreased, whereas, the intensity increased, especially in the middle and lower reaches. Furthermore, all of these variabilities caused the frequency of flood events increased in these regions. In China, the Haihe River basin possesses special important status in politics, economy, and culture. In recent years, the contradiction between water demand and water supply becomes more and more serious, which is partly caused by the global warming and superfluous groundwater exploitation. It is very urgent to study how to maintain the sustainable utilities of water resources under the climate change. For this need, the research has not been done enough in Haihe River basin partly due to the limited access to data and research instruments (Liu, 1999). In addition, the existed studies mainly focused on the analysis of specific weather condition causing flood and drought events (Ping et al., 2003); the analysis of the weather condition and water vapor transfer over the Haihe River basin (Fan and Liu, 1992; Zhang et al., 2008); the analysis of the historic trend and forecast of the future trend of runoff and water resources, etc. (Yuan et al., 2005; Liu et al., 2004; Shi, 1995). The study by Ren (2007) showed that the decreased amount of precipitation in the Haihe River basin is the largest among ten major river basins in China. The results of Zhang and Wang (2007) gave the similar conclusion. Liu et al. (2004) pointed out that the relationship between precipitation and runoff is different in different regions of the Haihe River basin, and we need to pay more attention to the influence of human activities. In China, large-scale precipitation observation data often come from two sources: the standard meteorological stations of China Meteorological Administration and the rain gauges of hydrological bureaus. The former has longer measuring period, and it is good to analyze the historical trend of precipitation; the latter has more stations but shorter observation periods, which is better to be used to calibrate and validate the hydrological models. In addition, precipitation data are managed by these two departments separately, which will impede the detailed description of their spatial-temporal distribution. Recognizing the above concerns, the objective of this paper is two-folds: (1) to compare the consistency and correlativity between the two precipitation data sets, i.e., from weather

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Journal of Geographical Sciences

stations (WS) and from rain gauges (RG), and to explore the feasibility of extending precipitation data of RG with the help of WS data; and (2) to obtain the detailed spatial–temporal variation of precipitation making good use of the advantages of these two data sets. The research will be useful to both the hydrology sectors and the meteorological sectors, and will provide some references to the related research in other river basins.

2

Data and methods

2.1

Data

The Haihe River basin is located between 112°–120°E and 35°–43°N, and has an area of about 31.8×104 km2, of which, hills and plateau occupy nearly 60% of the total area, and the remaining 40% belongs to the plain area. To the north of the watershed is the Yanshan Mountain, to the west is the Taihang Mountain, and to the east is the vast North China Plain. From north to south, the Haihe River basin can be divided into three parts: Haihe, Luanhe and Tuhaimajiahe, and their areas are 2.32×104 km2, 4.45×104 km2 and 3.18×104 km, respectively. For the convenience of study, we divide the whole catchment into 283 sub-basins (Figure 1). In the basin, there are 30 weather stations with 50 years (1958–2007) of data, which are provided by the China Meteorological Administration, and 248 rain gauges for 10 years (1995–2004) obtained from the hydrological bureaus. 2.2

Methods

In this paper, 5-year moving average and Figure 1 The location of weather stations, rain gauges linear regression methods were used to de- and 283 sub-basins in the Haihe River basin tect the linear trend pattern of time series (Zhang et al., 2008a, 2009a); Mann-Kendall (Zheng, 2001; Jiang, 2005; Zhang et al., 2008a, 2009a; Wang, 2008) method was used to do the significance test of the non-linear changing pattern; Kolmogorov-Smirnov test was applied to check the distribution pattern (Xu, 2001), and Z and F test were used to check the equality of mean value and variance between the two data sets, respectively. In addition, some other statistical indicators were calculated and compared which are presented in the Results section. Given the time series {xi}, i = 1, 2,…, n, some of the used methods are explained as follows. 2.2.1

Mann-Kendall trend test

The study of Yue and Wang (2002) show that the higher the auto-correlation in the time se-


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ries, the larger the error one may expect in using Mann-Kendall test. Generally, the auto-correlation in time series needs to be removed, which is done in the following procedure. At first, calculate the 1st order auto-correlation coefficient:

1 n −1 ∑ ( xt − x )( xi +1 − x ) Cov( xi , xi +1 ) n − 2 i =1 ρ1 = = Var ( xi ) 1 n ( xi − x ) 2 ∑ n − 1 i =1 Then, remove the auto-correlation from the original time series: xi′ = xi − ρ1 xi −1

(1)

(2)

Simply, the transferred series ( xi′), i = 1, 2, ..., n is still noted as ( xi ), i = 1, 2, ..., n . Second, calculate Kendall indicator, τ, variance, σ τ2 , as well as normalized variable U (Zheng, 2001):

τ=

4p −1 n(n − 1)

(3)

2(2n + 5) 9n(n − 1)

(4)

σ τ2 =

U = τ / στ (5) where p is the number of occurrence of dual observation in precipitation time series. U can be used to reflect the trend in hydrological or meteorological time series. The larger the |U|, the more obvious the changing trend is. If U > 0, there is an increasing trend, and vice versa. Given the significance level α, the critical value Uα/2 can be obtained from the standard normal-distribution table; if |U| > Uα/2, reject the hypothesis of no trend, and suppose the changing trend is significant. For example, given α = 0.05, then, Uα/2 = U0.025 = 1.96; if U > 1.96, the increasing trend is significant, if U < –1.96, the decreasing trend will be significant. 2.2.2

Kolmogorov-Smirnov (K-S) test

The objective of this test is to statistically verify whether the distribution of the observation data is similar to some known distribution patterns. This test is based on the difference between cumulative frequency curve of observation and theoretical frequency curve of expectation (Xu, 2001). At first, calculate the cumulative frequency of the theoretical distribution, i.e., Fe(x), and calculate the cumulative frequency based on the data, i.e., Fo(x): Fo(x) = k/n (6) where k is the number of observations less than or equal to x, and n is the total number of observations. Then, calculate the maximum deviation D: D = max|Fe(x)–Fo(x)| (7) Given the hypothesis to be tested as: H0: Fe(x)=Fo(x), Ha: Fe(x)≠Fo(x) The hypothesis of the observation following the decided distribution is rejected if

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D≥Dα(n), in which, Dα(n) is the critical value and α is the significance level. 2.2.3

Z test

Given the hypothesis to be tested as: H0: μ1–μ2 = δ, H1: μ1–μ2 ≠ δ where, δ is set to be zero for testing the equality of the two means μ1 and μ2. Calculate the statistics: x − y −δ z= s12 s22 + n1 n2

(8)

The hypothesis of the two means are identical is rejected if |z| ≥ zα/2. Given α = 0.05, then, zα/2 = z0.025 = 1.96. In which, s12 , s22 , n1 , n2 are variances and lengths of the two data sets,

respectively. 2.2.4

F test

Given the hypothesis to be tested as: H 0 : σ 12 = σ 22 , H1 : σ 12 ≠ σ 22 Calculate the statistics: F=

s12 s22

where s12 > s22

(9)

The hypotheses of the two variances are the same is rejected if F≥Fα(n1–1,n2–1). Given the significance level α = 0.05, and n1=n2=120, then, Fα(n1–1,n2–1)=F0.05(119,119)=1.35 will be found from the F-distribution table.

3 3.1

Results Temporal trend of precipitation in the Haihe River basin

For the daily precipitation of 30 weather stations from 1958 to 2007, the area average annual and seasonal precipitation are obtained by simple averaging method; then, the temporal trends of seasonal and annual area-average precipitation are calculated (Figure 2). It is seen that in winter (a), the precipitation is decreasing with the rate around 0.5 mm/10a, which is not significant at the 5% significance level; in spring (b), there is a minor increase, and the increasing trend is not significant at 5% significance level; in summer (c), the decreasing trend in precipitation is significant at the 5% significance level, and the average decreasing rate is about 22 mm/10a; in autumn (d), the precipitation is decreasing with the rate about 2.7 mm/10a, which is not significant at 5% significance level. In total, the annual precipitation (e) is decreasing with a rate of 23 mm/10a, and this trend is significant at 5% significance level. 3.2

Spatial and temporal relationship of precipitation in the Haihe River basin

As mentioned above, the long-term precipitation data from WS can describe the temporal changing trend of precipitation in the whole river basin, however, it can not picture the de-


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Figure 2 Temporal trend of the area-average precipitation in Haihe River basin from 1958 to 2007: a) winter; b) spring; c) summer; d) autumn; e) annual. The p value is the significance level of the linear regression equation.

tailed local characters because the number of stations is limited. At the same time, the number of RG is much more than WS in the same catchment, which can reflect the local distribution features. However, the time span is always shorter, which will limit the accuracy of the analysis for the temporal trend of time series. Consequently, it is important to study how to couple the advantages of the two data sets, and how to obtain the detailed information about precipitation in the Haihe River basin adequately. At first, the distribution patterns of precipitation of the two data sets are tested to see if

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they both follow the normal distribution. For illustrative purpose, the test of RG data of the Xingtai station is presented here and the results are shown in Figure 3, in which, the mean value is x =

1 n 1 n xi = 529.11 , and the standard deviation is s = ∑ ∑ ( xi − x )2 = 191.72. n i =1 n − 1 i =1

Given α=0.05, n=10, then, Dα(n)=0.409 can be read from the K-S Table. From Figure 3 we get the maxD(x)=0.1808 1.96, the arrowhead is upward, if U < –1.96, the arrowhead is downward, otherwise, the station is described by a dot.


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opposite is true in the rear; the total annual precipitation ranges from 175 to 570 mm. In the past 50 years, there is distinct decreasing trend in most of the regions. In autumn (Figure 7d), the precipitation pattern is similar to that in spring, and varies between 55 to 195 mm. Annually (Figure 7e), the overall pattern of precipitation in the Haihe River basin shows that the precipitation decreases from south to north, ranging from 285 to 870 mm; Wutaishan station and Zunhua-Qinglong regions (in far west and east regions) seem to be the most precipitation-rich regions. In the past 50 years, most of the regions have obvious decreasing trend. In summary, the extended rain gauges data can describe more details about the spatial and temporal distribution of precipitation.

4

Conclusions

The abnormal seasonal variability and spatial distribution of precipitation are always the direct reasons for the flood or draught events. The spatial and temporal variability of precipitation in the river basin has been paid more and more attention. In this study the difference and similarity of precipitation in the Haihe River basin measured by weather stations of China Meteorological Administration and rain gauges of hydrology bureau are compared. Based on the comparison results, the short records of rain gauges are extended by using the data from weather stations, and the extended data are used to study the spatial distribution of the temporal trend of the precipitation in the region. The following conclusions are drawn from the study: (1) In the past 50 years (1958–2007), the precipitation is largely decreasing except for the spring; the spatial distribution pattern of precipitation in summer is similar to the annual values. (2) The annual precipitation from both data sets satisfy the normal distribution; the mean values and variances are statistically equal to each other at 5% significance level; the correlation between these two data sets is very close, the precipitation from RG can be extended with the help of WS data. (3) The extended precipitation can well describe the spatial distribution of precipitation. Taking the Yanshan and Taihang mountains as boundary, there are precipitation-rich regions in front of the boundary, while the opposite is true behind the boundary. In addition, the precipitation is decreasing from south to north, from coastal zone to inland. (4) The annual and summer precipitation in most regions of the Haihe River basin have been decreasing during the past 50 years, in winter and autumn the precipitation in the west part of the basin has been decreasing while the majority of the basin has no significant changing pattern. In spring, precipitation is decreasing in west part of the basin and increasing in the middle part. (5) This study showed that coupling the advantages of the weather station precipitation data and the rain gauge data provides good description of spatial-temporal distribution of precipitation, as well as great help to the study of impact of climate change on water resources in the region.

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