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

A. Herrnstein, T. Dowling

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

Which is the Least Believable Entity (LBE)?

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, I’m still reading papers,

and am just glad to be here.)

-or-

*

* 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.

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 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.

• The hybrid approach allows terrestrial and gas-giant planets to be treated equally well by the same model.

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 )

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.

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

Venus with Topography

nk x nj x ni = 20 x 32 x 64

ptop = 1 mb, dlat = 5.2, dlon = 5.6

Venus with Topography

Using the forcing of Lee, Lewis, and Read (2005)

Spinup takes 18,000 (Earth) days…

That’d be just over 49 (Earth) years…

Nie unto half a century…

8,640,000 3-minute timesteps, give or take.

Will you accept 19 years and running, and a copy of our purchase order for a faster computer?

HELP.

Just arrived: a new 8-way dual computer that is worth mentioning (16 CPUs on one motherboard).

Venus with Topography

COMPLINE (April 2002)40 nodes X 1 CPU/node

COMPLINE 2 (January 2006)1 node X 16 CPU/node

vs.

Now about 18 days (wallclock) to do a 49-yr Venus LLR05 spinup

Flat bottom, Lon = 0

Topography, Lon = 0

U (m/s), Zonal Mean

Eliassen-Palm (EP)Flux Divergence

Wind Vectors at p ~300 mbar, Flat Bottom

Wind Vectors at p ~300 mbar, Topography

Wind Vectors in Bottom Layer, Flat Bottom

Wind Vectors in Bottom Layer, Topography

Summary

• Hybrid EPIC yields positive results for Held-Suarez benchmark

• Topography speeds up spinup; enhances EP flux divergence

• Good agreement between EPIC and Oxford GCMs with LLR05 Venus forcing

• Mountains generate standing eddies and prevailing winds; increase near-surface winds by x10

Research funded by NSF Planetary Astronomy Program

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.

Hybrid Vertical Coordinate

Two Bad Ideas and One Good One

• Theta Blending

gdiag (1 g)prog f () (1 g)prog

Numerically unstable in practice

• Theta Nudging

prog ;prog

t

g

coord

(prog diag )

Numerically unstable in practice

• Just use

diag

everywhere it is available, and = prog in the pure-sigma region(and vice versa for p).

Works extremely well in practice

Hybrid Vertical Coordinate

• Potential temperature, , varies on surfaces

• Previous hybrid models used = prog from

dprog

dt

Ý Q

,

CpT

.

• We ask: Why downgrade from the coordinate all the way to a prognostic variable? Why not treat it as a diagnostic variable?

diag f ()

g(), g( ) 0.