R n À G ¼ H þ LE
ð4:11Þ
where R n is the radiative budget components of small and large wavelength, G the
heat flux in soil, H the sensible heat flux, and latent heat flux, LE. The Bowen ratio,
b, is defined by
b ¼
H
LE
¼
q c p DT
q L Dq
ð4:12Þ
where L is the latent heat of water vaporization, and q the specific humidity (water
vapor mass per unit mass of humid air) given by
q ¼
v
q
¼
M w e
RT
=q
ð4:13Þ
where T and v are the temperature and absolute air humidity (mass of water vapor
per unit volume of humid air), R is the constant for ideal gases, and q the density of
humid air. Considering that this density is the weighted sum of the density of its
components, we have
q ¼ M w e þ M A ðp À eÞ
ð
Þ =RT
ð4:14Þ
where p is the total air pressure, and e the partial pressure of water vapor in humid
air, Eq. (4.13) can be written as
q ¼
v
q
¼
M w e
M w e þ M A ðp À eÞ
ð4:15Þ
where e = 0.622 is the molecular ratio between the molecular weight of water vapor
M w and of air M a
Dq ¼
Dv
q
¼
e De
e e þ ðp À eÞ
%
eD e
p
ð4:16Þ
Equation (4.12) can be written
b ¼
c p DT
LDq
¼
pc p DT
LeDe
¼ c
DT
De
ð4:17Þ
116
4 Exchange of Energy and Mass Over Forest Canopies