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The transient evolution of prediction errors in the short to intermediate time regime is considered under the combined effect of initial condition and model errors. Some generic features are brought out and connected with intrinsic properties. Under the assumption of small uncorrelated initial errors and of small parameter errors, the conditions of existence of a time at which the mean quadratic error reaches a minimum and of a crossover lime at which the contribution of initial condition errors matches that of model errors are determined. The results are illustrated and tested on representative low-order models of atmospheric dynamics exhibiting bistability, saddle-point behavior, and chaotic behavior.

The different modes of the early stages of the response of a forecasting model to a small error in the boundary conditions are analyzed. A general formulation of the problem based on the use of Green's functions is developed and implemented on systems in which the operators acting on the spatial coordinates of the fields involved are diffusion-like and advection-like. It is shown that the generic behavior displays a nonanalytic structure not reducible to a power of time for short times.

The dynamical and probabilistic aspects of model error arising from the neglect of unresolved scales and the concomitant reduction of phase space dimensionality of a reference system are analyzed. A general expression of the mean quadratic error involving the time correlation function of the excess phase space velocity is derived. In the short time regime, this expression reduces to the sum of a [t.sup.2] contribution reflecting the structure of the invariant distribution of the reference system and of a [t.sup.3] part bearing the signature of the Lyapunov exponents of both the reduced and the reference models. The approach is illustrated on two classes of systems involving, successively, multiple time and space scales. A comparison between the purely deterministic analysis and the one in which the model system is augmented by error sources assimilated to Gaussian random noises is carried out. It is shown that such a representation leads to a deterioration of the predictive skill of the model as far as mean values are concerned, but may enhance its variability properties, bringing them closer to the variability of the reference system.

A systematic formulation of model error is developed accounting for both its dynamical and probabilistic aspects. Some generic features, largely independent of the particular model under consideration, are brought out in connection with power-law behavior in the short time regime. The lifetime of this regime is shown to be related to the spectrum of the Lyapunov exponents and the decay characteristics of the time correlation functions involved. The results are illustrated and tested on representative low-order models of atmospheric dynamics exhibiting oscillations, bistability, and chaotic behavior.

A dynamical approach to atmospheric analogs extending the statistical formulation by Toth and Van den Dool is developed. Explicit analytical formulas for the probability and the mean recurrence time of analogs displaying the system's intrinsic time scales are provided for both discrete and continuous time dynamical systems and are evaluated numerically on a representative model. The analysis reveals strong dependence of recurrence times of analogs on the local properties of the attractor and a pronounced variability around their mean. Finally, the formulation is extended to stochastically forced systems such as a red noise atmosphere.

The authors report a systematic study on the short and intermediate time predictability properties of a quasigeostrophic T21L3 model in which emphasis is placed on the role of the Lyapunov vectors in the growth patterns of generic initial error fields. It is found that under scale-independent small-amplitude initial perturbations the evolution of the mean error is intimately related to the spectral distribution of the Lyapunov vectors. In the case of perturbations at a particular scale of motion the picture turns out to be more involved, particularly as far as mean error growth over all wavenumbers is concerned, and must appeal to coupling mechanisms between different scales. The role of the norm used for the measure of the mean error growth and the specific predictability properties at different vertical levels of the model are also analyzed.

Traditionally, climate is defined by the properties of the averages of the meteorological fields over an appropriate time interval. In this paper the properties of the time-averaged observables of a red noise atmosphere and of a simplified model of thermal convection are investigated both analytically and numerically and are compared to those of the original finescale variables. It is shown that averaging tends to reduce the domain of variability and the attractor dimension favors persistence of initial correlations and enhances predictability. The implications of these findings in the real-world atmosphere are briefly assessed.

Spatial distribution of stations in a global observational network is examined for the dynamics displayed by the atmospheric fields. Presence of an optimal distribution that can elicit the intricacy of this dynamics, with a negligible specified error, is analyzed. This observational error is examined for the influence of deviations of the network distribution from homogeneity. Non-homogeneous distribution might produce a more realistic record than a homogeneous distribution for scantily distributed stations such as those of the contemporary network.

The early stages of self-assembly of the elementary building blocks of nanophase materials are studied. The relative roles of entropic and energetic factors in determining the relative abundance of the final products present is analyzed using both a kinetic mean field model and a mesoscopic approach in which self-assembly is viewed as an encounter-controlled process on a discrete lattice. The relevance of the results in zeolite synthesis in connection with the ordered liquid phases recently discovered in these materials is discussed. [ABSTRACT FROM AUTHOR]

Evaluates thermodynamic entropy production in different parts of the attractor of two representative reactive models giving rise to periodic and chaotic behavior. Variability patterns observed as the system runs over the attractor; Comparison with the variability of indicators of the intrinsic complexity of the dynamics such as the local Lyapunov exponents.

The formalism of irreversible thermodynamics is applied to the shallow water model. Entropy production and entropy flow terms are identified, describing the ways dissipation and exchange processes unfold in space and time. Explicit evaluations are carried out in the case of Lorenz's nine-mode truncation and in the quasigeostrophic limit of the model. A number of systematic trends are identified by studying the way dissipation and kinetic energy vary as the forcing is increased and the system undergoes qualitative changes of behavior between different regimes, from simple symmetric flow to intermittent chaos. The constraints imposed by thermodynamics on the structure of the model equations and, especially, on the parameterization schemes are brought out.