1. National Center for Atmospheric Research
EVALUATION OF DYNAMICAL CORES INTENDED FOR GLOBAL ATMOSPHERIC CLIMATE MODELS
David L. Williamson
National Center for Atmospheric Research
Boulder, Colorado, USA

2. Global NWP Models = Global Climate Models
Climate = statistics of weather
NWP – deterministic evolution from observed Initial Conditions
before predictability is lost to chaos
Climate – statistics of a calculated evolution
after predictability is lost to chaos (IC irrelevant)
and when model has developed its own equilibrium
NWP – very high resolution, short time periods (weeks)
detailed fine scales
Climate – low resolution, very long time periods (decades – centuries)
large scale statistics

3. Climate models conceptually divided into:
Dynamical core – resolved fluid flow
Sub-grid scale parameterizations – forcing
What numerical method is “best” for the dynamical core?
Climate models not in a convergent regime
Climate models are in a forced-dissipative equilibrium
Solutions depend on both dynamical core and parameterizations

4. With a given parameterization suite:
What resolution of one scheme is equivalent to
what resolution of a different scheme?

5. AQUA-PLANET SIMULATIONS
Atmospheric model with complete parameterization suite
Idealized surface
no land (or mountains), no sea ice
specified global sea surface temperatures everywhere
longitudinally symmetric
latitudinally well resolved
Free motions, no forced component

6. SEA SURFACE TEMPERATURE

7. Community Atmosphere Model (CAM3) Eulerian Spectral Transform
Finite Volume
CAM3 Parameterization Package
T85 setting of adjustable constants
5 minute time step
14 month simulations, analysis over last 12 months

8. 2 degree Finite Volume is equivalent to
T42 Spectral Transform with 2.8 degree transform grid
1 degree Finite Volume is equivalent to
T85 Spectral Transform with 1.4 degree transform grid

9. GLOBAL AVERAGE, TIME AVERAGE
LONGITUDINAL AVERAGE, TIME AVERAGE
TEMPORAL EDDY COVARIANCES
TROPICAL WAVE ACTIVITY
FREQUENCY DISTRIBUTION OF TROPICAL PRECIPITATION
(A brief diversion on double versus single ICTZ)
KINETIC ENERGY SPECTRA (?)

19. PRECIPITATION

21. PRECIPITATION

22. Meridional average |7.5| to |17.5|
Examine averages over the subsidence region poleward of the upward branch of the Hadley cell
Meridional average |7.5| to |17.5|
Zonal average

23. RELATIVE HUMIDITY
CLOUD
LONGWAVE RADIATION

24. PBL
MOIST PROCESSES

25. Evolution of 60-level simulation
starting from a state from a 26-level simulation
T – T(0)
q – q(0)
RELATIVE HUMIDITY

26. CLOUD
CLOUD LIQUID
RADIATION

27. PBL
SHALLOW
PROG CLOUD WATER

28. FRACTION OF UNSTABLE POINTS
26 levels
60 levels

30. Evolution of 60-level simulation from a 26-level simulation
Shallow convection initially turns off
PBL continues to deposit water vapor between 850 and 900 mb
Relative humidity clouds increase between 850 and 900 mb
Longwave radiation cooling increases and destabilizes atmosphere
Shallow convection turns back on
BUT ATMOSPHERIC STATE IS NOT REALISTIC
CANNOT INCREASE VERTICAL RESOLUTION
NEED PARAMETERIZATIONS WHICH ARE NOT DEPENDENT ON GRID

32. EULERIAN SPECTRAL FINITE VOLUME
From Figures 5.5 and 5.7 of Jablonowski and Williamson, NCAR TN-469+STR, 2006

33. T85 EULERIAN SPECTRAL
DAY 9
DEL 4
DEL 4
DEL 6
DEL 6
DEL 8
DEL 8

35. 2 degree Finite Volume is equivalent to T42 Spectral Transform
In CAM3
2 degree Finite Volume is equivalent to T42 Spectral Transform
1 degree Finite Volume is equivalent to T85 Spectral Transform
Proportional relation does not hold at lower resolution
4 degree Finite Volume is not equivalent to T21 Spectral Transform

36. With aqua-planet can establish equivalent resolutions
of different schemes
for unforced component
But must use same parameterization suite
Has been used with additional cores
e.g. Mark Taylor with spectral element
Need method for forced component