Environmental Engineering Reference
In-Depth Information
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Figure 5.6
Scheme of lumped model. The A
D represent land cover or ecosystem types,
Veg
and
Soil
are vegetation and soil
properties (Adapted with permission from Chen, B., Chen, J.M., Mo, G.
et al
. (2007) Modeling and scaling coupled energy, water,
and carbon fluxes based on remote sensing: an application to Canada's landmass.
Journal of Hydrometeorology
, 8, 123-43
→
American Meteorological Society).
environmental parameters. Since an area is taken as a
whole to calculate the model result, a lumped model is
like a zero-dimensional representation of spatial features
(Maidment, 1993). A major concern in using a lumped
model is the possibility of obtaining a single value of a
spatially changeable parameter that allows amodel to pre-
dict the mean response of the modelled area (Moore and
Gallant, 1991; Chen
et al
., 2007). To address a lumped
system in upscaling studies, parameters are aggregated
using various approaches (as described in the section
of scaling parameters) to represent the spatial hetero-
geneities. As a result, one single set of model calculations
is applied across the whole area to get an estimate without
information about the spatial distribution (Figure 5.6).
A number of practical approaches can be used to
determine relatively homogeneous areas. First, a straight-
forward method is to run the model in each grid cell
across a region. It is assumed that each grid cell is homo-
geneous and fits the modelling scale no matter what the
size of the cell is. For example, land vulnerability to water
erosion was assessed directly by running a plot model on
a0
5
◦
dataset by Batjes (1996).
Secondly, to apply distributed models more reason-
ably, the concept of representative elementary area (REA)
is proposed in studying rainfall and runoff (Wood
et al
.,
1988, 1990) (see also Chapter 2). The REA is defined as
the 'smallest discernible point which is a representative
of the continuum and is employed for finding a certain
preferred time and spatial scale over which the process
representations can remain simple and at which the
distributed catchment behaviours can be represented
without the apparently undefinable complexity of local
heterogeneity.' This concept provides a motivation for
measurements of spatial variability as it highlights the
interaction between scale and variability. It indicates
that the variances and covariances of key variables are
invariant in land units above a certain threshold size. It is
difficult in practice, however, to determine the size of the
REA because it is strongly controlled by environmental
characteristics (Bloschl
et al
., 1995).
Thirdly, in regional hydrological modelling, the con-
cept of a hydrological response unit (HRU) has been
developed. The HRU is a distributed, heterogeneously
structured entity having a common climate, land use and
underlying pedo-topo-geological associations controlling
their hydrological dynamics. The crucial assumption for
each HRU is that the variation of the hydrological process
dynamics within the HRU must be small compared with
.
5.5.2.4 Distributed (partitioning) method
In a distributed model, a study area is divided into many
grid cells (or subareas, patches and strata) with relatively
homogeneous environmental conditions. Each grid cell is
represented by mean values of environmental processes
in the computation of regional and global estimates, such
as in a grid-based approach. The heterogeneity (variance)
within a grid cell is minimized while it is maximized
between cells. The environmental behaviour in a large
area is determined as the areally weighted average of the
behaviour of all those cells after a local model is then
employed in each grid cell (Figure 5.7). The resultant
value in a large area can be estimated using Equation 5.6:
i
=
k
F
=
p
i
f
(
x
i
)
(5.6)
i
=
1
where
p
i
is the
p
roportion of the total area that stratum
i
occupies, and
x
i
is the mean of
x
in the stratum
i
.
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