The basic equations - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 37

500-1,000 s and U 10m s 1 ,

where L is the horizontal scale. For

5 10 3 -10 4 m ¼ 5-10 km, which makes sense from what we know
about the wind field in convective storms.
Although we reject sound waves as being dynamically unimportant, there is
some evidence that convective storms, and intense vortices such as tornadoes
in particular, can generate detectable sound waves in the infrasound region.
Al Bedard of the former Wave Propagation Laboratory (WPL) in Boulder,
Colorado did some seminal work in this area, backed by earlier work by Roy
Arnold and collaborators during the 1970s and stimulated by the theoretical work
of Abdul Abdullah at NCAR in the mid-1960s. More recently, David Schecter at
North West Research Associates has numerically simulated infrasound in
convective storms.
In any event, three-dimensional cloud models have been developed that permit
sound waves and, thus, do not make use of the Boussinesq or anelastic approxi-
mation. Numerical procedures such as ''time-splitting'' have been developed that
allow one to include the full effects of compressibility without actually represent-
ing all the terms in the model equations at the highest frequencies: relatively low-
frequency processes such as advection and buoyancy are separated from relatively
high-frequency, sound wave propagation processes such as the pressure gradient
force and divergence, each of which is integrated using different time steps. For
diagnostic purposes, it is sucient though to use the Boussinesq approximation to
examine most dynamical effects.
Although we have carefully determined how well the Boussinesq and anelastic
approximations work and noted what their benefits and liabilities are, we must be
aware that we have not yet determined if energy is conserved for the full set of
equations. Since the purpose of this text is to understand dynamics—not how to
construct a numerical model—we will defer discussions of energy conservation
elsewhere (see the list of references).

L U

2.3.3 Water substance

Conservation of mass is extended to include water vapor and the various forms of
water substance through the following equation:
Dq = Dt ¼ JE ð qv Þþ q v þ E þ S C D ð 2 : 46 Þ

JE

where q is the specific humidity; E is the evaporation rate per unit mass of moist
air; S is the sublimation rate; C is the condensation rate; D is the deposition rate;
and the first two terms on the right-hand side come from the advective term. The
various types of water substance can be broken down into many more categories
(e.g., the deposition and sublimation rates can be specified separately for different
types of ice crystals and other forms of frozen water) than those represented in
(2.46), which is a highly simplified representation of what actually happens in the
atmosphere. Additional relations can be specified for conversion rates from ice to
liquid water (e.g., due to melting, etc.), the shedding of water on the surface of
melting hailstones, etc. Our inability to make in situ measurements of cloud par-