Climate Response and Fluctuation Dissipation

Leith, C. E.

doi:10.1175/1520-0469(1975)032<2022:crafd>2.0.co;2

Cited by 325 publications

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“…19. Second, there is a growing literature in developing theory (11,(21)(22)(23)(24) and algorithms for FDT (25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35). In fact, the earliest applications that tested the original suggestion of Leith (28) utilized the kicked perturbations in Eq.…”

Section: General Comments On the Linkmentioning

confidence: 99%

Link between statistical equilibrium fidelity and forecasting skill for complex systems with model error

Majda

Gershgorin

2011

Proc. Natl. Acad. Sci. U.S.A.

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Understanding and improving the predictive skill of imperfect models for complex systems in their response to external forcing is a crucial issue in diverse applications such as for example climate change science. Equilibrium statistical fidelity of the imperfect model on suitable coarse-grained variables is a necessary but not sufficient condition for this predictive skill, and elementary examples are given here demonstrating this. Here, with equilibrium statistical fidelity of the imperfect model, a direct link is developed between the predictive fidelity of specific test problems in the training phase where the perfect natural system is observed and the predictive skill for the forced response of the imperfect model by combining appropriate concepts from information theory with other concepts based on the fluctuation dissipation theorem. Here a suite of mathematically tractable models with nontrivial eddy diffusivity, variance, and intermittent non-Gaussian statistics mimicking crucial features of atmospheric tracers together with stochastically forced standard eddy diffusivity approximation with model error are utilized to illustrate this link.P redicting the long-range behavior of complex systems in nature in diverse disciplines ranging from climate change science (1, 2) to materials (3) and neuroscience (4) is an issue of central importance in contemporary engineering and science. Accurate predictions are hampered by the fact that the true dynamics of the system in nature are actually unknown due to inadequate scientific understanding or inadequate spatiotemporal resolution in the imperfect computer models used for these predictions; in other words, there are significant model errors compared to the true signal from nature. Recently, information theory has been utilized in different ways to systematically improve model fidelity and sensitivity (5, 6), to quantify the role of coarse-grained initial states in long-range forecasting (7,8), and to make an empirical link between model fidelity and forecasting skill (9, 10). Imperfect models for complex systems are constrained by their capability to reproduce certain statistics in a training phase where the natural system has been observed; for example, this training phase in climate science is roughly the 60-y dataset of extensive observations of the Earth's climate system. For long-range forecasting, it is natural to guarantee statistical equilibrium fidelity for an imperfect model, and a framework using information theory is a natural way to achieve this in an unbiased fashion (5-8, 10). First, equilibrium statistical fidelity for an imperfect model depends on the choice of coarse-grained variables utilized (5, 6); second, equilibrium model fidelity is a necessary but not sufficient condition to guarantee long-range forecasting skill (8). For example, ref. 11, Sect. 2.6, extensively discusses three very different strongly mixing chaotic dynamical models with 40 variables and with the same Gaussian equilibrium measure, the TBH, K-Z, and IL96 models, so that al...

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Section: General Comments On the Linkmentioning

confidence: 99%

Link between statistical equilibrium fidelity and forecasting skill for complex systems with model error

Majda

Gershgorin

2011

Proc. Natl. Acad. Sci. U.S.A.

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“…by the fluctuation-dissipation theorem (FDT), perhaps with simple Gaussian approximation (12,13,15,16). This procedure defines a memory-dependent non-Markovian control δF (t) for the statistical energy.…”

Section: B)mentioning

confidence: 99%

“…6. Use the FDT (12,13,15,22) to replace the response in the mean, δū, using the mean response operator…”

Section: Statistical Response For the Mean State From Statistical Linearmentioning

confidence: 99%

“…The parameter α > 0 is introduced to add a balance between the two components in energy E and control C. The larger value of α adds more weight on the control parameter in the process. [14] according to the cost [15].…”

Section: Effective Statistical Control Of the L-96 Modelmentioning

confidence: 99%

“…Now, we derive the optimal energy control C * (t) for time interval [0, T ] with varying cost depending on α. It is well-known (17, 18) that the scalar control problem in [14] and [15] is solved by a scalar Riccati equation: that is,…”

Section: Remark 1 the Statistical Control Problem In [14] Is Quite Umentioning

confidence: 99%

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Effective control of complex turbulent dynamical systems through statistical functionals

Majda

2017

Proc. Natl. Acad. Sci. U.S.A.

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Turbulent dynamical systems characterized by both a highdimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering, including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline. In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy, and new control strategies are needed. The goal of this paper is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle and statistical linear response theory. We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.statistical energy principle | response theory | statistical control T urbulent dynamical systems characterized by both a highdimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering (1-4), including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change (5, 6) or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline (7,8). In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy (9), and new control strategies are needed.The goal here is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle (10, 11) and statistical linear response theory (12-14). We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 (L-96) model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.i) The statistical control theory proposed here has the goal and theoretical steps in its design. A) Goal and statistical energy. The statistical energy, E , is the sum of the energy of the statistical mean and the trace of the statistical covariance (10, 11). A turbulent dynamical system is subjected to poorly known external forcing, and the goal of the statistical control strategy is to find an effective deterministic feedback control to drive the statistical energy measured at some time...

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Emergent constraints on climate‐carbon cycle feedbacks in the CMIP5 Earth system models

et al. 2014

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An emergent linear relationship between the long-term sensitivity of tropical land carbon storage to climate warming (γ LT ) and the short-term sensitivity of atmospheric carbon dioxide (CO 2 ) to interannual temperature variability (γ IAV ) has previously been identified by Cox et al. (2013) across an ensemble of Earth system models (ESMs) participating in the Coupled Climate-Carbon Cycle Model Intercomparison Project (C 4 MIP). Here we examine whether such a constraint also holds for a new set of eight ESMs participating in Phase 5 of the Coupled Model Intercomparison Project. A wide spread in tropical land carbon storage is found for the quadrupling of atmospheric CO 2 , which is of the order of 252 ± 112 GtC when carbon-climate feedbacks are enabled. Correspondingly, the spread in γ LT is wide (À49 ± 40 GtC/K) and thus remains one of the key uncertainties in climate projections. A tight correlation is found between the long-term sensitivity of tropical land carbon and the short-term sensitivity of atmospheric CO 2 (γ LT versus γ IAV ), which enables the projections to be constrained with observations. The observed short-term sensitivity of CO 2 (À4.4 ± 0.9 GtC/yr/K) sharpens the range of γ LT to À44 ± 14 GtC/K, which overlaps with the probability density function derived from the C 4 MIP models (À53 ± 17 GtC/K) by Cox et al. (2013), even though the lines relating γ LT and γ IAV differ in the two cases. Emergent constraints of this type provide a means to focus ESM evaluation against observations on the metrics most relevant to projections of future climate change.

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Climate Response and Fluctuation Dissipation

Cited by 325 publications

References 0 publications

Link between statistical equilibrium fidelity and forecasting skill for complex systems with model error

Link between statistical equilibrium fidelity and forecasting skill for complex systems with model error

Effective control of complex turbulent dynamical systems through statistical functionals

Emergent constraints on climate‐carbon cycle feedbacks in the CMIP5 Earth system models

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