On quantifying the climate of the nonautonomous Lorenz-63 model

Daron, Joseph; Stainforth, David A.

doi:10.1063/1.4916789

Cited by 17 publications

(15 citation statements)

References 45 publications

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“…Both taking temporal statistics and a finite ensemble size have been pointed out there to yield biases in general; and the authors suggested that "ensembles of several hundred members may be required to characterize a model's climate". Daron and Stainforth [51] provided further evidence of the biases and discrepancies between temporal and ensemble-wise statistics, and demonstrated the initial-condition-dependence of "transient" convergence properties of ensembles. Pierini [52] and Pierini et al [53] considered a periodically forced reduced double-gyre model described by four variables and determined sample measures, while Chekroun et al [54] studied the pullback attractor and its measure in a delay differential model of ENSO.…”

Section: Ensemble View In Other Conceptual Modelsmentioning

confidence: 94%

The Theory of Parallel Climate Realizations

et al. 2019

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Based on the theory of "snapshot/pullback attractors", we show that important features of the climate change that we are observing can be understood by imagining many replicas of Earth that are not interacting with each other. Their climate systems evolve in parallel, but not in the same way, although they all obey the same physical laws, in harmony with the chaotic-like nature of the climate dynamics. These parallel climate realizations evolving in time can be considered as members of an ensemble. We argue that the contingency of our Earth's climate system is characterized by the multiplicity of parallel climate realizations rather than by the variability that we experience in a time series of our observed past. The natural measure of the snapshot attractor enables one to determine averages and other statistical quantifiers of the climate at any instant of time. In this paper, we review the basic idea for climate changes associated with monotonic drifts, and illustrate the large number of possible applications. Examples are given in a low-dimensional model and in numerical climate models of different complexity. We recall that systems undergoing climate change are not ergodic, hence temporal averages are generically not appropriate for the instantaneous characterization of the climate. In particular, teleconnections, i.e. correlated phenomena of remote geographical locations are properly characterized only by correlation coefficients evaluated with respect to the natural measure of a given time instant, and may also change in time. Physics experiments dealing with turbulent-like phenomena in a changing environment are also worth being interpreted in view of the attractor-based ensemble approach. The possibility of the splitting of the snapshot attractor to two branches, near points where the corresponding time-independent system undergoes bifurcation as a function of the changing parameter, is briefly mentioned. This can lead in certain climate-change scenarios to the coexistence of two distinct sub-ensembles representing dramatically different climatic options. The problem of pollutant spreading during climate change is also discussed in the framework of parallel climate realizations. Keywords Climate dynamics • Nonautonomous systems • Ensembles • Snapshot attractors • Natural measures Communicated by Valerio Lucarini.

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Section: Ensemble View In Other Conceptual Modelsmentioning

confidence: 94%

The Theory of Parallel Climate Realizations

et al. 2019

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“…years. Daron and Stainforth ([2015]) and Selten et al ([2004]) and Smith ([1987]) also argue that it is plausible that there is no convergence for prediction lead times of interest, and they underscore this with evidence from Lorenz's 1963 model and a community climate systems model. Furthermore, even if climate models had strong physical measures, projections could not be independent of initial conditions ensembles.…”

Section: Dynamical Conditions Justifying Independence Of Initial Condmentioning

confidence: 99%

“…The research that has been carried out is sobering and suggests that a large number of initial conditions (and not just a few) are needed to reliably estimate projections. For instance, Daron and Stainforth ([2013]) using a low-dimensional nonlinear system that exhibits behaviour similar to that of the atmosphere and ocean found that several hundred initial conditions are needed (see also Daron and Stainforth [2015]; Kay et al [2014]). Similarly, Deser et al ([2012]) perform simulations with one of the CMIP5 models, and argue that large initial conditions ensembles are needed.…”

Section: Projectionsmentioning

confidence: 99%

“…However, in practice only very few initial conditions are considered (rarely more than ten; CMIP5 requires just three - Taylor et al [2012]). The research that has been carried out is sobering and suggests that a large number of initial conditions are needed to reliably estimate preditions (Daron and Stainforth [2013]; Daron and Stainforth [2015]; see also Kay et al [2014]). Hence there is considerable initial conditions uncertainty of the second kind.…”

Section: Predictionsmentioning

confidence: 99%

See 1 more Smart Citation

Initial-Condition Dependence and Initial-Condition Uncertainty in Climate Science

Werndl

2019

The British Journal for the Philosophy of Science

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This article examines initial-condition dependence and initial-condition uncertainty for climate projections and predictions. The first contribution is to provide a clear conceptual characterization of predictions and projections. Concerning initial-condition dependence, projections are often described as experiments that do not depend on initial conditions. Although prominent, this claim has not been scrutinized much and can be interpreted differently. If interpreted as the claim that projections are not based on estimates of the actual initial conditions of the world or that what makes projections true are conditions in the world, this claim is true. However, it can also be interpreted as the claim that simulations used to obtain projections are independent of initial-condition ensembles. This article argues that evidence does not support this claim. Concerning initial-condition uncertainty, three kinds of initial-condition uncertainty are identified (two have received little attention from philosophers so far). The first (the one usually discussed) is the uncertainty associated with the spread of the ensemble simulations. The second arises because the theoretical initial ensemble cannot be used in calculations and has to be approximated by finitely many initial states. The third uncertainty arises because it is unclear how long the model should be run to obtain potential initial conditions at pre-industrial times. Overall, the discussion shows that initial-condition dependence and uncertainty in climate science are more complex and important issues than usually acknowledged. 1Introduction2Projections and Predictions 2.1Predictions2.2Projections3Initial-Condition Dependence 3.1Projections 3.1.1Dynamical conditions justifying independence of initial conditions?3.1.2What projections can and cannot provide3.2Predictions4Initial-Condition Uncertainty 4.1Projections4.2Predictions5ConclusionAppendix

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“…indexed by the parameter λ = (σ, b). Note that the model (6.5) and assumption (6.4) are relevant in some climate models, see for example [9]. In particular, the function r(t) can be a finite sum of sinusoidal functions.…”

Section: The Lorenz Systemmentioning

confidence: 99%

Continuity of pullback and uniform attractors

Hoang

Olson

Robinson

2018

Journal of Differential Equations

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We study the continuity of pullback and uniform attractors for non-autonomous dynamical systems with respect to perturbations of a parameter. Consider a family of dynamical systems parameterized by λ ∈ Λ, where Λ is a complete metric space, such that for each λ ∈ Λ there exists a unique pullback attractor A λ (t). Using the theory of Baire category we show under natural conditions that there exists a residual set Λ * ⊆ Λ such that for every t ∈ R the function λ → A λ (t) is continuous at each λ ∈ Λ * with respect to the Hausdorff metric. Similarly, given a family of uniform attractors A λ , there is a residual set at which the map λ → A λ is continuous. We also introduce notions of equi-attraction suitable for pullback and uniform attractors and then show when Λ is compact that the continuity of pullback attractors and uniform attractors with respect to λ is equivalent to pullback equi-attraction and, respectively, uniform equi-attraction. These abstract results are then illustrated in the context of the Lorenz equations and the two-dimensional Navier-Stokes equations.

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On quantifying the climate of the nonautonomous Lorenz-63 model

Cited by 17 publications

References 45 publications

The Theory of Parallel Climate Realizations

The Theory of Parallel Climate Realizations

Initial-Condition Dependence and Initial-Condition Uncertainty in Climate Science

Continuity of pullback and uniform attractors

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