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Official Journal of the Asia Oceania Geosciences Society (AOGS)

Table 2 The theoretical value rα, the calculated value ri and the relative error δ (%) under different half-amplitudes Bi (i = 1, 2,…,30)

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

Bi rα ri δ (%)a Bi rα ri δ (%) Bi rα ri 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
  1. aThe relative error \(\delta = \frac{{\left| {r_{i} - r_{a} } \right|}}{{r_{a} }} \times 100(\% )\)