A View for Atmospheric Unpredictability

Based on Chaotic Dynamics, this paper illustrated the necessity of research and the objective existence of atmospheric unpredictability. Actually, inaccurate forecast happens all the time in both operational weather forecasting and climate prediction in which atmospheric unpredictability hides. By means of Discrete Mathematics, this paper also defined the Degree of Hesitation and the Predictable Days with which to discuss and compare the relationship between the predictability and unpredictability of several different forecast objects. In addition, this paper discussed the approaches of evaluating the atmospheric predictability and unpredictability, emphatically showed the Experience Assessment Method. At the last, this paper also proved the existence of atmospheric unpredictability by an example.

A New Theoretical Framework for Understanding Multiscale Atmospheric Predictability

Here we present a new theoretical framework that connects the error growth behavior in numerical weather prediction (NWP) with the atmospheric kinetic energy spectrum. Building on previous studies, our newly proposed framework applies to the canonical observed atmospheric spectrum that has a −3 slope at synoptic scales and a −5/3 slope at smaller scales. Based on this realistic hybrid energy spectrum, our new experiment using hybrid numerical models provides reasonable estimations for the finite predictable ranges at different scales. We further derive an analytical equation that helps understand the error growth behavior. Despite its simplicity, this new analytical error growth equation is capable of capturing the results of previous comprehensive theoretical and observational studies of atmospheric predictability. The success of this new theoretical framework highlights the combined effects of quasi-two-dimensional dynamics at synoptic scales (−3 slope) and three-dimensional turbulence-like small-scale chaotic flows (−5/3 slope) in dictating the error growth. It is proposed that this new framework could serve as a guide for understanding and estimating the predictability limit in the real world.

Atmospheric Predictability of the Tropics, Middle Latitudes, and Polar Regions Explored through Global Storm-Resolving Simulations

The predictability of the atmosphere has important implications for weather prediction, because it determines what forecast problems are potentially tractable. Even though our general understanding of error growth and predictability has been increasing, relatively little is known about the detailed structure of atmospheric predictability, such as how it varies between climate regions. The present study addresses this issue by exploring error growth and predictability in three latitude zones, using model output from a previous global storm-resolving predictability experiment by Judt published in 2018. It was determined that the tropics have longer predictability than the middle latitudes and polar regions (tropics, >20 days; middle latitudes and polar regions, a little over 2 weeks). Each latitude zone had distinct error growth characteristics, and error growth was broadly consistent with the underlying dynamics of each zone. Evidence suggests that equatorial waves play a role in the comparatively long predictability of the tropics; specifically, equatorial waves seem to be less prone to error growth than middle-latitude baroclinic disturbances. Even though the generality of the findings needs to be assessed in future studies, the overall conclusions agree with previous work in that current numerical weather prediction procedures have not reached the limits of atmospheric predictability, especially in the tropics. One way to exploit tropical predictability is to reduce model error, for example, by using global storm-resolving models instead of conventional models that parameterize convection.

Insights into Atmospheric Predictability through Global Convection-Permitting Model Simulations

Global convection-permitting models enable weather prediction from local to planetary scales and are therefore often expected to transform the weather prediction enterprise. This potential, however, depends on the predictability of the atmosphere, which was explored here through identical twin experiments using the Model for Prediction Across Scales. The simulations were produced on a quasi-uniform 4-km mesh, which allowed the illumination of error growth from convective to global scales. During the first two days, errors grew through moist convection and other mesoscale processes, and the character of the error growth resembled the case of [Formula: see text] turbulence. Between 2 and 13 days, errors grew with the background baroclinic instability, and the character of the error growth mirrored the case of [Formula: see text] turbulence. The existence of an error growth regime with properties similar to [Formula: see text] turbulence confirmed the radical idea of E. N. Lorenz that the atmosphere has a finite limit of predictability, no matter how small the initial error. The global-mean predictability limit of the troposphere was estimated here to be around 2–3 weeks, which is in agreement with previous work. However, scale-dependent predictability limits differed between the divergent and rotational wind component and between vertical levels, indicating that atmospheric predictability is a more complex problem than that of homogeneous, isotropic turbulence. The practical value of global cloud-resolving models is discussed in light of the various aspects of atmospheric predictability.

Intrinsic versus Practical Limits of Atmospheric Predictability and the Significance of the Butterfly Effect

Limits of intrinsic versus practical predictability are studied through examining multiscale error growth dynamics in idealized baroclinic waves with varying degrees of convective instabilities. In the dry experiment free of moist convection, error growth is controlled primarily by baroclinic instability under which forecast accuracy is inversely proportional to the amplitude of the baroclinically unstable initial-condition error (thus the prediction can be continuously improved without limit through reducing the initial error). Under the moist environment with strong convective instability, rapid upscale growth from moist convection leads to the forecast error being increasingly less sensitive to the scale and amplitude of the initial perturbations when the initial-error amplitude is getting smaller; these diminishing returns may ultimately impose a finite-time barrier to the forecast accuracy (limit of intrinsic predictability and the so-called “butterfly effect”). However, if the initial perturbation is sufficiently large in scale and amplitude (as for most current-day operational models), the baroclinic growth of large-scale finite-amplitude initial error will control the forecast accuracy for both dry and moist baroclinic waves; forecast accuracy can be improved (thus the limit of practical predictability can be extended) through the reduction of initial-condition errors, especially those at larger scales. Regardless of the initial-perturbation scales and amplitude, the error spectrum will adjust toward the slope of the background flow. Inclusion of strong moist convection changes the mesoscale kinetic energy spectrum slope from −3 to ~−5/3. This change further highlights the importance of convection and the relevance of the butterfly effect to both the intrinsic and practical limits of atmospheric predictability, especially at meso- and convective scales.