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Analysis of Land Use Change: Theoretical and Modeling Approaches
Helen Briassoulis, Ph.D.
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4.6.4. Input-Output-Based Integrated Models
The broad framework of Input-Output (I-O) Analysis as been used for the analysis of the economy-environment interactions in several instances, a short account of which will be given shortly. In the particular case of the analysis of the land use change, the literature contains contributions utilizing input-output models although not with the frequency with which other analytical frameworks are being used. Two general directions in the use of I-O analysis for the study of the economy-environment-land use relationships can be distinguished. The first involves the integration within the structure of an I-O table and model of environmental and land use considerations; this is the case of building a compact model and it is explained briefly below. The second involves the linking of an I-O model of an economy with other models describing its environment and land use system; this is the case of a modular model. These are detailed below.
4.6.4A Compact Input-Output Models
The earlier attempts to use the I-O model beyond the narrow confines of economic analysis are found in the models proposed by Cumberland (1966), Daly (1968), Leontief (1970), Isard (1972) and Victor (1972). The common thread of thought in all these attempts is to augment the standard economic I-O table with rows and columns which represent somehow the inputs and outputs of elements of the environmental system to and from the economic system. In the following, only a few of these attempts are discussed. The reader may refer to Lonergan and Cocklin (1985) and Bolton (1989) for additional analyses of these and other similar efforts. Leontief (1970) proposed an adaptation of the basic I-O model to accommodate the "environmental repercussions of the economic structure". The interindustry matrix of the basic I-O table is augmented with extra rows and columns, the rows representing the generation of pollutants by the economic sectors and columns representing anti-pollution economic sectors established to remove the pollutants generated by the economic system. This augmented table is suitable for the analysis of pollution caused by economic activities. The analysis of land use change, however, is not addressed by this framework. In fact, changes in land requirements are estimated exogenously based on the results of the augmented I-O table. An application of this approach by Leontief et al. (1977) is briefly described below.
The United Nations World Model
Leontief et al. (1977) designed and applied the United Nations World Model (mentioned previously) in a global modeling exercise commissioned by the United Nations for the study of the interactions of the world economy with the environment. All countries of the world were grouped into 15 regions. In each region, 48 producing and consuming sectors were distinguished connected with each other and with the economies of the other regions by means of I-O relationships. A multi-regional Input-Output system was set up consisting of 2626 equations that describe the interrelations between production and consumption of various goods and services within each region as well as interregional relationships (imports and exports). On the basis of various assumptions as regards basic macroeconomic magnitudes, the model projected the output of the economic sectors for a range of alternative future development scenarios to the year 2000.
Consumption coefficients measure the amounts of specific agricultural products, among others, consumed per unit dollar of additional total expenditure. The specific agricultural products considered are animal and milk products, cereals, high-protein crops and root crops. These were measured in physical units. Their consumption was estimated and projected from region-specific consumption functions published by FAO which take into account the income elasticity of demand for these products. All other agricultural products were labelled "residual agriculture" and their output is measures in value units. The following equation (4.107) was used to assess the cultivated land requirements for the projected levels of agricultural output.
SLAND = K* AGS + K * AGR (4.107)
where,
| SLAND | cultivated land area |
| AGS | selected agricultural products |
| AGR | residual agriculture |
| K | capital coefficients |
Capital coefficients reflects each year’s investment in equipment, land, plant, and irrigation. In the case of agriculture, the levels of investment in land development and irrigation are set exogenously. Land-input coefficients (the inverse of yield ratios) were held at the 1970 levels given the difficulties to project agricultural yields satisfactorily for the different regions of the world. In this respect, Leontief et al. (1977, 21) note that the projections offered can be "viewed as showing the combination of yield improvements and/or increases in cultivated area needed to realize the projected levels of agricultural output." The agricultural output and the associated food consumption projections were made on the assumption that the extent of self-sufficiency of each country will not change from its 1970 level. Based on these projections, a land/yield index, an arable land index and a land productivity index were estimated. The land/yield index measures the changes in land under cultivation, as compared with the base year 1970, required to achieve the predicted levels of agricultural output assuming that the productivity of land is at the 1970 levels. This index is essentially an index of agricultural production weighted by land per unit of output. Combining this index with exogenous estimates of new land brought into cultivation in the individual regions, the arable land index was calculated. This measures total arable land in 2000 as compared to 1970. Finally, the land productivity index gauges the increases in production that must be sought by means of technological change, and the use of high-yield crop varieties, pesticides and fertilizers.
Economic-Ecologic Models
Walter Isard (1972) offered a more complete adaptation of the I-O framework for the economic- ecological analysis of a region as shown in Figure 4.2o. Isard’s proposal is conceptually similar to the models proposed by Cumberland (1966) and Daly (1968). The extended I-O table has four quadrants which represent four two-way types of relationships between economic sectors and ecological processes. Vertically, the conventional economic sectors are identified in the first block of columns. The second block of columns is devoted to ecological processes classified broadly as biotic and abiotic. Biotic processes are further classified into fauna and flora-related while abiotic processes are further classified into climatic, geologic, physiographic, hydrologic, and soils. Horizontally, the first block of rows represents again the conventional economic sectors while the second block of rows represents ecological commodities which are classified broadly into biotic and abiotic. Biotic commodities are further distinguished into plant and animal life-related while abiotic commodities are further distinguished as the corresponding abiotic ecological processes. Observe that "land area" (and "water area") is introduced as one row of the extended I-O table. The first quadrant of the extended table is the typical matrix of interindustry coefficients of a conventional, economic I-O table. The second quadrant, designated as "economic sectors re: ecologic commodities" (i.e. economic sectors related to ecologic commodities), represents the production of pollutants by the economic sectors and forced on the environment. The third quadrant, designated as "ecologic processes re: economic sectors" (i.e. ecologic processes related to economic sectors), refers to economic commodities which are produced and used by ecological processes (this quadrant contains very few entries). The fourth quadrant, designated as "ecologic system: interprocesses", refers to the inputs and outputs exchanged during ecologic processes in the environment.
The Isard extended I-O table is an idealized representation of the economy-environment system characteristic of the early-1970s efforts to model holistically the interplay between the economy and the environment. It presents both conceptual as well as practical problems whose discussion is beyond the present purposes. Suffice to mention that the fourth quadrant is the most problematic of all as it contains the whole set of still unknown environmental processes which do not necessarily have an I-O (linear) representation. In addition, the treatment of the constituents of the environment in ways similar to the treatment of the material inputs and outputs of the economic system poses deep conceptual questions as well as methodological and practical problems of handling, measuring and interpreting the resulting coefficients. From the point of view of the analysis of land use, land area may be included in this framework but its mechanistic and linear treatment – as it is the case with all economic and ecological commodities and processes in I-O analysis – leaves much to be desired from the perspective of a comprehensive and meaningful analysis of land use and its change.
An extended I-O framework for the study of the economy-environment interactions similar to that proposed by Isard above was suggested and used by Victor (1972). The differences between Victor’s and Isard’s schemes are: (a) Victor uses the commodity-by-industry version of the economic I-O table instead of the industry-by-industry version, (b) the interpretation of the second quadrant is that the entries represent the amounts of ecological quantities used to satisfy interindustry and final demand, (c) similarly, the interpretation of the third quadrant is that the entries represent the amounts of ecologic commodities which are the outputs of interindustry and final demand activities, and (d) the fourth quadrant (Figure 4.2o.) is blank in Victor’s scheme (!). Victor defines as ecologic commodities all material inputs from the environment on their first introduction to the economy and classifies them according to the main environmental compartments of land, air and water. Similarly, the waste products of the economic system which are returned to the environment are also ecologic commodities. The "land" compartment accounts for material (land area included) and ecosystem inputs to the economic system as well as for the material and ecosystem outputs of the economic system (i.e. the environmental modifications effected by economic activities). Another characteristic of Victor’s use of the I-O framework is that he defines a number of accounting identities which must hold for both the economic and the ecologic commodities to ensure that the economic-ecologic system is in equilibrium. The identities concerning the ecologic commodities are considered material balance identities following from the law of the conservation of mass (the First Law of Thermodynamics ).
The models referred to above are compact models which attempt to force the spirit of the I-O accounting framework on the economy-environment interactions. From the perspective of the analysis of land use and its change, several observations should be made. First, there does not seem to exist any real world application of this modeling approach to the analysis of the land use impacts of economic activity. Most of the applications refer to pollutants (i.e. flows) generated by the economic system and abated by the anti-pollution sectors of the same system. Even in this case, the compact I-O modeling framework is not capable of handling a host of other environmental impacts either because they are intangible or because the restrictions of the I-O model (mostly the linearity and stability of the technical coefficients) do not provide for a realistic representation of the ecological processes as well as for the economic-environmental interactions over space and time.
Second, there are particular conceptual problems with handling land use and its change in the compact I-O model in addition to those associated with its handling of economic-environmental relationships in general. Land use conceptualized as area of land occupied by an economic activity is a stock concept, a form of capital, which can be considered as a "primary input" in the I-O model – i.e. it does not enter the interindustry matrix. If, however, the resources (or the services, products, qualities or other attributes) associated with a given land use are considered as flows, they can be incorporated in an interindustry matrix and treated like the economic interindustry coefficients. Still, there has to be a reasonable interpretation of these "flow" items to use the extended I-O meaningfully for the analysis of land use change which results from changes in the economic structure. Finally, it has to be kept in mind that I-O analysis in general is predicated on a demand-driven model of economic development which does not account for supply side factors, a particularly sensitive and critical issue when it comes to the constraints imposed by land use and the environment.
4.6.4B Modular Models with an Input-Output Component
Another direction in the use of I-O analysis for building integrated economy-environment models in which land use and its change are included is the design of modular models in which the economic system is represented by an I-O model. Several modular models for the study of the economy-environment interactions have been proposed since the mid-1970s (see, for example, Bolton 1989, Braat and van Lierop 1987, Briassoulis 1986, Hafkamp 1983, Lakshmanan and Bolton 1986, Lonergan and Prudham 1994). A schematic structure of such a model is shown in Figure 4.2p for a single-region case. The economic system in these models can be specified by means of several alternative functional forms one of which is an I-O model which provides for a complete picture of the interindustry relations. One such modular model has been already mentioned previously in the context of the application of the cellular automata modeling approach (Engelen et al. 1995). This model is rather simple compared to more elaborate modular integrated models. Another integrated model where the I-O model is used for modeling the regional economy and it is linked to other models representing the environmental system – including land use change models – is presented next.
The model built for Mauritius was designed at IIASA (International Institute for Applied Systems Analysis) by a research team led by W. Lutz (Lutz 1994a). The underlying philosophy of the model is termed the "PDE approach" (which stands for Population, Development, and Environment). The purpose of this modeling approach is to facilitate, through modeling, the study of the interactions between population change, socio-economic development and the environment. The sequence Population, Development, Environment is not arbitrary. According to Lutz (1994b)" "Population is taken as the point of departure as one of the basic driving forces that – together with many other factors – has an impact on development within environmental constraints.. Rather than viewing population-environment linkages in terms of a linear causal chain, it should be visualized as a series of concentric rings where the sphere of development ….. is intermediate between the demographic aspects of the human population and the natural environment" (Lutz 1994b , 210-211). This philosophy is depicted in Figure 4.2q. Drawing on Lutz (1994a) the broad modeling framework which has been designed to express the above philosophy is presented in the following. Its structure is modular, the three constituent modules being the population, the economy (or development) and the environment modules (Figure 4.2r.). These are described briefly next.
The population module (Lutz and Prinz 1994) is perhaps the most elaborate of all three given the importance attributed to the quantitative and the qualitative aspects of the demographic structure of an area within the PDE approach. The core of the module is a multi-state population model – an elaboration of the multi-regional demographic model transferred to the study of many population groups defined along any criterion of interest. In the present case, population groups were distinguished by education and labor force participation status. Population dynamics is studied along four main dimensions: age, sex, education and labor force participation which are considered as the most important in the study of the interactions between population and the environment. A distinction is drawn between determinants and characteristics of population change. The basic demographic determinants of population change are fertility, mortality and migration, their effects being not always immediate but working through birth and death age-specific rates. However, the parameters of the population system are significantly affected by local and supra-local physical, economic, social, cultural, and political conditions and, in their turn, may affect some of these conditions. The characteristics of population change – which are the outputs of the population module – include: total population size, growth rate, density, age distribution (mean age and dependency ratios), sex ratio, and regional population distribution. These impact on the economic and the environmental systems variously. Usually, population change affects the environment via the economy although in several instances the population-environment relationship is direct as it is the case with the use of land for housing or the use of water by private households.
The economic module (Wils 1994) is an input-output (I-O) model for a small, open economy. The economy mediates the relationship between population and the environment as the economic activities of the population use the resources and sink functions and services of the environment. Especially with respect to the uses of land, the economic structure is a critical determinant of the allocation of land to various activities which, in their turn, impact on environmental resources and receptors. The (I-O) model is demand driven. The final demand for the output of the economic sectors determines the total production of each sector according to the basic I-O identity:
X = (I-A)-1 Y (4.108)
where,
| X | is a nX1 vector of the output of the n economic sectors |
| Y | is the nX1 vector of final demand for the output of each sector |
| A | is an nXn matrix of inter-industry technical coefficients and |
| (I-A)-1 | is the nXn Leontief inverse matrix of sectoral multipliers |
For an exposition of I-O analysis the reader is referred to Hewings (1985), Miller and Blair (1985), and Schaffer (1999). For each sector, labor and environmental coefficients are specified; e.g. number of workers per unit value of output by sector, area of land per unit value output by sector, volume of water demanded per unit value of output by sector, and so on. In the complete model, these coefficients are frequently adjusted to produce consistent projections of population, economic activity and environmental conditions.
In the particular application in Mauritius, where a very open (and small) economy is to be modeled, prices are assumed to be fixed. The exogenous information provided to the I-O model includes:
The I-O model is a series of single-period models which operates under the assumption that all goods produced are sold within the same year. The model outputs are: (a) total production by sector with endogenous investment and (b) total production by sector with endogenous investment and private consumption. More details on the treatment of consumption as well as of other population characteristics in the economic module are provided in Wils (1994).
The land use model (Holm 1994) – a component of the environmental module of the Mauritius model – assesses the distribution of land to various land use categories as a function of the demands made by the economy, competition among land uses (basically, competition among the economic activities using land), and environmental constraints on the availability of land which is suitable for specific purposes. Land is assumed to be a form of capital a certain amount of which is necessary to produce a unit of sectoral output. Because the I-O model used employs linear production functions without returns to scale, no substitution between inputs is permitted. Hence, the land use requirements of a sector s (within a certain time period t), LDst, are found by simply multiplying the sectoral output estimated by the I-O model (within a certain time period t), Gst, by the inverse land productivity coefficient, lst (monetary value of output per square kilometer) as follows:
LDst = (1/lst) Gst (4.109)
As it was the case with the economic model, the land use model accepts exogenous input for land productivity which may be changed between time-periods. It, then, produces the land use distribution which is constrained by the amount of land available and the amount of water available for irrigation. In the case of a land or water conflict (over-prediction of demand for land or water basically), a solution is found by iteration. In other words, if there is a land shortage, the model changes final demand endogenously until a production mix is achieved which satisfies the land constraints. This procedure is detailed below.
The land use model distinguishes four aggregate types of land use: sugar cane land (the main economic good produced), other agricultural land, urban land, and beaches. Certain rules for land conversion from one land use type to another are established to guide the land allocation process. These rules draw from the experience of historical land transformation in the island as well as from logically derived sequences of possible transformations. Hence, sugar cane land and other agricultural land can be traded and transformed into urban land. Beach land cannot be transformed. The model is not spatially explicit; hence, transitions from one type to another are not specified by location. Although this lack of spatial specificity in the case of Mauritius did not create problems, it is generally preferable to have spatially-explicit (or, geo-referenced) models which produce more reliable land use changes as they reflect the actual spatial variability of various constraints on land transformations.
The assessment of the area of the four types of land use distinguished above is done separately for each type taking into account its particularities and applicable constraints. For example, in the case of agricultural land which is distinguished between sugar cane and other, demand for land is estimated initially by equation (4.109). However, if there is a water shortage, land productivity decreases. The impact of water shortage is reflected in a user-specified elasticity measure which shows how much land productivity will decline in the case of water shortage. The estimate of the new land productivity coefficient is used to adjust the demand for land by the particular sector (which is impacted by water shortage).
Urban land is considered an absorbing state; i.e. once agricultural land is converted to urban land the reverse change is not possible. The only source for new urban land is agricultural land (which was historically the case). Urban land is distinguished into residential and commercial. The demand for commercial land is directly estimated by equation (4.90). For residential land, the demand is estimated as a function of household consumption and land price as follows:
LDst = [h1Pt + (h2 Ct/h3)] 10-6 (4.110)
where,
| s | is the residential sector only |
| h1 | is the minimum residential space per person (by default 10 m2) |
| P | is total population |
| h2 | is the share of private consumption spent on housing (by default 9%) |
| C | is private consumption |
| h3 | is unit price of residential land |
All parameters are user specified and the per capita income elasticity of housing demand is assumed to be 1.
As regards beaches, these are assumed to be the key resource for tourism on the island. Therefore, all economic activity in the hotel and restaurant sectors are directly related to the length of the beaches (although these may not be located necessarily along the beach). Beaches are distinguished into two classes. The "strip" is currently used and it is considered the best; hence it is not changed at all in the model. What does change as a response to increased demand is the density of use of these beaches. There is another class of secondary beaches which can be converted to beach use for tourism. Finally, the "other land" type contains natural features and is used to assist the model user to redefine the amounts of available agricultural or urban land by transferring some land to and from the "other land" category.
Because of differences in land profitability among uses, the actual allocation of land to alternative uses is governed by economic factors, by now a common knowledge based on experience and urban land market theory (see Chapter 3 and the utility maximization models). The land use model of Mauritius employs a market mechanism for resolving land use conflicts which mimics a market bidding process (as in Alonso’s model). However, in addition to a market-based conflict resolution mechanism, the model accepts the possibility of public intervention in settling conflicts which involve the public interest. Because the model does not include market demand and supply for land and the corresponding prices (the rent profile) to employ an Alonso-like bidding process, it uses the production per unit of land as a substitute for the relative worth of the different types of land use, as profit per unit of land is almost proportional to production in this model. Based on value-added figures for the different economic sectors, the land use types are ranked from higher to lower priority for conversion and this ranking is assumed to remain constant over time. Hence, following Holm (1994), the decision rules adopted are: (a) in case of conflict, urban land demand wins over agricultural land demand unless a policy to preserve agricultural land is stipulated; (b) if no policy is specified, and if the land available for sugar and other agriculture is less than demanded when the urban land demand is satisfied, then the output of both agricultural sectors decrease proportionally. The decrease in demand for sugar land is initiated by decreasing export demand for sugar proportional to the land shortage. Decrease in other agricultural land demand is initiated by proportional decreases in export demands and in domestic household demand for food. This decrease is exactly compensated by an increase in import demand from households. Urban land is not allowed to decrease, regardless of the development of land demand. Consequently, agricultural land cannot increase but it can remain constant.
The land use model is used to simulate the land use and economic impacts of various types of plausible policies such as a "sugar policy" and an "agricultural policy". Finally, the model calculates the changes in population and in the total size of urban areas on the island as a function of specific scenario assumptions regarding population change, economy, land use, and the environment. On the basis of user-supplied assumptions, the spatial distribution of the population is projected. Two main assumptions are considered: (a) distribution proportional to the initial number of inhabitants, an assumption without enough empirical and theoretical support and (b) distribution proportional to population change in 1985-1990. For information on modeling the water systems in Mauritius in the context of the integrated model the reader is referred to Toth (1994).
The integrated model presented above presents another alternative way of modeling land use change in an integrated context. It may lack the sophistication of several other models reviewed before although here is nothing in the model structure to prevent more sophisticated treatment of model components. It seems that in the case of Mauritius – a relatively simple spatial system compared to complex urban or global systems – the level of sophistication employed was adequate for the problem at hand. The PDE modeling approach is distinct for its elaborate treatment of the population component whose detailed analysis provides the basis for a better representation of the socio-economic and environmental dynamics. The model adopts a coarse land classification system and it is not spatially explicit but again there does not seem to be any conceptual problem for its incorporating more spatial and land use detail. The land allocation module attempts to simulate a realistic land conversion, rule-based, process by taking into account environmental constraints. A similar procedure was used also by Engelen et al. (1995) in the context of their cellular automata modeling approach.
4.7. Other modeling approaches
The four main categories of models presented in the previous sections cover more or less the majority of models of land use and land use change. However, there are several other approaches which, on the one hand, do not fit easily into these categories and, on the other, cannot constitute a separate category by themselves as their application is either specialized or sparse, or very recent. In this section, certain of these other approaches are brought together and discussed. These are loosely grouped into: (a) natural-sciences-oriented approaches, (b) Markov modeling of land use change and (c) GIS-based approaches.
4.7.1. Natural-sciences-oriented modeling approaches
Modeling of land use change has been undertaken primarily in the disciplines of geography, regional science, and urban and regional economics. Planning and related fields have mostly borrowed from these principal disciplines although exceptions do exist especially in contemporary times when disciplinary boundaries become blurred and fuzzy. Modeling of land use change, however, has been historically and is currently the subject of other disciplines such as ecology, landscape ecology, forest science, soil science, and environmental science, in general. The models developed in these disciplines have a common characteristic; namely, they are natural sciences-based placing a heavy emphasis on the bio-physical aspects (determinants and impacts) of land use change and, at times, almost ignoring the socio-economic, institutional, political, and other determinants. They cover a variety of levels on the spatial and the temporal scales. Frequently, they are called land cover change or land use/cover change (and not land use change) models as, at higher spatial levels especially, land cover dominates which may or may not be associated with land use (as it is the case with natural vegetation). A brief indicative overview of these models is offered below, drawing on several reviews of the literature, to show the range and variety of the modeling studies available.
Landscape ecology models is a general category which includes models used to analyze landscape patterns, associated characteristics and processes, and change. Depending on the particular component of a natural ecosystem being studied (e.g. a plant or animal species, a particular ecosystem, a watershed) there is a wide variety of these models (see, for example, Baker 1989, Turner and Gardner 1991a). Two notable, interrelated characteristics of all approaches to the analysis of landscape change are mentioned. First, is their emphasis on the level of the spatial and temporal scale at which the analysis is performed as it has a determining influence on the patterns and processes of change identified and analyzed (Turner and Gardner 1991b). A variety of data analysis techniques have been developed and utilized in landscape models to address the issue of scale appropriately (Turner et al. 1991, Quattrochi and Pelletier 1991, Dunn et al. 1991, Milne 1991). The second characteristic is the spatial explicitness of landscape models which has been greatly improved with the advent of remote sensing techniques and GIS.
Sklar and Constanza (1991) distinguish two major categories of landscape models: stochastic and process-oriented. Stochastic landscape models employ Markov or semi-Markov processes to the study of changes in a study area which is subdivided into cells. Transitions in the state of each cell (e.g. the state of vegetation) are modeled by estimating transition probabilities which account for interactions between neighboring cells. The impact of climatic and other environmental factors can be incorporated also in estimating these transitions for a more realistic representation of the dynamics of landscape change. Process-oriented landscape models simulate spatial structure by compartmentalizing the landscape into a number of geometric areas and, then, describing abiotic and biotic flows between compartments according to certain location-specific algorithms. Various processes can be analyzed such as habitat succession, land use change, etc.
Although the majority of landscape models analyze change in terms of environmental determinants, the introduction of the human dimension in these models has been attempted also. Parks (1991) distinguished three groups of models of forested and agricultural landscapes which take into account the influence of socio-economic factors is the analysis of landscape change: (a) inventory/descriptive models, (b) engineering/optimization models, and (c) statistical/econometric models. These models can take into account various socio-economic factors such as returns per acre, net economic benefits, prices of inputs and outputs (products) associated with land use conversion (Parks 1991, Pfaff 1999). However, they are not based explicitly always on economic theory as it was the case with the discrete statistical models reviewed in section 4.3.1. (Bockstael 1996, Bockstael and Bell 1997, Irwin and Bockstael 1999).
A variety of solution techniques are employed in landscape models of land use/cover change. Most common among them are techniques which require the subdivision of the study area into cells (called also patches in landscape models) and estimate transition probabilities among different states of land use in each cell. The use of Markov and semi-Markov chain models is widespread especially when the data analyzed are obtained from remote sensing and related sources. GIS-based models are employed also for the same reasons. These two types of models are presented in the following sections. The main point with respect to these techniques is that they lack explanatory power as the causal relationships underlying the transitions studies are left unexplored. Transition probabilities are estimated as proportions of cells which have changed state from one point in time to another. This appears to remain the most handy way to estimate these probabilities despite the development of procedures for estimating transition probabilities on the basis of more complex, scientific considerations (Baker 1989). Other techniques used include statistical, regression models (Parks 1991, Pfaff 1999) as well as fractal models (Milne 1991). The latter provide appropriate tools for modeling the heterogeneity and complexity of landscape structure and processes of change. Fractal models belong to the same modeling tradition as the cellular automata models of urban spatial structure which were discussed in section 4.6.3B before. These models are also poor in explanatory power and grounding in economic, sociological or some other type of theory.
Turner et al. (1995) cite ecological modeling approaches that have been applied to model vegetation cover and soil organic matter dynamics in managed (and unmanaged) grassland ecosystems. These include the CENTURY model (Parton et al. 1987, 1993) as well as SAVANNA (Coughenour 1993 cited in Turner et al. 1995, 42), a process-oriented model of pastoral ecosystems. Similarly, livestock models and the underlying vegetation dynamics models of those linked explicitly to rangeland management contribute to studying land use change in specific ecosystem types. Global vegetation models employed for the study of biophysical relationships of plant canopies and global natural vegetation models employed for the study of natural vegetation as a function of climate (Meyer and Turner 1994, 74) are, in one way or another, related to the analysis of land use change from the particular disciplinary perspective of the life sciences.
Forest models are employed also to analyze land use changes, especially as regards the impacts of human colonization and deforestation in forest areas. Related studies include Brondizio et al. (1994), Pfaff (1999), and cited in Turner et al. (1995, 42) include Grainger (1990), Dale et al. (1993), Southworth et al. (1991) and Lambin (1994); the latter reviews modeling approaches applicable to deforestation processes.
Soil erosion and desertification represent important processes which effect land use changes in the course of time. Various physical models exist which account for these processes as well as for their close and critical interactions with other environmental factors – e.g. vegetation, water resources, climate. At times, interactions with socio-economic factors are also taken into account. These models contribute to the analysis of land use change especially in agricultural, rangeland, and sensitive (erosion-prone) areas (see, for example, Thornes and Brandt 1996). A number of recent research projects produce models developed in this direction such as MEDALUS I, II, III (see, Thornes and Brandt 1996 and the MEDALUS website in Appendix 1.B) and IMPEL (Rounsevell 1999).
Models have been used to study the impacts of climate change on the location and extent of natural ecosystems and agro-ecosystems. Related studies cited in Turner et al. (1995, 41) include Bultot et al. (1992), Emanuel et al. (1985), Parry et al. (1988a, 1988b). Climate change models – starting with IMAGE 1.0 (Rotmans 1990; see, also, Alcamo 1994) and developing into the ESCAPE framework (CRU and ERL 1992 cited in Turner et al. 1995, 41) have been linked to several impact models such as sea-level rise, agriculture and ecosystems which relate to the analysis of land use change in particular environments (usually the tropics and sensitive ecosystems).
The above brief account of natural-sciences-based modeling approaches to the analysis of land use change is simply indicative of the broad spectrum which needs to be covered for a comprehensive account of the related phenomena. These modeling efforts – as several others described in the preceding sections – have their own particularities and are suited to the study of special aspects of more general phenomena and processes. Further discussion of these models and additional references are found in various sources (see, for example, Turner and Meyer 1990, Meyer and Turner 1994, Turner et al. 1995). Their value lies in that they clarify particular aspects of the natural world dynamics and, hence, they make possible their integration, or the knowledge they provide, into more sensitive integrated models of land use change at various spatial and temporal scales.
4.7.2. Markov chain modeling of land use
change
Markov chain modeling (henceforth called Markov modeling, or Markov analysis, for brevity) is basically a simulation technique which has been applied to the analysis of land use change but it is not as widespread as other simulation techniques for reasons which will be discussed shortly. Its use in landscape models of land use change has been mentioned already in the previous section. It is worth noting, however, that the application of Markov analysis for the prediction of long-term land use changes is included among the proposals of the LUCC Implementation Plan (LUCC 1999). For preliminary applications see, also, Geoghegan et al. (1998).
The application of Markov analysis to the study of land use change was proposed in the geographic literature as early as 1965 for the study of the movement of central city rental housing areas (Clark 1965). Subsequent applications concerned mainly the study of land conversion processes mostly in urban contexts such as suburbanization, neighborhood housing turnover, land use change (Drewett 1969, Gilbert 1972, Bell 1974, 1975, Bell and Hinojosa 1977) and more special theoretical issues such as the process of land use succession (Bourne 1971). Other applications concerned the use of Markov chain analysis in the context of land use impact assessment of large public investments such as dams (Vandeveer and Drummond 1978) and of analyzing the historical dynamics of urbanization in agricultural areas (Muller and Middleton 1994). More recently, Markov analysis has been applied to problems of assessing the impacts of land use/cover changes on local climate (Lein 1989) and of projecting changes in organic carbon stores caused by land use changes (Howard et al. 1995). Finally, Markov analysis of land use change has been combined with GIS to create a tool for visualizing and projecting the probabilities of land use change (the transition probabilities) among categories of land use (Logsdon et al. 1996). The following discussion presents briefly the basics of Markov chain analysis as applied to issues of land use change and comments on issues related to its applicability.
Markov chain analysis belongs to the analytical methods of stochastic processes . A Markov process is a stochastic process with particular characteristics which distinguish it from other stochastic processes. For a system of interest, say a parcel of land, there is a set of discrete states (or classes) – S1, S2,…. Sn (say, different types of land use). The process can be in one and only one of these states at a given time. It moves successively from one state to the other with some probability which depends only on the current state and not on the previous states. This is a characteristic assumption of Markov processes (or, otherwise stated, this is a process without memory; see, Bell and Hinojosa 1977). The probability of moving from one state i to another state j is called a transition probability, Pij, and it is given for every ordered set of states. These probabilities can be represented in the form of a transition matrix, P, as shown below:
(4.111)
"Since the elements of the matrix are non-negative, and the sum of the elements in each row are equal to 1, each element of the matrix is called a probability vector and the matrix P is a stochastic or probability matrix" (Judge and Swanson cited in Clark 1965, 352).
This idea is easily transferred to the case of an area subdivided into a number of cells each of which can be occupied by a given type of land use at a given time. Transition probabilities are then computed on the basis of observed data between time periods which show the probability that a cell will change (or, move) from one land use type to another within the same period in the future. This probability depends only on the state in which a cell is at any given point in time - i.e. its current land use type – and not on the land use types by which it was occupied in the past. Obviously, the plausibility and acceptability of this assumption depends on the time span considered. For example, this may be true for long time spans (e.g. for more than 50 years although, in general, the longer the time span the more plausible this assumption becomes). Given the matrix P of transition probabilities, its use to project future changes in land use is as follows. A vector, l0, depicting the distribution of land uses among the different types at the beginning of the period is required. The vector, lt, showing the distribution of land use types at the end of the projection period is found by the following formula:
lt = l0 P (4.112)
The distribution of land use types after k time periods (of a given length) is found by powering matrix P:
ltk = l0 Pk (4.113)
If a Markov chain is regular (i.e. the entries of each row are non-negative and sum to one), then it can be used also to compute the equilibrium vector of land use distribution – i.e. this land use pattern in which net movements from one land use type to another are zero (Vandeveer and Drummond 1978). The resulting matrix has identical rows, each row representing the equilibrium distribution of land use types in the area. This equilibrium matrix is found either by raising matrix P to successive powers until the rows do not change or by following a more efficient procedure proposed by Judge and Swanson (1961 cited in Vandeveer and Drummond 1978).
Markov chains are classified variously depending on their properties. One such important property for its application in the analysis of land use change is the property of stationarity. A Markov chain is called temporally homogenous if the transition probabilities are identical for two time periods of elapsed time of the same duration occurring at different points in time. The concept of stationarity is closely related to the concept of temporal homogeneity and they are sometimes used synonymously. "A temporally homogeneous process is stationary when the (unconditional) probabilities of the system being in the different states at future points in time are constant" (Bell and Hinojosa 1977). A non-stationary Markov process is one in which the condition of stationarity does not hold – i.e. the transition probabilities are not constant at different time periods. Most of the applications of Markov analysis to the study of land use change assume that the process is stationary although this is not easy to prove in practice, the most important reason being the lack of data to test if the process is stationary.
Most of the applications of Markov analysis of land use change pursue a procedure more or less similar to the one described above. However, Markov analysis is a rather involved statistical method of analysis and its use requires thorough understanding of the mathematics and statistics involved as well as rigorous tests of the basic assumptions made; namely, that the observed processes are Markov processes and, in particular, stationary Markov processes. One of the reasons these basic assumptions are difficult to test is the lack of sufficient time series data on changes of land use between time periods to set up the transition probability matrices and then test the stability of the transition coefficients over time. Most applications admit to the presence of this difficulty and caution the reader against the limitation of the analysis in the case this test cannot be undertaken (Clark 1965, Bell 1977, Sklar and Constanza 1991). Therefore, a valid application of Markov analysis for the projection of land use changes requires a prior rigorous test of these basic assumptions. Once these tests are done and show that the assumptions are met in the particular case being studied, the procedure described above (and several versions of it found in the literature) can be applied. It is noted that the recent availability of remote sensing images as well as of GIS makes easier the testing and application of this type of analysis. An interesting application by Logsdon et al. (1996) proposes the procedure of "probability mapping" with the use of GIS to facilitate the visualization of the process of past change in space (the mapping of the transition probabilities) as well as its projection into the future (see, also, Geoghegan et al. 1998).
Markov analysis of land use change is an aggregate, macroscopic modeling approach as it does not account for any of the drivers of land use change; instead, it assumes that all forces that worked to produce the observed patterns and governed their transition probabilities will continue to do so into the future. Of course, advanced applications of Markov analysis relax the assumption of stationarity and make possible the exploration of alternative futures produced by changing appropriately the original transition probabilities to simulate different probabilities of transition among land use types. However, these applications presuppose high competency in the related mathematics and statistics. If the assumption of stationarity can be assumed to be valid – something which is time- and place-specific – then Markov analysis can be used in three different ways: (a) for ex-post impact assessment of land use (and associated environmental) changes of projects or policies in the spirit of Vadeveer and Drummond’s (1978) application; (b) for projecting the equilibrium land use vector as well as for approximating the time horizon at which it may be obtained; and (c) projecting land use changes at any time in the future given an initial transition probability matrix as it is commonly done in most applications. It has to be noted, however, that, in addition to the assumptions mentioned above, the type of Markov analysis presented here does not incorporate constraints on possible transitions or other types of constraints (e.g. availability of land and other resources). Future research may attempt to relax this and other constraints and provide versions of this simulation technique which can accommodate more plausible and defensible assumptions about reality.
4.7.3. GIS-based modeling approaches
A last group of modeling approaches is currently under development and the related applications to the study of land use change are still to be evaluated compared to the more established modeling techniques discussed so far. These are termed here GIS-based modeling approaches, a term that will be qualified shortly. The development of GIS in the last 20 years has opened new horizons for the management and manipulation of spatial data sets. However, as Fotheringham and Rogerson (1994) observe: "the field of GIS had too long ignored the potential contribution to be made by integrating some of the achievements of theoretical and quantitative geographers with the emergent technological developments in hardware and software…. While developments often focused upon the storage, retrieval and display of spatial information, few advances were made in providing (GIS) with the capability for spatial statistical analysis and modeling… (In another sense) … GIS technology could play a role in the development of new techniques for spatial analysis or, promulgate the use of existing exploratory and data-driven techniques" (Fotheringham and Rogerson 1994, 175). To explore the types of GIS-based modeling approaches for the analysis of land use change, it is necessary to take a brief look at the issues of spatial data, the functions of GIS for the analysis of these data, and the broad field of spatial analysis.
Spatial data sets have two distinctive traits. First, they describe the locations of objects in space (and their topological relationships) – called topological and positional data. Second, they describe non-spatial attributes of the objects recorded – called attribute or thematic data (Fischer et al. 1996).
GIS have four main functions related to spatial data:
Spatial analysis has evolved considerably over the last 40 years offering a multitude and diversity of procedures for the analysis of spatial phenomena. Two main directions can be distinguished broadly:
The analysis of land use change, based on available sets of geo-referenced (spatial) data, in a GIS environment involves the coupling (or, interfacing) of spatial analytic models with a GIS. This coupling may take two forms, in general: (a) tight coupling or (b) loose coupling (Goodchild 1992, Batty and Longley 1996, Fischer et al. 1996, Nyerges (1993) cited in Jankowski 1995, 264).
Tight coupling may be either full or close. Full coupling has not been achieved yet as it involves complete integration of spatial analytic models and techniques within the GIS or vice versa. Close coupling appears more realistic as it involves exchange of various types of information between spatial analytic models and GIS. However, several issues related to the interfacing of these tools are yet to be resolved. Finally, loose coupling is the current, widespread practice at present. Spatially-explicit models are linked to a GIS either to retrieve input spatial data and/or to display graphically the model results in map form. Several of the models presented before, especially those which are rule-based such as the cellular automata approach, the CLUE models, the USTED models, IIASA’s LUC model, and Markov modeling, among others, have already developed or are developing linkages with GIS.
However, if a separate group of modeling approaches to the analysis of land use change is to be distinguished – the GIS-based modeling approaches referred to in the beginning of the section – then these should refer to the tight coupling of spatial analytic models and GIS. This means that a spatial analysis and modeling technique is fully integrated with a GIS which performs the required analytical procedures and operations as part of its overall structure in addition to spatial data manipulation and map generation. At this point, a natural question that arises concerns the types of modeling approaches which are capable of being incorporated into GIS. Aspinall (1994) distinguishes four types:
Rule-based approaches employ rules to weight data sets in the geographic database. Knowledge-based approaches employ equations/relationships – developed outside the GIS – to data sets in the geographic database. Inductive-spatial approaches employ spatial analytical techniques (spatial statistics) to identify relationships between data sets in the geographic database (see, for example, LeSage 1999). Finally, geographic approaches are spatial statistical descriptive approaches which describe patterns in data sets in the geographic database in terms of location. All four approaches are relevant to the analysis of land use change although a strict reading of the term "location" would exclude the fourth group (see the extensive arguments offered in the beginning of this chapter on considering location theory and the related models as land use theory and models proper).
Of the four approaches, rule-based modeling is perhaps the most widely used GIS-based approach in the form of map overlay analysis which has many applications in planning contexts. Data pertaining to several attributes of a study area (elevation, slope, climate, hydrology, land uses) are stored in layers in a GIS. Different layers are overlain to generate maps showing "unique conditions" in McHarg’s (1969) tradition. Overlay analysis is used also to predict a new map as a function of the distribution of observed attributes (Unwin 1996). However, the caveats of the map overlay technique which Hopkins (1977) has so succinctly analyzed should be borne in mind irrespective of whether this is applied on a luminescent table or in a GIS. As Batty and Longley (1996) note: "(The layer model) … is a product of the notion that data can be separated in a clear spatial way, and although this may be possible, there is no guarantee that data should be put back together in the same way though simply adding layers… No one would pretend that the world works through such simplistic merging. Moreover, the notion that the addition of layers is the central modeling capability of GIS simply illustrates that GIS is based not upon the definition and representation of processes but simply upon static structures." (Batty and Longley 1996, 349-350).
Applied to the analysis of land use change, rule-based approaches can, in principle, contribute to three of the four major purposes of analysis: description, prediction (and conditional prediction), and evaluation. Whether explanation is feasible in this context is an open question. Description of land use change can be performed by overlaying land use maps from different time periods to identify the location and assess the magnitude of change. The accuracy of the description provided depends on the detail of the land cover classification employed which at the time of this writing is not sufficient to match the needs of actual decision making on land use issues (see, for example, the contributions in Liverman et al. 1998). Prediction of land use change – at least, particular types such as degradation, desertification, abandonment, urbanization, suburbanization – can be performed by combining various characteristics which are assumed to determine these kinds of changes (such as soil conditions, slope, climatic conditions, migration, economic stagnation). Utilizing scenarios to define future values of particular characteristics or different weightings of these characteristics, conditional predictions of such changes can be obtained (see, for example, Despotakis 1991, Despotakis et al. 1993). Finally, evaluation of proposed or expected future patterns of land use change is a function which can be undertaken in the context of a GIS also but it is a subject beyond the scope of this contribution (see, for example, Jankowski 1995, Pereira and Duckstein 1993)
Within the general trend to integrate GIS with spatial analysis and modeling techniques (see, for example, the contributions in Issue No.3, Vol.1 of the journal Geographical Systems), knowledge-based approaches have a great potential to contribute to the design of meaningful integrated systems for spatial analysis and decision making (see also, Fischer and Nijkamp 1993). Several of the land use models – especially those which are spatially explicit such as the spatial interaction, the linear programming and many more models – which have been presented in this chapter may be suitable pools of knowledge which can be used to guide the manipulation and analysis of the related spatial data. This is a future research area whose outcomes are difficult to envision and much more difficult to evaluate at present. What is visible, however, is that spatial decision support systems (SDSS) are going to proliferate in the near future given the enabling functions of technological developments, their rapid diffusion, and the various facilities they offer to interested users – researchers and modelers included (see, for example, Densham 1991). It remains to be seen whether these SDSS will be simply technical aids devoid of theoretical content and meaning or whether they will develop into multifaceted and sophisticated platforms for carrying out integrated analyses of land use change grounded on rigorous theories of how land use interacts with its socio-economic and bio-physical determinants in space and time.
4.8. A summary evaluation of models of land use change
The models reviewed in this chapter may not represent the whole universe of models which have been built and/or are actually used for the analysis of land use change. Several models have never been published in books or scientific journals. Others are built and never used however valuable they might have been if adopted. With these observations in mind, this chapter closes with a broad assessment of the models presented in the previous section. This is not an easy task as they exhibit a considerable diversity ranging from comparatively simple and single-sector or single-activity models to integrated models of complex environmental and socio-economic systems. Models are built for a variety of purposes, with differing available human, technical and financial resources, and at historic times when required basic knowledge may not be well developed across all aspects of a model’s structure. Hence, it is not possible to judge whether a model is "good" or "bad" – except for extreme cases of technical inefficiencies and caveats – as everything depends on the constellation of circumstances leading to model building and use. From a practical point of view, an elementary test of a model’s "worth" may be its adoption and sustained use. But even in this case, one should look for the particular circumstances accounting for this fact to get to meaningful explanation. And, naturally, practical "worth" does not imply theoretical and methodological rigor.
For the above reasons, this section offers a summary account of the main model characteristics along the principal (interrelated) aspects of the models which were covered before: (a) model purpose and object of study, (b) level of aggregation – spatial, sectoral/land use, temporal, (c) dynamics, (d) underlying theory, (e) functional specification – mostly, solution techniques and spatial explicitness, (g) data issues, (f) real world applications. The very important issue of the use of models for policy support is left for discussion in the last chapter.
A. Model purpose and object of study
A major distinction among models can be drawn on the basis of their purpose and the object of their study, two aspects which are closely related. As regards model purpose, models are frequently distinguished broadly into positive and normative. The former concern mostly descriptive, predictive (or forecasting) and impact assessment models. The second refer to prescriptive models which are favored in planning contexts. Early models of land use and its change were basically descriptive or prescriptive (like the very early model of von Thunen). Very soon, however, forecasting models of land use became popular as, together with prescriptive models, they played important functions in planning. In the post-1970s period, impact assessment models became widespread as they facilitated the assessment of land use impacts (usually associated with plan and/or program implementation) and, consequently, the environmental impacts associated with land use change. Explanatory models are the least frequent as explanation is most difficult to ensure in its deep, theoretical sense and not in the narrow, superficial sense of statistical explanation. However, several models claim explanatory status like the spatial interaction models and the economic theory-based models. These are deductive models which postulate an explanatory schema – mostly narrow and accounting for only a few economic determinants of land use change – and then use data to verify the model’s theoretical statement. In a sense, they force reality to fit into the model as critiques of urban modeling have so forcefully and cogently demonstrated (D. Lee 1973, Sayer 1979a, 1979b, Cooke 1983).
As regards their object of study, the models reviewed here refer to the analysis of land use change in general but even within this broad area models are distinguished by the particular nature of the spatial entity of reference – urban areas, rural areas, large regions, nations, groups of regions or nations, the world as a whole. A very large number of models, especially those built in the early decades of model building – the 1950s and the 1960s – refer to urban or to large metropolitan areas. Progressively, they have moved from partial to general or integrated approaches (Batty 1976), their post-1970s versions being the integrated land use/transportation models given the close relationships between both individual and collective land use and transportation decisions at least in urbanized settings. Land use models for other types of spatial entities were until recently less frequent and it is surprising that the bulk of modeling in geography and economics did not pay enough attention to the land use modeling needs of other types of areas such as agricultural regions, forest and mixed regions and so on. As Turner et al. (1995) note, at these larger scales, "what pass for land use models are typically models of economic sectors predicting changes in production at the country level …... They need to be better linked to outputs of locationally specific land use and land cover" (p. 28). The recent developments in land use change modeling (e.g. IIASA’s integrated modeling studies, the CLUE group’s models, etc.) tend to meet this last requirement but there is still a long way ahead to producing fully integrated models at various spatial scales and for the whole variety of socio-economic and environmental spatial settings.
B. Level of aggregation – spatial and functional
Early land use models already employed a system of zones to represent the distribution of land use types in the study area. This is perhaps the distinguishing characteristic of these models as a spatial system of reference is essential for modeling land use and its change which has characteristic spatial variability following the variability of its drivers. It is important to emphasize the determining role the particular zonal system exerts on the results of the analysis; namely, the number of zones, the shape of zones and the (implicit, at least) assumption of the homogenous distribution of modeled characteristics within zones. The level of detail of the spatial system of reference is not unrelated to other model characteristics and to the theoretical framework adopted. Different levels of spatial detail are suitable for modeling land use change at different spatial levels and relating this change to its determinants at the particular spatial level. Veldkamp and Fresco (1996b), among others, have specifically explored the effects of spatial scale on modeling land use change. The exploration of the effect of scale on the analysis of land use change is a central concern also in landscape ecology models (see, for example, the contributions in Turner and Gardner 1991).
Recently, there is a growing tendency towards spatially-explicit models in several scientific fields such as geography, urban and regional economics, ecological economics, landscape ecology. These models use the individual land parcel, the farm, or very small patches of landscape as units of analysis. Focusing on the individual land parcel – which in most cases is the decision making unit in the context of land use change, makes possible the use of micro-economic theory as well as micro-level theories from the environmental sciences to support modeling of land use change. Although the desirability of these detailed models is unquestionable, the important issue of spatial aggregation has to be thoroughly explored. The point is that several of the factors which impinge on the individual level of decision making operate at higher levels (see Blaikie and Brookfield 1987, LUCC 1999) and they are assessed by means of models operating at these higher scales. The results of these models have to be downscaled to lower levels which raises the issue of validity of the resulting estimates. The same is true with aggregating individual level model results to higher levels of the spatial and temporal scale.
Functional aggregation refers here to the particular sectors represented as well as to the associated land uses. In this sense, the level of functional aggregation in models of land use change is relatively low as it depends on the land using sectors being modeled, technical (solution) considerations, and, most critically perhaps, on the availability of appropriate, disaggregate sectoral data. The same applies to the level of land use detail employed. As regards the first point, models of a particular use of land – e.g. residential, commercial, agricultural – usually represent only the land use and the related sector of interest as well as those uses of land most closely associated with them. This is the case, for example, in residential land use models where residential and employment areas are targeted, the latter being modeled in differing degrees of detail. Large-scale models employ coarser land use and sectoral classification schemes and the same is true for several simulation models. Progress in GIS, computing equipment, and data dissemination systems may facilitate the use of more disaggregate information. Two points should be born in mind, however. Increasing the level of functional and spatial aggregation in models of land use change may improve the representation of the underlying processes but at the expense of computational efficiency and, from the user’s point of view, of the ability to interpret, comprehend and use effectively the models’ results. Hence, a trade-off is almost unavoidable between level of disaggregation and ease of use of model results. In addition, improving the level of functional and spatial aggregation should raise the question of whether the adopted theoretical framework and model specification are appropriate to modeling phenomena at other levels of detail than those for which they are fit as well as the issue of cross-scale interactions.
C. Dynamics
Naturally, the study of land use change dictates the explicit treatment of time – the temporal relationships among land use and its various determinants – in the respective models. The models presented in this contribution, however, are static or quasi-static although issues of dynamics have been discussed at times. The design of dynamic models encounters considerable difficulties in several respects: conceptual/ theoretical, computational, availability of data. This is not to say that no attempts have been and are being made at building dynamic models. Dynamic versions of spatial interaction models – interpreted as entropy models, of the Lowry model, and EMPIRIC, among others, have been proposed (Batty 1976, Wilson 1974, Batten and Boyce 1986, Bennett and Hordijk 1986). Moreover, several other types of dynamic models of spatial systems have been proposed (Andersson and Kuenne 1986, Miyao 1986, Fischer et al. 1996). Integrated land use-transportation models attempt to introduce the feedbacks from changes in transportation network characteristics on land use patterns. However, taking into account even the most essential feedbacks and two-way relationships between land use and its bio-physical and socio-economic determinants represents a significantly complex modeling task. In all cases, a trade-off between model tractability and realism has to be made eventually. A (relatively) simple, analytically tractable model reduces the real world variety to the point that the model may lose its utility as a decision support tool. On the other hand, adding complexity into a dynamic model increases both the computational burden and the ability to comprehend model results.
A compromise between static and dynamic are the quasi-static models which simulate the passage of time usually through the choice of suitable (lagged) variables, functional forms, pooling cross-sectional and time series data, and solution procedures. A common practice is to solve a static model sequentially using a time step of, say one- or two-year time interval, over the specified time horizon. It is, thus, possible to observe the changes which occur over time and to make adjustments ( exogenously specified or endogenously provided) to certain model variables to reflect the changes which occur from one time step to another. It is also common to provide for user-intervention during the sequential solution of a model; the user can change model parameters to simulate changes in particular conditions, foreseeable "surprises", or the implementation of policy measures which cannot be accommodated in the model’s structure. An even more advanced form of user intervention is offered by interactive models of land use change which are suited specifically for use in planning and policy making contexts; the user continuously interacts with the model – through appropriate model-user interfaces – modifying parameters, providing requisite information (e.g. on preferences, priorities, etc.) and choosing among model solutions those which most closely match the problem under study.
D. Underlying theory
The issue of theory is perhaps one of the two most important considerations in model building in general, the other one being availability of proper data sets. Although the use of theory (about the system being modeled) in model building seems indispensable, several model builders – especially of integrated economic-environmental models – acknowledge the lack of theory which would assist them in making important choices during model specification. Looking at the several theories of land use change which were presented in Chapter 3, it is surprising that a relatively small number of them have been used to support and guide operational model building. Some theories and models have been conceived simultaneously; hence, the use of the terms "theory" and "model" either interchangeably or to denote a set of conceptual and operational statements about reality (e.g. the urban land market theory and model). But the majority of theories are still without modeling (not necessarily mathematical) counterparts and the reverse is also true. Several models are devoid of theoretical foundations. The reasons for this gap are explored later in this section.
Models of land use change can be distinguished broadly into these which are based on a theory of some kind and those which are not. The first group includes economic theory-based models as well as spatial interaction/entropy models especially when derived from economic principles. In fact, the dominant theoretical frameworks employed are those of (mostly neoclassical) economic theory. The other group comprises all other models which either make no claim to any theory or that adopt an instrumental approach to theory (Sayer 1979a); i.e. they justify the choice of spatial, temporal and functional specification on the basis of certain theoretical statements and assumptions. In fact, there is a gray area between the two extremes of models based on theory and those which do not with models employing some form of theoretical assumptions and considerations to justify various choices related to model specification as well as to interpret model results. At this point, it is important to note that the role of theory is critical not only during model specification but also during interpretation of model results. In this respect, even economic theory is not adequate as land use change is not governed exclusively by economic considerations. At one extreme, that of individual decision making, many other personal and idiosyncratic factors will intervene and shape the final decision about the use of land . At the other extreme, that of global land use change, environmental factors seem to dominate the global patterns of change (although human roles in causing climatic change may prove to be very important in the future).
In all cases, the theoretical underpinnings and the related assumptions of a model bear importantly on its performance and the results it yields. Several of the models presented in this chapter have been criticized for their assumptions which do not always hold as they abstract heavily from the real world. Examples are von Thunen’s and Alonso’s land rent theories and models with their assumption of a monocentric plane with uniform properties and characteristics in all directions. Linear regression and linear programming models are based on a fundamental assumption of linear relationships between land use change and its determinants, an assumption which frequently is violated in reality. The same is true for the Input-Output models where the production relationships used are linear (as well as constant and inelastic to changes in output, technology and so on). Various modeling efforts have had and are having as their point of departure extant models with the purpose of relaxing some of their restrictive assumptions and, thus, making them more responsive to reality and more useful in applications. Two main concerns about a model’s assumptions are emphasized here. The first has to do with interpreting a model’s results in the context of its assumptions and the second with the linkage between spatial scale and model assumptions.
With respect to the first issue, the influence of a model’s assumptions on the model’s output is not always examined. This is particularly obvious in the "new generation" models which exhibit an strong tendency to produce practical modeling tools without questioning some fundamental assumptions made to produce results (e.g. the overlay technique in GIS-based models). From the point of view of a model’s use, interpreting a model’s results in the context of its assumptions and other limitations (e.g. available data, level of aggregation, etc.) makes the model more reliable and trustworthy than it is the case otherwise as it shows the range of its applicability and makes possible further improvements. With respect to the second issue, a model’s assumptions refer, explicitly or implicitly, to a given spatial level (and, more broadly, to particular socio-spatial structures). It is reasonable to posit that, once these assumptions are made, the model’s results refer to the respective spatial level. Therefore, when transferring models from one scale to the other (space and time), several of their assumptions may not hold. This may be one reason for invalid model results. For example, the theory of consumer utility maximization makes assumptions about individual consumers who, more or less, act at the lowest level, the individual, of decision making. At this level, the socio-economic determinants of land use relate to micro-behavioral factors and the bio-physical determinants relate similarly to micro-climatic and local environmental factors. These assumptions may be valid at this particular level (although critiques of "rational economic man" contend to the opposite). Applying these same assumptions to macro-models of land use change (e.g. at the urban and regional or even the global level) necessitates aggregation of consumer preferences along assumptions about individual behavior as well as aggregation of several other land use determinants from the micro to macro levels. The question which arises is whether model results obtained in this way are valid when the validity of their assumptions at a different scale than the one to which they are fit is questionable. Veldkamp and Fresco (1996b), among others, have explored this issue which bears importantly on a model’s essential usefulness in practical decision making. Needless to say that what has been said about the particular issue of assumptions in relation to spatial scale applies to several other model assumptions whose discussion is beyond the scope of this contribution.
Finally, the gap in the relationship between theories and models is discussed briefly. Of the several explanations for this discrepancy, two are mentioned here. The first, most important perhaps, reason is that the epistemological bases of several theories are not congruent with the idea of mathematical, symbolic modeling. More generally, theory and model builders adopt differing epistemological positions. Usually models move in the positivist epistemological tradition while theories cover a much broader spectrum of epistemologies. A sharp reflection of these differences is the way land is usually being conceptualized in theory and in models. A related reason is that reality is so complex; land use change comes about under the influence of many macro and micro factors, acting and interacting within varying time frames. Land use change problems are essentially metaproblems . Therefore, the reduction and simplification of this real world diversity to serve the purposes of model building is extremely difficult. The result may be either a very crude representation of reality or, on the contrary, a very complicated model structure that is impossible to handle within the bounds of reasonable time and other resources available to answer practical questions. A second reason is that many theories are cast in abstract terms which make their operationalization difficult. Abstract theories are, in part, a reflection of real world complexity and of inability, on the part of the theoretician, to disentangle the complex world and discover order behind the apparent chaos.
E. Functional specification
The models reviewed exhibit a considerable variability in terms of functional forms but some of them are more widely used than others basically because of their relative simplicity and ease of application. Hence, statistical models as well as linear programming models are more common compared to other functionally more sophisticated and involved model forms (e.g. nonlinear statistical and programming models). The most recent trend in land use modeling is the use of heuristic modeling techniques linked to GIS for easier manipulation and visual presentation of model input and output. In addition, it seems that, gradually, integrated models of various types and levels of integration are gaining ground as the demand for realism in modeling land use change cannot be met by single-sector or mono-dimensional, in general, models.
Another characteristic of the functional specification of land use change models, from the early to their most recent versions, is their spatial explicitness. All models employ a zonal system – a subdivision of the study area into smaller spatial units – however simple this may be. The advent of GIS and improvements in data processing technology facilitate the design of complete spatially explicit models. In this case, spatial detail may refer even to the level of the individual land parcel. In several countries (e.g. the United States, England, Canada) building block and parcel-level data are increasingly becoming available in GIS format which make possible the very detailed analysis of land use change. However, these developments point to the need for parallel developments in the techniques of spatial data analysis and their application to the particular issue of land use modeling. Spatial statistics and other techniques of spatial analysis have experienced a considerable growth in the last two decades but their widespread application remains to be seen. In the present context, several models of land use change analyze spatial data with conventional statistical techniques which apply to aspatial data; i.e. they do not account for the particular characteristics of spatial data such as spatial autocorrelation. The need for the application of spatial statistical techniques in the context of the analysis of land use change is emphasized, among others in the 1999 LUCC Implementation Plan (LUCC 1999). What is needed, however, is research on the adaptation of many more modeling techniques to the analysis of geo-referenced data.
F. Data issues
The second most important consideration in model building, together with the issue of the underlying theory, is the availability of proper data sets. Of course, the term "proper" needs qualification in each particular situation. The issue of data has been always the "headache" of modelers and it continues to be despite improvements in data collection and dissemination. The reason is that models are now called to meet more demanding tasks in terms of detail and integration. In general, data sets for meaningful analysis of land use change are presently considered those which are geo-referenced. The issues which relate to the availability of proper geo-referenced data to meet the needs of land use change modeling have been the theme of special initiatives on the part of organizations active in the analysis of land use change. In particular, LUCC, a core project/research programme jointly sponsored by IGBP and IHDP, has included among its activities an integrating activity concerning data and classification and intends to integrate the data collection efforts of the IGBP and IHDP DIS (Data Information Systems Offices). DAPLARCH (DAta Plan for LAnd use and land cover change ResearCH) was the main initiative within the LUCC programme whose aim was to define the data needs and convey them to the responsible agencies (in the 1996-1999 period). It organized four workshops to complete the first actions in the direction of addressing the main issues of data needs for LUCC studies. Other related activities were undertaken by research projects funded by the European Union. For information the reader is referred to CLAUDE (1997), LUCC (1997), LUCC (1998) and to the LUCC website (listed in Appendix 1.B).
The main data issues surrounding the comprehensive analysis of land use change are summarized below while for more information the reader is referred to LUCC (1997) and Briassoulis (1997), among others. Four groups of issues can be distinguished along four main data dimensions: spatial dimension, temporal dimension, definitions, and data collection. Chief concerns in all four groups are: data consistency, compatibility, reliability, availability, ease and cost of data collection/finding, and data transferability among spatial levels.
With respect to the spatial dimension, the spatial systems of reference used for collecting land use, economic, environmental, and other data frequently suffer from lack of compatibility and consistency in terms of level of spatial resolution, coverage and spatial definition. The spatial units usually follow administrative boundaries which, although appropriate for policy implementation, may not be meaningful for all types of data (e.g. the environmental). For certain variables, the spatial system of reference may not be standard and explicit at all. Moreover, spatial systems of reference change over time, a fact that may account for variations in the value of a variable over time. Making assumptions to aggregate or disaggregate different types of data (i.e. transferring data among spatial scales) in order to use them at the required spatial system of reference may generate inconsistencies among data sets. Compatible and consistent data sets are usually available relatively easily and at reasonable cost for larger scales mostly and for selected (but not all) variables of interest. Geo-referenced (and longitudinal) data exist for recent time periods only. All data problems become more acute when comparing different jurisdictions or when multi-jurisdictional areas are analyzed.
With respect to the temporal dimension, the temporal systems of reference (unit of temporal aggregation, spacing, timing and number of observations, etc.) which are appropriate for various types of variables are not always compatible and consistent and, consequently, reliable. Temporal systems of reference may change over time also, a fact seriously affecting their compatibility and consistency especially when aggregating or disaggregating such data. The greater the length of the time period analyzed, the greater the difficulty of ensuring the temporal compatibility, consistency and availability of the required data. This is especially critical for land use data which are collected from various sources such as past records, historical records, past maps, aerial photographs, and satellite data. These issues are more serious for policy data for which the exact timing and length of the policy intervention is critical in the analysis. Availability and cost of obtaining proper longitudinal data depends on the lack of: (a) agency coordination responsible for collecting different categories of data; (b) users of data and/or feedback from users of data; (c) organizational continuity in the data collecting agencies; (d) funds; (e) systematic data collection procedures and rules. In the case of different jurisdictions or study areas composed of segments of different jurisdictions all previous problems are compounded.
With respect to (operational) definitions of the concepts employed in models, the compatibility of the definitions of land use types, economic sectors, social variables, etc. are critical aspects of the validity and reliability of the whole analytical effort. Usually, definitions differ among jurisdictions and time periods especially at lower levels of aggregation. Aggregate definitions are impossible to disaggregate for particular spatial entities and time periods. Moreover, definitions change over time giving rise to problems of compatibility and consistency of the data collected. These problems are more serious with historical data. Usually, for aggregately defined variables data are available easily and at reasonable cost.
Finally, data collection and management procedures and rules are not always compatible and consistent among agencies in the same or in different countries as well as over time with the exception of internationally standardized data (e.g. population). Lack of systematic data collection procedures affects significantly the precision of measurements taken. Incorrect and imprecise collection and recording of field observations, intentional or unintentional omission or concealing of true data, untrained personnel, etc. generate unreliable data and makes their transfer among spatial and temporal scales problematic. Historical data, specifically, should be closely scrutinized. Moreover, the lower the spatial level, the fuzzier and less reliable the available information becomes. Data collected systematically, regularly and with the use of standardized techniques are usually more easily available and less costly than it is the case otherwise.
G. Real world applications
Several of the models presented in this chapter have been used in real world applications which are mentioned in the relevant references. The information available, however, refers mostly to industrialized countries and there is not enough information about model applications in other countries with the exception of models commissioned and/or used by international organizations. Shortage of adequate information makes difficult the assessment of the frequency of model applications over time. It is conjectured, however, that two periods of intense modeling and land use change model use activity can be discerned. The first coincides with the "highs’" of the quantitative revolution and the explosion of modeling activity in the 1960s to 1970s. The second started in the late 1980s and continues to the present. This latter resurgence of modeling activity and use is spurred by changes in perceptions and needs of important environmental and economic problems which are associated, in one way or another, with changes in land use.
Closing this summary account of land use change models, the last issue
addressed is: what makes a model of land use change "successful"? Setting aside
the philosophical analysis of the meaning of "success", a model’s success
operationally relates to its acceptance (not necessarily its adoption) as a
guide to thinking and acting in real world decision and problem settings. In
this perspective, it is suggested that a successful model is one that matches
satisfactorily purpose, theory, specification, available data and other
resources (such as know-how, expertise, money, time, effort). Frequently, there
is a mismatch between any two or more of these factors and models are found
unsatisfactory and in need of improvement. The spatial and socio-cultural
variety of land use contexts and of the corresponding decision making entities
are such that it seems that not many "successful" models exist to date. This is
reflected in the research agenda on (regional and global mostly) models
proposed in the 1999 LUCC Implementation Plan (LUCC 1999) whose main points
include: (a) coping with heterogeneity and scales in regional models, (b)
improving the environment-economy linkage, (c) dealing with technological
change, (d) representing the regulatory contexts in regional models of land
use/cover change (policies and institutions). Hence, the agenda for land use
change models is full and awaiting for modelers to respond to the
challenge!
