Correlation-aided method for identification and gradation of periodicities in hydrologic time series

Geoscience Letters

Official Journal of the Asia Oceania Geosciences Society (AOGS)

Table 4 Groups of six parameters, the sample length n, the mean value \(\overline{u}\) and the variation coefficient Cv_u of the stochastic component, the half-amplitude B, the periodicity length T and the initial phase t₀ of the periodic component, used in statistical tests for investigating their influences on the identification of periodicities

Test	N	\(\overline{u}\)	Cv_u	B	T	t₀
1	100, 150, 200, 250, 300, 350, 400, 450, 500	100	0.2	30	25	0
2	200	100, 150, 200, 250, 300, 350, 400, 450, 500	0.2	30	25	0
3	200	100	0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45	30	25	0
4	200	100	0.2	1.0, 1.5, 2.0, 2.5, 3.0^a	25	0
5	200	100	0.2	30	5, 10, 15, 20, 25, 30	0
6	200	100	0.2	30	300	0, ± 0.25π, ± 0.5π, ± 0.75π, π^b

^aThe half-amplitude should be comparable with the stochastic fluctuation. Therefore, let B = A × M, where A = |quantile (x(t), 3/4) − quantile (x(t), 1/4)|. The quantile (x(t), 1/4) and quantile (x(t), 3/4) here are the upper and lower quartiles of time series x(t), respectively. M is a coefficient representing multiple relation between B and A
^bAs t₀ = π and t₀ = − π represent the same phase for the sinusoidal function, only t₀ = π is tested