System Identification of the Global Climate Temperature by Output Error Method

Abstract

Global warming is a fact that has been announced by the Intergovernmental Panel on Climate Change (IPCC) since the eighties. Modeling the global terrestrial temperature through system identification is a very challenging task. The fractional integration operator is well adapted to model diffusion or propagation phenomena with few parameters and thanks to its long memory property. It is also known that fractional models are well suited for modeling thermal systems and especially for solving the heat equation. Also, it is quite natural to use the fractional operator to model the global climate temperature. To this aim, system identification by using fractional order models has been recently proposed for continuous-time multiple-input single-output (MISO) models. When differentiation orders are assumed known, coefficients are estimated by using the output error method for continuous-time fractional models extended to the MISO case. When unknown, a gradient-based algorithm is proposed for differentiation order estimation. Finally, model parameters are estimated on real input/output data and provide a very accurate goodness fit for the global earth temperature modeling.