System Identification of the Global Climate Temperature by Output Error Method

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.

[1]  R. Malti,et al.  System identification of MISO fractional systems: Parameter and differentiation order estimation , 2022, Autom..

[2]  P. Melchior,et al.  Long-memory recursive prediction error method for identification of continuous-time fractional models , 2022, Nonlinear Dynamics.

[3]  R. Malti,et al.  Output Error MISO System Identification Using Fractional Models , 2021, Fractional Calculus and Applied Analysis.

[4]  Zhe Gao,et al.  System identification with measurement noise compensation based on polynomial modulating function for fractional-order systems with a known time-delay. , 2018, ISA transactions.

[5]  Xin-Ping Guan,et al.  Parameter identification of fractional order systems using block pulse functions , 2015, Signal Process..

[6]  Boling Guo,et al.  Parameter identification in fractional differential equations , 2013 .

[7]  T. Crowley,et al.  Technical details concerning development of a 1200 yr proxy index for global volcanism , 2012 .

[8]  R. Neely,et al.  The Persistently Variable “Background” Stratospheric Aerosol Layer and Global Climate Change , 2011, Science.

[9]  Sirish L. Shah,et al.  Continuous-time model identification of fractional-order models with time delays , 2011 .

[10]  F. Ljungqvist.  A new reconstruction of temperature variability in the extra‐tropical northern hemisphere during the last two millennia , 2010 .

[11]  Rachid Mansouri,et al.  Optimal low order model identification of fractional dynamic systems , 2008, Appl. Math. Comput..

[12]  Alain Oustaloup,et al.  Advances in System Identification Using Fractional Models , 2008 .

[13]  C. Loehle.  A 2000-Year Global Temperature Reconstruction Based on Non-Treering Proxies , 2007 .

[14]  Greg Kopp,et al.  The Total Irradiance Monitor (TIM): Science Results , 2005 .

[15]  K. Holmgren,et al.  Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data , 2005, Nature.

[16]  Michael E. Mann,et al.  Global surface temperatures over the past two millennia , 2003 .

[17]  Philippe de Larminat,et al.  Earth climate identification vs. anthropic global warming attribution , 2016, Annu. Rev. Control..

[18]  Rachid Mansouri,et al.  Multivariable fractional system approximation with initial conditions using integral state space representation , 2010, Comput. Math. Appl..

[19]  R. Malti,et al.  Subspace method for continuous-time fractional system identification , 2009 .

[20]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[21]  D. Matignon.  Stability properties for generalized fractional differential systems , 1998 .

[22]  Heinrich Schwabe,et al.  Sonnen — Beobachtungen im Jahre 1843 , 1844 .