Geoscience Reference
In-Depth Information
Hence for short precipitation events that are not long enough to saturate the vegetation,
Equation (3.7) produces a loss
D
D
L
i
=
c
Pdt
−
Odt
for
S
≤
S
ic
(3.10)
0
0
Equation (3.10) is valid as long as the cumulative precipitation is smaller than the amount
needed to saturate the vegetation, and (3.6) is valid after that, when
S
=
S
ic
.
To allow the practical implementation of Equations (3.6) and (3.10), various assumptions
have been proposed by different authors, regarding
c
,
E
i
, and
O
. The main difficulties in
assessing these assumptions are the complexity of the vegetation cover precluding more
thorough analysis and the absence of experimental support for most of the processes involved
in interception. Some of these assumptions are briefly discussed in the following.
Some common assumptions
The fractional vegetation cover
c
is often assumed to be simply related with the free through-
fall coefficient
p
,as
c
=
(1
−
p
); this coefficient is the portion of the precipitation that
reaches the ground without hitting the canopy (Gash and Morton, 1978). Both
c
and
p
can
be measured (see Section 3.4.3). The drainage rate
O
has been estimated in various ways.
The simplest way to describe it is with the assumption that as long as the canopy is partly
saturated there is no drip, and that once it is saturated at the end of the storm the amount
of water on the canopy rapidly falls to its storage capacity
S
ic
(Gash, 1979; Noilhan and
Planton, 1989). These can be written as
O
=
0
for
S
<
S
ic
(3.11)
and, from Equation (3.8)
cP
−
E
i
−
O
=
0
for
S
=
S
ic
(3.12)
The rate of evaporation from the intercepting vegetation
E
i
is the most critical but also the
most difficult variable to determine. For operational purposes, it is now commonly (Noilhan
and Planton, 1989; Gash
et al
., 1995) assumed that, when the vegetation is saturated, it can
be estimated by means of a suitably chosen potential evaporation
E
po
(see Chapter 4) from
the fraction
c
of the surface occupied by intercepting vegetation and that the evaporation
from the remaining fraction (1
−
c
) can be ignored. For partly saturated surfaces during
the wetting up phase of the interception process, it has mostly (see Rutter
et al
., 1971)
been assumed that the evaporation is proportional to the relative saturation (
S
/
S
ic
). (This
assumption is an application of Equation (4.33) with (4.34).) Both assumptions can be
combined as
E
i
=
c
(
S
/
S
ic
)
E
po
(3.13)
The main problem with these underlying assumptions is that it is still not very clear exactly
how this potential evaporation should be defined or estimated; this issue will require fur-
ther study. In any event, these assumptions lead now to the following expressions for the
interception loss. If
t
0
denotes the time to saturation, the loss for short precipitation events
