Predictability – a problem partly solved

Lorenz, Edward N.

doi:10.1017/cbo9780511617652.004

Cited by 827 publications

(1,447 citation statements)

References 13 publications

Supporting

Mentioning

1,416

Contrasting

Unclassified

Order By: Relevance

“…For the above formalism to work, the right-hand side of the averaged system in (2.2) must not be O(ε); otherwise, higher-order homogenization techniques are needed [31]. We choose the two-scale forced damped Lorenz model [1,2,11,14,18] for the computational study of the dynamical properties of a two-scale slow-fast process with generic features of atmospheric dynamics, such as the presence of linearly unstable waves, strong nonlinearity, forcing, dissipation, chaos, and mixing. The two-scale forced damped Lorenz model is given bẏ…”

Section: A Remarkable Behavior Of the Two-scale Lorenz Modelmentioning

confidence: 99%

“…Originally in [11,14,18] there was no constant forcing F y term in the equation for y-variables in (2.4), however, in its absence the behavior of the y-variables is strongly dissipative [1,2]. Here, as in [2], we add a constant forcing F y in the right-hand side of the second equation in (2.4) to induce the strongly chaotic behavior of the y-variables with large positive Lyapunov exponents.…”

Section: A Remarkable Behavior Of the Two-scale Lorenz Modelmentioning

confidence: 99%

“…In Section 2 we start with a numerical experiment with an appropriately rescaled two-scale Lorenz model [2,11,14,18], which demonstrates that, for only slightly affected one-point statistics such as the mean state and variance, the chaos at the slow variables is suppressed by the increasing turbulent mixing at the fast variables through the forcing parameter. In Sections 3-5 we develop a mathematical framework for the slow averaged dynamics on the tangent subspaces.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

Abramov

2012

Communications in Mathematical Sciences

View full text Add to dashboard Cite

Abstract. Chaotic multiscale dynamical systems are common in many areas of science, one example being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger mixing system would result in general increase of chaos at the slow variables.

show abstract

Section: A Remarkable Behavior Of the Two-scale Lorenz Modelmentioning

confidence: 99%

Section: A Remarkable Behavior Of the Two-scale Lorenz Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

Abramov

2012

Communications in Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…We consider as our test bed a stochastic version of the Lorenz 95 system (Lorenz, 1995) whose state vector x = (x 1 , x 2 , x 3 , . .…”

Section: F C Cooper Et Al: Response Of High Dimensional Systemsmentioning

confidence: 99%

Estimation of the local response to a forcing in a high dimensional system using the fluctuation-dissipation theorem

Cooper

Esler

Haynes

2013

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

The fluctuation-dissipation theorem (FDT) has been proposed as a method of calculating the response of the earth's atmosphere to a forcing. For this problem the high dimensionality of the relevant data sets makes truncation necessary. Here we propose a method of truncation based upon the assumption that the response to a localised forcing is spatially localised, as an alternative to the standard method of choosing a number of the leading empirical orthogonal functions. For systems where this assumption holds, the response to any sufficiently small non-localised forcing may be estimated using a set of truncations that are chosen algorithmically. We test our algorithm using 36 and 72 variable versions of a stochastic Lorenz 95 system of ordinary differential equations. We find that, for long integrations, the bias in the response estimated by the FDT is reduced from ~75% of the true response to ~30%

show abstract

“…Details of the ensemble prediction and parameter estimation system (EPPES) can be found in Laine et al (2012), which applied the algorithm to a modified Lorenz-95 system (Lorenz, 1995;Wilks, 2005). The implementation here follows closely the one presented in Ollinaho et al (2013), which used an EPS emulator.…”

Section: Implementation Of the Estimation Algorithmmentioning

confidence: 99%

Parameter variations in prediction skill optimization at ECMWF

Ollinaho

Bechtold

Leutbecher

et al. 2013

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract. Algorithmic numerical weather prediction (NWP) skill optimization has been tested using the Integrated Forecasting System (IFS) of the European Centre for MediumRange Weather Forecasts (ECMWF). We report the results of initial experimentation using importance sampling based on model parameter estimation methodology targeted for ensemble prediction systems, called the ensemble prediction and parameter estimation system (EPPES). The same methodology was earlier proven to be a viable concept in low-order ordinary differential equation systems, and in large-scale atmospheric general circulation models (ECHAM5). Here we show that prediction skill optimization is possible even in the context of a system that is (i) of very high dimensionality, and (ii) carefully tuned to very high skill. We concentrate on four closure parameters related to the parameterizations of sub-grid scale physical processes of convection and formation of convective precipitation. We launch standard ensembles of medium-range predictions such that each member uses different values of the four parameters, and make sequential statistical inferences about the parameter values. Our target criterion is the squared forecast error of the 500 hPa geopotential height at day three and day ten. The EPPES methodology is able to converge towards closure parameter values that optimize the target criterion. Therefore, we conclude that estimation and cost functionbased tuning of low-dimensional static model parameters is possible despite the very high dimensional state space, as well as the presence of stochastic noise due to initial state and physical tendency perturbations. The remaining question before EPPES can be considered as a generally applicable tool in model development is the correct formulation of the target criterion. The one used here is, in our view, very selective.Considering the multi-faceted question of improving forecast model performance, a more general target criterion should be developed. This is a topic of ongoing research.

show abstract

Predictability – a problem partly solved

Cited by 827 publications

References 13 publications

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

Estimation of the local response to a forcing in a high dimensional system using the fluctuation-dissipation theorem

Parameter variations in prediction skill optimization at ECMWF

Contact Info

Product

Resources

About