Stochastic Nature of Physical Parameterizations in Ensemble Prediction: A Stochastic Convection Approach

Abstract In this paper it is argued that ensemble prediction systems can be devised in such a way that physical parameterizations of subgrid-scale motions are utilized in a stochastic manner, rather than in a deterministic way as is typically done. This can be achieved within the context of current physical parameterization schemes in weather and climate prediction models. Parameterizations are typically used to predict the evolution of grid-mean quantities because of unresolved subgrid-scale processes. However, parameterizations can also provide estimates of higher moments that could be used to constrain the random determination of the future state of a certain variable. The general equations used to estimate the variance of a generic variable are briefly discussed, and a simplified algorithm for a stochastic moist convection parameterization is proposed as a preliminary attempt. Results from the implementation of this stochastic convection scheme in the Navy Operational Global Atmospheric Prediction Sys...

[1]  R. Smith.  A scheme for predicting layer clouds and their water content in a general circulation model , 1990 .

[2]  D. Randall,et al.  Evaluation of Statistically Based Cloudiness Parameterizations Used in Climate Models , 1996 .

[3]  Vincent E. Larson,et al.  Supplying Local Microphysics Parameterizations with Information about Subgrid Variability: Latin Hypercube Sampling , 2005 .

[4]  J. Neelin,et al.  Toward stochastic deep convective parameterization in general circulation models , 2003 .

[5]  T. Hogan,et al.  The Description of the Navy Operational Global Atmospheric Prediction System's Spectral Forecast Model , 1991 .

[6]  D. Baumhefner,et al.  Predictability Experiments Using a High-Resolution Limited-Area Model , 1987 .

[7]  George L. Mellor,et al.  The Gaussian Cloud Model Relations , 1977 .

[8]  Timothy F. Hogan,et al.  Boundary layer clouds in a Global Atmospheric model: Simple cloud cover parameterizations , 2002 .

[9]  Roger Davies,et al.  A fast radiation parameterization for atmospheric circulation models , 1987 .

[10]  Peter Bechtold,et al.  A Simple Cloud Parameterization Derived from Cloud Resolving Model Data: Diagnostic and Prognostic Applications , 2002 .

[11]  Roberto Buizza,et al.  Impact of Ensemble Size on Ensemble Prediction , 1998 .

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

[13]  T. Palmer.  A nonlinear dynamical perspective on model error: A proposal for non‐local stochastic‐dynamic parametrization in weather and climate prediction models , 2001 .

[14]  Eugenia Kalnay,et al.  Ensemble Forecasting at NMC: The Generation of Perturbations , 1993 .

[15]  P. D. Thompson,et al.  Uncertainty of Initial State as a Factor in the Predictability of Large Scale Atmospheric Flow Patterns , 1957 .

[16]  J. Garratt.  The Atmospheric Boundary Layer , 1992 .

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

[18]  P. Bechtold,et al.  A Simple Parameterization of Cloud Water Related Variables for Use in Boundary Layer Models , 1995 .

[19]  Vincent E. Larson,et al.  A PDF-Based Model for Boundary Layer Clouds. Part I: Method and Model Description , 2002 .

[20]  David A. Randall,et al.  High-Resolution Simulation of Shallow-to-Deep Convection Transition over Land , 2006 .

[21]  Z. Toth,et al.  Short-Term Dynamics of Model Errors , 2002 .

[22]  C. Leith.  Theoretical Skill of Monte Carlo Forecasts , 1974 .

[23]  J. Deardorff,et al.  Subgrid-Scale Condensation in Models of Nonprecipitating Clouds , 1977 .

[24]  Kerry Emanuel,et al.  Development and Evaluation of a Convection Scheme for Use in Climate Models , 1999 .

[25]  C. Nicolis,et al.  Dynamics of Model Error: Some Generic Features , 2003 .

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

[27]  Kevin Judd,et al.  Time Step Sensitivity of Nonlinear Atmospheric Models: Numerical Convergence, Truncation Error Growth, and Ensemble Design , 2007 .

[28]  T. Rosmond.  A Technical Description of the NRL Adjoint Modeling System , 1997 .

[29]  A. P. Siebesma.  An Advection-Diffusion scheme for the convective boundary layer: description and 1d-results , 2000 .

[30]  P. L. Houtekamer,et al.  A System Simulation Approach to Ensemble Prediction , 1996 .

[31]  Warren J. Wiscombe,et al.  An algorithm for generating stochastic cloud fields from radar profile statistics , 2004 .

[32]  I. Troen,et al.  A simple model of the atmospheric boundary layer; sensitivity to surface evaporation , 1986 .

[33]  J. Sprott,et al.  Chaos and Predictability , 2005 .

[34]  Roger Daley,et al.  NAVDAS: Formulation and Diagnostics , 2001 .

[35]  João Paulo Teixeira,et al.  An eddy‐diffusivity/mass‐flux parametrization for dry and shallow cumulus convection , 2004 .

[36]  Eugenia Kalnay,et al.  Atmospheric Modeling, Data Assimilation and Predictability , 2002 .

[37]  R. Hodur.  The Naval Research Laboratory’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS) , 1997 .

[38]  Andrew J Majda,et al.  Stochastic and mesoscopic models for tropical convection , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[39]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[40]  T. N. Palmer,et al.  Predictability of the Atmosphere and Oceans: From Days to Decades , 1996 .

[41]  David A. Randall,et al.  Similarity of deep continental cumulus convection as revealed by a three-dimensional cloud-resolving model , 2002 .

[42]  Melinda S. Peng,et al.  Recent Modifications of the Emanuel Convective Scheme in the Navy Operational Global Atmospheric Prediction System , 2004 .

[43]  A. P. Siebesma,et al.  A Large Eddy Simulation Intercomparison Study of Shallow Cumulus Convection , 2003 .

[44]  A. Tompkins.  A Prognostic Parameterization for the Subgrid-Scale Variability of Water Vapor and Clouds in Large-Scale Models and Its Use to Diagnose Cloud Cover , 2002 .

[45]  J. Morcrette,et al.  A fast, flexible, approximate technique for computing radiative transfer in inhomogeneous cloud fields , 2003 .

[46]  S. Klein,et al.  How might a statistical cloud scheme be coupled to a mass‐flux convection scheme? , 2005 .

[47]  R. Stull.  An Introduction to Boundary Layer Meteorology , 1988 .

[48]  Kerry Emanuel,et al.  A Parameterization of the Cloudiness Associated with Cumulus Convection; Evaluation Using TOGA COARE Data , 2001 .

[49]  David A. Randall,et al.  Implementation of the Arakawa-Schubert Cumulus Parameterization with a Prognostic Closure , 1993 .