Hindawi Publishing Corporation Advances in Meteorology Volume 2012, Article ID 579764, 7 pages doi:10.1155/2012/579764 Research Article Analysis and Modeling of Time-Correlated Characteristics of Rainfall-Runoff Similarity in the Upstream Red River Basin 1, 2 1, 2 3 2 Xiuli Sang, Jianxin Xu, Kun Zhang, and Hua Wang Quality Development Institute, Kunming University of Science and Technology, Kunming 650093, China Engineering Research Center of Metallurgical Energy Conservation and Emission Reduction Ministry of Education, Kunming University of Science and Technology, Kunming 650093, China Hydrology and Water Resources Bureau of Yunnan, Kunming 650106, China Correspondence should be addressed to Jianxin Xu, xujianxina@163.com Received 25 October 2012; Revised 30 November 2012; Accepted 30 November 2012 Academic Editor: Luis Gimeno Copyright © 2012 Xiuli Sang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We constructed a similarity model (based on Euclidean distance between rainfall and runoﬀ)tostudy time-correlated characteristics of rainfall-runoﬀ similar patterns in the upstream Red River Basin and presented a detailed evaluation of the time correlation of rainfall-runoﬀ similarity. The rainfall-runoﬀ similarity was used to determine the optimum similarity. The results showed that a time-correlated model was found to be capable of predicting the rainfall-runoﬀ similarity in the upstream Red River Basin in a satisfactory way. Both noised and denoised time series by thresholding the wavelet coeﬃcients were applied to verify the accuracy of model. And the corresponding optimum similar sets obtained as the equation solution conditions showed an interesting and stable trend. On the whole, the annual mean similarity presented a gradually rising trend, for quantitatively estimating comprehensive inﬂuence of climate change and of human activities on rainfall-runoﬀ similarity. 1. Introduction correlated and consistent. However, this correlation often displayed a large ﬂuctuation, and the joint eﬀect of climate Understanding the relationships between rainfall and runoﬀ change and human activities on ecological environment was was vital for eﬀective management and utilization of scarce responsible for the rainfall-runoﬀ relation in the upstream water resources. Especially, it was important in Yunnan Red River since 2001. where water shortage and drought prevailed in three consec- Previous studies [2–5] focused on modeling the rainfall- utive years. runoﬀ relations. Generally, these models involved simulation In Red River Basin, the changes of watercourse and of runoﬀ in a given rainfall sequence. However, most of these hydrologic regime, soil erosion, sediment deposition, water studies illustrated that rainfall and runoﬀ presented similar pollution, loss of biodiversity, and other cross-border issues variability. In [6], plots of standardized 1970–2005 annual have attracted international attention [1]. The protection, runoﬀ and rainfall per basin revealed similar variability. Zhang et al. [7] found the rainfall and runoﬀ trends were rational management, and exploitation of water resources were becoming key issues of the strategic planning in a similar on the whole. But due to complex climate and human national level. In the last half century, deforestation and soil activities in diﬀerent regions, the correlation coeﬃcient of erosion were the root causes of drought in Yunnan. Under rainfall and runoﬀ showed some ﬂuctuations. the inﬂuences of climate change and human activities, the Therefore, the rainfall-runoﬀ similarity was inevitable ecological environment conditions of the upstream Red River and should be investigated. Our objective was to deﬁne Basin deteriorated further, which directly aﬀected the status rainfall-runoﬀ ﬂow similarity relationships. In fact, the of water resources of the middle and lower reaches of the Red inﬂuence of ecological deterioration and human activities River Basin. Precipitation was the main source of Red River on similarity of rainfall and runoﬀ became more and more Basin water resources. As we all know, rainfall and runoﬀ was prominent. Exploring some time-correlated regularity of 2 Advances in Meteorology information in upstream Yuanjiang River of Red River basin, providing services for the protection and exploitation of water resources, ﬂood control, drought, and disaster mitigation. 2.2. Data Processing. The time series of daily rainfall and runoﬀ were obtained from the hydrology stations of Dadongying (Figure 1). The record ranged from 2001 to 2010, as showed in Figure 2. For time series data, periodical change caused by noise or some mechanism should be determined. We need to ﬁnd a method to eliminate noise and reﬂect real trend of hydrological data. Wavelet analysis has been applied in the investigation of the rainfall-runoﬀ relationship [7–9]. In this paper, a denoised time series XD of input signal X was obtained by thresholding the wavelet coeﬃcients. Signal-to-noise ratio (often abbreviated SNR or S/N) was a measure used in science and engineering that compared the level of a desired signal to the level of background noise. It was deﬁned as the ratio of signal power to the noise power. A ratio higher than 1 : 1 indicates more signal than noise and can be applied to any form of signals. We deﬁned SNR as Figure 1: Water system diagram of Red River Basin of China. |X| SNR = . (1) |X − XD| these ﬂuctuations of rainfall-runoﬀ similarity was a very interesting and challenging work. X represented the vector signal, and the XD indicated the Our main contributions are as follows. denoised version of input signal. Figure 3 showed the time series plots of the denoised (1) We constructed a similarity model based on rainfall and runoﬀ values by wavelet method. By selecting Euclidean distance between rainfall and runoﬀ diﬀerent parameters in wavelet function, a higher signal-to- (Section 3). noise ratio was determined. The SNR of rainfall time series (2) We presented a detailed evaluation of the time was 18.31, and the SNR of runoﬀ series was 64.25. correlation of rainfall-runoﬀ similarity (Section 3). Obviously, rainfall and runoﬀ presented periodic change (3) We proposed the annual mean similarity for estimat- [10, 11]. However, runoﬀ data showed obvious oscillation ing the joint eﬀects of climate change and of human and instability, which indicated that runoﬀ was inﬂuenced activities on ecological environment (Section 4). by other factors such as evaporation capacity and vegetation coverage [11]. 2. Data Acquisition 3. Modeling To investigate the time-correlated characteristics of rainfall- runoﬀ similarity in the upstream Red River Basin of China, An analysis of the equal environments assumption should we performed a detailed investigation using 10 years (2001– be made. The data of rainfall and runoﬀ were obtained 2010) of daily measurements of rainfall and runoﬀ data as from the hydrology stations of Dadongying in the upstream follows. Red River Basin. Rainfall and runoﬀ in diﬀerent areas were not analyzed. The numerical similarity between rainfall and 2.1. Study Area. Figure 1 was the water system diagram runoﬀ was just investigated. The results showed that this of Red River Basin. The Da-dong-yong hydrologic station numerical similarity based on Euclidean distance was linear. marked with red circle was located in Najian County of Particularly, the annual mean similarity increase indicated ◦ ◦ Yunnan Dali Prefecture, at 100 34 east longitude, 25 04 the inﬂuence of ecological deterioration and human activities north latitude. In 1958 this station was established by the on similarity of rainfall and runoﬀ. In addition, for the Water Conservancy Bureau of Agriculture Department of noised data, wavelet analysis was used to decrease noise. And Yunnan Province. Since 1988, basic cross-section migrated signal-to-noise ratio was measured to determine noise level. 87 meters upward, and river basin area reached 2628 square In Section 4, this paper discussed the impact of noise data on kilometers. It was a typical provincial important hydrometric the key parameters of modeling. station in upstream Red River Basin of China. The station First, in this paper the data sets were chosen for exploring was mainly responsible for collecting basic hydrological the close relationship between rainfall and runoﬀ.More Advances in Meteorology 3 80 300 40 150 0 0 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 Days Days Figure 2: Time series plots of the observed rainfall and runoﬀ values. (SNR = 18.31) (SNR = 64.25) −50 −10 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 Days Days Figure 3: Time series plots of the denoised rainfall and runoﬀ values. and more studies [6, 7] showed that this relationship was Step One. The original and denoised rainfall-runoﬀ signals important and valuable to acquire the inﬂuence of environ- by thresholding the wavelet coeﬃcients was obtained, as mental changes and human activities on the ecology. Second, shown in Figures 2 and 3. similarity analysis could also be performed by estimating Euclidean distance parameters [12], then the minimum Step Two. A normalized data from 10 years of annual rainfall distance between rainfall and runoﬀ sets was deﬁned as and runoﬀ values was obtained by a linear transformation: similarity, which was obtained by calculating the objective Y = 20X − 100. (2) function with absolute value therefore, the particular sets in Table 1 were obtained as the equation solution conditions. As shown in Figure 4. Third, the parameters of similarity model were determined by least square method to ﬁt the minimum distance. Step Three. The Euclidean distance between the normalized The rainfall-runoﬀ modeling contained so many meth- rainfall and runoﬀ was calculated, and the minimum value ods [13–19]. This paper investigated a relationship of of distance sum was deﬁned as the similarity of rainfall and similarity. Based on the similarity between rainfall and runoﬀ. runoﬀ, we need to construct a map for normalizing the data. We deﬁned the annual rainfall in 2001 as “a,” whose coor- This mapping could not change the shape of curve, so we dinate was expressed as (2001, a). The rest of annual rainfall used Euclidean distance between the rainfall and runoﬀ to were represented by “a.” For example, the coordinate in 2002 quantify the similarity relation. was written as (2002, a+821.89). Similarly, the annual runoﬀ Rainfall (mm) Rainfall (mm) 8 3 8 3 Runoﬀ (10 m /s) Runoﬀ (10 m /s) 4 Advances in Meteorology Table 1: The corresponding constraints of similarity model in 10 years. 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 0 [0, 821] 821 [389, 821] 389 [0, 389] 0 [−35, 0] −35 [−35, 0] 0 [0, 780] 780 [352, 780] 352 [0, 352] 0 [−85, 0] −85 [−85, 0] 4. Results and Discussions ×10 2.5 A simple similarity model was established to calculate the minimum value of Euclidean distance between rainfall and runoﬀ. The solution results showed that the corresponding constraint or range also presented an interesting and stable trend as shown in Table 1. For the even-numbered years, 1.5 the corresponding constraint condition was a range or interval, and for the odd-numbered years, the corresponding constraint condition was just the boundary value of range. The minimum values of similarity between rainfall and runoﬀ by calculating the objective function were shown in 0.5 Figure 5. It was noticed that the evolution of the minimum value of similarity versus the time approximately followed the linear distribution. The least-squares method was used to ﬁt the initial and denoised time series. A model of rainfall and 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 runoﬀ similarity relation in the upstream Red River Basin Year was determined. The formula was as follows: Rainfall (transformed) Runoff δ = m × t − c. (7) Figure 4: The runoﬀ and transformed rainfall data. Then we take parameters’ sensitivities on the results into consideration. In case of long data (9 years) with noise, m = 1350.7, and c = 2703600, and in denoised case, 1 1 in 2001 was deﬁned as “b,” and its coordinate was expressed m = 1339.2, and c = 2680500, while, in case of short data 1 1 as (2001, b). The rest were represented by “b.” For example, (8 years) with noise, m = 1276.6, and c = 2555200, and 1 1 the Euclidean distance of corresponding points (2001, a)and in denoised case, m = 1265.8, and c = 2533500. Clearly, 1 1 2 2 (2001, b) was calculated by (2001 − 2001) +(a − b) . the key parameters of this model showed some ﬂuctuations. However, this method of modeling could be applied in other Using this transformation, the shape of annual rainfall- runoﬀ curves remained unchanged. The similarity model regions. based on the distance between the rainfall and runoﬀ was In diﬀerent regions, the rainfall-runoﬀ similarity still existed [6, 7]. Although this paper investigated the upstream built to compute the minimum value σ of the objective function (deﬁned as Φ). Red River Basin, other sets of values in other regions also The objective function is could be calculated by using this model, but the parameters of model would not be the same. The following ﬁgures showed the ﬁtting curves and Φ = |X − Y |. (3) i i correlation coeﬃcients. i=1 In order to verify the accuracy of the model, we calculated The similarity function is the relative error using the data of 2010. The predicting value of similarity was 11307, and the observed value was 12172. σ = min Φ. (4) In fact an accumulated error from 2001 to 2010 was obtained with the annual error at 86.5. We acquired the relative error X represented the annual runoﬀ values, and Y was the i i 0.0071, by the ratio between the annual error and observed annual rainfall values. In this paper, the “n”refersto10years value. from 2001 to 2010. One has Figure 7 clearly showed that the annual mean similarity 2 2 took a gradually rising trend. Even if it was diﬃcult to ( ) ( ) Φ = 2001 − 2001 + a − b +··· (5) separate which part of this annual mean similarity increase was due to climate changes alone or to human impact on + (2010 − 2010) + (a − b + c ) ecological environment. According to the historical data Let a−b = Q, then the objective function could be simpliﬁed records, in 2005, it was often the wettest in the summer. as However, Yunnan Province in China suﬀered the most serious early summer drought in the past 50 years. Figure 6 Φ =|Q| + |Q + c | +··· + |Q + c |. 1 9 (6) showed clearly the rainfall was increasing, and the runoﬀ Advances in Meteorology 5 14000 14000 12000 12000 8000 8000 6000 6000 δ δ 4000 4000 0 0 −2000 −2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Year Year De-noising data Original data Fitting curve Fitting curve (a) (b) Figure 5: Fitting of initial (a) and de-noising (b) data with the correlation coeﬃcient 0.982 and 0.983. 4 4 ×10 ×10 2.4 2.24 2.2 2.22 2.2 2.18 1.8 2.16 1.6 2.14 1.4 2.12 1.2 2.1 2.08 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Year Rainfall Year Runoﬀ (upper) Rainfall Runoﬀ (lower) Runoﬀ (upper) Runoﬀ (lower) Figure 6: The similar patterns of rainfall and runoﬀ at the minimum distance from 2001 to 2010. was decreasing. At the same time, this index of annual mean to study the changes of our ecological environment by similarity presented a ﬂuctuation from 2005. comparison of similarity between rainfall and runoﬀ. In addition, according to water resources bulletin of Yunnan Province from 2002 to 2004, the years 2002 and 2004 5. Summary belonged to years of average river water level. But the year of 2003 was relatively dry, which suﬀered the most serious In this paper, we studied the rainfall-runoﬀ similar patterns drought in the last ﬁve years. Clearly in Table 1, the particular in the upstream Red River Basin. The normalized rainfall- sets from 2002 to 2004 showed some ﬂuctuations. While in runoﬀ values were obtained by a simple linear transfor- 2003, the constraint condition of similarity model arrived the mation. A model of rainfall-runoﬀ similarity was built to maximum point. Figure 7 further showed the ﬂuctuation of determine the minimum of the Euclidean distance between the annual mean similarity in 2003. It was very interesting rainfall and runoﬀ. Both original and denoised time series 2001.9 2002.1 2002.2 2002.3 2002.4 2002.5 2002.6 2002.7 2002.8 2002.9 6 Advances in Meteorology b: Annual runoﬀ in 2001 Y : The annual rainfall values Q:Thediﬀerence of a and b. Acknowledgments This research is supported by the National Natural Science Foundation of China (Grant no. 51174105). The authors also deeply appreciate the helpful review comments and suggestions by anonymous reviewers. References [1] D. M. He, S. H. Wu, and H. Peng, “A study of ecosystem changes in Longitudinal Range-Gorge Region and trans- 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 boundary eco-security in southwest China,” Advances in Earth Years Science, vol. 20, no. 3, pp. 338–344, 2005. 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Published: Dec 19, 2012
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