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

2016 ◽  
Vol 73 (3) ◽  
pp. 1419-1438 ◽  
Author(s):  
Y. Qiang Sun ◽  
Fuqing Zhang
Keyword(s):  
Large Scale ◽  
Initial Perturbation ◽  
Forecast Accuracy ◽  
Initial Condition ◽  
Moist Convection ◽  
Error Growth ◽  
Initial Error ◽  
Baroclinic Waves ◽  
Atmospheric Predictability ◽  
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.

scholarly journals Mesoscale Predictability of Moist Baroclinic Waves: Convection-Permitting Experiments and Multistage Error Growth Dynamics

2007 ◽  
Vol 64 (10) ◽  
pp. 3579-3594 ◽  
Author(s):  
Fuqing Zhang ◽  
Naifang Bei ◽  
Richard Rotunno ◽  
Chris Snyder ◽  
Craig C. Epifanio
Keyword(s):  
Large Scale ◽  
Random Noise ◽  
Baroclinic Instability ◽  
Growth Dynamics ◽  
Small Scale ◽  
Moist Convection ◽  
Error Growth ◽  
Baroclinic Waves ◽  
Convective Scale ◽  
Shear Production

Abstract A recent study examined the predictability of an idealized baroclinic wave amplifying in a conditionally unstable atmosphere through numerical simulations with parameterized moist convection. It was demonstrated that with the effect of moisture included, the error starting from small random noise is characterized by upscale growth in the short-term (0–36 h) forecast of a growing synoptic-scale disturbance. The current study seeks to explore further the mesoscale error-growth dynamics in idealized moist baroclinic waves through convection-permitting experiments with model grid increments down to 3.3 km. These experiments suggest the following three-stage error-growth model: in the initial stage, the errors grow from small-scale convective instability and then quickly [O(1 h)] saturate at the convective scales. In the second stage, the character of the errors changes from that of convective-scale unbalanced motions to one more closely related to large-scale balanced motions. That is, some of the error from convective scales is retained in the balanced motions, while the rest is radiated away in the form of gravity waves. In the final stage, the large-scale (balanced) components of the errors grow with the background baroclinic instability. Through examination of the error-energy budget, it is found that buoyancy production due mostly to moist convection is comparable to shear production (nonlinear velocity advection). It is found that turning off latent heating not only dramatically decreases buoyancy production, but also reduces shear production to less than 20% of its original amplitude.

Atmospheric Predictability: Why Butterflies Are Not of Practical Importance

2014 ◽  
Vol 71 (7) ◽  
pp. 2476-2488 ◽  
Author(s):  
Dale R. Durran ◽  
Mark Gingrich
Keyword(s):  
Kinetic Energy ◽  
Turbulence Model ◽  
Large Scale ◽  
Mesoscale Model ◽  
Practical Importance ◽  
Absolute Magnitude ◽  
Error Growth ◽  
Initial Error ◽  
Initial Errors ◽  
Relative Errors

Abstract The spectral turbulence model of Lorenz, as modified for surface quasigeostrophic dynamics by Rotunno and Snyder, is further modified to more smoothly approach nonlinear saturation. This model is used to investigate error growth starting from different distributions of the initial error. Consistent with an often overlooked finding by Lorenz, the loss of predictability generated by initial errors of small but fixed absolute magnitude is essentially independent of their spatial scale when the background saturation kinetic energy spectrum is proportional to the −5/3 power of the wavenumber. Thus, because the background kinetic energy increases with scale, very small relative errors at long wavelengths have similar impacts on perturbation error growth as large relative errors at short wavelengths. To the extent that this model applies to practical meteorological forecasts, the influence of initial perturbations generated by butterflies would be swamped by unavoidable tiny relative errors in the large scales. The rough applicability of the authors’ modified spectral turbulence model to the atmosphere over scales ranging between 10 and 1000 km is supported by the good estimate that it provides for the ensemble error growth in state-of-the-art ensemble mesoscale model simulations of two winter storms. The initial-error spectrum for the ensemble perturbations in these cases has maximum power at the longest wavelengths. The dominance of large-scale errors in the ensemble suggests that mesoscale weather forecasts may often be limited by errors arising from the large scales instead of being produced solely through an upscale cascade from the smallest scales.

scholarly journals Understanding the Predictability within Convection-Allowing Ensemble Forecasts in East China: Meteorological Sensitivity, Forecast Error Growth and Associated Precipitation Uncertainties Across Spatial Scales

Atmosphere ◽  
2020 ◽  
Vol 11 (3) ◽  
pp. 234 ◽  
Author(s):  
Xiaoran Zhuang ◽  
Naigeng Wu ◽  
Jinzhong Min ◽  
Yuan Xu
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Forecast Error ◽  
Strong Relationship ◽  
Ensemble Forecast ◽  
Observation System ◽  
Dabie Mountains ◽  
Moist Convection ◽  
Error Growth ◽  
Error Energy

This study investigates the practical predictability of two simulated mesoscale convective systems (MCS1 and MCS2) within a state-of-the-art convection-allowing ensemble forecast system. The two MCSs are both controlled by the synoptic Meiyu-front but differ in mesoscale orographic forcing. An observation system simulation experiment (OSSE) setup is first built, which includes flow-dependent multiple-scale initial and lateral boundary perturbations and a 12 h 30-member ensemble forecast is thereby created. In combination with the difference total energy, the decorrelation scale and the ensemble sensitivity analysis, both forecast error evolution, precipitation uncertainties and meteorological sensitivity that describe the practical predictability are assessed. The results show large variabilities of precipitation forecasts among ensemble members, indicative of the practical predictability limit. The study of forecast error evolution shows that the error energy in the MCS1 region in which the convection is blocked by the Dabie Mountains exhibits a simultaneous peak pattern for all spatial scales at around 6 h due to strong moist convection. On the other hand, when large-scale flow plays a more important role, the forecast error energy in the MCS2 region exhibits a stepwise increase with increasing spatial scale. As a result of error energy growth, the precipitation uncertainties evolve from small scales and gradually transfer to larger scales, implying a strong relationship between error growth and precipitation across spatial scales, thus explaining the great precipitation variability within ensemble members. These results suggest the additional forcing brought by the Dabie Mountains could regulate the predictability of Meiyu-frontal convection, which calls for a targeted perturbation design in convection-allowing ensemble forecast systems with respect to different forcing mechanisms.

Dynamics and Structure of Mesoscale Error Covariance of a Winter Cyclone Estimated through Short-Range Ensemble Forecasts

2005 ◽  
Vol 133 (10) ◽  
pp. 2876-2893 ◽  
Author(s):  
Fuqing Zhang
Keyword(s):  
Short Range ◽  
Large Scale ◽  
Small Scale ◽  
Horizontal Distance ◽  
Moist Convection ◽  
Error Growth ◽  
State Variables ◽  
Ensemble Forecasts ◽  
Error Covariance ◽  
Cross Covariance

Abstract Several sets of short-range mesoscale ensemble forecasts generated with different types of initial perturbations are used in this study to investigate the dynamics and structure of mesoscale error covariance in an intensive extratropical cyclogenesis event that occurred on 24–25 January 2000. Consistent with past predictability studies of this event, it is demonstrated that the characteristics and structure of the error growth are determined by the underlying balanced dynamics and the attendant moist convection. The initially uncorrelated errors can grow from small-scale, largely unbalanced perturbations to large-scale, quasi-balanced structured disturbances within 12–24 h. Maximum error growth occurred in the vicinity of upper-level and surface zones with the strongest potential vorticity (PV) gradient over the area of active moist convection. The structure of mesoscale error covariance estimated from these short-term ensemble forecasts is subsequently flow dependent and highly anisotropic, which is also ultimately determined by the underlying governing dynamics and associated error growth. Significant spatial and cross covariance (correlation) exists between different state variables with a horizontal distance as large as 1000 km and across all vertical layers. Qualitatively similar error covariance structure is estimated from different ensemble forecasts initialized with different perturbations.

scholarly journals Insights into Atmospheric Predictability through Global Convection-Permitting Model Simulations

2018 ◽  
Vol 75 (5) ◽  
pp. 1477-1497 ◽  
Author(s):  
Falko Judt
Keyword(s):  
Isotropic Turbulence ◽  
Weather Prediction ◽  
Baroclinic Instability ◽  
Complex Problem ◽  
Finite Limit ◽  
Wind Component ◽  
Moist Convection ◽  
Error Growth ◽  
Growth Regime ◽  
Atmospheric Predictability

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.

scholarly journals Rethinking convective quasi-equilibrium: observational constraints for stochastic convective schemes in climate models

2008 ◽  
Vol 366 (1875) ◽  
pp. 2579-2602 ◽  
Author(s):  
J. David Neelin ◽  
Ole Peters ◽  
Johnny W.-B Lin ◽  
Katrina Hales ◽  
Christopher E Holloway
Keyword(s):  
Water Vapour ◽  
Large Scale ◽  
Climate Models ◽  
Sensitivity Study ◽  
Continuous Phase ◽  
Quasi Equilibrium ◽  
Moist Convection ◽  
Spatial Averaging ◽  
Substantial Impact ◽  
Long Range Correlations

Convective quasi-equilibrium (QE) has for several decades stood as a key postulate for parametrization of the impacts of moist convection at small scales upon the large-scale flow. Departures from QE have motivated stochastic convective parametrization, which in its early stages may be viewed as a sensitivity study. Introducing plausible stochastic terms to modify the existing convective parametrizations can have substantial impact, but, as for so many aspects of convective parametrization, the results are sensitive to details of the assumed processes. We present observational results aimed at helping to constrain convection schemes, with implications for each of conventional, stochastic or ‘superparametrization’ schemes. The original vision of QE due to Arakawa fares well as a leading approximation, but with a number of updates. Some, like the imperfect connection between the boundary layer and the free troposphere, and the importance of free-tropospheric moisture to buoyancy, are quantitatively important but lie within the framework of ensemble-average convection slaved to the large scale. Observations of critical phenomena associated with a continuous phase transition for precipitation as a function of water vapour and temperature suggest a more substantial revision. While the system's attraction to the critical point is predicted by QE, several fundamental properties of the transition, including high precipitation variance in the critical region, need to be added to the theory. Long-range correlations imply that this variance does not reduce quickly under spatial averaging; scaling associated with this spatial averaging has potential implications for superparametrization. Long tails of the distribution of water vapour create relatively frequent excursions above criticality with associated strong precipitation events.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

scholarly journals Forecasting of solar irradiance and ramp events with all-sky imagers

2021 ◽  
Author(s):  
Stavros-Andreas Logothetis ◽  
Vasileios Salamalikis ◽  
Stefan Wilbert ◽  
Jan Remund ◽  
Luis Zarzalejo ◽  
...  
Keyword(s):  
Solar Irradiance ◽  
Large Scale ◽  
Forecast Error ◽  
Forecast Accuracy ◽  
Short Term ◽  
Event Prediction ◽  
High Penetration ◽  
Spanish Research ◽  
Short Term Forecasting ◽  
Solar Resource

<p>Cloud cameras (all sky imagers/ASIs) can be used for short-term (next 20 min) forecasts of solar irradiance. For this reason, several experimental and operational solutions emerged in the last decade with different approaches in terms of instrument types and forecast algorithms. Moreover, few commercial and semi-prototype systems are already available or being investigated. So far, the uncertainty of the predictions cannot be fully compared, as previously published tests were carried out during different periods and at different locations. In this study, the results from a benchmark exercise are presented in order to qualify the current ASI-based short-term forecasting solutions and examine their accuracy. This first comparative measurement campaign carried out as part of the IEA PVPS Task 16 (https://iea-pvps.org/research-tasks/solar-resource-for-high-penetration-and-large-scale-applications/). A 3-month observation campaign (from August to December 2019) took place at Plataforma Solar de Almeria of the Spanish research center CIEMAT including five different ASI systems and a network of high-quality measurements of solar irradiance and other atmospheric parameters. Forecasted time-series of global horizontal irradiance are compared with ground-based measurements and two persistence models to identify strengths and weaknesses of each approach and define best practices of ASI-based forecasts. The statistical analysis is divided into seven cloud classes to interpret the different cloud type effect on ASIs forecast accuracy. For every cloud cluster, at least three ASIs outperform persistence models, in terms of forecast error, highlighting their performance capabilities. The feasibility of ASIs on ramp event detection is also investigated, applying different approaches of ramp event prediction. The revealed findings are promising in terms of overall performance of ASIs as well as their forecasting capabilities in ramp detection.  </p>

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