By revealing two kinds of attractor coexistence within Lorenz models, we suggest that the entirety of weather possesses a dual nature of chaos and order with distinct predictability. Over 50 years since Lorenz’s 1963 study and a follow-up presentation in 1972, the statement ``weather is chaotic’’ has been well accepted. Such a view turns our attention from regularity associated with Laplace’s view of determinism to irregularity associated with chaos. In contrast to single type chaotic solutions, recent studies using a generalized Lorenz model (GLM) have focused on the coexistence of chaotic and regular solutions that appear within the same model using the same modeling configurations but different initial conditions. The results, with attractor coexistence, suggest that the entirety of weather possesses a dual nature of chaos and order with distinct predictability. In this study, based on the GLM, we illustrate the following two mechanisms that may enable or modulate two kinds of attractor coexistence and, thus, contribute to distinct predictability: (1) the aggregated negative feedback of small-scale convective processes that can produce stable non-trivial equilibrium points and, thus, enable the appearance of stable steady-state solutions and their coexistence with chaotic or nonlinear oscillatory solutions, referred to as the 1^st and 2^nd kinds of attractor coexistence; and (2) the modulation of large-scale time varying forcing (heating) that can determine (or modulate) the alternative appearance of two kinds of attractor coexistence. Based on our results, we then discuss new opportunities and challenges in predictability research with the aim of improving predictions at extended-range time scales, as well as sub-seasonal to seasonal time scales.

In this study, based on the number of modes, the original three-dimensional Lorenz model (3DLM) is generalized with two additional modes [five-dimensional Lorenz model (5DLM)] to examine their role in the predictability of the numerical solutions and to understand the underlying processes that increase the solution stability. As a result of the simplicity of the 5DLM with respect to existing generalized Lorenz models (LMs), the author is able to obtain the analytical solutions of its critical points and identify the role of the major nonlinear term in the solution’s stability, which have previously not been documented in the literature. The nonlinear Jacobian terms of the governing equations are analyzed to highlight the importance of selecting new modes for extending the nonlinear feedback loop of the 3DLM and thus effectively increasing the degree of nonlinearity (i.e., the nonlinear mode–mode interactions) in the 5DLM. It is then shown that numerical solutions in the 5DLM require a larger normalized Rayleigh number r for the onset of chaos and are more predictable than those in the 3DLM when r is between 25 and 40 and the Prandtl number σ is 10. The improved predictability is attributable to the negative nonlinear feedback enabled by the new modes. The role of the (negative) nonlinear feedback is further verified using a revised 3DLM with a parameterized nonlinear eddy dissipative term. The finding of the increased stability in the 5DLM and revised 3DLM with respect to the 3DLM is confirmed with the linear stability analysis and the analysis of the Lyapunov exponents using different values of r and σ. To further understand the impact of an additional heating term, results from the 5DLM and a higher-dimensional LM [e.g., the six-dimensional LM (6DLM)] are analyzed and compared.

To assess the fidelity of general circulation models (GCMs) in simulating cloud liquid water, liquid water path (LWP) retrievals from several satellites with passive sensors and the vertically‐resolved liquid water content (LWC) from the CloudSat are used. Comparisons are made with ECMWF and MERRA analyses, GCM simulations utilized in the IPCC 4th Assessment, and three GCM simulations. There is considerable disagreement amongst the LWP estimates and amongst the modeled values. The LWP from GCMs are much larger than the observed estimates and the two analyses. The largest values in the CloudSat LWP occur over the boundary‐layer stratocumulus regions; this feature is not as evident in the analyses or models. Better agreement is found between the two analyses and CloudSat LWP when cases with surface precipitation are excluded. The upward vertical extent of LWC from the GCMs and analyses is greater than CloudSat estimates. The issues of representing LWC and precipitation consistently between satellite‐derived and model values are discussed.

A high‐resolution finite volume general circulation model (fvGCM), resulting from a development effort of more than ten years, is now being run operationally at the NASA Goddard Space Flight Center and Ames Research Center. The model is based on a finite volume dynamical core with terrain‐following Lagrangian control volume discretization and performs efficiently on massive parallel architectures. The computational efficiency allows simulations at a resolution of a quarter of a degree, which is double the resolution currently adopted by most global models in operational weather centers. Such fine global resolution brings us closer to overcoming a fundamental barrier in global atmospheric modeling for both weather and climate, because tropical cyclones can be more realistically represented. In this work, preliminary results are shown. Fifteen simulations of four Atlantic tropical cyclones in 2002 and 2004, chosen because of varied difficulties presented to numerical weather forecasting, are performed. The fvGCM produces very good forecasts of these tropical systems, adequately resolving problems like erratic track, abrupt recurvature, intense extratropical transition, multiple landfall and reintensification, and interaction among vortices.

In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the streamfunction is referred to as a secondary streamfunction mode, while the two additional modes, which appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc) is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74), but slightly smaller than the one in the 5DLM (rc ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): "If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado." The implications of this and previous work, as well as future work, are also discussed.