A kinetic energy backscatter algorithm for use in ensemble prediction systems

Physical justification is provided for the use of kinetic energy backscatter in forecast models, particularly in respect of ensemble prediction systems. The rate of energy backscatter to scales near the truncation limit is controlled by a total energy dissipation function involving contributions from numerical diffusion, mountain drag and deep convection. A cellular automaton is used to generate evolving patterns that, together with the dissipation function, define a stream‐function forcing field. Each member of the European Centre for Medium‐Range Weather Forecasts (ECMWF) ensemble forecast system is perturbed by a different realization of this backscatter forcing, and the resulting increase in ensemble spread, if not excessive, has a beneficial impact on probabilistic measures of forecast skill. The input of small‐scale kinetic energy by the backscatter algorithm also helps to correct a known problem with the energy spectrum in the ECMWF model—the absence of the observed −5/3 spectral slope in the mesoscales. Copyright © 2005 Royal Meteorological Society.

[1]  Ragnar Fjørtoft,et al.  On the Changes in the Spectral Distribution of Kinetic Energy for Twodimensional, Nondivergent Flow , 1953 .

[2]  P. Kennedy,et al.  The Energy Budget in a Clear Air Turbulence Zone as Observed by Aircraft , 1975 .

[3]  B. Hoskins,et al.  The Life Cycles of Some Nonlinear Baroclinic Waves , 1978 .

[4]  M. Macvean.  The effects of horizontal diffusion on baroclinic development in a spectral model , 1983 .

[5]  Douglas K. Lilly,et al.  Stratified Turbulence and the Mesoscale Variability of the Atmosphere , 1983 .

[6]  M. Cullen,et al.  An Extended Lagrangian Theory of Semi-Geostrophic Frontogenesis , 1984 .

[7]  G. D. Nastrom,et al.  A Climatology of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft , 1985 .

[8]  Steven A. Orszag,et al.  Analytical theories of turbulence and the ε expansion , 1987 .

[9]  Harold Ritchie,et al.  Application of the Semi-Lagrangian Method to a Spectral Model of the Shallow Water Equations , 1988 .

[10]  Jean Côté,et al.  A Two-Time-Level Semi-Lagrangian Semi-implicit Scheme for Spectral Models , 1988 .

[11]  A Quantitative Analysis of the Dissipation Inherent in Semi-Lagrangian Advection , 1988 .

[12]  M. Tiedtke.  A Comprehensive Mass Flux Scheme for Cumulus Parameterization in Large-Scale Models , 1989 .

[13]  A Semigeostrophic Eady-Wave Frontal Model Incorporating Momentum Diffusion. Part II: Kinetic Energy and Enstrophy Dissipation , 1990 .

[14]  D. Thomson,et al.  Stochastic backscatter in large-eddy simulations of boundary layers , 1992, Journal of Fluid Mechanics.

[15]  D. Stephenson.  The northern hemisphere tropospheric response to changes in the gravity-wave drag scheme in a perpetual January GCM , 1994 .

[16]  G. Shutts,et al.  A numerical modelling study of the geostrophic adjustment process following deep convection , 1994 .

[17]  David B. Stephenson,et al.  The impact of changing the horizontal diffusion scheme on the northern winter climatology of a general circulation model , 1995 .

[18]  G. Vallis,et al.  Balanced mesoscale motion and stratified turbulence forced by convection , 1997 .

[19]  Jorgen S. Frederiksen,et al.  Eddy Viscosity and Stochastic Backscatter Parameterizations on the Sphere for Atmospheric Circulation Models , 1997 .

[20]  Johnny Wei-Bing Lin,et al.  Influence of a stochastic moist convective parameterization on tropical climate variability , 2000 .

[21]  K. Tung,et al.  The k−3 and k−5/3 Energy Spectrum of Atmospheric Turbulence: Quasigeostrophic Two-Level Model Simulation , 2001 .

[22]  K. Browning,et al.  Measurements of dissipation rate in frontal zones , 2001 .

[23]  Johnny Wei-Bing Lin,et al.  Considerations for Stochastic Convective Parameterization , 2002 .

[24]  Nonlinear interactions of fast and slow modes in rotating, stratified fluid flows , 2003 .

[25]  in Geophysics , 2022 .

[26]  T. Palmer,et al.  Stochastic representation of model uncertainties in the ECMWF ensemble prediction system , 2007 .