Multifractality And Nonstationarity Analysis Based On High Frequency Water Level Data

Studying the characteristics of hydrological and physical processes and their evolution over time can reveal the inherent hydrodynamic mechanism of hydrology,and can provide a scientific basis for forecasting and making corresponding water resources dispatching and flood prevention measures,which has important research value and practical significance.Based on the high frequency water level data measured in a river in northern China,this thesis studies long-rang dependence,multifractality and its reason,and the trend of non-stationary.Specific work as follows:(1)Based on high frequency sampling(sampling period of 6 minutes)to complete the water level long time sequence memory recognition.The multi-scale wavelet estimation method is used to estimate the Hurst exponent H of high-frequency river water level data.The results show that the Hurst exponent estimation of all observation sites satisfies H>0.5,indicating that the river water level have obvious long memory behavior.Moreover,the power law features corresponding to different time scales have some differences,and there is some correlation with the wavelet scale.(2)It is found and proved that there is consistency between the sampling time and the wavelet scale,which further confirming the multi-scale behavior and the fractal characteristic of the water level data.That is,wavelet scale(j1,j2)and sampling time l satisfies H(l + 1,j1,j2)=H(l,j1+ 1,j2 + 1).Comparing the measured data with the exponential long range dependent process,it is found that the multi-scale behavior only exists in the water level data.This indicates that there may be multi-fractal in the water level data,and then the wavelet multi-scale plot comfirms the existence of multi-fractal characteristics in the measured data.(3)A multi-fractal model of water level data was constructed and a fingerprint feature using parameters a,b,?? as a multi-fractal feature was proposed.A generalized binomial multifractal model is established and the stage time and daily average water level were extracted based on high frequency data.The generalized Hurst index of all observation stations calculated by MF-DFA and WLMF methods was greater than 0.88 and average multi-fractal intensity ??ave>1,which indicats that the measured data have significant mulitifractal characteristics.(4)Cause analysis of multifractal characteristics of water level.The original sequence was reconstructed by two methods of random shuffling(shuffled series)and phase reconstructing(surrogate series)to test the two main factors that may cause multifractal:fluctuation correlation and fluctuation distribution characteristics.The MF-DFA is used to calculate the generalized Hurst exponents of the two reconstructed sequences to obtain their empirical distributions and two hypothesis testing methods for these two major causes is proposed.This method can explain the cause more than using a single rearrangement or reconstructed sequence,and can show more details than the test method by constructing the statistics ?hsf??r,sf 2??r,sg 2.The results of two hypothesis testing methods show that the factors that affect the multifractal characteristics of water level are the correlation of sequence fluctuations and the probability distribution characteristics of small fluctuations.(5)The non-stationary metrics NS are introduced to quantitatively characterize the non-stationary nature of water level data,and it is concluded that the water level data is mainly composed of differential stationary process.An AMK method is proposed for the fitting of water level data,which NS is used to achieve ARIMA model selection and Mann-Kendall method is used to find the break points in the sequence to locate the incidents' time.Under the condition of satisfying the minimum sum of squared residuals,a gradient descent ARIMA method is proposed to fit the differential stationary process.Actual fitting accuracy exceeds 93%.