A FIRST-ORDER ANALYSIS OF THE HEAT WAVE IN THE
SOIL
DARIO CAMUFFO
CNR-Istituto di Chimica e Tecnologia dei Radioelementi, Corso Stati Uniti, /-35020 Camin Padova, Italy
and
SERGIO VINCENZI and LEONARDO PILAN
CNR-Istituro per lo Studio della Dinamica delle Grandi Masse, S.Polo 1364,/-30125 Venezia, Italy
(Received January 2, 1984; revised February 29, 1984)
Abstract. On the basis of a realistic distribution of the net radiative flux density (composed of a half sinusoid
for the shortwave contribution plus a term dependent on the soil surface temperature for the longwave
contribution), the solutions regarding the propagation of both the diurnal thermal wave and the heat flux
density in the soil are analyzed. The more relevant differences from the analytical solutions obtained under
the classical hypothesis of pure sinusoidal forcing waves on the boundary are therefore pointed out.
List of Symbols
a albedo
al, a2, a 3 coefficients in Equation (2)
A absorbed fraction of R
A 0 daylight amplitude of incoming shortwave radiation
e~ Fourier coefficients
D (KIo)) 112
g constant in Equation (1)
G soil heat flux density
h adimensional depth z/D x/~
H sensible heat flux density
H(y) Heaviside function ofy
k soil conductivity
K soil diffusivity
L$, L~" incoming and outcoming long, wave radiation
LE latent heat flux density
N daylight duration
q 7D/k
r Sun-Earth distance
r* respondance
R global solar radiation
S solar constant
t time
t* retention-time
T soil temperature
x adimensional time nt/12
x o effective adimensional daylight duration nN/12
z depth
Z Sun's zenith angle
~/ parameter defined in Equation (7)
b solar declination
Wasp, Air, and SoiI Pollution 23 (1984) 441-454. 0049-6979/84/0234-0441501.90.
© 1984 by D. Reidel Publishing Company.