Introduction to Parametrization of Sub-grid Processes Anton Beljaars ([e-mail] room 114)

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Introduction to Parametrization of Sub-grid
Processes Anton Beljaars(anton.beljaars_at_ecmwf.
int room 114)

• What is parametrization?
• Processes, importance and impact.
• Testing, validation, diagnostics
• Parametrization development strategy

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Why parametrization

• Small scale processes are not resolved by large
  scale models, because they are sub-grid.
• The effect of the sub-grid process on the large
  scale can only be represented statistically.
• The procedure of expressing the effect of
  sub-grid process is called parametrization.

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What is parametrization and why is it needed

• The standard Reynolds decomposition and
  averaging, leads to co-variances that need
  closure or parametrization
• Radiation absorbed, scattered and emitted by
  molecules, aerosols and cloud droplets play an
  important role in the atmosphere and need
  parametrization.
• Cloud microphysical processes need
  parametrization

• Parametrization schemes express the effect of
  sub-grid processes in resolved variables.
• Model variables are U,V,T,q, (l,a)

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Reynolds decomposition
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Space and time scales
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Space and time scales
1 hour
100 hours
0.01 hour
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Numerical models of the atmosphere
Hor. scales Vert. Scales time range

• Climate models 200 km 500 m 100 years
• Global weather prediction 20 km 200 m 10 days
  
• Limited area weather pred. 10 km 200 m 2
  days
• Cloud resolving models 500 m 500 m 1 day
• Large eddy models 50 m 50 m 5 hours

Different models need different level of
parametrization
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Parametrized processes in the ECMWF model
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Applications and requirements

• Applications of the ECMWF model
• Data assimilation T1279L91-outer and
  T95/T159/T255-inner loops 12-hour 4DVAR.
• Medium range forecasts at T1279/L91 (16 km) 10
  days from 00 and 12 UTC.
• Ensemble prediction system at T639L62 (32 km) for
  10 days, and T319 (65 km) up to day 15
  2x(501) members.
• Short range at T1279L91 (15 km) 3 days, 4 times
  per day for LAMs.
• Seasonal forecasting at T95L40 (200 km) 200 days
  ensembles coupled to ocean model.
• Monthly forecasts (ocean coupled) at T159L61
  Every week, 501 members.
• Fully coupled ocean wave model.
• Interim reanalysis (1989-current) is under way
  (T255L60, 4DVAR).

• Basic requirements
• Accommodate different applications.
• Parametrization needs to work over a wide range
  of spatial resolutions.
• Time steps are long (from 10 to 60 minutes)
  Numerics needs to be efficient and robust.
• Interactions between processes are important and
  should be considered in the design of the schemes.

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Importance of physical processes

• General
• Tendencies from sub-grid processes are
  substantial and contribute to the evolution of
  the atmosphere even in the short range.
• Diabatic processes drive the general
  circulation.
• Synoptic development
• Diabatic heating and friction influence synoptic
  development.
• Weather parameters
• Diurnal cycle
• Clouds, precipitation, fog
• Wind, gusts
• T and q at 2m level.
• Data assimilation
• Forward operators are needed for observations.

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Global energy and moisture budgets
Hartman, 1994. Academic Press. Fig 6.1 and 5.2
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Sensitivity of cyclo-genesis to surface drag
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T-tendencies
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T-Tendencies
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T-Tendencies
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T-Tendencies
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T-tendencies
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T-Tendencies
Imbalance (physics dynamics) due to (a) Fast
adjustment to initial state (data assimilation
problem) (b) Parametrization deficiencies
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Validation and diagnostics

• Compare with analysis
• daily verification
• systematic errors e.g. from monthly averages
• Compare with operational data
• SYNOPs
• radio sondes
• satellite
• Climatological data
• CERES, ISCCP
• ocean fluxes
• Field experiments
• TOGA/COARE, PYREX, ARM, FIFE, ...

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Day-5, T850 errors
Viterbo and Betts, 1999. JGR, 104D, 27,803-27,810
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Diurnal cycle over land
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History of 2m T-errors over Europe in the ECMWF
model (step60/72)
RMS (day/night)
Bias (day/night)
LESS STABLE BL DIFFUSION

• Model temperature errors are influenced by many
  processes.
• Observations at process level are needed to
  disentangle their effect

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TSR JJA 24 hour forecasts (CY31R1/23R4 - CERES)
CY31R1 - CERES
CY23R4 - CERES
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Lat. Heat Flux-DJF (ERA_40_Step_0_6 vs. DaSilva
climatology)
ERA40 model
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PYREX experiment
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PYREX mountain drag (Oct/Nov 1990)
Lott and Miller, 1995. QJRMS, 121, 1323-1348
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Latent heat flux ERA-40 vs. IMET buoy
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Cloud fraction (LITE/ECMWF model)
Cross section over Pacific 45N/120E 45S/160W
(16-09-1994)
Model
LITE
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Parametrization development strategy

• -Invent empirical relations (e.g. based on
  theory, similarity arguments or physical insight)
• To find parameters use
• Theory (e.g. radiation)
• Field data (e.g. GATE for convection PYREX for
  orographic drag HAPEX for land surface Kansas
  for turbulence ASTEX for clouds BOREAS for
  forest albedo)
• Cloud resolving models (e.g. for clouds and
  convection)
• Meso scale models (e.g. for subgrid orography)
• Large eddy simulation (turbulence)
• Test in stand alone or single column mode
• Test in 3D mode with short range forecasts
• Test in long integrations (model climate)
• Consider interactions

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Measure diffusion coefficients
stable
unstable
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Convert to empirical function
Diffusion coefficients based on Monin Obukhov
similarity
MO-scheme (less diffusive)
Operational CY30R2
MO-scheme (less diffusive)
Operational CY30R2
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Column test
Cabauw July 1987, 3-day time series
Observations versus model (T159, 12-36 hr
forecasts)
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T2-difference DJF (ensemble of 6 integrations)
Effect of MO-stability functions instead of LTG
Contours at 1, 3, 5, K
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Test in 3D model Data assimilation daily
forecasts over 32 days March 2004
Effect of MO-stability functions
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Concluding remark

• Enjoy the course

and Dont hesitate to ask questions