Scientific discipline and tradition have caused two distinctly different approaches to emerge in the field of land use studies. Researchers in the social sciences have a long tradition of studying individual behaviour at the micro-level, some of them using qualitative approaches (Bilsborrow and Okoth Ogondo, 1992; Bingsheng, 1996) and others using the quantitative models of micro-economics and social psychology. Rooted in the natural sciences rather than the social, geographers and ecologists have focussed on land cover and land use at the macro-scale, spatially explicit approaches linking remote sensing and GIS, and using macro-properties of social organisation in order to identify social factors connected to the macro-scale patterns. Due to the poor connections between spatially explicit land use studies and the social sciences, the land use modellers have a hard time tapping into the rich stock of social science theory and methodology. This is compounded by the ongoing difficulties within the social sciences to interconnect the micro and macro levels of social organization (Coleman, 1990; Fox et al., 2002; Geoghegan et al., 1998; Watson, 1978).
Models based on the micro-level perspective are based on the simulation of the behaviour of individuals and the up-scaling of this behaviour, in order to relate it to changes in the land use pattern. Two of the most important approaches will be discussed here: multi-agent simulation and micro-economic models.
Multi-agent models simulate decision-making by individual agents of land use change explicitly addressing interactions among individuals. The explicit attention for interactions between agents makes it possible for this type of model to simulate emergent properties of systems. Emergent properties are macro-scale attributes that are not predictable from observing the micro-units in isolation. Such properties 'emerge' if there are important interactions between the micro-units that feed back on the micro-behaviour. If the decision rules of the agents are set such that they sufficiently look like human decision-making they can simulate behaviour at the meso-level of social organisation, i.e., the behaviour of in-homogeneous groups of actors (Parker et al., 2003). Multi-agent models can shed light on the degree in which system-level properties simply emerge from local evolutionary forces and the degree to which those local processes are influenced and shaped by their effect on the persistence and continued functioning of ecosystems or the biosphere (Levin et al., 1998). Until recently, mathematical and computational capacity limited the operation of this type of models. Recently research teams have developed applicable simulation systems, most often for totally different purposes than land use change modelling (Cubert and Fishwick,
1998; DIAS, 1995; Lutz, 1997). The best known such system that is readily adaptable for ecological and land use simulation is the SWARM environment developed at the Santa Fe Institute (Hiebler et al., 1994).
Multi-agent models should be based on detailed information of socioeconomic behaviour under different circumstances (Conte et al., 1997; Tesfatsion, 2001). This information can be obtained from extensive field studies by sociologists. The relevant importance of the different processes influencing land use change can be tested by sensitivity analysis and a link to higher levels of aggregation can be made. Simulated behaviour at the aggregate level can foster the development of new theories linking individual behaviour to collective behaviour. Meso-level studies typically show how individual people interact to form groups and organise collective action, and how such collective decisions vary with group size, collective social capital, and so on.
Most current multi-agent models are only able to simulate relatively simplified landscapes, as the number of interacting agents and factors that need to be taken into account, is still too large to comprehensively model (Kanaroglou and Scott, 2001). More recently a larger number of multi-agent modellers have begun to focus on land-use change processes and provide insights on the microlevel dynamics of these systems (Barreteau and Bousquet, 2000; Berger, 2001; Bousquet et al., 1998; Bura et al., 1996; Huigen, 2004; Manson, 2000; Polhill et al., 2001; Rouchier et al., 2001; Sanders et al., 1997; Vanclay, 1998).
A wide variety of land use models based on micro-economic theories exist as reviewed by Kaimowitz and Angelsen (1998) and Irwin and Geoghegan (2001). Most economic land use change models begin from the viewpoint of individual landowners who make land use decisions with the objective to maximize expected returns or utility. In turn such models use economic theory to guide model development, including choice of functional form and explanatory variables (Ruben et al., 1998). The assumptions on behaviour arise from the micro level. This limits these models to applications that are able to discern all individuals. Difficulties arise from scaling up these models, as they have primary been designed to work at the micro-level. Jansen and Stoorvogel (1998) and Hijmans and Van Ittersum (1996) have shown the problems of scale that arise when this type of models are used at higher aggregation levels.
Studies that use the macro-level perspective are often based on macro-economic theory or apply the systems approach. A typical example of an economic model that uses the macro-perspective is the IIASA LUC model developed for China (Fischer and Sun, 2001). The model has a low spatial resolution (8 regions in China) and is very data demanding due to the multiple sectors of the economy that are taken into account. It is designed to establish an integrated assessment of the spatial and inter-temporal interactions among various socio-economic and biophysical forces that drive land use and land cover change. The model is based on recent advances in applied general equilibrium modelling. Applied general equilibrium modelling uses input-output accounting tables as the initial representation of the economy and applies a dynamic welfare optimisation model. In mathematical terms, the welfare optimum levels of resource uses and transformations are a function of the initial state of the economy and resources, of the parameterisation of consumer preferences and production relations, and of (exogenously) specified dynamics and constraints such as population growth and climate changes.
Other land use change models are based on an analysis of the spatial structure of land use; therefore, they are not bound to the behaviour of individuals or sectors of the economy. Among these models are the CLUE model (Verburg and Veldkamp, 2004; Verburg et al., 1999); GEOMOD2 (Pontius et al., 2001; Pontius and Malanson, 2005); LOV (White and Engelen, 2000) and LTM (Pijanowski et al., 2002).
The above discussion on the micro- and macro-level research perspective referred to the issue of scale. Scale is the spatial, temporal, quantitative, or analytic dimension used by scientists to measure and study objects and processes (Gibson et al., 2000). All scales have extent and resolution. Extent refers to the magnitude of a dimension used in measuring (e.g., scope of area covered on a map) whereas resolution refers to the precision used in this measurement (e.g., grain size). For each process important to land use and land cover change, a range of scales may be defined over which it has a significant influence on the land use pattern (Dovers, 1995; Meentemeyer, 1989). These processes can be related to exogenous variables, the so-called 'driving forces' of land use change. Often, the range of spatial scales over which the driving forces and associated land use change processes act correspond to levels of organisation. Level refers to level of organisation in a hierarchically organised system and is characterised by its rank ordering in the hierarchical system. Examples of organizational levels include organism or individual, ecosystem, landscape and national or global political institutions. Many interactions and feedbacks between these processes occur at different levels of organisation. Hierarchy theory suggests that processes at a certain scale are constrained by the environmental conditions at levels immediately above and below the referent level, thus producing a constraint 'envelope' in which the process or phenomenon must remain (O'Neill et al., 1989).
Most land use models are based on one scale or level exclusively. Often, this choice is based on arbitrary, subjective reasons or scientific tradition (i.e., micro-or macro-level perspective) and not reported explicitly (Gibson et al., 2000; Watson, 1978). Models that rely on geographic data often use a regular grid to represent all data and processes. The resolution of analysis is determined by the measurement technique or data quality instead of the processes specified. Other approaches chose a specific level of analysis, e.g., the household level. For specific data sets optimal levels of analysis might exist where predictability is highest (Goodwin and Fahrig, 1998; Veldkamp and Fresco, 1997). Unfortunately these levels are not consistent, therefore, it might be better not to use a priori levels of observation, but rather extract the observation levels from a careful analysis of the data (Gardner, 1998; O'Neill and King, 1998).
The task of modelling socio-cultural forces is difficult because humans act both as individual decision makers (as assumed in most econometric models) and as members of a social system. Sometimes these roles have conflicting goals. Similar scale dependencies are found in biophysical processes. Often the aggregated result of individual processes cannot be straightforwardly determined. Rastetter et al. (1992) and King et al. (1989) point out that the simple spatial averaging of fine-scale non-linear functional forms of ecosystem relationships, or of the data required to compute the spatially aggregate versions of such functional forms, can lead to substantial aggregation errors. This is widely known as the 'fallacy of averages'.
Besides these fundamental issues of spatial scale, another scaling issue relates to scales of observation, and is, therefore, more related to practice. Due to our limited capacities for the observation of land use, extent and resolution are mostly linked. Studies at large spatial extent invariably have relatively coarse resolution, due to our methods for observation, data analysis capacity and costs. This implies that features that can be observed in small regional case studies are generally not observable in studies for larger regions. On the other hand, due to their small extent, local studies often lack information about the context of the case study area that can be derived from the coarser scale data. Scales of observation usually do not correspond with the scale/level at which the process studied operates, causing improper determination of the processes (Bloschl and Sivapalan, 1995; Schulze, 2000).
The discussion of scale issues can be summarised by the three aspects of scaling important for the analysis of land use change:
• Land use is the result of multiple processes that act over different scales. At each scale different processes have a dominant influence on land use.
• Aggregation of detailed scale processes does not straightforwardly lead to a proper representation of higher-level processes. Non-linearity, emergence and collective behaviour cause this scale-dependency.
• Our observations are bound by the extent and resolution of measurement causing each observation to provide only a partial description of the whole multi-scale land use system.
Although the importance of explicitly dealing with scaling issues in land use models is generally recognised, most existing models are only capable of performing an analysis at a single scale. Many models based on micro-economic assumptions tend to aggregate individual actions but neglect the emergent properties of collective values and actions (Riebsame and Parton, 1994). Approaches that implement multiple scales can be distinguished by the implementation of a multi-scale procedure in either the structure of the model or in the quantification of the driving variables. The latter approach acknowledges that different driving forces are important at different scales and takes explicit account of the scale dependency of the quantitative relation between land use and its driving forces. Two different approaches to quantifying the multi-scale relations between land use and driving forces are known. The first is based on data that are artificially gridded at multiple resolutions; where at each individual resolution the relations between land use and driving forces are statistically determined (de Koning et al., 1998; Veldkamp and Fresco, 1997; Verburg and Chen, 2000; Walsh et al., 2001; Walsh et al., 1999). The second approach uses multi-level statistics (Goldstein, 1995). The first applications of multi-level statistics were used in the analysis of social science data of educational performances in schools (Aitkin et al., 1981). More recently it was found that this technique could also be useful for the analysis of land use, taking different driving forces at different levels of analysis into account. Hoshino (2001) analysed the land use structure in Japan by taking different factors at each level into account using data for municipalities (level-1 units) nested within prefectures (level-2 units). A similar approach was followed by Polsky and Easterling (2001) for the analysis of the land use structure in the Great Plains of the USA. Also in this study administrative units at different hierarchical levels were used.
A number of land use change models are structured hierarchically, thus taking multiple levels into account. In its simplest form, the total amount of change is determined for the study area as a whole and allocated to individual grid-cells by adapting the cut-off value of a probability surface (Pijanowski et al., 2002). The demand-driven nature of land use change could be used as a rationale for this approach. Population and economic developments change the demand for different land use types at aggregate levels whereas the actual allocation of change is determined by regional and local conditions. This structure is also implemented in the CLUE modelling framework (Verburg et al., 1999). However, this framework uses three scales: the national scale for demand calculations and two spatially explicit scales to take driving forces at different scales into account. Apart from the top-down allocation a bottom-up algorithm is implemented to feed back local changes to the regional level.
A unifying hypothesis that links the ecological and social realms, and an important reason for pursuing integrated modelling, is that humans respond to cues both from the physical environment and from their socio-cultural context and behave to increase both their economic and socio-cultural well-being. Land use change is therefore often modelled as a function of a selection of socioeconomic and biophysical variables that act as the so-called 'driving forces' of land use change (Turner II et al., 1993). Driving forces are generally subdivided in three groups (Turner II et al., 1995): socio-economic drivers, biophysical drivers and proximate causes (land management variables). Although biophysical factors mostly do not 'drive' land use change directly, they can cause land cover changes (e.g., through climate change) and they influence land use allocation decisions (e.g., soil quality). At different scales of analysis, different driving forces have a dominant influence on the land use system. At the local level this can be the local policy or the presence of small ecological valuable areas whereas at the regional level the distance to the market, port or airport might be the main determinant of the land use pattern.
Driving forces are most often considered exogenous to the land use system to facilitate modelling. However, in some cases this assumption hampers the proper description of the land use system, e.g., if the location of roads and land use decisions are jointly determined. Population pressure is often considered to be an important driver of deforestation (Pahari and Marai, 1999), however, Pfaff (1999) points out that population may be endogenous to forest conversion, due to unobserved government policies that encourage development of targeted areas, or that population may be collinear with government policies. If the former were the case, then including population as an exogenous 'driver' of land use change would produce a biased estimate and lead to misleading policy conclusions. If the latter were the case, then the estimates would be unbiased, but inefficient, leading to a potential false interpretation of the significance of variables in explaining deforestation. Other examples of endogeneity of driving forces in land use studies are given by Chomitz and Gray (1996), Mertens and Lambin (2000) and Irwin and Geoghegan (2001).
The temporal scale of analysis is important in deciding which driving forces should be endogenous to the model. In economic models of land use change, demand and supply prices and associated functions are the driving forces of land use change. However in the short term prices can be considered exogenous to land use change even though they are endogenous on longer time spans.
The selection of driving forces is very much dependent on the simplification made and the theoretical and behavioural assumptions used in modelling the land use system. In most economic approaches optimisation of utility is the assumed behaviour, leading to bid-rent models. Most economic models of land use change are, therefore, related to the land rent theories of Von Thunen and Ricardo. Any parcel of land, given its attributes and location, is assumed to be allocated ,to the use that earns the highest rent (e.g., Chomitz and Gray, 1996, Jones and O'Neill, 1992). In its most simple form, the monocentric model, the location of a central city or business district to which households commute, is the main factor determining the rent of a parcel. All other features of the landscape are ignored. Individual households optimise their location by trading off accessibility to the urban centre and land rents, which are bid up higher for locations closer to the centre. The resulting equilibrium pattern of land use is described by concentric rings of residential development around the urban centre and decreasing residential density as distance from the urban centre increases. In this case 'distance to urban centre' is the most important driving variable. The limitation of the monocentric model is partly due to its treatment of space, which is assumed to be a 'featureless plain' and is reduced to a simple measure of distance from the urban centre. Others explain spatial variability in land rent by differences in land quality that arise from a heterogeneous landscape, but abstract from any notion of relative location leading to spatial structure. Many models that try to explain land values, for example, hedonic models combine the two approaches by including variables that measure the distance to urban centre(s) as well as specific location features of the land parcel (Bockstael, 1996).
Models of urban and peri-urban land allocation are, generally, much more developed than their rural counterparts (Riebsame et al., 1994). More recent urban models are no longer solely based upon economic modelling using either equilibrium theory or spatial disaggregated intersectoral input-output approaches. Rather than utility functions they use discrete choice modelling through logit models (Alberti and Waddell, 2000; Landis, 1995). This also allows a greater flexibility in behavioural assumptions of the actors. Conventional economic theory makes use of rational actors, the Homo economicus, to study human behaviour. This powerful concept of the rational actor is not always valid and various modifications to this conception of human choice have been suggested (Janssen and Jager, 2000; Rabin, 1998). Examples of such modifications of the concept of the rational actor include the difficulty that people can have evaluating their own preferences, self-control problems and other phenomena that arise because people have a short-run propensity to pursue immediate gratification and the departure from pure self-interest to pursue 'other-regarding' goals such as fairness, reciprocal altruism and revenge.
Models that integrate the analysis of different land use conversions within the same model commonly use a larger set of driving forces. Apart from the drivers that determine urban land allocation, such as land value and transportation conditions, they need information on the suitability of the land for agricultural production (e.g., soil quality and climatic variables, market access). Also the extent of the study area influences the selection of variables. In larger areas it is common that a larger diversity of land use situations is found, which requires a larger variety of driving forces to be taken into account, whereas in a small area it might be only a few variables that have an important influence on land use.
Three different approaches to quantify the relations between land use change and its driving forces can be distinguished. The first approach tries to base all these relations directly on the processes involved, using theories and physical laws (deductive approach). Examples are economic models based on economic input-output analysis (Fischer and Sun, 2001; Waddell, 2000) or utility optimisation (Ruben et al., 1998). For integrated land use change analysis this approach is often not very successful due to the difficulty of quantifying socio-economical factors without the use of empirical data. Therefore, the second approach uses empirical methods to quantify the relations between land use and driving forces instead (inductive approach). Many econometric models rely therefore on statistical techniques, mainly regression, to quantify the defined models based on historic data of land use change (Bockstael, 1996; Chomitz and Gray, 1996; Geoghegan et al., 1997; Pfaff, 1999). Also other models, not based on economic theory, use statistical techniques to quantify the relationships between land use and driving forces (Mertens and Lambin, 2000; Mertens et al., 2000; Pontius et al., 2001; Pontius and Schneider, 2001; Serneels and Lambin, 2001; Turner et al., 1996; Veldkamp and Fresco, 1996; Wear and Bolstad, 1998 and many more). Most of these approaches describe historic land use conversions as a function of the changes in driving forces and location characteristics. This approach often results in a relatively low degree of explanation due to the short time-period of analysis, variability over this time period and a relatively small sample size (Hoshino, 1996; Veldkamp and Fresco, 1997). Cross-sectional analysis of the actual land use pattern, which reflects the outcome of a long history of land use changes, results in more stable explanations of the land use pattern (de Koning et al., 1998; Hoshino, 2001). A drawback of the statistical quantification is the induced uncertainty with respect to the causality of the supposed relations.
The third method for quantifying the relations between driving forces and land use change is the use of expert knowledge. Especially in models that use cellular automata, expert knowledge is often used. Cellular automata models define the interaction between land use at a certain location, the conditions at that location and the land use types in the neighbourhood (Clarke and Gaydos, 1998; Engelen et al., 1995; Silva and Clarke, 2002; Wu, 1998). The setting of the functions underlying these cellular automata is hardly ever documented and largely based upon the developer's knowledge and calibration.
Land use patterns nearly always exhibit spatial autocorrelation. The explanation for this autocorrelation can be found, for a large part, in the clustered distribution of landscape features and gradients in environmental conditions that are important determinants of the land use pattern. Another reason for spatially autocorrelated land use patterns are the spatial interactions between land uses types itself: urban expansion is often situated right next to an already existing urban area, as is the case for business parks etc. Scale economies can provide an explanation for such patterns. In agricultural landscapes adoption of particular farming technologies or cultivation patterns might also exhibit observable spatial effects. Other land use types might preferably be located at some distance from each other, e.g., an airport and a residential area, causing a negative spatial autocorrelation. The importance of such structural spatial dependencies is increasingly recognized by geographers and economists. Spatial statistical techniques have been developed to quantify spatial dependencies when using econometrics (Anselin, 2002; Bell and Bockstael, 2000).
Spatial autocorrelation in land use patterns is scale dependent. At an aggregate level residential areas are clustered, having a positive spatial autocorrelation. However, Irwin and Geoghegan (2001) found that, at the scale of individual parcels in the Patuxent watershed, there was evidence of a negative spatial interaction among developed parcels, implying that a developed land parcel 'repels' neighbouring development due to negative spatial externalities that are generated from development, e.g., congestion effects. The presence of such an effect implies that, ceteris paribus, a parcel's probability of development decreases as the amount of existing neighbouring development increases. The existence of different causal processes at different scales means that spatial interactions should again be studied at multiple scales while relations found at a particular scale can only be used at that scale.
Spatial interactions can also act over larger distances: a change in land use in the upstream part of a river might affect land use in the downstream part through sedimentation of eroded materials leading to a functional connectivity between the two areas. Another example of spatial connectivity is the migration of companies from one part of the country to another part when all available land area is occupied at the first location. Analysis of these interactions is essential to understand the spatial structure of land use. Globalisation of the economy will cause these interactions to have a large spatial extent, leading to connectivity in land use between continents.
Cellular automata are a common method to take spatial interactions into account. They have been used in studies of urban development (Clarke and
Gaydos, 1998; Li and Yeh, 2002; White et al., 1997; Wu and Webster, 1998) but have now also been implemented in land use models that are able to simulate multiple land use types (White and Engelen, 2000). Cellular automata calculate the state of a pixel based on its initial state, the conditions in the surrounding pixels, and a set of transition rules. Although very simple, they can generate a rich behaviour (Wolfram, 1986).
The Urban Growth Model (Clarke and Gaydos, 1998), a classical cellular automata model for urban expansion was combined with so-called 'deltatrons' that enforce even more spatial interaction than achieved with cellular automata alone in order to achieve the desired degree of spatial and temporal autocorrelation (Candau, 2000; Herold et al., 2003).
Neighbourhood interactions are now also increasingly implemented in econometric models of land use change. Although this implementation can be done through advanced measures of autocorrelation (Bell and Bockstael, 2000; Brown et al., 2002; Walker et al., 2000), more often simple measures of neighbourhood composition, e.g., the area of the same land use type in the neighbourhood, are included as explanatory factors in regression models explaining land use change (Geoghegan et al., 1997; Munroe et al., 2001; Nelson and Hellerstein, 1997).
A different method for implementing spatial interaction, especially interaction over larger distances, is the use of network analysis. In many models, driving forces have been included that indicate travel times or distances to markets, ports and other facilities that are important to land use. Often models that are based on economic theory take travel costs to a market into account (Jones, 1983). Most often simple distance measures are used. However, it is also possible to use sophisticated techniques to calculate travel times/costs and use the results to explain the land use structure. This type of calculations are often included in combined urban-transportation models (Miller et al., 1999).
Spatial interactions can also be generated more indirectly through the hierarchical structure of the model. Multi-scale models like CLUE (Veldkamp and Fresco, 1996) and Environment Explorer (White and Engelen, 2000) can generate spatial interactions through the feedback over a higher scale. If a certain, regional, demand cannot be met at the local level (due to a location condition or policy, e.g., nature reserve), it will feedback to the regional level and allocation to another location will proceed. This type of modelling can indicate the trade-off of a measure at a certain location for the surrounding area.
Temporal dynamics: trajectories of change
The previous sections all dealt with spatial features of land use change. Many of the issues addressed are also relevant for the temporal dimension of land use change. Changes are often non-linear and thresholds play an important role. Nonlinear behaviour requires dynamic modelling with relatively short time steps. Only then can land use change analysis take into account the path-dependency of system evolution, the possibility of multiple stable states, and multiple trajectories. Land use change cannot be simply explained as the equilibrium result of the present set of driving forces. In other words, land use change may be dependent on initial conditions, and small, essentially random events may lead to very different outcomes, making prediction problematic. Exemplary is the effect of transportation infrastructure on the pattern of development. Road expansion and improvement not only lead to more development but may also lead to a different pattern through a reorganisation of the market structure, which then feeds back to further infrastructure development. Thus, certain trajectories of land use change may be the result of 'lock in' that comes from systems that exhibit autocatalytic behaviour.
Connected to the temporal dimension of models is the issue of validation. Validation of land use change models is most often based on the comparison of model results for a historic period with the actual changes in land use as they have occurred. Such a validation exercise requires land use data for another year than the data used in model parameterisation. The time period between the two years for which data are available should be sufficient to actually compare the observed and simulated dynamics. Ideally this time period should be as long as the period for which future scenario simulations are made. Such data are often difficult to obtain and even more often data from different time periods are difficult to compare due to differences in the classification scheme of land use maps or the resolution of remote sensing data. Methods for validation of model performance should make a clear distinction in the model performance concerning the quantity of change and the quality of the spatial allocation of the land use changes. Appropriate methods for validation of land use change models are described by Pontius (2002), Costanza (1989), Pontius and Scheider (2001).
In a number of models, temporal dynamics are taken into account using initial land use as a criterion for the allowed changes. Cellular automata approaches do this explicitly by including decision rules that determine the conversion probability. In the CLUE-S model (Verburg et al., 2002) a specific land use conversion elasticity is given to each land use type. This elasticity will cause some land use types to be more reluctant to change (e.g., plantations of permanent crops) whereas others easily shift location (e.g., shifting cultivation). The SLEUTH urban growth model (Clarke and Gaydos, 1998) employ explicit functions to enforce temporal autocorrelation that also take the 'age' of a new urban development centre into account. The economic land allocation model of the Patuxent Landscape Model (Irwin and Geoghegan, 2001) also explicitly considers the temporal dimension. The land use conversion decision is posed as an optimal timing decision in which the landowner maximises expected profits by choosing the optimal conversion time. That time is chosen so that the present discounted value of expected returns from converting the parcel to residential use is maximized. These latter two model implementations of temporal dynamics already take account of a longer time span than most models, which only account for the initial state. However, most models are currently unable to account for land use change as influenced by land use histories over longer time scales. For a proper description of certain land use types, e.g., long fallow systems, or feedback processes such as nutrient depletion upon prolonged use of agricultural land, incorporation of land use histories could make an important improvement (Priess and Koning, 2001).
The combination of temporal and spatial dynamics often causes complex, non-linear behaviour. However, a large group of models do not account at all for temporal dynamics. These models are simply based on an extrapolation of the trend in land use change through the use of a regression on this change (Geoghegan et al., 2001; Mertens and Lambin, 2000; Schneider and Pontius, 2001; Serneels and Lambin, 2001). This type of model is therefore not suitable for scenario analysis, as they are only valid within the range of the land use changes on which they are based. The validity of the relations is also violated when confronted with a change in the competitive conditions between land use types, e.g., caused by a change in demand. This critique does not apply to all models based on statistical quantification. When these models are based on the analysis of the structure (pattern) of land use instead of the change in land use and are combined with dynamic modelling of competition between land use types, they have a much wider range of applications.
Land use change decisions are made within different time scales, some decisions are based on short term dynamics (such as daily weather fluctuations), and others are only based on long-term dynamics. Most land use models use annual time steps in their calculations. This means that short-term dynamics are often ignored or, when they can have an additive effect, are aggregated to yearly changes. However, this aggregation can hamper the linkage with the actual decision making taking at shorter time scales. The need for multi-scale temporal models was acknowledged in transportation modelling, where short-term decisions depend on the daily activity schedules and unexpected events (Arentze et al., 2001; Arentze and Timmermans, 2000). The link between this type of transportation models and land use is straightforward. If changes in the daily activity schedule are required on a regular basis, individuals will adjust their activity agenda or the factors affecting the agenda, for example by relocation. Such a decision is a typical long-term decision, evolving from regular changes in short-term decisions.
Land use systems are groups of interacting, interdependent parts linked together by exchanges of energy, matter, and information. Land use systems are therefore characterised by strong (usually non-linear) interactions between the parts, complex feedback loops that make it difficult to distinguish cause from effect, and significant time and space lags, discontinuities, thresholds, and limits (Costanza and Wainger, 1993). This complexity makes the integration of the different sub-systems one of the most important issues in land use modelling. Generally speaking, two approaches for integration can be distinguished. The first approach involves a rather loose coupling of sub-systems that are separately analysed and modelled. To allow the dissection of system components, it must be assumed that interactions and feedbacks between system elements are negligible or the feedbacks must be clearly defined and information between sub-systems must be achieved through the exchange of input and output variables between sub-system models. The second approach takes a more holistic view. Instead of focussing all attention on the description of the sub-systems explicit attention is given to the interactions between the sub-systems. In this approach, more variables are endogenous to the system and are a function of the interactions between the system components. The approach chosen is very much dependent on the time-scale (endogeneity assumptions) and the purpose for which the model is built. Generally speaking, integration only adds value as compared with disciplinary research when feedbacks and interactions between the sub-systems are explicitly addressed. An appropriate balance should be found, as the number of interactions that can be distinguished within the land use system is very large and taking all of those into account could lead to models that are too complex to be operational.
The group of models commonly referred to as integrated assessment models are models that attempt to portray the social, economic, environmental and institutional dimensions of a problem (Rotmans and van Asselt, 2001). In practice, most integrated assessment models are directed to the modelling of climate change and its policy dimensions (reviewed by Schneider, 1997). Some integrated assessment models, e.g., the IMAGE2 model (Alcamo et al., 1998) contain land use modules, but these are often much less elaborated than models that are specifically developed for land use studies. For integrated assessment models the same conclusions hold as for land use models: many large models consist of linked subsystems that are not fully integrated. This means that these models are complicated but not complex, as a result of which their dynamic behaviour is almost linear and does not adequately reflect real world dynamics (Rotmans and van Asselt, 2001).
An example of a fully integrated model is the IIASA-LUC model (Fischer and Sun, 2001). Although this model incorporates many sub-systems, interactions and feedbacks, it has become complex to operate and, above-all, difficult to parameterise due to the high data requirements (see Briassoulis, 2001 for a discussion of data needs). Another disadvantage of highly complex, integrated models is that the degree and type of integration often appears to be subjective based on the modeller's disciplinary background. As a fully integrated approach, qualitative modelling (Petschel-Held et al., 1999) allows a focus on the system as a whole, however, also this approach is completely based on the knowledge of the developer about the existence and importance of the feedbacks important to the studied system, so it is likely to be biased and incomplete.
An integrated approach that models the behaviour of the different subsystems individually but includes numerous connections between these sub-models is the Patuxent Landscape Model (Geoghegan et al., 1997; Voinov et al., 1999) that is designed to simulate fundamental ecological processes on the watershed scale, in interaction with a component that predicts the land use patterns. Land use change is dealt with in the economic module (Bockstael, 1996; Irwin and Geoghegan, 2001) whereas all hydrological and ecological processes in the watershed are simulated in the ecological module. The ecological module integrates all processes involved based on the General Ecosystem Model (Fitz et al., 1996). The coupling between the economic module and the ecological module is less elaborated. Output of the economic module, land use change patterns, is used as input in the ecological module whereas the possibility exists that output of the ecological module, e.g. water table depths, habitat health etc., should be used as inputs of the economic module, allowing for feedbacks within the system. Also in other integrated land use-ecosystem models, the ecological sub-models tend to be far more integrated than the associated land use models (McClean et al., 1995).
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