Mathematical and physical ideas for climate science

Lucarini, Valerio; Blender, Richard; Herbert, Corentin; Ragone, Francesco; Pascale, Salvatore; Wouters, Jeroen

doi:10.1002/2013rg000446

Cited by 136 publications

(179 citation statements)

References 274 publications

Supporting

Mentioning

178

Contrasting

Order By: Relevance

“…(11.3.7) See a discussion of these results in a geophysical context in [263,102,340]. These results provide some explicit formulas for studying rigorously extremes in a timedependent setting.…”

Section: Extremes Coarse Graining and Parametrizationsmentioning

confidence: 88%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

Self Cite

178

253

View full text Add to dashboard Cite

ii 4.1.2 The New Conditions 44 4.1.3 The Existence of EVL for General Stationary Stochastic Processes under Weaker Hypotheses 46 4.1.4 Proofs of Theorem 4.1.4 and Corollary 4.1.5 48 4.2 Extreme Values for Dynamically Defined Stochastic Processes 53 4.2.1 Observables and Corresponding Extreme Value Laws 55 4.2.2 Extreme Value Laws for Uniformly Expanding Systems 59 4.2.3 Example 4.2.1 revisited 61 4.2.4 Proof of the Dichotomy for Uniformly Expanding Maps 63 4.3 Point Processes of Rare Events 64 4.3.1 Absence of Clustering 64 4.3.2 Presence of Clustering 65 4.3.3 Dichotomy for Uniformly Expanding Systems for Point Processes 67 4.4 Conditions Д q (u n ), D 3 (u n ), D p (u n ) * and Decay of Correlations 68 4.5 Specific Dynamical Systems where the Dichotomy Applies 71 4.5.1 Rychlik Systems 72 4.5.2 Piecewise Expanding Maps in Higher Dimensions 73 4.6 Extreme Value Laws for Physical Observables 74

show abstract

Section: Extremes Coarse Graining and Parametrizationsmentioning

confidence: 88%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

Self Cite

178

253

View full text Add to dashboard Cite

show abstract

“…One of the outstanding scientific challenges of the last decades has been to attempt to provide a comprehensive theory of climate, able to explain the main features of its dynamics, describe its variability, and predict its response to a variety of forcings, both anthropogenic and natural [1][2][3]. The study of the phenomenology of the climate system is commonly approached by focusing on distinct aspects like:…”

Section: Introductionmentioning

confidence: 99%

“…See [7] for a detailed analysis of the relationship between response, fluctuations, and dissipation at different scales. Altogether, the climate can be seen as a thermal engine able to transform heat into mechanical energy with a given efficiency, and featuring many different irreversible processes that make it non-ideal [2,8,9].…”

Section: Introductionmentioning

confidence: 99%

“…A typical IPCC-like climate change experiment consists in simulating the system in a reference state (a stationary preindustrial state with fixed parameters, or a realistic simulation of the present-day climate), raising the CO 2 concentration (as well as, in general, the concentration of other greenhouse gases such as methane) in the atmosphere following a certain time modulation within a given time window, and then fixing the CO 2 concentration to a final value, in order to observe the relaxation of the system to a new stationary state. Each time-modulation of the CO 2 forcing defines a scenario, and it is a representation of the expected change in the CO 2 concentration resulting from a specific path of industrialization and change in land use. Note that the attribution of unusual climatic conditions to specific climate forcing is far from being a trivial matter [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…Adding noise in the equations in the form of stochastic forcing-as in the case of using stochastic parametrizations [24] in multiscale system-provides a way to regularize the problem, but it is not entirely clear how to treat the zero noise limit. Additionally, one should provide a robust and meaningful derivation of the model to be used for constructing the noise: a proposal in this direction is given in [2,25,26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns

Lucarini

Ragone

Lunkeit³

2016

J Stat Phys

Self Cite

132

View full text Add to dashboard Cite

The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(10 5 ) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is nonautonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting-at any lead time and in an ensemble sense-the change in climate properties resulting from increase in the concentration of CO 2 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change.Paper prepared for the special issue of the Journal of Statistical Physics dedicated to the 80th birthday of Y.

show abstract

Combining satellite observations and reanalysis energy transports to estimate global net surface energy fluxes 1985–2012

et al. 2015

View full text Add to dashboard Cite

Two methods are developed to estimate net surface energy fluxes based upon satellite-derived reconstructions of radiative fluxes at the top of atmosphere and the atmospheric energy tendencies and transports from the ERA-Interim reanalysis. Method 1 applies the mass-adjusted energy divergence from ERA-Interim, while method 2 estimates energy divergence based upon the net energy difference at the top of atmosphere and the surface from ERA-Interim. To optimize the surface flux and its variability over ocean, the divergences over land are constrained to match the monthly area mean surface net energy flux variability derived from a simple relationship between the surface net energy flux and the surface temperature change. The energy divergences over the oceans are then adjusted to remove an unphysical residual global mean atmospheric energy divergence. The estimated net surface energy fluxes are compared with other data sets from reanalysis and atmospheric model simulations. The spatial correlation coefficients of multiannual means between the estimations made here and other data sets are all around 0.9. There are good agreements in area mean anomaly variability over the global ocean, but discrepancies in the trend over the eastern Pacific are apparent.

show abstract

Mathematical and physical ideas for climate science

Cited by 136 publications

References 274 publications

Extremes and Recurrence in Dynamical Systems

Extremes and Recurrence in Dynamical Systems

Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns

Combining satellite observations and reanalysis energy transports to estimate global net surface energy fluxes 1985–2012

Contact Info

Product

Resources

About