Environmental Engineering Reference
In-Depth Information
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Figure 5.7 Schematic illustration of distributed model. The A
D represent relatively homogeneous region (or layer L) which could
be a grid cell, ecosystem type, representative elementary area, hydrological response unit, etc. Veg and Soil represent vegetation, soil
properties, and other environmental variables (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).
the dynamics in a different HRU (Fl ugel, 1995; Bracken
and Kirkby, 2005).
Fourthly, geostatistics, such asmeasures of spatial auto-
correlation between data values, provides a methodology
of determining a relative homogeneous size for environ-
mental modelling. Homogeneous areas are seen as having
high spatial autocorrelation such that a coarse spatial
resolution would be appropriate, whereas heterogeneous
areas are seen as having low spatial autocorrelation so
that a fine spatial resolution would be needed (Curran
and Atkinson, 1999). Analysing the variogram change
with spatial resolution can help to identify the predom-
inant scale of spatial variation, at which might be an
optimal scale for environmental modelling. Several sta-
tistical models can potentially identify the optimum scale
of a variable. The average local variance estimated from
a moving window is a function of measurement scale
(Woodcock and Strahler, 1987). The scale at which the
peak occurs may be used to select the predominant scale
of variables. Similar to the local variance method, the
semi-variance at a lag of one pixel plotted against spa-
tial resolution is an effective means of determining the
optimal scale. For example, when using the semi-variance
technique with remote sensing data, Curran and Atkin-
son (1999) found that a spatial scale of 60m was suitable
for the analysis of urban areas whereas 120m was suit-
able for agricultural areas. The dispersion variance of
a variable defined on a spatial scale within a specified
region may also be applied to link information pertinent
to the choice of optimal scale (Van der Meer, 1994). All
above approaches are acceptable for dealing with scaling
problems that arise due to spatial heterogeneity combined
with process nonlinearity, but are not valid when there
are interactions between adjacent grids (or areas). For
example, Muller et al . (2008) demonstrated how param-
eters related to different processes can vary over different
scales in a very small area.
5.5.2.5 Routing approach
The model structure in a routing approach remains the
same across scales while the variables (fluxes) for the
models are spatially and temporally modified. Such inter-
actions always occur in hydrological processes, where the
model output at large scales is far from being the simple
sum of each grid cell. When water flow and sediment
move from the divide to the outflow of a catchment and
from a small catchment to a large catchment, the values
of related hydrological variables in a grid are affected
not only by the environmental characteristics within this
grid but also by properties in the surrounding grid cells.
The runoff in a pixel is determined by the precipitation
and infiltration within this grid, and water arriving from
and discharging to neighbouring grids. The amount of
sediment deposited or detached in a grid cell is strongly
dependent on the movement of both water and sed-
iment in surrounding neighbouring grids. Hence the
routing approach is usually employed after calculating
the drainage direction on the basis of the steepest descent
of topography (Figure 5.8a). This technique has been
effectively employed in runoff and sediment-transport
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