A Unified Shape Model For Sunspot Number Cycles

Abstract

Modelling and prediction of sunspot number time series is an unavoidable activity in the space object re-entry prediction community. Different mathematical functions have been proposed in the literature as sunspot number cycle model, since the McNish-Lincoln regression fit. Since many models are available in the literature, a new mathematical function which fits the sunspot number cycle does not add any additional value unless it have a greater predictive power or simplicity in model. Hence, we propose in this paper, a model which unify many models in literature and show that the shape of sunspot number cycle can be described as a product of a polynomial and a negative exponential function. The proposed model has certain free parameters, which need to be estimated from the observed sunspot number data. Since all the models reviewed in this paper are a product of a polynomial and a negative exponential along with a number of parameters, we have seen that all these models can be derived from a modified generalized Gamma probability density function by transforming certain parameters and fixing certain parameters. In this paper, we estimate the parameters of the model from the revised monthly averaged sunspot numbers available in the SIDC website. In addition, an attempt has been made to test the goodness of fit of the model using the coefficient of determination. Finally a preliminary level prediction have also been attempted to forecast the characteristics of sunspot number cycle 25.

Keywords

• sunspot numbers, gamma distribution,free parameter