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Analysis and Modeling of Time-Correlated Characteristics of Rainfall-Runoff Similarity in the Upstream Red River Basin

Analysis and Modeling of Time-Correlated Characteristics of Rainfall-Runoff Similarity in the... 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. Original data [2] W.A.Welderufael,P.A.L.LeRoux, andM.Hensley,“Quan- Denoised data tifying rainfall-runoff relationships on the Dera Calcic Fluvic Regosol ecotope in Ethiopia,” Agricultural Water Management, Figure 7: Plots of annual mean similarity versus years. vol. 95, no. 11, pp. 1223–1232, 2008. [3] O. Kisi, J. Shiri, and M. Tombul, “Modeling rainfall-runoff process using soft computing techniques,” Computers & Geosciences, vol. 51, pp. 108–117, 2013. [4] D. Labat, R. Ababou, and A. Mangin, “Rainfall-runoff rela- by thresholding the wavelet coefficients were applied to tions for karstic springs—part I: convolution and spectral verify this model. The results indicated that the rainfall- analyses,” Journal of Hydrology, vol. 238, no. 3-4, pp. 123–148, runoff similarity was of a good time-correlated characteristic with a high correlation coefficient. When the minimum [5] M. P. Rajurkar, U. C. Kothyari, and U. C. Chaube, “Modeling value of similarity model was obtained, the corresponding of the daily rainfall-runoff relationship with artificial neural constraint or range also presented an interesting and stable network,” Journal of Hydrology, vol. 285, no. 1–4, pp. 96–113, trend. The annual mean similarity showed a gradually rising trend; in other words, the minimum distance between [6] W. Sven Lavado Casimiro, J. Ronchail, D. Labat, J. C. Espinoza, rainfall and runoff patterns in the upstream Red River and J. L. Guyot, “Basin-scale analysis of rainfall and runoff in Peru (1969–2004): Pacific, Titicaca and Amazonas drainages,” Basin was increasing. All these changes were caused by the Hydrological Sciences Journal, vol. 57, no. 4, pp. 625–642, 2012. comprehensive influences of climate change and human [7] J.C.Zhang,J.Jiang,D.P.Liu,and L. Donald DeAngelis, activities on rainfall-runoff similarity. “Vegetation coverage influence on rainfall-runoff relation Studying the similar relations of rainfall and runoff was based on wavelet analysis,” Journal of American Science, vol. of great significance. According to our research results, the 5, no. 2, pp. 97–104, 2009. constraint or range for meeting the minimum distance of [8] T. Partal and M. Kuc ¨ ¸uk, ¨ “Long-term trend analysis using dis- rainfall-runoff similarity was getting smaller and smaller. crete wavelet components of annual precipitations measure- However, the objective function value of similarity of rainfall ments in Marmara region (Turkey),” Physics and Chemistry of and runoff always followed a linear distribution, and the next the Earth, vol. 31, no. 18, pp. 1189–1200, 2006. annual similar relationship of rainfall and runoff could be [9] J. Wang and J. Meng, “Research on runoff variations based predicted. In particular, the trend of annual mean similarity on wavelet analysis and wavelet neural network model: a case reflected the impact of external environment changes on study of the Heihe River drainage basin (1944-2005),” Journal of Geographical Sciences, vol. 17, no. 3, pp. 327–338, 2007. hydrology and water resources system. [10] W. C. Boughton, “Effect of data length on rainfall-runoff modeling,” Environmental Modelling & Software, vol. 22, no. 3, pp. 406–413, 2007. List of Symbols [11] L. H. C. Chua and T. S. W. Wong, “Improving event-based rainfall-runoff modeling using a combined artificial neural X: Input signal network-kinematic wave approach,” Journal of Hydrology, vol. XD: Denoised time series 390, no. 1-2, pp. 92–107, 2010. SNR: Signal-to-noise ratio [12] G. Alaerts, J. van Erps, S. Pieters et al., “Similarity analyses of a: Annual rainfall in 2001 chromatographic fingerprints as tools for identification and X : The annual runoff values quality control of green tea,” Chemometrics in Chromatograph, n: Years from 2001 to 2010 vol. 910, pp. 61–67, 2012. c : The constant [13] G. F. Lin and C. M. Wang, “A nonlinear rainfall-runoff model σ: The minimum value of objective function embedded with an automated calibration method—part 1: the Φ: Objective function model,” Journal of Hydrology, vol. 341, no. 3-4, pp. 186–195, Y : Normalized data Annual mean similarity Advances in Meteorology 7 [14] J. Yu, C. Yang, C. Liu et al., “Slope runoff study in situ using rainfall simulator in mountainous area of North China,” Journal of Geographical Sciences, vol. 19, no. 4, pp. 461–470, [15] G. Cao, J. Wang, L. Wang, and Y. Li, “Characteristics and runoff volume of the Yangtze River paleo-valley at Nanjing reach in the Last Glacial Maximum,” Journal of Geographical Sciences, vol. 20, no. 3, pp. 431–440, 2010. [16] X. Lin, Y. Zhang, Z. Yao et al., “The trend on runoff variations in the Lhasa River Basin,” Journal of Geographical Sciences, vol. 18, no. 1, pp. 95–106, 2008. [17] J. Li and P. Feng, “Runoff variations in the Luanhe River Basin during 1956–2002,” Journal of Geographical Sciences, vol. 17, no. 3, pp. 339–350, 2007. [18] Y. Jiang, C. Zhou, and W. Cheng, “Streamflow trends and hydrological response to climatic change in Tarim headwater basin,” Journal of Geographical Sciences, vol. 17, no. 1, pp. 51– 61, 2007. [19] G. Mahe´ and J. E. Paturel, “1896-2006 Sahelian annual rainfall variability and runoff increase of Sahelian Rivers,” Comptes Rendus Geoscience, vol. 341, no. 7, pp. 538–546, 2009. 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Analysis and Modeling of Time-Correlated Characteristics of Rainfall-Runoff Similarity in the Upstream Red River Basin

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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.
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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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