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**Read this article to learn about various models used in geography: significance, needs, features, types and general classification of models! **

In the post-Second World War period, the definition of geography, geographic thought, and geographic methodology have undergone great transformation.

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In order to put the subject on a sound footing and to command respect in sister disciplines, geographers have increasingly concentrated in the last few decades on the theme of geographic generalization, formulation of models, theories and general laws. This geographic generalization is also known as ‘model-building’.

The term ‘model’ has been defined differently by different geographers. In the opinion of Skilling (1964), a model is “either a theory, a law, a hypothesis, or a structured idea. Most important, from the geographical point of view, it can also include reasoning about the real world (physical and cultural landscape) by means of relation in space or time. It can be a role, a relation or an equation”.

In the opinion of Ackoff, “a model may be regarded as the formal presentation of a theory or law using the tools of logic, set theory and mathematics”. According to Haines-Young and Petch, “any device or mechanism which generates a prediction is a model”. Accordingly, modeling, like experimentation and observation, is simply an activity which enables theories to be tested and examined critically.

Most of the geographers of the post-Second World War period have widely conceived models as idealized or simplified representation of reality (geographic landscape and man-nature relationship).

**Significance of ****Model:**

Geography is a discipline which deals with the interpretation of man-nature relationship. The earth—the real document of geographical studies—is however, quite complex and cannot be comprehended easily. The earth’s surface has great physical and cultural diversity.

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In geography, we examine location, landforms, climate, soils, natural vegetation and minerals’ spatial distribution and their utilization by mankind which lead to the development of cultural landscape. Moreover, geography is a dynamic subject as the geographical phenomena change in space and time.

The subject matter of geography, i.e., the complex relationship of man and environment can be examined and studied scientifically by means of hypotheses, models and theories. The basic aim of all models is to simplify a complex situation and thus render it more amenable to investigations. In fact, models are tools which allow theories to be tested. A more restricted view of models is that they are predictive devices.

**Need of Modelling in Geography**:

Geographers are interested in making laws and theories in their discipline like those in physical, biological and social sciences. Model is a device for understanding the vast interacting system comprising all humanity and its natural environment on the surface of the earth. This is of course not attainable except in a highly generalized manner.

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**Modelling in geography is, therefore, done due to the following reasons: **

1. A model-based approach is often the only possible means for arriving at any kind of quantification or formal measurement of unobserved or unobservable phenomena. Models help in estimations, forecasts, simulations, interpolation and generation of data. The future growth and density of population, use of land, intensity of cropping, migration pattern of population, industrialization, urbanization and growth of slums may be predicted with the help of such models. These are very useful in the forecast of weather, change of climate, change in sea level, environmental pollution, soil erosion, forests depletion and evolution of landforms.

2. A model helps in describing, analyzing and simplifying a geographical system. Locational theories of industries, zoning of agricultural land use, patterns of migration and stages of development of landforms can be easily understood and predicted with the help of models.

3. Geographical data are enormous and with every passing day these data are becoming more and more difficult to understand. Modelling is undertaken for structuring, exploring, organizing and analyzing the obtained enormous data through discriminating pattern and correlation.

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4. Alternative models can be used as ‘laboratories’ for surrogate observation of systems of interest which cannot be observed directly, and for experimenting and estimating the effects and consequences of possible changes in particular components as also for generating future scenario of evolution and end states of system of interest.

5. Models help in improving the understanding of causal mechanism, relationships between micro and macro properties of a system and the environment.

6. Models provide framework within which theoretical statements can be formally represented and their empirical validity then put under scrutiny.

7. Modelling provides linguistic economy to geographers and social scientists who understand their language.

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8. Models help in the building of theories, general and special laws.

**Features of a ****Model:**

**The main features of a model are as under: **

1. The geographical reality of the earth’s surface and man-environment relationship are quite complex. Models are the selective pictures of the world or part of it. In other words, a model does not include all the physical and cultural attributes of a macro or micro region. In fact, model is a highly selective attitude to information.

2. Models give more prominence to some features and obscure and distort some others.

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3. Models contain suggestions for generalization. As stated above, predictions can be made about the real world with the help of models.

4. Models are analogies as they are different from the real world. In other words, models are different from reality.

5. Models tempt us to formulate hypothesis and help us in generalizing and theory-building.

6. Models show some features of the real world in a more familiar, simplified, observable, accessible, easily formulated or controllable form, from which conclusions can be drawn.

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7. Models provide a framework wherein information may be defined, collected and arranged.

8. Models help in squeezing out the maximum amount of information from the available data.

9. Models help to explain how a particular phenomenon comes into existence.

10. Models also help us to compare some phenomena with the more familiar ones.

11. Models cause a group of phenomena to be visualized and comprehended which otherwise could not be comprehended because of its magnitude or complexity.

12. Models form stepping-stones to the building of theories and laws.

**Types of ****Models:**

As described earlier, the term ‘model’ has been used in a great variety of contexts. Owing to the great variety, it is difficult to define even the broad types of models without ambiguity. One division is between the descriptive and the normative. The descriptive model is concerned with some stylistic description of reality whereas the normative model deals with what might be expected to occur under certain stated or assumed conditions. Descriptive models may be concerned with the organization of empirical information, and termed as data, classificatory (taxonomic), or experimental design models. Contrary to this, normative models involve the use of a more familiar situation as a model for a less familiar one, either in a time (historical) or a spatial (geographical) sense and have a strongly predictive connotation.

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On the basis of stuff (data) from which they are made, models may also be classified into hardware, physical or experimental models. The physical or experimental model may be iconic (idol-shaped) in which the relevant properties of the real world are presented with the same properties with only a change in scale. For example, maps, globes and geological models are physical or experimental models. Models may be an analogue (simulation) having real world properties represented by different properties. Analogue or simulation models are concerned with symbolic assertion of a verbal or mathematical kind in logical terms.

**General Classification of ****Models:**

As stated at the outset, complexity of geographical landscapes and geographical situations is such that models are of particular importance in studying geography. A large number of models have been designed, adopted and applied by geographers.

**A more simple classification of models illustrated with examples has been given as follows:**

**Scale Models****:**

Scale models, also called hardware models, are perhaps the easiest type to appreciate as they are direct reproductions, usually on a smaller scale of reality. Scale models may be either static, like the model of a land surface of a geological model, or dynamic, like a wave tank or river flume. Dynamic models are perhaps more interesting and useful in geographical work. The great advantage that a dynamic model has over reality is that the operative processes can be controlled. This allows each variable to be studied separately.

In a wave tank, the effect of material size, wave length and wave steepness on a beach slope can be measured quite accurately if two variables are held constant while the third is varied. If the resultant beach slope angle is plotted against each variable in turn the points obtained in each case may either fall in a nearly straight line indicating a significant relationship, or in a diffused scatter suggesting little or no relationship. Close relationships revealed by the model may not be apparent on a natural beach where the wave variables cannot be controlled.

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There are, however, difficulties in applying the results of model studies of this type to a natural situation. One of these is the problem of scale. If wave size and material size are scaled up in the same proportion, then the sand of the model would become large cobbles in nature—and these two materials do not react similarly to waves. Again if sand in nature is scaled down to model size, it would be silt or clay which also responds differently from sand under wave action.

Despite such difficulties scale models have yielded very useful results in many fields of enquiry. The fact that engineers make a scale model before embarking upon any major project such as river improvement, dam construction, canal excavation, landslides, tidal surges, flood forecast, or harbour works scheme, demonstrates the value of this type of model.

Scale models are often used by physical geographers and especially by geomorphologists. In fact, geomorphologists have carried out fundamental research with scale models in order to investigate processes that are difficult to observe under natural conditions, such as river action, glacial movement, wind erosion, marine processes and erosion by underground water.

**Map****s:**

Maps are the models that are most familiar to geographers. They are a special type of scale model which become increasingly abstract as the scale becomes smaller. At one end of the spectrum is the stereo-pair vertical air-photograph which provides virtually a true scale model of the real world. It is, however, static and represents only the area shown at one instance of time. A simple vertical air photograph loses the impression of height but still shows all the visible elements of the landscape virtually true to scale.

A large-scale map loses much of the detail of the landscape although it can show buildings, roads and other features of this size accurately. As the scale is reduced the information becomes more symbolic and can no longer be shown true to scale; even more detail must be omitted. The map can, however, give an indication of the relief by means of contours, hill shading and hachures; this is missing from the simple vertical air photograph. Another advantage which maps also have over reality is that they show a very large area simultaneously, so that mutual space relationships can be much more easily appreciated and compared than on the ground.

Many maps use symbols to show specific features or distributions such as population density; these are even more abstract and further removed from reality that they represent. A new insight into a familiar area can be given by drawing a diagrammatic map where the scale is not correct for an area, but is adjusted to show population or some other variable to scale.

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Modifications in area, distance and direction are also needed in maps covering the world or large parts of it. A curved surface cannot be correctly reproduced on a plane or flat piece of paper. In fact, it is impossible to show a three dimensional earth on a two dimensional plane or sheet of paper. The earth may be truly represented on a globe, but globes have very little utility in geographical studies.

**Simulation and Stochastic ****Models:**

Simulation means imitating the behaviour of some situation or process by means of a suitably analogous situation or apparatus, especially for the purpose of study or personal training. Stochastic means: randomly determined or that which follows some random probability distribution or pattern, so that its behaviour may be analyzed statistically but not predicted precisely.

Simulation and stochastic models have been developed to deal with dynamic situations rather than with a static state shown on a map. This type of model simulates particular processes by means of random choices, hence the term ‘stochastic’, one which is connected with chance, occurrences. It can be illustrated by its application to drainage development.

Starting with a pattern of grid squares it is assumed that a stream source exists at the centre of certain randomly chosen squares. Random numbers are again used to determine in which of the four possible directions, each stream will flow and a line is drawn to represent its course as far as the centre of the adjacent square.

By repeating the process (with certain reservations that approximate to reality) there emerges a complete drainage network which shows many similarities to natural drainage patterns. Thus a conclusion can be reached that the natural drainage pattern has some element of chance about its make-up.

Simulation models can also be of use as a means of analyzing a large number of variables, which is a recurring problem in geography. For instance, the development of coastal spit can be shown to depend on a number of distinct processes or wave types. These different processes can be built into a model in such a way that each of them is allocated a specific range of random numbers. Each random number that comes up results in the operation of the appropriate process. In this way, the spit can be built up by the action of different processes in a random order, but in specific proportions. If the simulated spit resembles the real one, then one can conclude that the processes probably operate in the proportion specific in the model. Once a realistic model has been found it can then be used to predict future development of the spit provided the processes continue to operate in similar proportions.

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Stochastic simulation models have also been successfully used in the field of human geography to study the spatial diffusion of a variety of phenomena, including the spread of population diseases such as malaria, smallpox, fever and AIDS or innovations such as the use of a particular piece of machinery, tractors, chemical fertilizers, pesticides and weedicides. The simulation is made realistic by imposing barriers that can be crossed with a varying degree of difficulty. Random numbers are used to determine the direction of spread and the effect of the barriers can then be assessed.

The term ‘Monte Carlo’ is used to describe some stochastic models, in which chance alone determines the outcome of each move within the conditions of the model.

The Monte Carlo model may be compared with the Markov Chain model in which each move is partially determined by the previous move.

The Markov Chain is exemplified in the random-walk drainage development model described above. Both types have been applied in many fields of geographical research.

**Mathematical ****Models:**

Mathematical models are considered to be more reliable but difficult to construct. They obscure many of the human values, normative questions and attitudes. Yet, they have symbolic assertions of a verbal or mathematical kind in logical terms.

**For example, suppose I offer the following arguments:**

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(1) A is larger than B, and (2) B is larger than C.

Now by virtue of (1) and (2) together, I offer the following theorem or conclusion: (3) Therefore, A is larger than C.

The logical validity of this conclusion will not change with the change in time. Logically, it had to be true in 3000 B.C., 2000 B.C., 1000 A.D., and it will be true in 2025 A.D., 3000 A.D., 4000 A.D. Thus, the validity of the conclusion does not depend on specific historical period. It is a historical.

In the same way, the logical validity of a theory is also spatial. If a theorem is logically valid, it must be locally valid in the United States, Germany, Russia, France as well as in India, Pakistan, China and Japan.

Mathematical models can be further classified according to the degree of probability associated with their prediction into deterministic and stochastic.

Mathematical models represent the equation of specific processes by means of mathematical equations which relate the operative process to the resultant situation. It is necessary, however, to have a sound knowledge of the physical processes concerned, and consequently, this type of model-building has been mainly the work of physicists. For example, a dynamic mathematical model of glacier flow has been constructed by J.F. Nye. He simplifies the basic assumptions as far as possible to make the equations sufficiently simple to solve.

Thus, the glacier bed is assumed to have a rectangular cross profiled (U-shaped valley) of uniform size and specific roughness. The ice is assumed to be perfectly plastic in its response to stresses. Then, given certain stresses, the response of the ice can be calculated by means of differential equations. These can predict specific flow patterns and ice profiles for given values of the assumed conditions.

The geomorphologist can play his part by measuring flow patterns and glacier dimensions in the field. The closeness with which these approximate to the calculated values is a measure of the success of the mathematical model. If the observed flow pattern agrees closely with the predicted one, then the model can be used with some confidence to provide values for flow in parts of the glacier that cannot readily be measured in the field, but which are very important in studying the effect of glaciers on the landscape.

The speed of basal flow is important in this context. Mathematical models have also advanced our knowledge of how rivers move their load and adjust their beds, and how waves operate on the coast. These models are usually in the form of differential equations largely based on known physical relationship, and it is essential to test their numerical results against observations made under natural conditions or in a scale hardware model. The models are only as successful as the assumptions and simplifications on which they are based are true and valid. They provide a very simplified situation, but one that can be expressed in precise numerical terms and hence is capable of suitable mathematical manipulation. For this reason such models are more suited to problems in physical geography.

There have, however, been somewhat different development of mathematical model in human geography. These are more in the nature of empirical relationships that can be expressed in mathematical terms. An example is the rank-size relationship. This relationship shows that within any class of occurrences there are usually a few large items and many small ones with a fairly regular distribution between them.

It has been applied to towns in many parts of the world. There are a few large towns but many more small ones, and between the two, a moderate number of medium ones; the relationship is approximately linear on a double logarithmic scale. Mathematical models have also been developed in economic geography, which is more susceptible to quantitative formulation than other branches of human geography. Such models are often not dynamic in the same way as are the differential equations in physical geography, although some deal with flow of goods, etc., from one region to another.

Another mathematical model is linear programming, which is relevant to many situations in economic geography. It is a method of finding the optimum solution to a problem in which several conditions must be fulfilled. A factory will have certain requirements of labour, raw materials, transport and access to markets and each of which determines conditions that can be expressed as mathematical equations and represented graphically on straightlines. When all the equations have been plotted they reveal the point of optimum value in terms of location. The procedure provides a definite solution based on the values assigned to the equations. If the values are accurate, then the optimum solution will be obtained.

**Analogue ****Models:**

Analogue models differ from those type of models which have already been described. In the analogue models, instead of using limitations of the original or symbols to represent it, the feature being studied is compared with some completely different feature by means of an analogy. An analogue model uses a better known situation or process to study a less well-known one. Its value depends on the researcher’s ability to recognize the element common to two situations. These elements constitute the positive analogy; the dissimilar or negative analogy and the irrelevant or neutral analogy are ignored.

Reasoning from analogy has long been a part of geographical study. James Hutton, in his major work published in 1795, recognized the similarity between the circulation of blood in the body and the circulation of matter in the growth and decay of landscapes.

A similar circulation can also be seen in the hydrological cycle. The Davis’ concept of ‘normal cycle of erosion’ and Ratzel’s concept of ‘state as a living organism’ are important examples in which landforms and state have been compared to living organism. Both these concepts are thus analogies. The analogy used to further geographical knowledge must be better understood than the feature being investigated.

The behaviour of metals under stress has been intensively studied, and this has allowed useful analogies to be drawn between metals and ice. Methods of dealing with one problem can often be transferred by analogy to a completely different situation. The study of kinetic waves has been applied to the movement of vehicles on crowded roads, to the movement of stones and flood waves in rivers, and to the formation of surges at a glacier snout. These very dissimilar problems have a common fact that they are one-dimensional flow phenomena and from this point of view they can be treated with the same technique.

Analogies have also proved fruitful in the study of problems in human geography; for example, those that draw on certain well-established relationships in physics. The gravity model is a good example of this type. It is based on the physical observation that the attractive force between two bodies is proportional to the product of their masses divided by the square of the distance between them. The value for the distance in the model is often squared to approximate more closely to the force of gravity as observed in physics.

The attractive force may be considered in terms of transactions between two places. The number of transactions is likely to increase as the size of the places, often measured in terms of population number, increases and as the distance between them decreases. This model presupposes that there is no other force involved to limit the transaction, such as an international or language barrier. Various other physical relationships used as analogue models include the patterns of a magnetic field and the second law of thermodynamics

**Theoretical ****Models:**

Theoretical models can be divided into two categories. The conceptual models provide a theoretical view of a particular problem allowing deductions from the theory to be matched against the real situation. This can be exemplified by the theoretical consideration of the effect of a rising and falling sea level upon the coastal zone if certain specific conditions are fulfilled. It is assumed that wave erosion is the only process operating, that waves can only erode rock to r. certain depth of the order of about 13 metres (40 feet) and that the waves erode a wave-cut platform to a certain gradient below which they cannot operate effectively. It is also assumed that the initial coastal slope is steeper than this gradient.

A consideration of the prolonged action of waves eroding under these conditions, with a rising and falling sea level, leads to the conclusion that only with a slowly rising sea level, can a wave-cut platform of great width be produced. The theoretical forms of the coastal zone under the various conditions specified can be established and then compared with actual coastal zones. Much more elaborate theoretical models of this conceptual type have been developed in the study of the evolution of slope profiles. These are based on the known or assumed effect of different slope processes.

A long series of stages of modification can be derived from this type of theoretical model, and these can again be matched with actual slopes.

The second type of theoretical model is associated with the word ‘theory’, when this is used to denote the overall framework of a whole discipline. The framework must not be too rigid or it will cramp the growing edges of the subject, where the most exciting work is going on. The ideal is a flexible framework that can contain a wide variety of geographical endeavour and yet give it coherence and purpose. Models are particularly valuable in this context as they are often common to all branches of the subject and so help to give it unity.

An analogy may help to illustrate the way in which the vast and growing amount of geographical data may be organized within a theoretical framework. Geography may be compared with a five-storeyed building, each storey being supported by the one below and supporting the one above (Fig. 11.1):

** **

(1) The lowest storey is the one which accommodates the data, the raw material of geographical study.

(2) The data lead up to the level of model where they are organized in a suitable way for analysis.

(3) The techniques of analysis, lying on the next storey, depend on the model adopted for the study.

(4) Analysis leads up to the next floor, concerned with the development of theories.

(5) The theories in turn lead up to formulation of tendencies and laws. These are located at the top as they are the ultimate aim of geographical methodology.

**Critical**** Views:**

For understanding and explaining complex geographical phenomena, models are of great importance. Modelling has, however, been criticized on many counts. Critical views on modelling vary from those which accept modelling but criticize the way in which modelling is done to those which reject modelling as a worthwhile activity in geography.

Those who agree with modelling in geography but do not agree with the way models are being prepared and hold the view that most of the models are prepared badly. The basic aim of the modeller is to represent complexity by something simpler. In the exercise of modelling, the modeller may simplify the complexities of geographical realities too much or too little. Oversimplification may mislead students and generate misunderstanding which may ultimately lead to bad prediction. Under simplification is of little use in teaching as it does not explain the reality and gives insufficient basis for prediction.

The second objection to modelling is that the modellers may concentrate on the wrong things. Sometimes models may neglect to fulfil the basic criterion of simplifying. They go for the principal component analysis, stepwise regression and Q-analysis. These techniques often produce models more complicated than the original data. Moreover, models may incorporate some of the salient points and omit others.

There are scholars who do not question the appropriateness of modelling as a generally applicable strategy in geography. There is a group of geographers who consider modelling as a worthwhile activity but hold the view that geographers should not be forced to apply modelling techniques to everything. According to them, modelling is not appropriate in some branches of geography, especially in human geography, regional geography, cultural geography and historical geography. In various branches of regional, cultural and historical geography, modelling strategies have distorted the subject by putting overemphasis on some topics and under emphasis on others. By this strategy, generalizations have been made on the basis of few cases and many a time at the expense of specific cases.

Those who out rightly reject modelling in geography say that geography is not a pure physical science, it has a very strong component of human beings and models may not properly adjust and interpret the normative questions like beliefs, values, emotions, attitudes, desires, aspirations, hopes, and fears, and therefore, models cannot be regarded as dependable tools for explaining correctly the geographical reality.

Criticism of modelling may also be based on objections to the generalization that modelling usually involves. It may be considered futile to construct general models to apply to geographical events, especially where idiosyncratic (regional) human actions and free will are concerned. Or, it may be that the geographer’s purpose is to predict or understand specific events and situations, his or her interests may be in the unique (specific, regional) case for which a general model is thought irrelevant.

Many of the models in geography have also been criticized on the grounds of application of sophisticated mathematical and statistical tools and techniques. Despite the quantitative revolution, few geographers feel comfortable with mathematical symbolism and ideas, and are thus largely unconscious of the generality, clarity and elegance that mathematical modellers appreciate in a good model. Geographers apart, even students, policy makers, clients and the public at large, may find mathematical models difficult to understand.

Another criticism is that no model is adequate by itself; any model must be continually subject to reassessment, modification and replacement. In Feyerabend’s words (1975):

Knowledge…is an ever-increasing ocean of mutually incompatible (and perhaps incommensurable) alternatives, each single theory, each fairy tale, each myth that is part of the collection forcing the other into greater articulation and all of them contributing, via this process of competition to the development of consciousness. Nothing is ever settled, no view can ever be omitted from a comprehensive account.

In fact, accountable growth of knowledge is not a well-regulated activity where each generation automatically builds upon the results achieved by earlier workers. It is a process of varying tension in which tranquil periods characterized by steady accretion of knowledge are separated by crises which can lead to an upheaval within subjects, disciplines and break in continuity.

Model-building also demands considerable reliable data. Such reliable data are rarely attainable in the developing and underdeveloped countries. As a matter of fact, any set of data collected in the developing countries have many pitfalls and shortcomings. Any model, theory, or law developed on the basis of weak and unreliable data is bound to give only a distorted and faulty picture of the geographical reality. It has also been found that generalizations done with the help of models and structured ideas are bringing exaggerated results leading to wrong predictions.

Most of the models have been developed in the advanced countries of Europe and America, and theories and models were constructed in these countries on the basis of data collected there. There is certainly a danger that the models developed in Europe and America may be elevated to general truth, and given the status of universal models. In reality we do not have universal human, cultural, industrial, agricultural and urban geography. There are different socio-cultural and agro-industrial processes, working in different parts of the world, which result into different cultural landscapes. Owing to these constraints, generalizations made on the basis of models may be misleading and faulty.

Moreover, the data used by the western experts are related to a period of about one hundred years. If these models, developed on the basis of data of developed countries, are applied in the developing countries, the results and predictions may be disastrous.

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