Geoscience Reference
In-Depth Information
(
L
e
E
)
−
2
Second
stage
(
L
e
E
0
)
−
2
First stage Transition
t=t
0
t=t
0
+
t
r0
Time,
t
(days)
Fig. 9.26 Sketch of a method to determine the two stages of drying by means of Equation (9.110).
(After Brutsaert and Chen, 1995.)
a time shift parameter. Then after fitting data of
E
−
2
against
t
, in accordance with (9.108)
or
E
−
2
=
(2
/
De
0
)
2
t
r
(9.110)
one can derive
De
0
and
t
0
from the slope and intercept as sketched in Figure 9.26. In order
to represent the cumulative evaporation as a function of
t
1
/
r
in the range of validity of
(9.108), the sketch illustrates that the starting point of the integration should be
t
r
=
t
r0
,
i.e.
t
=
(
t
0
+
t
r0
), marking the end of the transition, rather than
t
r
=
0. At
t
=
(
t
0
+
t
r0
), the
variable
E
−
2
starts its linear relation with
t
r
. The cumulative evaporation after the onset of
the desorptive regime is then
E
2
=
De
0
(
t
1
/
2
r
−
t
1
/
2
r0
)
(9.111)
in which the subscript 2 indicates the second stage of drying. The value of
t
r0
, marking the
beginning of the second stage, can be related to the value of the cumulative evaporation at
the end of the first stage, or of the transition if there is one, say
E
1
, as follows
E
1
/
De
0
2
t
r0
=
(9.112)
Thus (9.111) can also be expressed as
E
2
=
De
0
t
1
/
2
r
−
E
1
(9.113)
As mentioned, (9.110) can be used as a regression equation with experimental data to
estimate the values of the effective parameters
De
0
and
t
0
; with a known or decided upon
value of
E
1
, Equation (9.113) allows the prediction of the cumulative evaporation after
the onset of the second stage of drying.
Conceptually, it can be seen that this procedure is in fact based on a time compression
assumption, which is analogous with that used to describe rainfall infiltration after the
