Geoscience Reference
In-Depth Information
The intention of applying the model in this macroscale context was to try to improve the
prediction of runoff production and routing in large-scale land surface parameterisations in
GCMs. It had two advantages in this respect: firstly in at least attempting to take account of some
of the heterogeneity in soil moisture storage and runoff generation at the large scale (which had
been lacking in earlier land surface parameterisations); and secondly the more realistic routing
of runoff enabled more rigorous comparisons with observed discharges from large basins. It is
also important in this context that these are achieved in a computationally efficient way, since
the complexity of individual components of GCMs is still constrained by the limitations of
currently available supercomputers. Applications to the Mississippi basin (Liston
et al.
, 1994),
Arkansas Red River basin (Abdulla
et al.
, 1996; Abdulla and Lettenmaier, 1997), Columbia River
Basin (Nijssen
et al.
, 1997) and Weser River (Lohmann
et al.
, 1998b) have been reported. VIC
was included in the Project for the Intercomparison of Landsurface Parameterisation Schemes
(PILPS) (see, for example, the comparison of runoff predictions reported in Lohmann
et al.
,
1998c) and in the Model Parameter Estimation Experiment (MOPEX) (Andreassian
et al.
, 2006).
The version of the model described here is the VIC-2L (two-layer) structure of Liang
et al.
(1994, see also Lohmann
et al.
, 1998a). The addition of a thin upper soil layer produces the
VIC-3L model (Liang and Xie, 2001). The form of the fast runoff production function is per-
haps seen most clearly in Figure B2.2.1. The curved function represents the distribution of
local total storage capacities in the basin. As rainfall is added more and more of the storage
capacities are filled and, once filled, any excess rainfall on that part of the catchment is as-
sumed to become fast runoff. Between rainstorms, it is assumed that all the storages gradually
drain, thereby setting up the antecedent conditions prior to the next storm. It is interesting to
note that one of the earliest ESMA models, the Stanford Watershed Model (Figure 2.7), had a
similar storage capacity function for the prediction of fast runoff but assumed that the distribu-
tion was always uniform between some minimum and maximum capacities across the basin.
The variable infiltration capacity form allows for a non-uniform distribution according to the
power function:
i
=
i
m
1
−
A
i
)
b
−
(1
(B2.2.1)
where
i
is the infiltration storage capacity,
i
m
is a maximum infiltration storage capacity for
the area,
A
i
is the fraction of the area with infiltration capacity less than
i,
and
b
is a shape
parameter controlling the formof the distribution. For
b
=
1 the infiltration capacity is uniformly
distributed, as assumed in the Stanford Watershed Model. This distribution function has two
parameters,
i
m
and
b
.
This equation is applied to the upper soil layer. For any level of storage in the upper soil
layer, an equivalent threshold for saturation,
i
o
, and the equivalent area of the catchment that
will be saturated,
A
s
can be calculated (see Figure B2.2.1). The distribution of local storage
deficits for the area that is not yet saturated can be then defined as:
d
i
=
i
−
i
o
=
i
m
1
−
A
i
)
b
−
(1
−
i
o
;
i>i
o
(B2.2.2)
During a rainstorm, average catchment rainfall in excess of any canopy interception losses is
added to the upper soil layer storage at each time step. The saturated area is calculated as that
part of the catchment for which upper layer storage exceeds
i
for that time step. Any rainfall in
excess of saturation is assumed to reach the stream as fast runoff. Evapotranspiration is assumed
to take place at the potential rate for the area that is saturated and at a reduced rate depending
on storage deficit for the remaining part of the area. At the end of the time step, the upper
layer storage is depleted by drainage to a lower soil water storage, assuming that drainage is
due to gravity alone and that the unsaturated hydraulic conductivity in the upper layer can
be described as a function of storage in that layer by the Brooks-Corey relation (see Box 5.4).
This requires three further parameters to be specified: a hydraulic conductivity,
K
s
, a residual
moisture content,
r
,
and a pore size distribution index,
B
.
