4.6 Rise time vs. amplitude (The Waldmeier Effect)

A number of relationships have been found between various sunspot cycle characteristics. Among the more significant relationships is the Waldmeier Effect (Waldmeier, 19351939) in which the time it takes for the sunspot number to rise from minimum to maximum is inversely proportional to the cycle amplitude. This is shown in Figure 26View Image for both the International Sunspot Number and the 10.7 cm radio flux data. Times and values for the maxima are taken from the 24-month Gaussian given in Table 4. Times for the minima are taken from the average dates given in Table 2. Both of these indices exhibit the Waldmeier Effect but with the 10.7 cm flux maxima delayed by about 6 months. This is larger than, but consistent with the delays seen by Bachmann and White (1994). The best fit through the Sunspot Number data gives
Rise Time (in months ) ≈ 35 + 1800 ∕Amplitude (in Sunspot Number ). (7 )
While this effect is widely quoted and accepted it does face a number of problems. Hathaway et al. (2002Jump To The Next Citation Point) found that the effect was greatly diminished when Group Sunspot Numbers were used (the anti-correlation between rise time and amplitude dropped from –0.7 to –0.34). Inspection of Figure 26View Image clearly shows significant scatter. Dikpati et al. (2008b) noted that the effect is not seen for sunspot area data. This is consistent with the date in Tables 3 and 4 which show that significantly different dates for maxima are found with sunspot area when compared to sunspot number. The dates can differ by more than a year but without any evidence of systematic differences (area sometimes leads number and other times lags).
View Image

Figure 26: The Waldmeier Effect. The cycle rise time (from minimum to maximum) plotted versus cycle amplitude for International Sunspot Number data from cycles 1 to 23 (filled dots) and for 10.7 cm Radio Flux data from cycles 19 to 23 (open circles). This gives an inverse relationship between amplitude and rise time shown by the solid line for the Sunspot Number data and with the dashed line for the Radio Flux data. The Radio Flux maxima are systematically later than the Sunspot number data as also seen in Table 4.

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