Summary of Resolving Convection in a Global Hypohydrostatic Model
by Garner, Frierson, Held, Pauluis, and Vallis, which appears
in Journal of the Atmospheric Sciences.
Primary arguments:
- Making a hypohydrostatic rescaling of the equations of motion in an
idealized moist GCM causes changes in the general circulation, provided
a large enough rescaling constant is used.
-
Many of the same changes as adding a convection scheme occur under this
rescaling, such as reduced Hadley circulation strength.
Discussion:
This paper followed up on the study of Pauluis et al
which studied the effect of a transformation to the vertical momentum equation in a non-hydrostatic
model (called DARE/RAVE by Kuang, Bretherton and Blossey). The transformation increases the scale of
convective motions, so may allow a lower resolution model to resolve convection.
The Pauluis et al paper took a pragmatic approach and studied whether this strategy is useful as opposed
to just running a coarse-resolution cloud-resolving model, unfortunately with somewhat unfavorable
results. In this paper, we use this hypohydrostatic rescaling within the idealized physics package
developed in my thesis and used in the
FHZ06 and
FHZ07 papers (although now with a non-hydrostatic
dynamical core that's used in the ZETAC model. We took more of an exploratory approach with this work, our
goal being to understand how convection affects the general circulation in a broad sense.
We test different values of the hypohydrostatic scaling parameter in the moist GCM, which causes convection
to appear at larger scales, but also causes convection to become more sluggish (i.e., convective growth rates
slow down). In the appendix of the paper, we show that making this transformation can be accomplished by
varying model parameters as well: for instance, changing the hypohydrostatic parameter is identically
equivalent to running the model on a planet with smaller gravity, smaller surface pressure and saturation
mixing ratios, and a larger drag coefficient. The latter set of transformations (which we call "deep Earth")
increase the scale height of the planet, and thus increases the aspect ratio, making convection larger. See
the appendix and my thesis for more information about
why the other changes are necessary to have an exact equivalence. One can make the identical transformation
by running the model on a smaller Earth, with increased rotation and increased diabatic forcing (Kuang et
al's Diabatic Acceleration and REscaling).
We ran the model globally using typical GCM resolutions (2x2.5 degrees, 44 levels).
A first remarkable result is that one must use a huge rescaling parameter to see any effect whatsoever.
Using a scaling parameter of alpha = 100 (which means the nonhydrostatic terms are multiplied by a factor of
10,000!) produces only minor changes in the general circulation. This essentially just means that typical
GCMs are very, very hydrostatic. Moving on to the dynamical effects of the hypohydrostatic transformation,
one can clearly see convective updrafts moving from the gridscale to larger scales as the rescaling parameter
is increased. The figure above shows a vertical cross section of instantaneous upward motion along the
equator for a control simulation (above) and a simulation with rescaling factor alpha = 300 (below).
Clearly the updrafts become much wider with the rescaling, as expected from the linear analysis.
In terms of the general circulation, one can see effects on the general circulation in a range of fields in
both the tropics and the midlatitudes. The latter is not surprising given the variety of studies we have
performed showing the effect of moisture and convection in determining the static stability in
midlatitudes (FHZ06, Frierson 2006 and
Frierson 2007c). Most remarkable is that adding the
hypohydrostatic transformation to make convection bigger causes similar changes to the general circulation
as adding a convection scheme, as in the Frierson 2007a
paper: the Hadley cell slows down, equatorial precipitation decreases, and subtropical precipitation
increases. Why would such changes occur?
One key to figuring this out is examining the typical depths of convective updrafts, as can be seen in the
figure above. Despite the fact that the convection is slower in the rescaled case, the updrafts reach
higher into the upper troposphere and lower stratosphere. The reason for this is that as the updrafts
become larger, they become less susceptible to entrainment of dry air. The entrainment occurs simply by
numerical diffusion in the model, but a similar effect occurs in the real atmosphere: if there is less
entrainment, updrafts are more likely to reach higher and convection occurs more easily. You can read
more about why deeper convection leads to a slower Hadley cell in the
Frierson 2007a paper.
Full citation:
Garner, S. T., Frierson, D. M. W., Held, I. M., Pauluis, O. M., and G. K. Vallis.
Resolving Convection in a Global Hypohydrostatic Model.
Journal of the Atmospheric Sciences, 64, 2061-2075, 2007.
The official journal link can be found
here.
A PDF download of the full paper can be found here.
This download is courtesy of the American Meteorological Society, who owns sole
rights to it.
The download is subject to copyright laws and statutes. For more
information, please visit the Allen Press/AMS Journals Online website.
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