Spatial Modelling and Scaling Issues - Environmental Modelling: Finding Simplicity in Complexity - page 68

different information in the different disciplines involved.
For example, the observed characteristics in biosphere
processes may represent leaf, plant and ecosystem respec-
tively when the spatial measurements are aggregated from
a small scale to a large scale.
A modelling (working) scale , building up an environ-
mental model, is partly related to processes and partly
to the application models. Typical hydrological mod-
elling scales in space include the local (plot) scale (1m),
the hillslope (research) scale (100m), the catchment scale
(10 km), and the regional scale (1000 km) (seeChapters 10
and 11). The corresponding temporal scales are the event
scale (1 day), the seasonal scale (1 year), and the long-term
scale (100 years: Figure 5.1; Dooge, 1986). In the assess-
ment of biospheric ecosystem function, data for fine-scale
physiologymodels aremeasured at leaf level over seconds.
The prediction of canopy photosynthesis for forest stands
is operated with daily climatic information and a spatial
scale from 1 to 10 ha. On the contrary, coarse-scale bio-
geochemical models are designed to estimate biosphere
processes over regional scale extrapolating to a 10 to
100 km 2 spatial resolution with monthly climate data
(McNulty et al ., 1996).
Application of environmental modelling always
involves four different scales. These are geographic scale
of a research area, temporal scale related to the time
period of research, measurement scale of parameters
(input data resolution), and model scale referring to both
temporal and spatial scales when a model was established.

the real world can be considered as the composition of
line, area and volume. To explain the scaling issue of non-
linearity, we use a unit side of lines to build up a square
and a cube, which leads to the same unit value for all three
objects. When the side scale changes by a factor of two, the
surface area increases by a factor of four and the volume
by a factor of eight. There is clearly a nonlinear process
of scaling properties between the side length, the square
surface and the cube volume. Considering such a problem
in hydrology, we should find how topographic attributes
change if we double the spatial resolution of a topographic
map, or how the drainage area changes if we double the
length of a stream (Dodds and Rothman, 2000).
The scaling issue in heterogeneous natural environ-
mental systems, on the other hand, can also be explained
in hierarchical land cover classification. If a given area
of 1

1km 2 is classified into 16 land-cover classes in a
high spatial resolution dataset, such as 30

×

30 m 2 . With
the reduction of measurement scale, only the dominant
class tends to remain while the minor classes may be
eliminated. With the continuous reduction of scale, there
will be only one class remaining eventually. The scaling
in heterogeneity of land-class categories is of subsequent
influences on climate models (Salmun et al ., 2009).
The parameter values in natural environments are
usually dependent on the measurement scales. This
dependence implies that the value of a parameter in
a large measurement scale cannot be simply calculated
from a small measurement scale. In order to reduce
or increase measurement scale, scaling studies in envi-
ronmental modelling are related to such a fundamental
question as how a model changes with the variation in
parameter-measurement scales. Hence it becomes crucial
to determine the linkage of both environmental param-
eters and models across scales using scaling techniques.
Upscaling refers to the environmental issues at a higher
scale based on the knowledge obtained from a lower scale,
whereas downscaling determines the issues at a lower scale
using knowledge at a higher scale (Figure 5.2).

×

5.2.2 Scaling
Scaling focuses on what happens to the characteristics of
an object when its scale (size/dimension) is changed pro-
portionately. What happens is mainly a function of spatial
processes of nonlinearity and heterogeneity. An object in

10 3 yr

Global

Knowledge
decrease

5.3 Causes of scaling problems

Regional

log(time)

Catchment

There are a number of conceptually distinct reasons
resulting in scaling problems (Heuvelink, 1998; Harvey,
2000; Peterson, 2000). First of all, the most common
and fundamental cause of scaling problems is the exis-
tence of both spatial heterogeneity and relevant process
nonlinearities. Spatial environmental models more or less
require both climatic/weather input data and land-surface

Ecosystem

Plot

Plant

Leaf

Second
cm

10 4 km

log(space)

Figure 5.1 Typical scales of environmental models.