ISSN:0094-243X    

DOI:10.1063/1.34272

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

The predictability problem arises because hydrodynamic flows with similar initial conditions may evolve differently, despite the continuous dependence of solutions on initial conditions.The central topological issues of predictability concern the dimensions of the spaces in which solutions and solution differences reside. Concentration on the attractors of the flow reveals that such spaces may be effectively finite dimensional, and that the relevant number of dimensions may not always be large.The mathematical approach utilizes eigenvalue problems and spectral decompositions to determine the expanding and contracting components of the flow, both directly, and through the construction of the unstable manifold via an extended version of the center manifold theorem.A common situation in hydrodynamics allows explicit estimation of the dimension of the attractors with Lyapunov exponents. The center manifold theorem demonstrates strong convergence of truncated spectral models in attractors that bifurcate from the origin.A version of the Poincare´ map is constructed along an evolving trajectory by resolving the error field into a component transverse of the trajectory and a phase error component. The resulting equations suggest an eigenvalue problem that will reveala priorithose regions of phase space in which large transverse or phase errors may be expected.

ISSN:0094-243X    

DOI:10.1063/1.34265

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

Measures of predictability are determined by various moments of the conditional probability distribution for the physical observables in a flow field. A general technique is introduced whereby anexactstochastic differential equation for the dynamics of a flow field is constructed from the primitive equations. This is a generalized Langevin equation which in the Markov limit can be replaced by a Fokker‐Planck equation. This latter equation is solved for the non‐equilibrium probability density for a simple model system thereby allowing one to calculate the predictability measures exactly.

ISSN:0094-243X    

DOI:10.1063/1.34291

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

The observation that the large‐scale motions of the atmosphere exhibit some of the features of two‐dimensional turbulent flow has been used to justify the study of atmospheric predictability using simplified turbulence models. Global FGGE data are used to investigate several aspects of large‐scale turbulence in the atmosphere. Two rather different flow regimes are found. The high wavenumber region is dominated by the transient component, there is approximate isotropy, the spectrum has a power‐law slope, the January and July spectra are remarkably similar, and there is a strong enstrophy flux down scale. This region has some of the features of an enstrophy cascading subrange. The low wavenumber region on the other hand is dominated by the stationary component, is markedly anisotropic and exhibits notable changes in the spectrum between January and July. There is a strong energy flux up scale. It is notable that there seems to be no barrier to the up scale transfer via the Rhines mechanism.An associated diagnostic study of the error at 24, 48, and 72 hours of the Canadian Meteorological Centre forecast model is carried out in wavenumber space. Error spectra and budget terms are obtained and compared with the results expected from theory. Error behavior at high wavenumbers and for short times is in reasonable accord with expectations. The source of error due to model imperfections is, however, a very important term at all scales. Error behavior differs in summer and winter and the behavior of error in the low wavenumber regime is crucial to the limit of predictability.

ISSN:0094-243X    

DOI:10.1063/1.34255

出版商:AIP    

年代:1984

数据来源: AIP

ISSN:0094-243X    

DOI:10.1063/1.34260

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

An outline is given of some recent and current research in the Geophysical Fluid Dynamics Laboratory of the UK Meteorological Office on the dynamics of rotating fluids and planetary atmospheres. Many of these investigations bear on the problem of creating a theoretical framework for atmospheric predictability studies.

ISSN:0094-243X    

DOI:10.1063/1.34261

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

We consider the equivalent barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Twenty‐five modes are retained in a spherical harmonics expansion of the stream function. Solutions are studied as a function of the nondimensional intensity of the forcing and dissipation.Stationary solutions show the nonlinear orographic resonance of Charney and DeVore. A second resonance at lower, more realistic values of the forcing appears as a result of the larger number of modes. Among the multiple equilibria associated with the second, more complex resonance are a zonal and a blocked flow pattern which present marked similarities with the synoptically defined normal and blocked Northern Hemisphere midlatitude flows.Wave‐wave interactions influence strongly the stability properties of the equilibria and time evolutions of nonequilibrium solutions. The latter show persistent sequences which occur in the phase‐space vicinity of the zonal and blocked equilibria. Composite flow patterns of the persistent sequences are similar to the equilibria nearby. The mean life times of the sequences are longer than in reality due to the lack of baroclinic processes in the model. A recurrent hyper‐predictable sequence with both persistent and agitated episodes, lasting a total of 500 simulated days, is also exhibited and discussed.

ISSN:0094-243X    

DOI:10.1063/1.34262

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

A low‐order model of quasi‐geostropic uniform potential vorticity is considered. The depth‐integrated total energy and the available potential energy on the boundaries are both conservative properties of the fluid motion. Energy exchanges between three scales of motion involving six Fourier amplitudes are analyzed. The exchange of energy between the wave components satisfies Fjo&slash;rtoft’s theorem on scale interactions at any instant. However, the system exhibits an inherent unpredictability, and the ordering of the large, intermediate and small‐scale waves changes with time. Consequently, the direction and rate of energy transfer between the wave components becomes unpredictable. It is demonstrated that these properties of the model are fundamentally different than those associated with a low‐order quasi‐geostropic model involving three amplitude equations with two quadratic constraints on the motion.

ISSN:0094-243X    

DOI:10.1063/1.34263

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

This paper examines the predictability properties of barotropic and baroclinic geostropic turbulence. By geostropic turbulence I mean rapidly rotating, stably stratified flow with many degrees of freedom, dominated to a greater or lesser extent by nonlinearity. Predictability here is concerned with the rate of divergence, measured by spectra of energy in the difference field, of two initially similar fields. In particular the paper examines the effects of a mean gradient of potential vorticity (the beta effect) and the effects of baroclinic instability on flow predictability. In barotropic (i.e., two‐dimensional) turbulence, beta increases predictability by slowing nonlinear energy transfer between scales. Two layer flow is not so affected, because beta increases the range of wavenumbers over which significant energy transfer occurs due to the modification of the linear stability properties of the system. In two layer flow baroclinic and barotropic effects each account for about half of the loss of predictability.

ISSN:0094-243X    

DOI:10.1063/1.34264

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

Recent studies based upon the output of the ECMWF operational forecasting model indicates that if, after the first day of a forecast, a perfect model could be substituted for the present model, forecasts as good as those presently produced at seven days would be realized at ten days. These studies do not reveal how much improvement in one‐day forecasting is possible.We hypothesize that if all other imperfections in the forecasting procedure could be removed, the inevitable initial uncertainties in observing the small‐scale features would, after D days, lead to error fields with amplitudes and spectra resembling those of the errors in present one‐day forecasts. The appropriate value of D is highly dependent upon the spectrum of actual atmospheric motions. Estimates with a crude model place D at about four days, thereby implying that the present forecasting success at one week may some day be realized at nearly two weeks.

ISSN:0094-243X    

DOI:10.1063/1.34266

出版商:AIP    

年代:1984

数据来源: AIP