Transcript J. Teixeira, C. A. Reynolds, B. Kahn, J. Goerss, J. Mclay and

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
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 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?
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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