Spatio-temporal evolution of global surface temperature distributions

Climate is known for being characterised by strong non-linearity and chaotic behaviour. Nevertheless, few studies in climate science adopt statistical methods specifically designed for non-stationary or non-linear systems. Here we show how the use of statistical methods from Information Theory can describe the non-stationary behaviour of climate fields, unveiling spatial and temporal patterns that may otherwise be difficult to recognize. We study the maximum temperature at two meters above ground using the NCEP CDAS1 daily reanalysis data, with a spatial resolution of 2.5° by 2.5° and covering the time period from 1 January 1948 to 30 November 2018. The spatial and temporal evolution of the temperature time series are retrieved using the Fisher Information Measure, which quantifies the information in a signal, and the Shannon Entropy Power, which is a measure of its uncertainty — or unpredictability. The results describe the temporal behaviour of the analysed variable. Our findings suggest that tropical and temperate zones are now characterized by higher levels of entropy. Finally, Fisher-Shannon Complexity is introduced and applied to study the evolution of the daily maximum surface temperature distributions.

[1]  S. Drijfhout,et al.  A novel probabilistic forecast system predicting anomalously warm 2018-2022 reinforcing the long-term global warming trend , 2018, Nature Communications.

[2]  R. Reynolds,et al.  The NCEP/NCAR 40-Year Reanalysis Project , 1996, Renewable Energy.

[3]  Sheila López-Rosa,et al.  Analysis of complexity measures and information planes of selected molecules in position and momentum spaces. , 2010, Physical chemistry chemical physics : PCCP.

[4]  Un Desa.  Transforming our world : The 2030 Agenda for Sustainable Development , 2016 .

[5]  J. Cattiaux,et al.  Describing the Relationship between a Weather Event and Climate Change: A New Statistical Approach , 2020, Journal of Climate.

[6]  E. F. Schuster.  Estimation of a Probability Density Function and Its Derivatives , 1969 .

[7]  James V. Zidek,et al.  Uncertainty, entropy, variance and the effect of partial information , 2003 .

[8]  Thomas M. Cover,et al.  Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing) , 2006 .

[9]  R. C. Macridis.  A review , 1963 .

[10]  Vijayan N. Nair,et al.  A REVIEW AND RECENT DEVELOPMENTS , 2005 .

[11]  Jorge Cadima,et al.  Principal component analysis: a review and recent developments , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  Prakasa Rao.  Nonparametric functional estimation , 1983 .

[13]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[14]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[15]  V. Alekseev.  Estimation of a probability density function and its derivatives , 1972 .

[16]  Amir Dembo,et al.  Information theoretic inequalities , 1991, IEEE Trans. Inf. Theory.

[17]  Frank H. P. Fitzek,et al.  The Medium is the Message , 2006, 2006 IEEE International Conference on Communications.

[18]  F. Doblas-Reyes,et al.  Retrospective prediction of the global warming slowdown in the past decade , 2013 .

[19]  C. Franzke.  Warming trends: Nonlinear climate change , 2014 .

[20]  H. Joe.  Estimation of entropy and other functionals of a multivariate density , 1989 .

[21]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[22]  C. Vignata,et al.  Analysis of signals in the Fisher – Shannon information plan , 2003 .

[23]  C. Tebaldi,et al.  Long-term Climate Change: Projections, Commitments and Irreversibility , 2013 .

[24]  Marshall McLuhan,et al.  The medium is the message , 2005 .

[25]  C. Masoller,et al.  Identifying large-scale patterns of unpredictability and response to insolation in atmospheric data , 2017, Scientific reports.

[26]  L. Györfi,et al.  Density-free convergence properties of various estimators of entropy , 1987 .

[27]  Jianping Huang,et al.  Evolution of land surface air temperature trend , 2014 .

[28]  Federico Amato,et al.  Advanced Analysis of Temporal Data Using Fisher-Shannon Information: Theoretical Development and Application in Geosciences , 2020, Frontiers in Earth Science.

[29]  Matthew P. Wand,et al.  Kernel Smoothing , 1995 .

[30]  M. C. Jones,et al.  A reliable data-based bandwidth selection method for kernel density estimation , 1991 .

[31]  Ian T. Jolliffe,et al.  Empirical orthogonal functions and related techniques in atmospheric science: A review , 2007 .

[32]  Juan Carlos Angulo,et al.  Fisher-Shannon plane and statistical complexity of atoms , 2008 .

[33]  G. North,et al.  Empirical Orthogonal Functions: The Medium is the Message , 2009 .

[34]  Yuriy G. Dmitriev,et al.  On the Estimation of Functionals of the Probability Density and Its Derivatives , 1974 .

[35]  Jean-François Bercher,et al.  Analysis of signals in the Fisher–Shannon information plane , 2003 .

[36]  Noel A Cressie,et al.  Spatio-Temporal Statistics with R , 2019 .

[37]  M. Requier-Desjardins,et al.  The 2030 Agenda for Sustainable Development , 2015, An Insider's Guide to the UN.

[38]  Christian P. Robert,et al.  Statistics for Spatio-Temporal Data , 2014 .