Spatial Modelling and Scaling Issues - Environmental Modelling: Finding Simplicity in Complexity - page 74

to translate ecological and environmental models across
spatial scales (King, 1991; Rastetter et al ., 1992; Bugmann
et al ., 2000; Harvey, 2000).

Trend

5.5.2.1 Calibration of a model
This approach is to adopt a model, which is applica-
ble at small scales, for application at large scales using
'calibration' values. The calibration technique is to set
up an empirically calibrated relationship between fine-
and coarse-scale data. This approach requires that both
fine- and coarse-scale data are available to perform the
calibration. The calibrated models may only be treated
as reliable within the ranges of input and output data
used for the calibration, and the incorporation of new
model variables requires recalibration of the relationship
(Rastetter et al ., 1992; Friedl, 1997). In practical terms,
it is difficult to carry out measurements for calibration
at various scales, especially very large scales. However,
because of the nonlinearity of the processes involved,
together with the heterogeneity of the natural system,
there is no reason to suppose that the use of calibration
values should be any more successful in reproducing the
areal average result (Beven, 1995).

Coverage

Commensurate

Resolution

Noise

Observation

Figure 5.5 Process scale versus observation scale. Source :
Bloschl and Sivapalan (1995). Reproduced by permission of
John Wiley & Sons, Ltd.

dependent variable are very changeable. The same result is
also identified byWalsh et al . (1997) when analysing a lin-
ear regression model between the Normalized Difference
Vegetation Index (NDVI) and elevation on a mountain.
Therefore, if a model is established at a process scale
and input parameters measured at the same scale, the
model output should be accurate and acceptable. The
relationship between process and measurement scale is
that processes larger than the coverage appears as trends
in the data, whereas processes smaller than the resolution
appear as noise (Figure 5.5; Bloschl and Sivapalan, 1995).

5.5.2.2 Multiscale models
Since processes change with various scales, a set of dif-
ferent models is required for various particular scales,
such as specifically used at field plot, watershed, regional
and global scales (David et al ., 1996; Kirkby et al ., 1996;
Poesen et al ., 1996). Separate scaling methods could be
developed for each individual process, and the rules for
transitions between them could be used to synthesize
these separate scaling methods into an aggregate scaling
methodwhich incorporates the behaviour of the ensemble
of scales (Peterson, 2000). The plot-scale environmental
models may represent physical and other processes in
detail whereas large-scale models can provide a potential
value, such as potential cumulative soil erosion at the
global scale (Kirkby and Cox, 1995; Kirkby et al ., 1996).
In doing so, the scale effects are included in each indi-
vidual model and the environment could be accurately
simulated. Unlike plot-scale models, however, accurate
regional- and global-scale models are rarely available.

5.5.2 Methods forupscalingenvironmental
models

If we could take the Earth as a unit to build up a global
model, it would produce a very accurate output of our
interests when each input and output is only one single
measured value at the global scale. However, global-scale
model operation should rely on scale linkages of environ-
mental objects to certain conceptual frameworks due to
the difficulties in making direct measurements at a large
scale. Although it is a challenge to scale a complex assem-
blage of parameters and models to corresponding process
scales, it is feasible to identify a few scalable parameters
within the complex environment in an attempt to reduce
the scale uncertainties of modelling. Any methods reduc-
ing the scaling effects would be a great improvement
of modelling results as it seems impossible to eliminate
completely the impact of scale on environmental mod-
elling (Luo, 1999). There are several methods available

5.5.2.3 Lumped models
The lumping method is carried out by integrating the
increased heterogeneity that accompanies the change
in model extent by aggregating across heterogeneity in