Qingping Zhu

Entropy-Based Wavelet De-noising Method for Time Series Analysis

The existence of noise has great influence on the real features of observed time series, thus noise reduction in time series data is a necessary and significant task in many practical applications. When using traditional de-noising methods, the results often cannot meet the practical needs due to their inherent shortcomings. In the present paper, first a set of key but difficult wavelet de-noising problems are discussed, and then by applying information entropy theories to the wavelet de-noising process, i.e., using the principle of maximum entropy (POME) to describe the random character of the noise and using wavelet energy entropy to describe the degrees of complexity of the main series in original series data, a new entropy-based wavelet de-noising method is proposed. Analysis results of both several different synthetic series and typical observed time series data have verified the performance of the new method. A comprehensive discussion of the results indicates that compared with traditional wavelet de-noising methods, the new proposed method is more effective and universal. Furthermore, because it uses information entropy theories to describe the obviously different characteristics of noises and the main series in the series data is observed first and then de-noised, the analysis process has a more reliable physical basis, and the results of the new proposed method are more reasonable and are the global optimum. Besides, the analysis process of the new proposed method is simple and is easy to implement, so it would be more applicable and useful in applied sciences and practical engineering works.

Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales

In this paper, the influence of four key issues on wavelet-based analysis of hydrologic series’ complexity under multi-temporal scales, including the choice of mother wavelet, noise, estimation of probability density function and trend of series data, was first studied. Then, the complexities of several representative hydrologic series data were quantified and described, based on which the performances of four wavelet-based entropy measures used commonly, namely continuous wavelet entropy (CWE), continuous wavelet relative entropy (CWRE), discrete wavelet entropy (DWE) and discrete wavelet relative entropy (DWRE) respectively, were compared and discussed. Finally, according to the analytic results of various examples, some understanding and conclusions about the calculation of wavelet-based entropy values gained in this study have been summarized, and the corresponding suggestions have also been proposed, based on which the analytic results of complexity of hydrologic series data can be improved.

Improved continuous wavelet analysis of variation in the dominant period of hydrological time series

Abstract Two key issues of continuous wavelet transform (CWT), the choice of wavelet basis function and the determination of analytic procedure of CWT, were studied and approaches to solve them proposed. Then, the improved CWT method was used to reveal the periodic characteristics of several typical hydrological series, including runoff and precipitation data measured at diverse sampling rates. Finally, the results of periods identified by three methods were compared, and the variation of the first main period (FMP) with length of the annual hydrological series was investigated. The results indicate that hydrological time series show both global and local characteristics. Comparatively, the latter are more complicated and difficult to describe, because of their frequent manifestations of irregular phenomena. Moreover, the variation of FMP just reflects the complicated local characteristics of the hydrological series. In summary, this study improves the understanding of complicated hydrological processes, whereas description and simulation of the local characteristics of hydrological series should be the focus of future research. Editor D. Koutsoyiannis Citation Sang, Y.F., Wang, D., Wu, J.-C., Zhu, Q.-P., and Wang, L., 2013. Improved continuous wavelet analysis of variation in the dominant period of hydrological time series. Hydrological Sciences Journal, 58 (1), 1–15.

A New Method of Periods' Identification in Hydrologic Series Based on EEMD

Identification of dominant periods is a very important but difficult task in hydrologic time series data analysis. In this paper, for improving the results of periods’ identification, a new method, called EEMD-MESA (ensemble empirical mode decomposition-maximum entropy spectral analysis), has been proposed, whose main idea is identifying the main intrinsic mode functions (MIMFs) in hydrologic series firstly, and then by using MESA to identify periods in each MIMFs, all periods in the hydrologic series can be gotten finally. By applying to an observed runoff series, advantages of the new method have been verified. Analyses results show that EEMD-MESA is as better as MSSA but much better than other methods (FFT and MESA); While compared with MSSA, EEMD-MESA is more convenient and time-saving. Therefore, the EEMD-MESA method would be more applicable to practical hydrologic works.

Hydrologic and hydraulic characteristics of the Yellow River and impact of flow and sediment diversion

wastewater. The contents of nitrogen and phosphorus of Ruppia maritima varied with the season. The most contents of nitrogen and phosphorus in the tissue ofRuppia maritima were up to 5.042% and 0.956%, respectively. It was observed that the community of Ruppia maritima was replaced gradually by the community of Potamogeton pectinatus in the coastal scenic watercourse of reclaimed wastewater from April 2004 to October 2005. The stable isotope technique was used to trace nitrogen by Ruppia maritima absorbed in water at laboratory. It was found that Ruppia maritima was capable of simultaneously absorbing two kinds of nitrogen sources such as ammonia and nitrate in the reclaimed water. The accumulation of nitrogen from ammonia (615NH4-N) and from nitrate (61sNO3-N) showed the logarithm and exponential relations with time, respectively. Higher nutrient loading in the coastal reclaimed wastewater may be a reason why the community ofRuppia maritima declines.