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Appendix regional modelling


Models are an abstraction and simplification of reality. A region may be represented by using models of increasing abstraction such as aerial photographs, a map, a diagram, or a series of equations representing the dynamics of the regional system. The method presented here is that of Odum and Odum (1976) which uses a series of diagrams to focus attention on key elements and interactions.

Modelling requires a macroscopic perspective to eliminate superfluous detail. Several relatively simple steps are employed.

Step 1. Identification of system limits. All ecosystems have arbitrary limits. However, the principle of integrative levels indicates that to understand a system such as a river and its flood plain, one should analyze the next higher encompassing system - watershed - in order to understand the internal interactions of the prior system.

Consequently, each person representing a different sector during the planning process should understand how a given boundary affects his analysis of the system as a whole. A boundary cutting across a statistical enumeration district or ecosystem can, of course, complicate the analysis. Political and other considerations may dictate other limits. Once lines are drawn, boundary conditions are established and internal interactions can be distinguished from exchanges with other systems.

Step 2. Definition of scale. The planning mandate determines the focus of the model. Finding a place to locate a highway requires a very different model than one for a general mandate to "optimize regional development." Scale, units of measure, quality and other characteristics of information, and compatible levels of detail in analysis depend upon the common constraints of the area's size, availability of time and funding and planning objectives.

Step 3. Identification of inputs and outputs. Once system limits have been established (Step 1), outside energies, materials and information which affect the system can be listed (Table 1). These may include sunlight, rainfall, tidal action, tectonic movement, fuels, goods, technology, infrastructure, finances, immigrants and policy decisions, all of which interact with other system components. Outputs include products, emigrants, water, pollutants, heat, etc. In a complex region, interdisciplinary discussions are essential for identification of components and external interactions.

Step 4. Identification of components (Subsystems) and interactions. It is useful to go into considerable detail in identifying components and interactions at the early stages of model elaboration. Later, components may be combined or eliminated if not critical to the analysis. The basic divisions in any regional model have to do with their relationships to man, especially the degree of intervention and energy subsidy applied. Therefore, natural components (both terrestrial and aquatic), managed systems such as in agriculture and silviculture, and man-created components such as cities, industries, and water control structures are considered (Table 2). At a later stage, new components proposed as development alternatives can be added.

Step 5. Preparing the diagram. Table 3 gives the basic symbols needed for system diagramming. Each symbol has a unique characteristic as described. When lines are drawn to represent flows of energy or materials and information with energy values, one has a conceptual model of the regional system. By quantifying the flows and storages, such a model can be expressed as a series of non-linear differential equations and computer simulated to test the effects of various management strategies.

Figures 1-4 shows the sequence in preparing a regional diagram. First, the system boundary is shown and the external forcing function or energy sources that have been identified in Step 3 are arranged clockwise beginning with the most dilute source, the sun, and ending with the most concentrated sources (Figure 1). Total systems respiration is shown by the heat sink and all exports by the arrow to the right. Second, the major components or subsystem within the system boundary identified in Step 4 are added (Figure 2). Third, the interaction of inputs to, and transfers between, components are generalized and shown without going into detail on the precise mechanism involved (Figure 3). Fourth, the same diagram in Figure 3 is redrawn to show the complexity of the internal interaction (Figure 4).

Table 1



System inputs

1. Technology, information and policy
2. Equipment, materials and all supplies
3. Services
4. Energy quantity and quality - fossil fuels, electrical, solar, wind, etc.
5. Water - rain and inflow from other systems
6. Sediments, organic matter, chemicals, etc. from upstream systems
7. Money - when an input involves an economic transaction
8. Immigrants

System outputs

1. Agricultural products
2. Water, air and water-bone contaminants, and sediments
3. Industrial products
4. Forest products and services to downstream systems such as water quality and hydroperiod regulation
5. Emigrants
6. Recycled gases, solids and liquids
7. Hydroelectric energy production

Background data

1. Physical and political maps
2. Soils, geomorphology, hydrology
3. Map and description of important ecosystems

Legislative regulation

1. Laws governing regional plans and planning
2. Regulation or zoning of landuse
3. Laws governing construction, mining, channelization, etc.
4. Laws regulating quantity and quality of the discharge of wastes into air, water and land
5. Permission requirements for clearing land, cutting timber, mining
6. Laws regulating commercial and sports fishing and hunting
7. Laws establishing and protecting parks
8. Requirements for permits and licenses

Official and private agencies serving the

1. Ministries or institutes with actual or potential functions in project area management
2. Research and teaching institutions
3. Private organizations and businesses with interest in environmental management

Table 2


1. Subsystems having components and processes that are predominantly man-made
Industry - extractive, processing, power transformation, etc.
People - demographic characteristics, cultural perceptions and interactions
Cities - structure and function, interactions with hinterland, intercity interactions
Institutions - structure and function, role in relation to all subsystems, actual capabilities
2. Subsystems that combine natural and man-made components and processes
Farms and ranches, silviculture, aquaculture-structure and function, area, location, human and institutional characteristics
3. Subsystems having components and processes that are predominantly natural
Terrestrial and aquatic - structure and function, diversity, extent, location, degree of intervention


1. Industrial production - interaction of materials, energy, water, labor, etc. Interaction of by-products such as heat, chemicals and particulates with man, agriculture and natural systems
2. Agricultural production - interaction of solar and fossil energy, water, chemicals, soil minerals, equipment and technology. Interaction of by-products such as chemicals and sediments with infrastructure and natural systems.
3. Natural systems - interaction of solar energy with water and inputs from other components such as runoff, sediments and wastes. Services to agriculture and man such as hydroperiod regulation, wind breaks, pest predator habitat, recreation, erosion control, etc.






Energy source or forcing function

Any source of energy or materials and information with energy content external to the system being studied. The sun and sun derived energies such as wind and rain are considered inexhaustable. Rates of flow are limited and can vary according to intrinsic controls of a predictable nature such as seasons. Earthquakes and hurricanes have frequencies intrinsic to an area. The other major class of energies are those of cultural origin, such as fossil fuels, materials, services, migration and information (technology). Input rates are determined either by policy decisions external to the system or by the ability of the system to attract. Flows are considered to be constant or to vary according to a given program during a given analysis or simulation run.

Energy storage

The tank-shaped symbol represents any storage of energy, materials or information within a system or system components. Scale may range from the instantaneous biomass of a single plant to that of an entire forest depending on the model. Storages have one or more inputs and outputs and a capacity set by the modeller. Tanks represent structure in many forms, such as a building, the capital assets of a city, ordered information stored in a library or the accumulated experience of a people. A tank without an inflow can represent non-renewable resources.

Energy transformation and storage

A special case of the previous energy storage symbol. The energy entering (a) via the small triangle is transformed and stored (b) in another form. In keeping with the second law of thermodynamics some of the incoming energy must be degraded (c) in the process of transformation. In Figure 8 incoming oil is transformed by fire partly into heat to warm the house and partly into heat going directly up the chimney.


The switch symbol represents an on/off control on an energy flow; switching action (a) determines whether flow (b)-(c) is on or off. Examples include the turning on of fish migration by some cue, the turning on of an irrigation system when soil moisture drops to a determined level and the activation of a crop subsidy.

Heat sink

The downward pointing arrow represents the degradation of energy into dispersed heat (entropy) associated with work processes in any system as dictated by the second law of thermodynamics. Every development process - the building of structure in a plant, a farm or a region - requires the loss or depreciation of part of the energy available. This is sometimes called an "entropy tax." Energy is constantly entering a system and being stored and transformed. Eventually it leaves the system as either dispersed heat or products bound for some other system. In a steady state inflows equal outflows. For the earth as a whole all energy entering leaves as dispersed heat.

Interaction or workgate

The workgate symbol represents the interaction of two energy flows in which flow (a) makes possible, increases or reduces (negative impact) flow (b) resulting in a new flow (c) at an entropy cost (d). In a plant, creation of biomass through photosynthesis is represented by a series of workgates in which sunlight interacts with water, CO, and nutrients. Agriculture adds additional work gates for cultivation, pest control, etc.


The downward pointing workgate combined with the heat sink symbol represents stress. This is a special case used to make a negative effect more obvious in a model. Disease is a stress on an organism diverting energy from useful work into waste heat. Excess water or drought have the same effect on a crop.


This symbol represents a single plant or an entire community which has its basis in photosynthesis. At the regional scale the symbol is used to represent individual ecosystems or combinations; crops, a farm or the agricultural sector.


The hexagonal symbol represents a consumer. A consumer can be a soil microbe, a cow, a human population, a city or an industry. All have in common an outside energy source, depreciation and the output of energy in the form of productions such as minerals, meat, work or tractors.

Economic transactor

In the part of the system in which man uses money as a means of accounting for flows of goods and services the transactor symbol represents the rate of exchange. Money always flows in the opposite direction to energy.

Non-defined process

The box is used when it is not important to represent the precise role of a component.


Odum, H.T. and E.C. Odum. 1976. Energy Basis for Man and Nature. McGraw Inc. 297 pp.

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