Spatial Modelling and Scaling Issues - Environmental Modelling: Finding Simplicity in Complexity - page 69

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Fine resolution Coarse resolution

Figure 5.2 Linkages of parameters across scales.

parameters, which are derived from the measurements
including precipitation, temperature, topography, soil
physical and chemical properties, land cover/land use
and hydrological properties. These data are considerably
variable both spatially and temporally, which result in
the difficulties of aggregating large-scale behaviour from
local processes.
Secondly, different processes are primarily dominant
at different scales, which means the correlations derived
at one scale might not be applicable at another and infor-
mation is often lost as spatial resolution becomes coarser.
Moreover, each environmental process may have its own
optimal spatial and temporal scales. Because of the exis-
tence of different dominant processes at various scales,
the effects of an increasing number of processes need to be
incorporated as a scaling method attempts to span over
a wider range of scales. Thirdly, feedback is associated
with the interaction between small-scale parameters of a
system and large-scale variables, as processes at different
scales affect each another. Processes operating at small
and fast scales are constrained by processes operating
at slow and large scales, while large and slow processes
are constructed and organized by the interactions of
many small fast processes (Ahl and Allen, 1996). These
cross-scale connections suggest that scaling should only
be applied over a limited range of scales and in spe-
cific situations. Fourth, emergent properties arise from
the mutual interaction of small-scale components among
themselves rather than some outside force. The processes
can abruptly reorganize themselves through time, render-
ing previously developed scaling relationships invalid as
the structure and processes that they incorporate cease to
exist. Fifth, when there is a temporal lag in the response of
a system to perturbation, the scaling problem may arise
because of the lack of information about process linkages
in a dynamic environment.

5.4 Scaling issues of input parameters
and possible solutions

5.4.1 Changeofparameterswithscale

Data required for spatial environmental modelling are
measured either at a point such as field measurements
of precipitation, temperature and soil properties, or over
a given continuous area such as with remotely sensed
observations. The reliability of the data value in an area is
affected by both its neighbours and internal heterogeneity.
Pixels in remote sensing imagery, which are the smallest
element of an electronic image, have been widely used to
estimate environmental properties. Nevertheless, sensors
are commonly centre-biased such that the reflectance
towards the centre of the field of view has most influence
on the reflectance (Fisher, 1997). It is poorly understood
whether the reflectance from one location on the ground
only influences the corresponding pixel, or whether it
may have an effect on values for surrounding pixels. On
the other hand, information in one pixel, especially a
large pixel, is usually the mixture of different ground
objects rather than presenting a true geographical object
(Settle and Drake, 1993; Fisher, 1997). As a result, the
extracted spatial environmental parameter only indicates
a representative value rather than a real physical meaning.
For example, if there are more than three types of soil or
land cover/land use within a large grid, the corresponding
categorical value is only a domain value which may
represent a proportion as less as one third of reality. It is a
snare and a delusion to take pixels with various resolutions
as a homogenous reality on the ground (Fisher, 1997).
Changing the scale of measurement has a significant
impact on the variability of object quantities. A land-
surface parameter at various scales represents the different
amount of details referring to both spatial patterns and