Geoscience Reference
In-Depth Information
5
4
De
0
3
( m m d
−
1 / 2
)
2
1
0
0
1 0
2 0
3 0
4 0
5 0
T e m p e r a t u r e , T (
o
C )
Fig. 9.25 The temperature dependency of the effective desorptivity
De
0
in mm d
−
1
/
2
, as measured by a
weighing lysimeter with loam in Arizona (open circles), and of the normalized water vapor
diffusivity (curve). The indicated temperature is the average of the five daily averages for the
first five days of the soil-limiting phase. (After Jackson
et al
., 1976.)
those portions of a field whose surface moisture content was below a certain threshold value;
however, they also found that
De
0
exhibits a strong dependency on temperature, varying by
a factor of about 2 from winter to summer. In Figure 9.25 these measured values of
De
0
can
be compared with the normalized temperature dependency of the water vapor diffusivity;
the similarity of both dependencies suggests that vapor diffusion contributes substantially
to the total water transport in the top layer of the soil.
In these three field studies with daily time steps, the transition between the first and second
stage of drying appears to have been relatively abrupt. Jackson
et al.
(1976) concluded that
at the field scale any gradual transition was mainly caused by the variability of the surface
soil moisture, so that the field was partly in the first and in the second stage of drying. In the
analyses of the bare-soil lysimeter measurements by Black
et al.
(1969) and by Parlange
et al.
(1992), the desorptive stage was assumed to have started immediately after the water
application had ceased, and the first stage was dispensed with.
Time compression approximation
In the two bare-soil lysimeter studies just mentioned, the desorption formulation was imple-
mented by simply plotting the cumulative evaporation
E
against the square root of time
t
1
/
2
to fit a linear relation through the origin, and the end of the precipitation or the irriga-
tion was taken as the starting point. Whenever the first stage is short or nonexistent, this
procedure may be acceptable. However, because Equation (9.108) is a nonlinear function
of
t
, the choice of the starting point of the second drying stage, i.e.
t
=
0, is critical for
its proper performance. In many situations considerable evaporation can take place under
first stage drying conditions and the transition can also be long; thus in general, this starting
point is not known and a different approach is needed.
To obtain a more objective procedure, it was proposed by Brutsaert and Chen (1995)
that Equation (9.108) should be recast in terms of a relative time
t
r
=
(
t
−
t
0
), in which
t
0
is
