Ma Weijie, Kang Yan, Song Songbai
College of Water Resources and Architectural Engineering, Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest Agriculture and Forest University, Yangling 712100, China.
Entropy (Basel). 2019 Dec 26;22(1):38. doi: 10.3390/e22010038.
The study on the complexity of streamflow has guiding significance for hydrologic simulation, hydrologic prediction, water resources planning and management. Utilizing monthly streamflow data from four hydrologic control stations in the mainstream of the Weihe River in China, the methods of approximate entropy, sample entropy, two-dimensional entropy and fuzzy entropy are introduced into hydrology research to investigate the spatial distribution and dynamic change in streamflow complexity. The results indicate that the complexity of the streamflow has spatial differences in the Weihe River watershed, exhibiting an increasing tendency along the Weihe mainstream, except at the Linjiacun station, which may be attributed to the elevated anthropogenic influence. Employing sliding entropies, the variation points of the streamflow time series at the Weijiabu station were identified in 1968, 1993 and 2003, and those at the Linjiacun station, Xianyang station and Huaxian station occurred in 1971, 1993 and 2003. In the verification of the above points, the minimum value of -test is 3.7514, and that of Brown-Forsythe is 7.0307, far exceeding the significance level of 95%. Also, the cumulative anomaly can detect two variation points. The -test, Brown-Forsythe test and cumulative anomaly test strengthen the conclusion regarding the availability of entropies for identifying the streamflow variability. The results lead us to conclude that four entropies have good application effects in the complexity analysis of the streamflow time series. Moreover, two-dimensional entropy and fuzzy entropy, which have been rarely used in hydrology research before, demonstrate better continuity and relative consistency, are more suitable for short and noisy hydrologic time series and more effectively identify the streamflow complexity. The results could be very useful in identifying variation points in the streamflow time series.
径流复杂性研究对于水文模拟、水文预测、水资源规划与管理具有指导意义。利用中国渭河干流四个水文控制站的月径流数据，将近似熵、样本熵、二维熵和模糊熵方法引入水文研究，以探究径流复杂性的空间分布和动态变化。结果表明，渭河全流域径流复杂性存在空间差异，沿渭河干流呈增加趋势，但林家川站除外，这可能归因于人为影响的增强。采用滑动熵方法，确定了魏家堡站径流时间序列在1968年、1993年和2003年出现变异点，林家川站、咸阳站和华县站分别在1971年、1993年和2003年出现变异点。在上述变异点的验证中，t检验最小值为3.7514，Brown-Forsythe检验最小值为7.0307，远超过95%的显著性水平。此外，累积异常法也能检测到两个变异点。t检验、Brown-Forsythe检验和累积异常检验强化了熵值用于识别径流变异性的有效性结论。结果表明，四种熵值在径流时间序列复杂性分析中具有良好的应用效果。此外，二维熵和模糊熵此前在水文研究中很少使用，它们表现出更好的连续性和相对一致性，更适合短序列和含噪水文时间序列，能更有效地识别径流复杂性。研究结果对于识别径流时间序列变异点具有重要意义。
