This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Nowadays, as the available water resources throughout the World are becoming depleted, in order to manage and plan water resource better, more and more attention is being paid into the fluctuating characteristics of water discharges. However, the preexisting research was mainly focused on the last half century. In this paper, the natural streamflow observed since 1470 at the Sanmenxia station in the middle Yellow River basin was collected, and the methods of variation coefficient, moving average, Mann-Kendall test and wavelet transform were applied to analyze the dynamic characteristics of the streamflow. The results showed that, (1) between 1470 and 2007, the natural streamflow changed 200–919 × 10^{8} m^{3}, and water discharge varied moderately; (2) in the middle Yellow River basin, it appears that the most severe and most persistent droughts during

Water is the base of the life on Earth, however, the available water resources throughout the world are becoming depleted, and this problem is aggravated by the increasing population, extending irrigation agriculture and developing industry. Nowadays, it is widely acknowledged that water is a major limiting factor for socio-economic development in the World [

River flow plays the central role in the development and management of water resources, but on the other hand, the distribution of streamflows is highly uneven on the temporal scale, so more and more researchers are paying attention to topics in this field, such as streamflow circulation, riverflow oscillation, discharge prediction,

In China, because the Yangtze and Yellow River are the two largest rivers in China, with a significant domestic status and the number of affected people is multitudinous, and their degraded eco-environments, these rivers have attracted the most attention in China.

In the Yangtze River, it is found that during the past 50 years, although the riverflow patterns were different, no significant trend (at 95% confidence level) was detected for annual water discharges at all hydrologic stations [

The preexisting researches were mainly focused on the last half century; but statistical analysis of the riverflow variation depends on the availability of long time series, as these include richer information. However, systematic measurement of discharges in the modern era started relatively late, and it is relatively difficult to collect the historical data over centuries. The objectives in this paper is, to analyze the oscillating character and change cycles in the middle Yellow River basin, based on the reconstructed historical data (1470–2007) from the Sanmenxia station, and discuss the influencing factors. The study will be helpful for policy-makers to manage the water resource more effectively.

The Yellow River (Huanghe) is the second largest river in China, with a total length of 5,464 km. It originates in the northeast of the Tibetan Plateau, runs across the Loess Plateau of North China and the Ordos Plateau, and flows eastwards to the Bohai Sea, via semi-arid and semi-humid regions (^{5} km^{2}) is one of the most important drainage areas in China, directly supporting a population of some 110 million people, mostly farmers and rural residents. The Yellow River basin covers nine provinces/autonomous regions, ^{3} of runoff (during the period of 1919–1975), accounting for 2% of the total runoff of China [

Since the late part of the last century, the middle and lower reaches of the Yellow River have periodically suffered from floods or droughts, which consequently have led to serious conflicts between ecological water supply and demand, and decreased the health level of the Yellow River ecosystem [

In the Yellow River basin, though the earliest official survey of water discharge started in 1919, some flood/drought events have been fortunately recorded in the local history logs. Wang

One-Sample Kolmogorov-Smirnov Test was conducted to detect the normal distribution. In order to detect the water discharge oscillation on the decadal scale, the 11-year moving average was used, and the average value among 11 years was placed into the 6th year position. In addition, the variation coefficient _{i}

In order to evaluate the persistence of drought over the period of 1470–2007, the streamflow series was de-noised using a range of multiyear center moving averages. According the references from Woodhous [

The rank-based Mann-Kendall method (MK), put forward by Mann and Kendall [_{1}, _{2}, …, _{n}) of the random variable _{k}

Under the null hypothesis of no trend, the statistic _{k}_{k}_{k}

Under the above assumption, the definition of the statistic index Zk is calculated as:

In a two-sided test for trend, the null hypothesis is rejected at the significance level of α if |_{(1−α/2)}, where _{(1−α/2)} is the critical value of the standard normal distribution with a probability exceeding α/2. A positive _{n}, _{n−1}, … , _{1}). Following the same procedure as shown in _{k}_{k}_{k}_{k} will be calculated for the retrograde sample. The _{1} and _{2}, respectively in this paper. The intersection point of the two lines, _{1} and _{2} (k = 1, 2, …, n) locates the time of abrupt change for time series, if the intersection point is between the two confidence lines. The null hypothesis must be rejected if the intersection point is significant at 5% significant level (

The basic objective of the wavelet transform is to achieve a complete time-scale (or shift-scale) representation of localized and transient phenomena occurring at different time scales. Based on the results of time-scale distribution, it is easy to analyze the periodicity of streamflow series. For time series ^{2} (_{f}

The key point of wavelet transform lies in the selection of wavelet function. The real part and imaginary part of complex wavelet has a phase difference of π/2, which can eliminate the modular vibration of wavelet transform coefficient of real form, so in this study, the Complex Morlet wavelet was adopted to analyze the periodic characteristics of natural streamflow in relation to time. The Complex Morlet wavelet is a single-frequency complex sinusoidal function tapered with a Gaussian window, and is expressed as:

Mann-Kendall assumed that sample data are serially independent, so a series with a positive serial correlation will inflate the variance of the estimated mean, and hence the effective sample size contains less information about the mean than a random series [_{i}_{k}

It follows that the critical level of correlation for 95% significance is

The results of serial correlation analysis indicated the natural streamflow at the Sanmenxia station had significant autocorrelation at the lag = 12 (

The result from the One-Sample Kolmogorov-Smirnov Test rejects the null hypothesis of normal distribution (

The variation coefficient

The natural streamflow amount is concentrated 200–919 × 10^{8} m^{3} during 1470–2007, the mean value is 510.37 × 10^{8} m^{3} (

According to the evaluated criterion, the distribution of single-year low flow events is fairly frequent over time (

Intervals of persistent drought become more evident when longer windows lengths are considered. In particular, the interval from circa 1868–1900 appears to be the most severe and most persistent drought on record (25-year windows). The 1470s–1490s, 1920s–1930s and 1990s–2000s also emerge as periods of sustained low flows. Several of the low flow events from the late 19^{th} century, such as 1877, 1928, 1901 and 2002 (several longest bar in

The results of the Mann-Kendall test are shown in _{1} > 0), but the trend is not significant at >95% confidence level; and after 1880 the natural streamflow presents a decreasing trend (Z_{1} < 0), and the trend is still not significant at >95% confidence. For the streamflow series at the Sanmenxia station, the intersection point of the Z_{1} and Z_{2} curves occurs at _{1} and _{2} gives the point of jumping change, which illuminates several abrupt points appeared during 14707–2007, and the result is consistent with

In order to reveal the long-term changes rather than rapid changes in the natural streamflow series, a longer time scale (250-year) is chosen. The wavelet coefficient contour map of the natural streamflow series is plotted based on the above method of Morlet wavelet transform. The intensity at each

When considering the natural streamflow at the Sanmenxia station, the real part of the wavelet transform is shown in

For the 50–75 scale, there are more than eight-cycle oscillations. The periods of 1470–1490, 1530–1570, 1595–1625, 1650–1680, 1725–1750, 1775–1800, 1830–1865, 1890–1925, 1960–1980 are the abundant-water periods, while 1491–1529, 1571–1594, 1626–1649, 1681–1724, 1751–1774, 1801–1829, 1866–1889, 1926–1959 and after 1980 are the low-water periods. For the 20–30 and 10-year scales, there are more cycle oscillations, and the oscillation frequencies of annual natural streamflow are higher and more complicated.

The wavelet variance of the streamflow at the Sanmenxia station is computed based on

Natural streamflow is the result by hydrological cycles of precipitation, infiltration, evapotranspiration and other components, which leads to the natural water discharge with periodicity and hydrological anomaly. Precipitation is the direct source of natural runoff, and provides the material source for water discharges. Due to the lack of corresponding historical precipitation records, and considering the basin upper Sanmenxia occupies more than 90% area of Yellow River basin, the correlation between natural streamflow (in Sanmenxia station) and precipitation (in Yellow River basin) during 1950–2007 was analyzed (

Temperature is another critical factor for natural water discharge, and the effect of temperature rises on water discharge is mainly evident in three aspects: the first is to increase potential and actual evaporation, which is unfavorable for discharge yield; the second is beneficial for the thawing of ice and snow, which will increases runoff in the short term; the third is to change the form of precipitation (temperature rising can change snowfall into rainfall) and then change the conditions for runoff generation. The negative correlation (P < 0.01) between natural streamflow and annual average temperature (in the whole Yellow River) was found in this research (

In addition, El Niño-Southern Oscillation (ENSO) and sunspots are undeniable influencing factors, their effects be implemented mostly through their effect on climatic and hydrological cycles. Mechoso and Iribarren [

Besides the above natural conditions, human activity is another influencing factor. However, when the natural streamflow is calculated, the water-consumed by human being, such as irrigation water, industrial water and domestic water,

Natural streamflow is influenced by precipitation, temperature, ENSO, sunspots, human activities,

As can be concluded, the natural streamflow at the Sanmenxia station presents moderate variability during the whole period 1470–2007, and it appears that some persistent drought intervals exist, when longer windows lengths, such as 1868–1900, 1470s–1490s, 1920s–1930s and 1990s–2000 are considered. By use of the Mann-Kendall test, it is found the natural streamflow during 1470–1880 and 1880–2007 present increasing and decreasing trends, respectively, however both trends are not significant at >95% confidence level. It is still found the streamflow series shoes an abrupt change

The authors wish to thank the research funding provided by the National Key Basic Special Foundation Project of China (No. 2007CB407202) and China Postdoctoral Science Foundation funded project (No. 20090450221). The autoregressive analysis described in the paper was carried out in the Matlab numerical software environment and made particular use of the CAPTAIN Toolbox for Matlab (see

Location of Sanmenxia station in the Yellow River basin.

Autocorrelation results.

Annual natural streamflow at the Sanmenxia station.

Distribution of natural streamflow at the Sanmenxia station.

Distribution of natural streamflow for the lowest 15th percentile over the period 1470–2007. Low rankings are indicated by the bars with different height, longer bar represents lower flow event.

Result of Mann-Kendall test.

Real part wavelet coefficient contour map of natural streamflow.

Wavelet variance figure of Morlet wavelet transform coefficients.

Correlation between natural streamflow and precipitation (a), temperature (b). The annual streamflow observes at the Sanmenxia station, the annual precipitation and temperature is the annual average value in the whole Yellow River basin.

Wavelet coefficient changes of natural streamflow at the Sanmenxia station and sunspots from 1700 to 2003 on a 60-year scale (cited from [