The Shape of Solar Cycle Described by a Modified Gaussian Function

Abstract

The shape of each sunspot cycle is found to be well described by a modified Gaussian function with four parameters: peak size A, peak timing t _m, width B, and asymmetry α. The four-parameter function can be further reduced to a two-parameter function by assuming that B and α are quadratic functions of t _m, computed from the starting time (T ₀). It is found that the shape can be better fitted by the four-parameter function, while the remaining behavior of the cycle can be better predicted by the two-parameter function when using the data from a few (about two) months after the starting time defined by the smoothed monthly mean sunspot numbers. As a new solar cycle is ongoing, its remaining behavior can be constructed by the above four- or two-parameter function. A running test shows that the maximum amplitude of the cycle can be predicted to within 15% at about 25 months into the cycle based on the two-parameter function. A preliminary modeling to the first 24 months of data available for the current cycle indicates that the peak of cycle 24 may probably occur around June 2013±7 months with a size of 72±11. The above results are compared to those by quasi-Planck functions.