Spatiotemporal stochastic forcing effects in an ensemble consisting of arrays of diffusively coupled Lorenz cells

Lorenzo, M. N.; Santos, M.; Pérez‐Muñuzuri, V.

doi:10.1063/1.1601791

Cited by 10 publications

(17 citation statements)

References 37 publications

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“…This peak seems to be the signature of a resonant behavior between the annual cycle period T ac and the noise correlation time as it will be shown later. For the limit case τ → 0 and finite G(0, 0), the noise intensity tends to zero and the noise vanishes (Lorenzo et al, 2003). In this way, the ensemble reduces to the case when only different random initial conditions were considered without stochastic physics, and the forecast scores tend to those calculated then (see Table I).…”

Section: Resultsmentioning

confidence: 96%

“…noise dispersion is not kept constant as is varied, Eq. A4) a decreasing of the scores with should be expected (Lorenzo et al, 2003). Spread and error increase faster with for the additive than for the multiplicative case.…”

Section: Resultsmentioning

confidence: 99%

“…Here again, the effect of multiplicative (a-c) or additive (d-f) contributions of the noise is analyzed. Although few resonant cases with changing spatial correlation scale have been described in the literature (Lorenzo et al, 2003;Santos and Sancho, 2001), we expected here to obtain different natural length scales as the vorticity changes and analyze its effect on the scores. Unfortunately, only a linear increase of the scores with the correlation length is obtained, although this is still a nontrivial effect, as for the trivial case (i.e.…”

Section: Resultsmentioning

confidence: 99%

“…The role of spatiotemporal stochastic forcing was previ-ously analyzed in simple nonlinear models of reduced dimensionality, where only local coupling among grid points was considered Pérez-Muñuzuri, 1999, 2001;Lorenzo et al, 2003). Following this idea, we have perturbed stochastically a simplified atmospheric global circulation model, PUMA (Portable University Model of the Atmosphere) developed at Hamburg University (Fraedrich et al, 1998).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Response of a global atmospheric circulation model to spatio-temporal stochastic forcing: ensemble statistics

Pérez‐Muñuzuri

Lorenzo

Montero

et al. 2003

Nonlin. Processes Geophys.

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Abstract. The response of a simplified global atmospheric circulation model (PUMA) to spatiotemporal stochastic forcing is analyzed using the statistical measures originally developed for ensemble forecast evaluation. The nontrivial effects of time and length correlations of the stochastic forcing on the ensemble scores (e.g. spread and 'error') are studied. A maximum for these scores is observed to occur for specific values of the correlation time. The effects of multiplicative and additive contributions of the correlated noise are analyzed in terms of the noise and PUMA parameters.

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Section: Resultsmentioning

confidence: 96%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Response of a global atmospheric circulation model to spatio-temporal stochastic forcing: ensemble statistics

Pérez‐Muñuzuri

Lorenzo

Montero

et al. 2003

Nonlin. Processes Geophys.

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show abstract

“…For example, Lorenzo et al (2003) demonstrated decreasing ensemble spread of an ensemble system consisting of chaotic Lorenz cells diffusively coupled, as the correlation scale of PE grows. If the growing perturbations rapidly adopt the horizontal scales comparable to that of the reference flow, the ensemble spread reaches an asymptotic value and then weakly changes.…”

Section: Discussionmentioning

confidence: 99%

On stochastic stability of regional ocean models to finite-amplitude perturbations of initial conditions

Ivanov

Chu

2007

Dynamics of Atmospheres and Oceans

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We consider error propagation near an unstable equilibrium state (classified as an unstable focus) for spatially uncorrelated and correlated finite-amplitude initial perturbations using short-(up to several weeks) and intermediate (up to 2 months) range forecast ensembles produced by a barotropic regional ocean model. An ensemble of initial perturbations is generated by the Latin Hypercube design strategy, and its optimal size is estimated through the Kullback-Liebler distance (the relative entropy). Although the ocean model is simple, the prediction error (PE) demonstrates non-trivial behavior similar to that existing in 3D ocean circulation models. In particular, in the limit of zero horizontal viscosity, the PE at first decays with time for all scales due to dissipation caused by non-linear bottom friction, and then grows faster than (quasi)-exponentially. Statistics of a prediction time scale (the irreversible predictability time (IPT)) quickly depart from Gaussian (the linear predictability regime) and becomes Weibullian (the non-linear predictability regime) as amplitude of initial perturbations grows. A transition from linear to non-linear predictability is clearly detected by the specific behavior of IPT variance. A new analytical formula for the model predictability horizon is introduced and applied to estimate the limit of predictability for the ocean model.

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Logarithmic bred vectors. A new ensemble method with adjustable spread and calibration time

2008

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[1] The breeding method is a conceptually simple and computationally cheap ensemble generation technique. Bred vectors (BV) are dynamically obtained from the nonlinear model and correspond to the spatial structures with fast-growing fluctuations at each time. These vectors have a characteristic localized spatial structure, with only a small number of significant values corresponding to the leading fluctuation areas. The temporal and spatial growth of the BV interacts making the spatial structure a key factor of the dynamics. In this paper we introduce a new breeding technique, Logarithmic Bred Vectors (LBV), which allows growing vectors with tuneable spatial structure, more (or less) localized. This yields ensembles with different spatiotemporal dynamics (different spread, etc.). This is done by introducing a new parameter (the geometrical mean) which controls the spatial correlation of the bred vectors, from uncorrelated vectors similar to random perturbations, to fully correlated and localized vectors similar to standard bred vectors. The new method increases the diversity of the ensemble and allows the spread to grow faster preserving the model performance in terms of the root mean square error. Consequently, the ensembles can be calibrated for a desired lead time (for instance a shorter forecast range). The concepts are illustrated using a chain of diffusively coupled Lorenz systems. Preliminary evidence of the possible application in operative weather prediction models is also presented.

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Spatiotemporal stochastic forcing effects in an ensemble consisting of arrays of diffusively coupled Lorenz cells

Cited by 10 publications

References 37 publications

Response of a global atmospheric circulation model to spatio-temporal stochastic forcing: ensemble statistics

Response of a global atmospheric circulation model to spatio-temporal stochastic forcing: ensemble statistics

On stochastic stability of regional ocean models to finite-amplitude perturbations of initial conditions

Logarithmic bred vectors. A new ensemble method with adjustable spread and calibration time

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