Spatial Modelling and Scaling Issues - Environmental Modelling: Finding Simplicity in Complexity - page 67

are not always available at a regional or global scale, the
moderate and coarse spatial and fine temporal resolution
datasets have been widely established. These databases
include 0

5.2 Scale and scaling

5.2.1 Meaningsof scale inenvironmental
modelling

5 ◦ and 1 ◦ soil types, vegetation types and land
use in the Global Ecosystems Database (GED), daily
1 km global Advanced Very High Resolution Radiometer
(AVHRR), 1 km MODerate Resolution Imaging Spec-
troradiometer (MODIS) products including land cover,
temperature, albedo, leaf-area index (LAI) and Fraction
of Photosynthetically Active Radiation (FPAR), and daily
climatic data in the Global Climate Data Center (Justice
et al ., 2002). Nevertheless, it is still not clear how these
data change with temporal and spatial scales and to what
extent they fit both environmental processes and models
from local to global scales.
The behaviour of the natural environment is sophisti-
cated and continuous while our spatial modelling process
is finite and discrete. Spatial modelling must partition a
geographic space into a finite number of grids (cells or pix-
els), which is themajor limitation in the simulation of nat-
ural environmental process. The parameters or attributes
in a grid are generally heterogeneous rather than homoge-
nous. Thus, many spatial models of environmental pro-
cesses and patterns are scale dependent. We currently
face two pairs of contradictions. One is that although
the local environmental processes can be simulated accu-
rately, many environmental managers and policy makers
require the environmental assessments at a regional or
global scale. Another is that most physically based models
have been developed and validated at uniform field-plot
scales or under laboratory conditions while the widely
available data formodel inputs are very coarse and hetero-
geneous. The scaling issues of environmental parameters
and modelling restrict the applicability of the principles
and theories learned under plot conditions to the assess-
ment of environmental risk at a regional or global scale.
These challenges arise because little understanding has
been achieved about the linkage between well-developed
models at fine (smaller and experimental) scales and
environmental processes operating at large scales.
This chapter discusses the scaling issues facing spatial
environmental modelling and the currently used meth-
ods reducing the scaling effects on both models and
their parameters. A case study is then presented on the
approaches to scale up a soil-erosion model established
at a plot scale to regional or global scales by scaling
land-surface parameters. This study intends to develop
a scale-invariant soil-erosion model by scaling the slope
and vegetation-cover factors that control erosion to fit
the modelling scale.

.

The term 'scale' refers to complex phenomena that vary
within space, time, or other dimensions in the real
world. This concept allows us to use finite and dis-
crete measurements to understand the infinitely variable
and continuous Earth system. It also provides us a means
to store, recall, and analyze information about environ-
mental features that would otherwise be impossible to
evaluate. However, scale is a confusing concept meaning
different things depending on the context and disciplinary
perspective. It is often misunderstood and the different
meanings of the word are used interchangeably (Bloschl
and Sivapalan, 1995; Goodchild and Quattrochi, 1997).
There are over 30 meanings of the word 'scale' (Curran
and Atkinson, 1999), but only the following fivemeanings
are commonly used in environmental analysis (Lam and
Quattrochi, 1992; Bloschl and Sivapalan, 1995). A carto-
graphic map scale refers to the proportion of a distance
on a map to the corresponding distance on the ground. A
large-scale map covers a smaller area generally with more
detailed information, while a small-scale map covers a
larger area often with brief information about the area.
In contrast, a geographic scale is associated with the size
or spatial domain of the study. A large geographic scale
deals with a larger area, as opposed to a small geographic
scale, which covers a smaller area.
An operational scale (process scale, characteristic scale)
is defined as the scale at which a physical process oper-
ates in the natural environment. This scale is associated
with the spatial extent and temporal duration (lifetime
and cycle) depending on the nature of the process (or
object). Observations and models conducted at their
operational scales produce the reality of an environmental
phenomenon.
A measurement scale (observational scale) is the spatial
resolution that is used to determine an object. At this scale
a construct is imposed on an object in an attempt to detect
the relevant variation (Collins, 1998). The measurement
scale can be defined as the spatial or temporal extent of a
dataset, the space (resolution) between samples, and the
integration time of a sample. The spatial scale is related to
the size of the smallest part of a spatial dataset, such as the
plot size in the field investigation, pixel size of remotely
sensed data and digital elevation data, and grid (or cell)
size in spatial modelling. With the change of measure-
ment scale, the environmental parameters may represent