By A. Ramachandra Rao, En-Ching Hsu (auth.)
The Hilbert-Huang rework ((HHT) is a lately constructed process that is used to investigate nonstationary info. Hydrologic and environmental sequence are, in general, analyzed through the use of innovations which have been built for desk bound information. This has resulted in difficulties of interpretation of the implications. Environmental and hydrologic sequence are usually nonstationary. the fundamental aim of the cloth mentioned during this publication is to investigate those info through the use of tools in accordance with the Hilbert-Huang rework. those effects are in comparison to the implications from the conventional tools akin to these in line with Fourier remodel and different classical statistical tests.
This ebook could be of price to researchers drawn to weather swap and complex graduate scholars in civil engineering, atmospheric sciences and statistics.
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1). 2) The significance of trends is tested by comparing the standardized test statistic Z = S/ V S with the standard normal variate at the desired significance level. 3) The n/n∗S is obtained by an approximation to the theoretical values. 4) where n is the actual number of observations and S i is the autocorrelation function of the ranks of the observations. The test result, which is the standardized test statistic Z, gives not only the information about stationarity or nonstationarity but also whether the trend is upward or downward.
Autocorrelation function is used to compare the persistence of simulated and the original data. The autocorrelation functions (Box and Jenkins, 1976) yn at are used to detect non-randomness in data. For given measurements, y1 y2 t=1 2 n, the lag k autocorrelation function is defined in Eq. 8). 8) yi − y¯ 2 i=1 In this section, method one, which is simulated only with random phase, is examined by using several sets of data. For different types of data, the results from one or two samples are used for demonstration.
For example, the degree of stationarity could be calculated over the piecewise span, T , such as 10, 50, and 100 time steps. Degree of stationarity is used to investigate the variation in frequency bins. The monthly temperature data in Europe is used as an example. Their degree of stationarity DS , Eq. 1) and degree of statistical stationarity DSS T (for T = 10 50 100 and 300 in Eq. 1. 1 while the others are DSS T. Overall, DS has the higher value than DSS T . DSS T decreases and approaches zero with decreasing length of T , especially in the high-frequency range.