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

Abstract

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.

Aircraft measurements of gravity waves in the upper troposphere and lower stratosphere during the START08 field experiment

“…The common characteristics and individual features of the wave variances and spectrum slope behaviors appear to be generally consistent with past studies on the spectral analysis of aircraft measurements, including Nastrom and Gage (1985) using the Global Atmospheric Sampling Program (GASP) flight data set, and Lindborg (1999) using the Measurement of Ozone and Water Vapor by Airbus In-Service Aircraft (MOZAIC) aircraft observations. In addition, our recent separate study of idealized moist baroclinic waves (Sun and Zhang, 2015) suggests that the presence of moist convection and mesoscale gravity waves, though probably non-isotropic, does appear to steer the mesoscale range of the spectral slope to be −5/3. (2) The vertical velocity component appears to be flat approximately within the range between ∼ 8 and ∼ 256 km.…”

“…Interestingly, the M1 segment immediately prior to the M2 segment did not record the event, probably due to the fast changing background flow. Spectral behaviors of atmospheric variables have also been studied by highresolution non-hydrostatic mesoscale numerical weather prediction (NWP) models (e.g., Skamarock, 2004;Tan et al, 2004;Waite and Snyder, 2013;Bei and Zhang, 2014).…”

“…This will help to distinguish whether the sampled mesoscale and small-scale variances are gravity waves or artifacts of the observing system. In addition, under the idealized controllable atmosphere with varying degrees of convective instability and baroclinic instability (e.g., Zhang, 2004;Wang and Zhang, 2007;Wei and Zhang, 2014;Sun and Zhang, 2015), high-resolution simulations of baroclinic jet-front systems will be employed to understand (1) how to constrain the parameterizations of jet-front gravity waves in general circulation models, (2) the role of gravity waves in mesoscale predictability, and (3) the contribution of gravity waves to mesoscale energy spectra in global wavenumber distribution or in multi-dimensional wavenumber distribution.…”

Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain

“…This relatively high resolution resolves most fine-scale terrain and, combined with non-hydrostatic dynamics, allows for the explicit representation of some mesoscale phenomena, including deep moist convection and part of the spectrum of thermally driven breezes. However, the lack of mesoscale detail in the initial conditions of the forecasts, the fast growth of forecast errors at small spatial scales [229,230], and the rapid downscale propagation of small initial errors at the large scales [231] imply that high-resolution predictions are not necessarily more skillful than low-resolution ones. In addition, parameterization schemes that are appropriate at coarse resolutions may be inadequate for km-scale or sub-km-scale simulations, in particular for ABL mixing [232].…”

On the Predictability and Error Sources of Tropical Cyclone Intensity Forecasts

“…In attempting to improve any type of numerical weather forecast, it is useful to be aware of fundamental and practical predictability limits imposed by the inherent chaotic nature of atmospheric behavior (Lorenz 1969;Zhang et al 2007;Rotunno and Snyder 2008;Palmer et al 2014) coupled with limitations on our ability to accurately observe our environment (Sun and Zhang 2016). One may reasonably expect models and data assimilation techniques to improve continuously over time, while the hope that observations will also improve must be tempered by finite economic and technological resources.…”