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 2 The theoretical value r_α, the calculated value r_i and the relative error δ (%) under different half-amplitudes B_i (i = 1, 2,…,30)

B_i	r_α	r_i	δ (%)^a	B_i	r_α	r_i	δ (%)	B_i	r_α	r_i	δ (%)
1	0.0349	0.0353	1.16	11	0.3637	0.3625	0.34	21	0.5983	0.5961	0.37
2	0.0713	0.0705	1.13	12	0.3926	0.3906	0.51	22	0.6157	0.6140	0.28
3	0.1064	0.1055	0.90	13	0.4187	0.4176	0.25	23	0.6324	0.6309	0.23
4	0.1407	0.1400	0.48	14	0.4447	0.4436	0.24	24	0.6493	0.6470	0.36
5	0.1770	0.1741	1.67	15	0.4706	0.4685	0.44	25	0.6637	0.6623	0.22
6	0.2072	0.2075	0.17	16	0.4954	0.4924	0.61	26	0.6782	0.6768	0.21
7	0.2419	0.2402	0.69	17	0.5173	0.5152	0.42	27	0.6933	0.6905	0.40
8	0.2724	0.2722	0.09	18	0.5385	0.5369	0.30	28	0.7064	0.7035	0.41
9	0.3037	0.3032	0.16	19	0.5598	0.5576	0.39	29	0.7189	0.7159	0.42
10	0.3350	0.3333	0.49	20	0.5796	0.5774	0.39	30	0.7295	0.7276	0.26

^aThe relative error \(\delta = \frac{{\left| {r_{i} - r_{a} } \right|}}{{r_{a} }} \times 100(\% )\)