## 5. ConclusionsData of the quarterly mean values of the sunspot area from the year 1875 to 1996 (cycles 12-22) are used to discuss the shape of the solar cycles in this paper. First, we describe our efforts to find a simpler function that might be used to reproduce the shape of the sunspot cycles, simpler in terms of having fewer free parameter. Our study clearly shows that the shape of the sunspot cycle can be adequately described using a simple function with only two parameters, the starting time and the amplitude of a cycle. This function is derived from a 4-parameter functional fit of the quarterly mean sunspot areas. Then we find that the values of the amplitude and the starting time are well determined early in the cycle. As a sunspot cycle progresses, the amplitude parameter can be better determined to within 10% at 4.3 years into its cycle, and the starting time can be well determined to within 0.3 year at 4.6 years into its cycle. This determination of the parameters provides an early estimate for the temporal behavior of the sunspot cycle over its remaining years including sunspot maximum. Characteristics of the sunspot cycle shape are investigated in this paper too. The shape of the sunspot area cycle is generally asymmetric, taking less time rising to maximum from minimum than reaching the next minimum from the maximum. Probably the most significant relation among the cycle shape characteristics is the Waldmeier effect: cycles with larger amplitude are more asymmetric and take less time to reach maximum. This effect, however, is modified for the sunspot area cycles, comparing with the cycles of the sunspot numbers. It is well known that the reliability of sunspot numbers is larger than that of sunspot areas because the former is easier to measure. In a recent paper by Pettauer & Brandt (1994) errors of sunspot areas determined even with sophisticated methods are given between and . The difference of the Waldmeier effects for the sunspot area cycles and for the sunspot relative number cycles is perhaps caused by the bigger uncertainty of the sunspot area © European Southern Observatory (ESO) 1999 Online publication: April 28, 1999 |