The basic equations - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 32

(liquid and frozen); and the specific volume . Diabatic heating from changes

in the phase of water substance, turbulent heat transfer from the surface, and radi-
ation causes changes in temperature and specific volume. The dynamics of
convective storms is affected most by the latent heat released or absorbed when
water droplets condense from water vapor, when water droplets evaporate, when
ice crystals form directly from water vapor, when water droplets freeze into ice, when
ice melts into water, and when ice particles sublimate (''to err is human, to change
phase, sublime''). The bulk change-in-phase processes (as opposed to changes to
individual particles) are referred to as ''cloud microphysics''. Since cloud microphy-
sical processes are not completely understood and not easily observable and
quantified, they are parameterized in terms of quantities that can in fact be meas-
ured, such as temperature, humidity, pressure, etc.
Turbulent sensible heat transfer from a heated land surface during the day
when the Sun is out or when cold air passes over a much warmer body of water is
often linked to cloud formation. Radiative cooling at cloud top, heating at cloud
base, or horizontal gradients in radiative heating (e.g., at cirrus anvil edges) can
also play significant roles, but are not of primary dynamical

¼ 1 =

importance for

convective storms.
The adiabatic form of the thermodynamic equation, expressed in terms of the
time rate of change of variables, is given by

C p DT = Dt 1 = Dp = Dt ¼ 0 ð 2 : 25 Þ

In this formulation changes in temperature following air parcel motion are related
only to changes in pressure following air parcel motion. The adiabatic form of the
thermodynamic equation is useful for describing the thermodynamic changes asso-
ciated with horizontal and vertical air motions outside of convective storms: rising
air is cooled and sinking air is warmed if the stratification is stable, the amount of
cooling/warming varying as the lapse rate of temperature.
It is useful to express the adiabatic form of the thermodynamic equation in
terms of potential temperature

R = C p

¼ T ð p = p 0 Þ ð 2 : 26 Þ

where D = Dt ¼ 0 (i.e., potential temperature is conserved). When the air is

saturated, e (equivalent potential temperature). From the

definition of potential temperature, the adiabatic form of the thermodynamic
equation (2.25) may be expressed as

is replaced by

1 = D = Dt ¼ 1 = pDp = Dt ð 2 : 27 Þ

This equation will be useful later when we analyze sound waves. In particular, the
left-hand side is part of the equation of continuity discussed in the following
section and allows us to relate changes in density to changes in pressure.