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∂ϑ
1
[
]
=
F
−
F
−
R
(41)
3
2
,
3
3
3
∂
t
D
3
where ϑ
i
is the volumetric soil water content (m
3
m
-3
) in the i
th
layer;
P
1
is infiltration rate of
precipitation into the upper soil moisture store (m s
-1
);
D
i
(m) is thickness of the i
th
soil layer;
F
i,i+1
is water flux between
i
and
i+1
soil layer (m s
-1
);
F
3
is gravitational drainage flux from
recharge soil water store (m s
-1
);
E
tf,1
and
E
tf,2
are canopy extraction of soil moisture by
transpiration from the rooted first and second soil layers (kg m
-2
s
-1
), respectively;
R
0
the
surface runoff (m s
-1
); and
R
i
is subsurface runoff from the i
th
soil layer (m s
-1
) (Figure 5). In
the model Eqs. (39)-(41) are solved using an explicit time scheme.
Figure 5. Schematic diagram of the LAPS scheme hydrology.
The precipitation
P
1
that infiltrates into the top soil layer is given by
(
)
⎧
min
P
,
K
ϑ
<
ϑ
P
=
0
s
1
2
(42)
1
0
ϑ
=
ϑ
1
2
where
K
s
is the saturated hydraulic conductivity (m s
-1
),
ϑ
is saturated volumetric soil water
content and
P
0
the effective precipitation rate on the soil surface (m s
-1
) given by
(
)
(43)
P
=
P
−
P
−
D
0
f
f
The rate of interception (inflow) for the canopy,
P
f
is given by
(
)
c
P
= 1
P
−
e
−
v
σ
(44)
f
where
P
is the precipitation rate (m s
-1
) above the canopy and
ν
is a constant depending on the
leaf area index assuming that the interception of the rainfall can be considered via the
expression describing the exponential attenuation [19] (Sellers et al., 1986). The rate of
drainage of water stored on the vegetation (outflow) for the canopy (m s
-1
),
D
f
, is given by
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