28.6 Methodological Implications
The most effective case studies are those for
which the available time series data on both societal and environmental processes permit analysis
of the patterns of change both within human and
environmental systems and the interaction between
them. Such information can include historical documentary material, detailed data on socioeconomic
change over a 10- to 20-year period, and comparable time series information on environmental
conditions using soil surveys, climatic records, and
remotely sensed data and air photographs.
Aggregation
Aggregations are made to reduce complexity. This
may be necessary for a variety of reasons, including parsimony in model building, cost constraints,
and the practicality of working with large numbers
of variables or observations.
Aggregation is a relatively uncomplicated process in which components have linear properties
and it is appropriate to add together information
from different units. Some additivities are unambiguous (e.g., number of people and livestock, area
under different land uses, and ecological zones).
When we have ratio variables or estimates from different sized populations, then weighting or some
other manipulation of the information may be required to maintain representativeness.
The concept of similarity is fundamental to the
process of aggregation. Similarity can be variously
defined by variables, indicators, proximity, processes, and history. When the processes at a finer
level are understood, then aggregation can be done
on a theoretically sound basis. There remains a
problem, however, in the application of models developed at the finer scale to interactions among
variables that represent aggregations of finer-scale
conditions. For example, "the leaves of a canopy
might be lumped and treated as a single "big leaf'
.... The fine-scale equations are often applied directly, or with minor changes, to describe the properties of this coarse-scale aggregate. The problem
with this approach is that the aggregate does not
generally behave the same way as the fine-scale
components from which it is constituted" (Rastetter et aI., 1992, p. 56). Criteria for aggregation may
include optimizing objective functions (minimizing
within-group variance, maximizing a regression
coefficient), contiguity, and administrative convemence.
The issue of aggregation requires attention to the
assumptions that have to be met to permit valid
generalizations. Aggregation changes the scale of
431
analysis. In the social and ecological sciences, it
may involve sampling a number of individual
cases, each with its own idiosyncrasies, to create a
sample size large enough to allow generalizations
to be made that are not unduly influenced by the
particular behavior of individuals.
Each discipline has its own literature on the issue. Parametric and nonparametric procedures and
spatial statistics all deal with the issue of aggregation and extrapolation from individual cases to populations. In single-discipline analyses, methods exist to explore interscalar issues, although they
remain problematic. When dealing with environmental issues that cut across and integrate many
disciplines, these methods are partially appropriate.
The conceptual frameworks and methodology for
such integration are emerging (see Chapters 10
through 21).
Scale and Time
The stimuli that create interaction from one scale
to another are not instantaneous. Time lags occur
that will vary in length depending on the characteristics of the processes involved. For example,
diffusion studies have examined the dynamics of
the spread of a phenomenon over space or within
populations. The rate of spread may accelerate or
decelerate at different times in the process and there
may be factors that facilitate or inhibit diffusion
(Morrill et aI., 1988).
The impact of the impulses between levels is
subject to time lags of different length depending
on the impulse. Thus an understanding of the interactions across scales requires appreciation of
temporal dynamics in the model:
Patterns of interaction not only exist over space but
through time. The outcomes of induced change in social,
political or economic conditions are recognized to involve both an interaction between them, a synergism, and
a recognition of time-lags such that the full impact of interactions may only become evident over a longer period
of time. Child health programs, for example, may have
rapid success in reducing child mortality rates but their
impact upon other aspects of the production system may
be long-delayed. Increased demand for land arising from
subsequent population growth may only appear fifteen
to twenty years later when the beneficiaries reach adulthood ....
The question of time becomes more complicated once
biophysical components are added to the developmental
framework. Climatic rhythms, processes of soil formation and erosion, and vegetation growth and decay have
The most effective case studies are those for
which the available time series data on both societal and environmental processes permit analysis
of the patterns of change both within human and
environmental systems and the interaction between
them. Such information can include historical documentary material, detailed data on socioeconomic
change over a 10- to 20-year period, and comparable time series information on environmental
conditions using soil surveys, climatic records, and
remotely sensed data and air photographs.
Aggregation
Aggregations are made to reduce complexity. This
may be necessary for a variety of reasons, including parsimony in model building, cost constraints,
and the practicality of working with large numbers
of variables or observations.
Aggregation is a relatively uncomplicated process in which components have linear properties
and it is appropriate to add together information
from different units. Some additivities are unambiguous (e.g., number of people and livestock, area
under different land uses, and ecological zones).
When we have ratio variables or estimates from different sized populations, then weighting or some
other manipulation of the information may be required to maintain representativeness.
The concept of similarity is fundamental to the
process of aggregation. Similarity can be variously
defined by variables, indicators, proximity, processes, and history. When the processes at a finer
level are understood, then aggregation can be done
on a theoretically sound basis. There remains a
problem, however, in the application of models developed at the finer scale to interactions among
variables that represent aggregations of finer-scale
conditions. For example, "the leaves of a canopy
might be lumped and treated as a single "big leaf'
.... The fine-scale equations are often applied directly, or with minor changes, to describe the properties of this coarse-scale aggregate. The problem
with this approach is that the aggregate does not
generally behave the same way as the fine-scale
components from which it is constituted" (Rastetter et aI., 1992, p. 56). Criteria for aggregation may
include optimizing objective functions (minimizing
within-group variance, maximizing a regression
coefficient), contiguity, and administrative convemence.
The issue of aggregation requires attention to the
assumptions that have to be met to permit valid
generalizations. Aggregation changes the scale of
431
analysis. In the social and ecological sciences, it
may involve sampling a number of individual
cases, each with its own idiosyncrasies, to create a
sample size large enough to allow generalizations
to be made that are not unduly influenced by the
particular behavior of individuals.
Each discipline has its own literature on the issue. Parametric and nonparametric procedures and
spatial statistics all deal with the issue of aggregation and extrapolation from individual cases to populations. In single-discipline analyses, methods exist to explore interscalar issues, although they
remain problematic. When dealing with environmental issues that cut across and integrate many
disciplines, these methods are partially appropriate.
The conceptual frameworks and methodology for
such integration are emerging (see Chapters 10
through 21).
Scale and Time
The stimuli that create interaction from one scale
to another are not instantaneous. Time lags occur
that will vary in length depending on the characteristics of the processes involved. For example,
diffusion studies have examined the dynamics of
the spread of a phenomenon over space or within
populations. The rate of spread may accelerate or
decelerate at different times in the process and there
may be factors that facilitate or inhibit diffusion
(Morrill et aI., 1988).
The impact of the impulses between levels is
subject to time lags of different length depending
on the impulse. Thus an understanding of the interactions across scales requires appreciation of
temporal dynamics in the model:
Patterns of interaction not only exist over space but
through time. The outcomes of induced change in social,
political or economic conditions are recognized to involve both an interaction between them, a synergism, and
a recognition of time-lags such that the full impact of interactions may only become evident over a longer period
of time. Child health programs, for example, may have
rapid success in reducing child mortality rates but their
impact upon other aspects of the production system may
be long-delayed. Increased demand for land arising from
subsequent population growth may only appear fifteen
to twenty years later when the beneficiaries reach adulthood ....
The question of time becomes more complicated once
biophysical components are added to the developmental
framework. Climatic rhythms, processes of soil formation and erosion, and vegetation growth and decay have