World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings : Volume 18, Issue 1 (12/01/2011)

By Lucarini, V.

Click here to view

Book Id: WPLBN0003974541
Format Type: PDF Article :
File Size: Pages 22
Reproduction Date: 2015

Title: A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings : Volume 18, Issue 1 (12/01/2011)  
Author: Lucarini, V.
Volume: Vol. 18, Issue 1
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Lucarini, V., & Sarno, S. (2011). A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings : Volume 18, Issue 1 (12/01/2011). Retrieved from

Description: Department of Meteorology, University of Reading, Reading, UK. The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

A statistical mechanical approach for the computation of the climatic response to general forcings

Abramov, R. and Majda, A. J.: Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems, Nonlinearity, 20, 2793–2821, 2007.; Arnold, V. I.: Catastrophe Theory, Springer, Berlin, 1992.; Baladi, V.: On the susceptibility function of piecewise expanding interval maps, Commun. Math. Phys., 275, 839–859, 2007.; Brayshaw, D. J., Hoskins, B., and Blackburn, M.: The storm track response to idealised SST perturbations in an aquaplanet GCM, J. Atmos. Sci., 65, 2842–2860, 2008.; Cacuci, D. G.: Sensitivity theory for nonliner systems. Part I. Nonlinear functional analysis approach, J. Math. Phys., 22, 2794–2802, 1981a.; Cacuci, D. G.: Sensitivity theory for nonliner systems. Part II. Extensions to additional classes of responses, J. Math. Phys., 22, 2803–2812, 1981b.; Cataliotti, F. S., Fort, C., Hänsch, T. W., Inguscio, M., and Prevedelli, M.: Electromagnetically induced transparency in cold free atoms: Test of a sum rule for nonlinear optics, Phys. Rev. A, 56, 2221–2224, 1997.; Cessac, B. and Sepulchre, J.-A.: Linear response, susceptibility and resonances in chaotic toy models, Physica D, 225, 13–28, 2007.; Chekroun, M. D., Simonnet, E., and Ghil, M.: Stochastic climate dynamics: Random attractors and time-dependent invariant measures, Physica D, in press, 2011.; Dolgopyat, D.: On differentiability of SRB states for partially hyperbolic systems, Invent. Math., 155, 389–449, 2004.; Eckmann, J.-P. and Ruelle, D.: Ergodic theory of choas and strenge attractors, Rev. Mod. Phys., 57, 617–655, 1985.; Errico, R.: What Is an Adjoint Model?, B. Am. Meteor. Soc., 78, 2577–2591, 1997.; Eyink, G. L., Haine, T. W. N., and Lea, D. J.: Ruelle's linear response formula, ensemble adjoint schemes and L�vy flights, Nonlinearity, 17, 1867–1889, 2004,; Fertig, E., Harlim, J., and Hunt, B.: A comparative study of 4D-Var and 4D ensemble Kalman filter: perfect model simulations with {Lorenz}-96, Tellus A, 59, 96–101, 2007.; Fraedrich, K., Jansen, H., Kirk, E., Luksch, U., and Lunkeit, F.: The Planet Simulator: Towards a user friendly model, Meteorol. Z., 14, 299–304, 2005.; Frye, G. and Warnock, R. L.: Analysis of partial wave dispersion relations, Phys. Rev., 130, 478–494, 1963.; Gallavotti, G.: Chaotic hypotesis: Onsanger reciprocity and fluctuation-dissipation theorem, J. Stat. Phys., 84, 899–926, 1996.; Gallavotti, G. and Cohen, E. D. G.: Dynamical ensembles in stationary states, J. Stat. Phys., 80, 931–970, 1995.; Gallavotti, G.: Nonequilibrium statistical mechanics (stationary): overview, in: Encyclopedia of Mathematical Physics, edited by: Françoise, J.-P., Naber, G. L., Tsou Sheung Tsun, Elsevier, Amsterdam, 530–539, 2006.; Giering, R. and Kaminski, T.: {R}ecipes for {A}djoint {C}ode {C}onstruction, ACM Trans. On Math. Software, 24, 437–474, 1998.; Ghil, M. and Malanotte-Rizzoli, P.: Data assimilation in meteorology and oceanography, Adv. Geophys., 33, 141–266, 1991.; Gritsun, A. and Branstator G.: Climate response using a three-dimensional operator based on the fluctuation-dissipation theorem, J. Atmos. Sci., 64, 2558–2575, 2007.; Gritsun A., Branstator G. and Majda A. J.: Climate response of linear and quadratic functionals using the fluctuation-dissipation theorem, J. Atmos. Sci., 65, 2824–2841, 2008.; Hall, M. C. G.: Application of adjoint sesnitivity theory to an atmospheric general circulation model, J. Atmos. Sci., 42, 2644–2651, 1986.; Hall, M. C. G. and Cacuci, D. G.: Physical interpretation of the adjoint functions for sensitivity analysis of atmospheric models, J. Atmos. Sci., 40, 2537–2546, 1983.; Hall, M. C. G., Cacuci, D. G., and Schlesinger, M. E.: Sensitivity analysis of a radiative-convective model by the adjoint method, J. Atmos. Sci., 39, 2038–2050, 1982.; Hallerberg, S., Pazò, D., Lòpez, J. M., and Rodr\'{i}guez, M. A.: Logarithmic bred vectors in spatiotemporal chaos: Structure and growth, Phys. Rev. E, 81, 066204, doi:10.1103/PhysRevE.81.066204, 2010.; Hasselmann, K.: Stochastic clim


Click To View

Additional Books

  • Regional and Inter-regional Effects in E... (by )
  • Albedo Parametrization and Reversibility... (by )
  • Oscillations in Critical Shearing, Appli... (by )
  • Lagrangian Transport in a Circular Lake:... (by )
  • Magnetic Holes in Plasmas Close to the M... (by )
  • Distinguishing the Effects of Internal a... (by )
  • An Attempt to Find Precursors in the Ulf... (by )
  • The Use of Artificial Neural Networks to... (by )
  • Effect of Interchange Instability on Mag... (by )
  • Direct Numerical Simulation of Intermitt... (by )
  • A New Method for Abrupt Change Detection... (by )
  • Comments and New Results About the Magne... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.