Handling the Topography of Venus with a Hybrid Sigma-Theta Coordinate GCM

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Handling the Topography of Venus with a Hybrid
Sigma-Theta Coordinate GCM

• A. Herrnstein, T. Dowling

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Which is the Least Believable Entity (LBE)?

1. A result for Venus from a model that is known for
   its simulations of gas giants?

-or-

• B. A statement about Venus made by a modeler who
  is known for his simulations of gas giants?

LBE B. (The model is working. But, Im still
reading papers, and am just glad to be here.)


Although, my wife and two young daughters,
who have never been to Key Largo, love the ocean,
but could not come because of work and school,
just called to inform me that, no, the flowers
did not get delivered, and yes, my sleeping bag
has been moved into the doghouse.
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Hybrid Vertical Coordinate
Converging results for Venus using different
vertical coordinates will be, and is, a positive
sign of progress.
An isentropic coordinate virtually eliminates
vertical truncation error. A terrain-following
coordinate is best near topography.
The hybrid approach allows terrestrial and
gas-giant planets to be treated equally well by
the same model.
The equatorial superrotation of Jupiter and
Saturn may or may not have something to do with
the superrotation of Venus and Titan. Having a
single model that can switch between all four is
valuable.
We have published a new hybrid-coordinate
algorithm that overcomes many of the technical
difficulties of its predecessors.
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Hybrid Vertical Coordinate

• Konor and Arakawa (1997, MWR), Dowling et al
  (2006, Icarus)
• f(?) g(?) ?
• where ? is the potential temperature (isentropic
  ds cp d log ?)

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Test Case Held-Suarez
We need this kind of clarity for the simple Venus
forcing models being published
even if the results
only partially resemble Venus.
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Test Case Held-Suarez
Hybrid EPIC model results (t 200 to 1200 days)
a) zonal wind, b) eddy variance of T, c) mean T,
d) mean ?
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Venus with Topography
nk x nj x ni 20 x 32 x 64 ptop 1 mb, dlat
5.2?, dlon 5.6?
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Venus with Topography
Using the forcing of Lee, Lewis, and Read (2005)
Spinup takes 18,000 (Earth) days
Thatd be just over 49 (Earth) years
Nie unto half a century
8,640,000 3-minute timesteps, give or take.
HELP.
Will you accept 19 years and running, and a copy
of our purchase order for a faster computer?
Just arrived a new 8-way dual computer that is
worth mentioning (16 CPUs on one motherboard).
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Venus with Topography
vs.
COMPLINE (April 2002) 40 nodes X 1 CPU/node
Now about 18 days (wallclock) to do a 49-yr Venus
LLR05 spinup
COMPLINE 2 (January 2006) 1 node X 16 CPU/node
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Flat bottom, Lon 0?
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Topography, Lon 0?
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U (m/s), Zonal Mean
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Eliassen-Palm (EP) Flux Divergence
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Wind Vectors at p 300 mbar, Flat Bottom
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Wind Vectors at p 300 mbar, Topography
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Wind Vectors in Bottom Layer, Flat Bottom
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Wind Vectors in Bottom Layer, Topography
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Summary
Hybrid EPIC yields positive results for
Held-Suarez benchmark
Good agreement between EPIC and Oxford GCMs
with LLR05 Venus forcing
Topography speeds up spinup enhances EP flux
divergence
Mountains generate standing eddies and
prevailing winds increase near-surface winds by
x10 Research funded by NSF Planetary
Astronomy Program
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Hybrid Vertical Coordinate
Traditional terrain-following coordinates ?
p/pbot bot 1, top 0 The mountains are
echoed in the coordinate all the way to the top.
Konor and Arakawa (1997, MWR). Hybrid ?-?,
with ? (p-pbot)/(ptop-pbot) bot 0, top
1
Dowling et al. (2006, Icarus). Hybrid ?-?,
with ? log(p/pbot)/log(ptop/pbot) bot 0,
top 1 The point of using log p is that
terrain is roughly the same in km for each
planet, but surface pressure is approx. 105,
103, and 101 mbar for Venus, Earth, and Mars.
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Hybrid Vertical Coordinate
Two Bad Ideas and One Good One
Theta Blending
Numerically unstable in practice
Theta Nudging
Numerically unstable in practice
Just use
Works extremely well in practice
everywhere it is available, and ? ?prog in the
pure-sigma region (and vice versa for p).
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Hybrid Vertical Coordinate
Potential temperature, ?, varies on ? surfaces
Previous hybrid models used ? ?prog from
We ask Why downgrade ? from the coordinate all
the way to a prognostic variable? Why not treat
it as a diagnostic variable?