
Toward the End of Cumulus Paramterization
Sensiitivity of radiativeconvective equilibrium simulations to
horizontal resolution
Olivier Pauluis
Courant Intitute of Mathematical Sciences
Abstract
The current generation of General Circulation Models can simulate
the global atmosphere with a resolution of the order of 50 km. Such a
resolution is insufficient to explicitly simulate the deep convective
motions that are responsible for the bulk of the vertical energy transport
in the atmosphere. To compensate for this limitation, climate models
have use various cumulus parameterizations to account for the effects of
convective motions on the atmospheric temperature, humidity and cloud
distribution. However, due to the continuous increase in computational
power, the next generation of global models might be run at a sufficiently
fine resolution as to make the use of cumulus parameterization unnecessary.
This paper investigates the impacts of horizontal resolution on the statistical
behavior of convection. An idealized radiativeconvective equilibrium is
simulated for model resolutions ranging between 2 and 50 km. The simulations
are compared based upon the analysis of the mean state, of the energy and
water vapor transport, and of the probability distributions functions for various
quantities. It is found that, despite some bias in temperature and humidity,
coarse resolution simulations are able to reproduce reasonably well the
statistical properties of deep convective towers. This is particularly apparent
in the cloud ice and vertical velocity distributions that exhibit a very robust
behavior at resolution up to 16 km.
A theoretical scaling for the vertical velocity as function of the grid resolution
is derived, based upon the behavior of an idealized air bubbles.The vertical
velocity of an ascending bubble is determined by its aspect ratio, with a wide,
flat parcel rising at a much slower pace than a narrow one. This theoretical
scaling law can explain the behavior of the numerical simulations, and be
used to renormalize the probability distribution functions for vertical velocity.
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