The Application Of Wavelet Method In The Problems On The Analysis Of Hydrologic Time Series

Through hydrometry lots of hydrological time series can be gained such as precipitation, runoff, peak discharge, and etc. They are the output of the hydrologic system influenced by meteorology, basin surface and human activities. They feature as uncertainty, periodicity, jumping, mutation, and tendency. A major research approach in hydrology is to employ the present analyzing techniques to describe hydrological time series so as to explore the developing pattern of hydrological system.Hydrological time series are of great uncertainty and complexity, and the common analyzing methods cannot ensure the clear understanding and precise prediction of their developing pattern and changing characteristics. Thus, we need to introduce new theories and methods. The wavelet analysis which has become wide used in 1980s is the method addressing the coarse and fine. Both the slight change and the great trend can be detected, and at the same time simple time series of different frequency range can be obtained. The adoption of wavelet analysis in the hydrological time series research, with the aid of other theories and methods, can disclose the changing patterns of hydrological system so that more basis can be provided for water resource development, exploitation and effective deployment.Wavelets are honored as the microscope of signal analyzing. This is a localized time-frequency signal analysis method with windows fixed in size but variable in shape. That means, it has high frequency resolution and low temporal resolution in low-frequency part, but low temporal resolution an high frequency resolution in the high-frequency part. In the past ten years, wavelet transformation has had more systematic theories and calculation methods. Other than stretching and paralleling, rotating has been introduced and used in high-dimension. It has been applied in lots of fields in natural science, which demonstrates its obvious priority and broad prospect.Hydrological time series are samples observed, which display various changing features. Different from the statistical method in researching the tendency and jumping of the hydrological series, the wavelet analyzing method brings in the idea of multiple dimensions. Thus, it commands excellent localization in spatial and frequency domain, and suits in the case of non-stationary signals. The wavelet method can reveal profoundly the changing features of hydrological time series such as mutation and tendency. Through its multi-resolution function the multi-time scale feature can be uncovered. Through the dissection and reconstruction hydrological time series can be modeled randomly and be used in hydrographic water resource analysis and calculation.This paper applies the wavelet method in hydrological time series analysis, and pays much effort in the analysis of the time series singularity, the denoising application, and the multi-time scale analysis.Through the wavelet analysis of the climate, hydrologic series from different areas and river basins, we can draw the following points:1)Based on the wave wavelet transformation and Lipshitz index analysis, the mutation feature of hydrologic time series is explored. This shows that the singular points of the series can be detected from the wavelet transformation modulus maxima, which always appear when there are modulus mutation. Therefore, the testing ends can be realized with the searching for the modulus maxima to check whether there is the singular point in messages. The Lipschitz index a can represent the size of singularity. That is, when a is greater, the smoothness of this point is higher and the singularity is smaller; when a is smaller, the singularity is greater. Based on the runoff process analysis during the past fifty years at Xingxiangshao reservoir hydrologic station, the annual runoffs of the fifty-one years possess twice greater mutation, which were in the year of 1971 and 1998. The Lipschitz indexes of these two points are below 1, which means that the singularity is great. That verifies the two points underwent mutations indeed. 2)Based on soft thresholding, the wavelet thresholding denoising method has an ideal de-noising effect. Useful time series are usually low-frequency signals (stationary signal), high-frequency noise signals are usually noises. The wavelet decomposition can separate the high-frequency elements from the low-frequency elements, threshold the separated high-frequency signals, and then reconstruct them with the low-frequency signals, and in this way the de-noising of the hydrologic time series can be achieved. Using DB2 wavelet to de-noising the precipitation in the past fifty years we can say that peaks in the series decrease obviously after the de-noising. Though the auto-correlation analysis of the noise series, it can be concluded that the auto-correlation series are evenly distributed, and show the property of cycling. That is to say, among the original series obvious white noise series exist, and the threshold de-noising method in wavelet analysis is effective in series de-noising.3)Wavelet analysis as a mathematical method bears the characteristic of time-frequency localization. This"focusing"nature can be employed to display the fine structure of the hydrologic time series, and provides a new approach to analyze multi time scale changes and distribution. From the results by Morlet wavelet transformation analysis on Da'an city's annual precipitation in the past fifty years, we learn that the wavelet transformation analysis can not only offer various time scales, the strength of the cycle and distribution and the trend of precipitation and mutation, but also the major cycles. The annual precipitation of Da'an city possesses the major cycle of twenty-five years and assisting cycle of fifteen years.