Global terrestrial temperature modeling by using fractional models

Abstract

Modeling the global climate system through the temperature output is a very challenging task. Knowing the fractional operator long memory property to well model diffusion phenomena with very few parameters, it is proposed in this paper to use fractional models for climate change modeling. System identification is applied for continuous-time system identification of multiple-input single-output (MISO) fractional order models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. Finally, the estimation with fractional models is carried out on real input/output data and provide a very good goodness fit of the global earth temperature.