We constructed a similarity model (based on Euclidean distance between rainfall and runoff) to study timecorrelated characteristics of rainfallrunoff similar patterns in the upstream Red River Basin and presented a detailed evaluation of the time correlation of rainfallrunoff similarity. The rainfallrunoff similarity was used to determine the optimum similarity. The results showed that a timecorrelated model was found to be capable of predicting the rainfallrunoff 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 rainfallrunoff similarity.
Understanding the relationships between rainfall and runoff was vital for effective management and utilization of scarce water resources. Especially, it was important in Yunnan where water shortage and drought prevailed in three consecutive years.
In Red River Basin, the changes of watercourse and hydrologic regime, soil erosion, sediment deposition, water pollution, loss of biodiversity, and other crossborder issues have attracted international attention [
Previous studies [
Therefore, the rainfallrunoff similarity was inevitable and should be investigated. Our objective was to define rainfallrunoff flow similarity relationships. In fact, the influence of ecological deterioration and human activities on similarity of rainfall and runoff became more and more prominent. Exploring some timecorrelated regularity of these fluctuations of rainfallrunoff similarity was a very interesting and challenging work.
Our main contributions are as follows.
We constructed a similarity model based on Euclidean distance between rainfall and runoff (Section
We presented a detailed evaluation of the time correlation of rainfallrunoff similarity (Section
We proposed the annual mean similarity for estimating the joint effects of climate change and of human activities on ecological environment (Section
To investigate the timecorrelated characteristics of rainfallrunoff similarity in the upstream Red River Basin of China, we performed a detailed investigation using 10 years (2001–2010) of daily measurements of rainfall and runoff data as follows.
Figure
Water system diagram of Red River Basin of China.
The time series of daily rainfall and runoff were obtained from the hydrology stations of Dadongying (Figure
The record ranged from 2001 to 2010, as showed in Figure
Time series plots of the observed rainfall and runoff values.
In this paper, a denoised time series
Signaltonoise 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
Time series plots of the denoised rainfall and runoff values.
Obviously, rainfall and runoff presented periodic change [
An analysis of the equal environments assumption should be made. The data of rainfall and runoff were obtained from the hydrology stations of Dadongying in the upstream Red River Basin. Rainfall and runoff in different areas were not analyzed. The numerical similarity between rainfall and runoff was just investigated. The results showed that this numerical similarity based on Euclidean distance was linear. Particularly, the annual mean similarity increase indicated the influence of ecological deterioration and human activities on similarity of rainfall and runoff. In addition, for the noised data, wavelet analysis was used to decrease noise. And signaltonoise ratio was measured to determine noise level. In Section
First, in this paper the data sets were chosen for exploring the close relationship between rainfall and runoff. More and more studies [
The corresponding constraints of similarity model in 10 years.
2001  2002  2003  2004  2005  2006  2007  2008  2009  2010 

0 

821 

389 

0 

−35 

0 

780 

352 

0 

−85 

The rainfallrunoff modeling contained so many methods [
The runoff and transformed rainfall data.
We defined the annual rainfall in 2001 as “
Using this transformation, the shape of annual rainfallrunoff curves remained unchanged. The similarity model based on the distance between the rainfall and runoff was built to compute the minimum value
The objective function is
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
The minimum values of similarity between rainfall and runoff by calculating the objective function were shown in Figure
Fitting of initial (a) and denoising (b) data with the correlation coefficient 0.982 and 0.983.
Then we take parameters’ sensitivities on the results into consideration. In case of long data (9 years) with noise,
In different regions, the rainfallrunoff similarity still existed [
The following figures showed the fitting curves and correlation coefficients.
In order to verify the accuracy of the model, we calculated the relative error using the data of 2010. The predicting value of similarity was 11307, and the observed value was 12172. In fact an accumulated error from 2001 to 2010 was obtained with the annual error at 86.5. We acquired the relative error 0.0071, by the ratio between the annual error and observed value.
Figure
The similar patterns of rainfall and runoff at the minimum distance from 2001 to 2010.
Plots of annual mean similarity versus years.
In addition, according to water resources bulletin of Yunnan Province from 2002 to 2004, the years 2002 and 2004 belonged to years of average river water level. But the year of 2003 was relatively dry, which suffered the most serious drought in the last five years. Clearly in Table
In this paper, we studied the rainfallrunoff similar patterns in the upstream Red River Basin. The normalized rainfallrunoff values were obtained by a simple linear transformation. A model of rainfallrunoff similarity was built to determine the minimum of the Euclidean distance between rainfall and runoff. Both original and denoised time series by thresholding the wavelet coefficients were applied to verify this model. The results indicated that the rainfallrunoff similarity was of a good timecorrelated characteristic with a high correlation coefficient. When the minimum value of similarity model was obtained, the corresponding constraint or range also presented an interesting and stable trend. The annual mean similarity showed a gradually rising trend; in other words, the minimum distance between rainfall and runoff patterns in the upstream Red River Basin was increasing. All these changes were caused by the comprehensive influences of climate change and human activities on rainfallrunoff similarity.
Studying the similar relations of rainfall and runoff was of great significance. According to our research results, the constraint or range for meeting the minimum distance of rainfallrunoff similarity was getting smaller and smaller. However, the objective function value of similarity of rainfall and runoff always followed a linear distribution, and the next annual similar relationship of rainfall and runoff could be predicted. In particular, the trend of annual mean similarity reflected the impact of external environment changes on hydrology and water resources system.
Input signal
Denoised time series
Signaltonoise ratio
Annual rainfall in 2001
The annual runoff values
Years from 2001 to 2010
The constant
The minimum value of objective function
Objective function
Normalized data
Annual runoff in 2001
The annual rainfall values
The difference of
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.