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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.

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