Crytic period analysis model of hydrological process and its application

Abstract

Abstract:It is difficult to analyse the crytic period of the hydrological process, because hydrological time series is probably characterized by heteroscedasticity. To find out the crytic period, a model is constructed as follows: (1) after using zero-mean transformation for the data, to do Augmented Dickey-Fuller stationary test for the sequence, to build the corresponding AR(p) model and then to do ARCH effects test and white noise test for residual series; (2) for those time series that cannot pass through ARCH test, using logarithm transformation to reduce the heteroscedasticity, and then to redo step (1) until they pass through ARCH test and stationary test; (3) using periodogram analysis to determine all the possible the prime periods and further to put forward three kinds of tests to determine significance level of those prime periods. As examples, the hydrological processes of streamflow from 1784 to 1997 for the gauging stations of Alaer and Xinquman along Tarim River are analysed. After reducing their heteroscedasticity, AR(4) and AR(2) models are developed, respectively. Our results show that the streamflows from the two gauging stations have the same cryptic period of 42Ð7 years. Furthermore, the reliability for the crytic period model is testified by variance analysis, which shows that the crytic period model is useful and reliable.

A revised range of variability approach considering the periodicity of hydrological indicators

“…There are many methods for determining periodic time, for example, the autocorrelation method, moving average method, periodogram method, fast Fourier transform, maximum entropy spectrum analysis, MLS, and wavelet analysis. There are also many revised methods incorporating the advantages of different approaches (Wang et al ., ; Sang et al ., ). Several methods are relatively simple, for example, autocorrelation, moving average, and periodogram, whereas others are more complex, for example, the MESA and wavelet analysis (Torrence and Compo, ).…”

“…The major periodic times are the reciprocal of these major frequencies. To identify these peak values, Fisher's test is used (Kottegoda et al ., ; Wang et al ., ). If there is no peak that passes the criteria of Fisher's test, no periodic time will be identified through this method.…”

“…Examination of periodicity of each IHA time series. The periodic component in a time series can be represented through a system of sinusoidal waves with specific periodic times and amplitudes after the trend component, if it exists, has been estimated and removed (Kottegoda et al, 2004;Wang et al, 2009). The periodic times corresponding to the waves with the largest amplitudes are considered to be the major periodic times (Brockwell and Davis, 2002;Kottegoda et al, 2004).…”

基于arma-Garch模型的水文过程不确定性分析

“…GARCH 模型时并没有对序列进行检验, 也并没有展 开进一步的探讨. 在国内, Wang 等人 [7,17] 首次针对水 文过程中的条件异方差现象进行了分析, 将异方差 检验用于水文过程的时序分析中, 利用数据变换消 除异方差的方式开展塔里木河历年径流隐含周期问 题的研究. 随后又提出了将基于 BX 数据生成的灰色 Markov 预测模型与 ARCH 模型相结合的方法, 以鲇 鱼山水文站年径流量为例进行了建模及应用 [10] .…”

Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis–Hastings Markov Chain Monte Carlo algorithm

“…Many efforts have been taken for quantification of the uncertainties from estimation of model parameters. Uncertainties are often estimated by confidence interval (Mishra, 2009;Smakhtin, 2001;Wang et al, 2009), which is based on asymptotic approximation quantify the lower bound and upper bound of modeling results given certain level of significance, usually 5% of significance.…”