1. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 1 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 Stochastic Parameterizations: From Satellite Observations to Ensemble Prediction Copyright 2009 California Institute of Technology. Government Sponsorship Acknowledged.

2. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 2 Physical parameterization problem in weather prediction models Temperature (K) probability e.g. pdf of temperature in grid-box longitude latitude Weather prediction models: Δx=Δy~ 10-100 km Δx Δy Essence of parameterization problem is the estimation of joint PDFs of the model variables (u,v,w,q,T)

3. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 3 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)

4. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 4 Stochastic parameterizations: a methodology Methodology for stochastic parameterizations A variable after being updated by a parameterization (e.g. moist convection) can be written: - mean value of the variable after convection - stochastic value after convection - normally distributed stochastic variable with mean standard deviation - standard deviation due to moist convective processes After discretizing the first term on the rhs, the following equation is obtained - mean value before the moist convection parameterization Teixeira and Reynolds, MWR, 2008

5. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 5 Stochastic convection: a simple approach - constant of proportionality - normally distributed stochastic variable with mean and standard deviation 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 Assuming standard deviation proportional to convection tendency leads to: Teixeira and Reynolds, MWR, 2008

6. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 6 US Navy NOGAPS ensemble spread due to stochastic physics only: 850 hPa Temperature  Perturbations grow in time  At 24 h: mostly in Tropics/Sub-tropics  At 144 h: mostly in Mid-latitudes  Similar for U at 250 and 850 hPa, Z at 500 hPa Teixeira and Reynolds, MWR, 2008

7. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 7 Stochastic convection: tropics versus extra-tropics NOGAPS stochastic convection after 5 to 10 days:  Saturation in Tropics  Synoptic (sub-synoptic) peak in NH Extra-tropics Total energy difference (function of wave number) for May 2005: ensemble member with stochastic convection - control simulation (no stochastic conv.) TropicsNH Extra-tropics Teixeira and Reynolds, MWR, 2008

8. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 8 359293239183139 Tropical Cyclone Forecast Error: Atlantic 2005 Number of Forecasts Stochastic Convection significantly improves NOGAPS ET performance ET: No Stoc. Conv. ET: Stoc. Conv. Multi-model Consensus Official Forecast Track error (nm) Goerss and Reynolds, AMS, 2008 See also Reynolds et al., MWR 2008

9. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 9 Liquid Water Path PDFs from GOES for different types of boundary layer clouds From Gaussian stratocumulus to skewed cumulus regimes 200 km LWP from visible channel, Δx=1km, Δt=30 min, 3 years of data (1999-2001)  100,000 snapshots of 200 km 2 Kawai and Teixeira, JCLI, 2009

10. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 10 PDFs of cloud water content from CloudSat: How large is the skewness? 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? Not Necessarily! Skewness of cloud water content (CWC) from CloudSat for different cloud types for SON 2006  Δx~1km, Δz~500 m Kahn et al, 2009

11. National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California 11 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 Acknowledgments: we acknowledge the support from a NOAA cooperative agreement for THORPEX Teixeira and Reynolds, MWR, 2008 and Reynolds et al., MWR, 2008