Empirical estimation of cycle durations from their amplitude characteristics

Estimation of a cycle duration Тс, along with calculation of the cycle maximum value Wm, is of importance to prediction problems of solar cycles or their reconstruction in the past. Several approaches connecting Тс with cycle characteristics are presented in the paper. Cycles of reliable Wolf-number sequence (cycles 10-22) are examined. The Waldmeier idea of regarding Wm as an independent variable is used in calculations. Experimental curves are approximated by expansions of type. Corresponding expansion coefficients are shown in the table. Simple Тс dependences on Wm are derived, and estimation of the duration of the 23rd cycle is given due to postulation and application of empirical relations between the cycle area and duration. The paper proves that the total duration of cycles, along with relative errors, should be compared to estimate Тс. The criteria obtained for cycles 10-22 are used for the estimation of reconstructed cycles 1-9; the estimation allowed establishing of significant differences.