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National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California Stochastic Parameterizations: From Satellite Observations to Ensemble Prediction J. Teixeira(1), C. A. Reynolds(2), B. Kahn(2), J. Goerss(2), J. Mclay(2) and H. Kawai(1) (1) Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California (2) Naval Research Laboratory, Monterey, California, USA Copyright 2009 California Institute of Technology. Government Sponsorship Acknowledged. 1 National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California Physical parameterization problem in weather prediction models Weather prediction models: Δx=Δy~ 10-100 km Δy Δx Temperature (K) e.g. pdf of temperature in grid-box longitude Essence of parameterization problem is the estimation of joint PDFs of the model variables (u,v,w,q,T) 2 National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California Stochastic nature of physical parameterizations in ensemble prediction For parameterizations: Ensemble prediction is fundamentally different from deterministic prediction Stochastic Parameterizations Parameterizations in ensemble prediction systems: No a priori reason for deterministic parameterizations (i.e. evolution of mean) Parameterizations also provide estimates of higher moments of PDF (e.g variance) Parameterizations in ensemble could provide probable values (stochastic) Stochastic values should be constrained by parameterization PDFs (e.g. variance) 3 National Aeronautics and Space Administration Stochastic parameterizations: a methodology Jet Propulsion Laboratory California Institute of Technology Pasadena, California Methodology for stochastic parameterizations A variable after being updated by a parameterization (e.g. moist convection) can be written: conv stoch conv conv - mean value of the variable after convection - stochastic value after convection - normally distributed stochastic variable with mean 0 standard deviation ,conv ,conv- standard deviation due to moist convective processes stoch conv After discretizing the first term on the rhs, the following equation is obtained t conv stoch conv t - mean value before the moist convection parameterization 4 Teixeira and Reynolds, MWR, 2008 National Aeronautics and Space Administration Stochastic convection: a simple approach Jet Propulsion Laboratory California Institute of Technology Pasadena, California Assuming standard deviation proportional to convection tendency leads to: stoch conv t 1 t conv - constant of proportionality - normally distributed stochastic variable with mean 0 and standard deviation t 0 1 1 t t conv conv stoch leads to Simple vertical correlation: single random number per column No horizontal or temporal correlations: Perturbations assumed much smaller than grid-size Parameterization variance already possesses a certain degree of correlation Physically unclear how to construct correlations 5 Teixeira and Reynolds, MWR, 2008 National Aeronautics and Space Administration US Navy NOGAPS ensemble spread due to stochastic physics only: 850 hPa Temperature Jet Propulsion Laboratory California Institute of Technology Pasadena, California Perturbations grow in time At 24 h: mostly in Tropics/Sub-tropics At 144 h: mostly in Mid-latitudes 6 Similar for U at 250 and 850 hPa, Z at 500 hPa Teixeira and Reynolds, MWR, 2008 Stochastic convection: tropics versus extra-tropics National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California Total energy difference (function of wave number) for May 2005: ensemble member with stochastic convection - control simulation (no stochastic conv.) TROPICS Total Energy MAY 05 NHX Total Energy MAY 05 Tropics 12 24 36 48 60 72 96 120 144 168 192 216 240 1.E-01 Energy (J/kg) NH Extra-tropics 1.E+01 1.E-02 1.E-03 1.E-04 1.E-05 12 24 36 48 60 72 96 120 144 168 192 216 240 1.E+00 Energy (J/kg) 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 0 20 40 60 80 100 120 0 20 40 Total Wave Number 60 80 100 120 Total Wave Number NOGAPS stochastic convection after 5 to 10 days: Saturation in Tropics Synoptic (sub-synoptic) peak in NH Extra-tropics 7 Teixeira and Reynolds, MWR, 2008 National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California Tropical Cyclone Forecast Error: Atlantic 2005 Stochastic Convection significantly improves NOGAPS ET performance 300 Track error (nm) 250 200 ET:EOMI No Stoc. Conv. 150 ET:ENMI Stoc. Conv. CONU Consensus Multi-model 100 OFCLForecast Official 50 See also Reynolds et al., MWR 2008 0 24 48 72 96 120 359 293 239 183 8 139 Number of Forecasts Goerss and Reynolds, AMS, 2008 National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California Liquid Water Path PDFs from GOES for different types of boundary layer clouds 200 km LWP from visible channel, Δx=1km, Δt=30 min, 3 years of data (1999-2001) 100,000 snapshots of 200 km2 200 km From Gaussian stratocumulus to skewed cumulus regimes 9 Kawai and Teixeira, JCLI, 2009 National Aeronautics and Space Administration PDFs of cloud water content from CloudSat: How large is the skewness? Jet Propulsion Laboratory California Institute of Technology Pasadena, California Skewness of cloud water content (CWC) from CloudSat for different cloud types for SON 2006 Δx~1km, Δz~500 m Large values of skewness of cloud water PDF in deep convection Does it imply that PDFs of water vapor and temperature are highly skewed as well? 10 Not Necessarily! Kahn et al, 2009 National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California SUMMARY Stochastic nature of parameterizations in ensemble systems: • Parameterizations in ensemble prediction should be stochastic • Stochasticity constrained by parameterization PDF A simple stochastic convection approach: • Standard deviation proportional to convection tendency • Perturbations grow in time + ‘migrate’ (tropics to extra-tropics) • Tropics: stochastic convection spread ~ init. cond. spread • Impact in tropical cyclone prediction Using high-resolution satellite data for PDF estimation FUTURE WORK… • More sophisticated variance estimation • Differents PDFs • Stochastic boundary layer, clouds • Feasibility of this type of approach in other NWP centers Teixeira and Reynolds, MWR, 2008 and Reynolds et al., MWR, 2008 Acknowledgments: we acknowledge the support from11 a NOAA cooperative agreement for THORPEX