Modeling Geographic
Phenomena as Processes
Femke Reitsma
Department of Geography
University of Wisconsin-Milwaukee
freitsma@uwm.edu
Abstract
The common approach to modeling geographic phenomena is based in the object-oriented paradigm. A paradigm that is argued here to be inappropriate and even unable to capture the spatio-temporal essence of the “things” we model. These phenomena include migration, erosion, urban sprawl, percolation, and development, which form the basis of a geographer’s education in processes as opposed to objects. Modeling such phenomena as a collection of objects that undergoes change upon a spatial plain ignores that change defines the process. An alternative basis for modeling spatio-temporal phenomena is proposed that involves developing a conceptual framework that takes change as its core, a framework defined by process. The redefinition of modeling rudiments recommends new approaches to observation and measurement of geographic phenomena in order to develop an example of modeling geographic phenomena as processes.
1. Introduction
We see much of the world constantly in flux. As Heraclitus reputedly once said, one can never step into the same river twice. The objective of this research (apart from completing a PhD) is to develop a modeling approach that takes this notion of flux, in the form of process, as geography’s primitive. Such an approach attempts to build from the bottom up, where a method of modeling geographical phenomena will be derived from an appropriate theory of geographic phenomena. As Couclelis stated, ‘the technical question of the most appropriate data structure for the representation of geographic phenomena begs the philosophical question of the most appropriate conceptualization of the geographic world’ (Couclelis 1992: 65, original italics). However the author does not intend to enter into any form of metaphysical debate, rather, recognizing that our observations of constant change in the “things” studied recommends an approach to modeling that is based on process, which takes change as its core.
The significance of such work comes from the recognition that Object Orientation is not the panacea to modeling spatio-temporal phenomena (Worboys 2001). The divide between the spatiality of GISs (geographic information systems) and the temporality of traditional modeling software remains (Clarke, Parks et al. 2001). Thus the author suggests an alternative framework that is grounded in change, which is inherently spatio-temporal, through the modeling of geographic processes as processes rather than a collection of objects.
The following begins by introducing what is meant by process in Section 2. Section 3 provides some justification as to the import of this approach to modeling geographic phenomena. A conceptual model of how modeling process might be modeled is then provided in Section 4, followed by Section 5, which explores the difficulty in presenting an example of a process specified according to the conceptualization developed in Section 4. Section 6 concludes the paper with direction towards implementation.
2. Primitive processes
Geography is the study of process. It is not purely about space, nor the areal differentiation of objects in that space, but the complex spatio-temporal nature of geographic phenomena. Here ‘nothing in the physical world is purely spatial or temporal; everything is process’ (Blaut 1961: 2). In an average undergraduate introduction to physical geography students learn about atmospheric and oceanic circulation, tropical cyclones, earthquakes, weathering processes, floods, desertification, glaciation, and longshore sediment transport. In a human geography equivalent, students learn about migration, the green revolution, transportation, urban sprawl, information flows, trade, sustainable development, Fordism, and growth. These are all processes.
Processes are defined by change in phenomena. Every thing involves change; even seemingly unchanging structures may simply be considered slow processes of long duration (Blaut 1961). Instead of describing the world as a set of objects that undergo change, we may describe the world as a set of processes that embody change. Thus change should be at the core of models of these processes, where modeling geographic phenomena as processes is considered more fundamental than as a collection of objects and relations, the current approach.
The ‘study of space-time processes concerns how spatial arrangements are modified by movement or spatial interaction’ (Gatrell 1983: 2). This dichotomy of structure and process, form and movement, is presented as structure explaining subsequent process, and process explaining subsequent spatial structure (Abler, Adams et al. 1971). Traditionally the focus has been to understand process through an analysis of the patterns or structures they produce (Getis and Boots 1978). Coffey (1981) argues for an alternative view, taken up in this paper, suggesting that process captures both structure and motion. Here, process involves ‘a feedback loop in which morphology is not only the result of changes, but to a large extent plays a causal role by setting the initial conditions or constraints for the processes’ (Coffey 1981: 12). Thus, function and structure cannot be separated (Koestler 1968). Indeed, structure may be considered paused process.
To clarify the notion of change recommended as the core construct, a number of foundational terms need be defined. These informal definitions form the basis on which a definition of change and process builds upon and forms a part of.
An Object is a human imposed categorization or abstraction of concrete or abstract things in the world, its definition being dependent on scale: spatial, temporal, and attribute.
Attributes are aspects of the object that define its state.
Space is the relationship between two objects at one instant of time, an instant of time being a point on an underlying temporal axis (for a more formal definition see Beguin and Thisse 1979).
Time is a measurement of changes in an object. It is the relationship between the state of an object (at an instant) and a changed state of that object (at another instant). Directionality is unnecessary.
Within this measure of time the term change is already used, and must therefore be defined. Change can then be defined on an object as the difference between that object’s spatial and/or attribute characteristics at one instant of time and the characteristics of that same object at another instant of time. This definition of change is completely dependent on the spatial, temporal, and attribute scale, whereby the finer the grain of each of these aspects the greater the potential for change to be evident or measured.
As the reader may have noticed, the definitions of space, time, and change were given in terms of objects. They may be redefined in terms of processes, as will be discussed in Section 4. However, a preliminary meaning is necessary to provide a starting point. Coffey (1981) defines process as the succession of actions or events through time, that is, an extended notion of change. However, this sequence of events must be connected by an explanatory mechanism (Harvey 1969). Any set of events cannot be considered a process without a logical connection between them. A Process is, then, a human imposed categorization or abstraction of a sequence of events that are logically connected, its definition also being dependent on scale: spatial, temporal, and attribute. Change can then be defined on a process in the same manner as on an object, that is as the difference between a process at one instant of time and that same process at another instant of time. As with objects, this definition of change is completely dependent on the spatial, temporal, and attribute scale, whereby the finer the grain of each of these aspects the greater the potential for change to be evident or measured.
3. Rationalization
The way this world is modeled limits our understanding of it and our ability to explain it. If we observe the world as constantly changing at multiple scales, to capture what we see happening “out there” requires appropriate modeling methods that reflect our observations of the phenomenon’s complex spatio-temporal nature. The following points provide a number of arguments for basing models of geographic phenomena on the concept of process:
3.1 Modeling processes as objects
Current modeling techniques have developed and continue to develop around the object-oriented paradigm. However, the question arises (Worboys 2001): can objects in the object-oriented view of the world model events or phenomena?
An object may be considered as being composed of state, behavior, and identity. The state of an object encompasses all of the attributes of the object as well as the current values of these attributes. The behavior of an object is how it acts and reacts, in terms of operators and state changes (Booch 1994). Objects model abstract and concrete things in the world, both static and dynamic. However, change is only handled implicitly in the variations of the attributes of the objects, where ‘the terms instance and object are interchangeable’ (Booch 1994: 83). What is needed is a dynamic modeling construct that is based explicitly on spatial, temporal, and attribute change.
3.2 Reciprocating structure and behavior of objects
The combined attributes and operations of the objects in the model define the structure of the model, a structure that can typically be altered only by external manipulation. The execution of the rules or operators defines the behavior of each object. Thus changes in the structure of the model directly impact on the behavior of the objects. However, there is no scope for changes in behavior to alter the structure of the model.
3.3 Spatio-temporal realities
Within the object oriented view space is the container. Objects operate over space, which is referred to through some form of spatial co-ordinate system. Space plays a role in their behavior, but it does so as a static backcloth upon which a temporal object moves. Furthermore, time is imported through the time steps needed to implement the behavior of the object. But in our measured reality, space and time directly influence objects and vice versa. This argument reflects that of absolute versus relative space (and time), which has been won philosophically by the relativists (Harvey 1969), yet implementation wise the balance has tipped in the favor of absolute representations. For example, static notions of space are problematic when attempting to model human movement, such as transport or pedestrian modeling, where the structure of the modeled world within which these agents interact is immutable regardless of the pressures exerted.
3.4 Technological Determinism
The specification of a geographic process model is necessary due to the limitations of current object-oriented tools to model the subject of geographic research. Rather than apply concepts and tools developed in different disciplines for different purposes, a modeling method must be developed for geography based on an apposite notion of geographic phenomena. What is needed is a bottom up approach based on a solid theoretical foundation, rather than a top down approach where the tools that are selected (typically from a narrow range of options) and applied were not developed with geographic phenomena in mind. For example, geographic information systems (GIS) are developed within the current object-oriented paradigm and are naturally focused on the needs of the commercial market rather than the academic geographer wishing to model their subject matter in a more appropriate manner. It is often not until much later that the fundamental assumptions and theory inherent in such tools are considered or questioned, as was evident in the social critique of GIS in the early 1990s, more than a decade after its widespread use within academia (see for example Pickles 1995).
Clearly there is a need for a geographic modeling foundation. Such a foundation is found in the concept of process. The basic organizing concept of the geographer has long been considered space, yet geography is no longer just about areal differentiation. The purpose of geography is to understand these spatial patterns of difference; such understanding can only be found when the temporal nature of phenomenon is considered. If process is considered as the basic organizing concept of geography, and is theoretically salient and tenable, then models must be developed based upon this concept.
4. Conceiving process rudiments
Conceptualizing processes requires a careful description of its varying aspects or rudiments. In what follows, statements in bold form the key concepts or the framework upon which a process model hangs.
The simplest, as opposed to the smallest, element in a process model is a functional attribute, that is, a functional attribute is the primary element of a process. This term functional attribute is coined here to differentiate it from structural attributes. The traditional notion of attribute (in GIS) is based on the object-orientation description of the world, defined here as structural attributes. These structural attributes are characteristics of objects, they are the measuring apparatus (Casti 1989), the aspects of the object that can be observed qualitatively or measured quantitatively by which we define the object in a certain state. Note the atemporal nature of such a definition. In comparison, a functional attribute is defined here as an attribute that is explicitly temporal. It is composed of a function, including thresholds, that is defined by and defines its relationship to other functional attributes.
As with temporality, functional attributes and processes are explicitly spatial. A functional attribute incorporates and modifies its neighborhood within its relational space. At a given point a functional attribute considers and changes its neighbors in its relational neighborhood and its own value, given the characteristics of that specific functional attribute.
Processes are defined by
relationships among a collection of functional attributes.
For example, the process of urban sprawl is determined by the interaction
of many sub processes, some of which might include,
urban growth, migration, and local government intervention.
Note the distinction made between determinism and causality (following
Casti 1989). These sub processes
are here defined as the functional attributes
of the process they compose. The
operation of a process depends on the values of the functional attributes,
such as in the form of thresholds.
For example, the process of longshore sediment transport
at a beach may be described by a number of functional attributes, such
as: angle of wave approach, wind direction, wind speed, depth, wave height,
etc. Given that the process of
longshore sediment transport depends on the functional attribute “depth”, the
spatial extent of its operation is limited by this
functional attribute.
Processes and functional attributes may be characterized by mathematical functions. A mathematical function maps a domain to a codomain; it is a relation that uniquely associates members of one set with members of another set. A function defines change, where change is the difference between the domain and the codomain. Change defines time. Time is therefore relative to the interaction between functional attributes. For example, the process of erosion on a hill slope is described as a function that maps the state of the hill slope at an instant of time to a future state of that hill slope after the process has changed that hill slope.
Processes influence the operation of each functional
attribute, either directly as a part of a functional attribute’s definition,
or indirectly through relations between other functional attributes that
are defined with reference to the process.
In turn, functional attributes define the nature of the process.
Thus, process and functional attributes have a reciprocal
relationship.
This relationship engenders change, thus processes can
change. Due to the influence
of other processes, or pressures exerted by functional attributes, processes
can change: a structural evolution (White
1988; O'Sullivan 2001).
For example Kay et al (1999)
and Kay (2000)
describe the change in processes occurring in Lake Erie in North America, a
two-attractor catastrophic cusp model for shallow lakes.
The two attractors identified are the pelagic and the benthic
attractor. Lakes have been found
that flip between these attractors, which are defined by different processes,
on a regular basis;
Functional attributes and processes form a hierarchy, that is, they may be described as being embedded in a functional hierarchy (Koestler 1968). Looking down this functional hierarchy, a process as a whole is described by its parts, its functional attributes. Looking up the functional hierarchy, that former whole is now a functional attribute of a whole above it in the hierarchy. For example, take the classification of channel geomorphology, which incorporates both the structural geomorphology and the functional geomorphic processes operating at each level (Montgomery and Buffington 1998). The processes operating in a channel unit are functional attributes of the processes operating in those of a channel reach, which are in turn functional attributes of the processes operating in a valley segment, and so forth within a watershed and a geomorphic province.
These hierarchies are not closed to the external environment of a process. Rather, processes are open systems. That is, processes are open to energy and mass from outside. Therefore, a process must have some external input and output. Each functional attribute includes a qualifier that imports or exports energy or mass if there is no spatial neighborhood defined in the model.
5. Stumbling over an example of process
There are a number of advantages of taking the notion of process, as outlined above, as the primitive in modeling geographic processes. Firstly, as a novel way of modeling the geographic phenomena studied it may provide new insights into how those geographic phenomena operate. As mentioned above, this approach also promotes a functional hierarchy of processes, where translation between processes at different levels of the hierarchy should not prove difficult, providing an avenue into research on scale. A further advantage of a process approach is the potential for snapping in other processes, Lego style, especially those with the same functional attributes. This may provide insight into the connections - through functional attributes - among processes. Finally, modeling processes in such a manner should be applicable to both field and discrete notions of space.
However, the author has not yet found an example that is formalized in such a way as to fit the above conceptualization of process. The requirements of such a specification for a geographic phenomena are that it be deterministic, whereby each variable is defined in terms of other variables, hierarchical (Haigh 1987), and that it explicitly incorporate space in the description of the interactions between its variables. The author conjectures that the lack of such a specification may be a consequence of a deeper epistemological incongruence. In an ontology built upon objects one can only describe the world within the ontology’s bounds. This then impacts on the data collected and the models developed. While not delving into the depths of metaphysics, the author recognizes processes metaphysics as a potential alternative (Rescher 2000).
In lieu of a formal example, then, a hypothetical illustration must suffice. Phillips (1999) provides an example of the process of discharge in a stream, which the following is taken from, that may be imaginatively extended to fit the process conceptualization presented above. He presents ‘a fully specified, completely determined system: that is, every variable can be described as some function of the other variables’ (Phillips 1999:75). This is described by the mass continuity equation
(1)
where Q is discharge (
/s), w is water surface width (m), d is mean
water depth (m), and v is mean velocity (m/s).
Additional variables that allow for a fully specified system are the
constant of the specific gravity if water (
), the Darcy-Weisbach friction factor (f) to describe
flow resistance, and the energy gradient or water surface slope (s)
(2)
where hydraulic radius 
. Equation 2
can be rewritten to solve for any variable on the
right of the equality.
This example is clearly aspatial. However, space cannot just be inserted into models, it must be inherent in the description of the phenomena, inherent to the data captured. Conceptually we may extend it by considering each variable a functional attribute that is “spatially aware” in the sense that it is acts upon and reacts to its relational neighborhood to which it is connected.
Thus the process Q is composed of and defined by a
collection of functional attributes, w, d, 
, g, R, s, f, that define each
other. The model
is initiated by raw data, which may define some or
all of the functional attributes and forms the basis for the spatiality of the
model whereby the raw data includes space.
This space is imported into the model
through each data point incorporating relations to its neighbors in a
relational space. The functioning
of the process and functional attributes will depend on these relations and on
thresholds that define the limits of the operation of the process and
functional attributes.
Furthermore, the location of process operation (defined by the data) will
import and export mass and energy defined by the process and functional
attributes through neighborhood relations.
6. A Beginning
The discussion of the problems of finding a suitable example suggests that to model geographic phenomena as processes requires the measurement of these phenomena in a manner that is amenable to the schema outlined in section 4. This then presents the task of developing new theory based on this new measurement approach. Following which, the conceptual model of the process and functional attributes may be specified with a functional programming language, such as Haskell, which is useful for the specification of conceptual models, leading towards implementation (Frank and Kuhn 1995).
In applying a functional language, the author considers Q-analysis as a likely method that could be extended to accommodate for the approach defined above (Atkin 1974a; Atkin 1974b). Q-analysis, also known as polyhedral dynamics, has been discussed and applied in geography in the past (Atkin 1978; Johnson 1981; Wilson 1981; Beaumont and Gatrell 1982; Gould 1982; Gatrell 1983; Fioretti 1996; Albrecht 1997). Regardless of past enthusiasm (Gould 1982), it has been rarely used since the hey days of systems theory optimism. This method may be well served by implementation tools such as Cellular Automata (CA), particularly graph based CA (O'Sullivan 2001), or Boolean Networks.
Attempting to step outside of the object-oriented paradigm conceptually has not proved an easy task. Clearly the formalisation and implementation of a process model will provide many challenges, particularly in the search for an example upon which to hang the theory. Hence, the next step is to either find a phenomena that has been observed and described in a manner that is amenable to the conceptualization of a process model, or to start from scratch.
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