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Analysis of Land Use Change: Theoretical and Modeling Approaches
Helen Briassoulis, Ph.D.
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4.6.3. Simulation Integrated Models
Many of the integrated models of land use can be classified basically as simulation models if simulation is defined broadly as a modeling activity aimed at analyzing impacts or making conditional predictions using some form of operational expression of a system’s components and of their interrelationships. Batty (1976) notes that "All mathematical models which involve the use of large-scale computational facilities are referred to as simulation models" (Batty 1976, 294). However, as a modeling technique, simulation has a more precise meaning. According to Wilson (1974), simulation techniques involve "a set of rules which enable a set of numbers to be operated upon, usually in the computer, although the rules and the consequences of applying them cannot be written down as a set of algebraic equations…. Sometimes, the simulation technique lends itself naturally to a problem. This happens, for example, when the underlying theory consists of a set of statements involving conditional probabilities ….We resort to simulation techniques for situations which are too complicated to be handled by more straightforward algebraic techniques" (Wilson 1974, 175).
Batty (1976) clarifies further the meaning of simulation by distinguishing between analytic and simulation methods of modeling: "Analytic methods of modeling involve the use of mathematical analysis to arrive at explicit equations representing the behaviour of the system. Simulation methods are used to derive the behavior of the system when the system is too complex to be modeled using the more direct analytic approach" (Batty 1976, 294). He further cites Elton and Rosenhead (1971) who "point out the essential characteristic of simulation when they say "… one does not arrive at explicit equations expressing the behavior of the system of this general type; rather one achieves a number of potential histories of the system from which the effects of possible modification to the system can be predicted" (Batty 1976, 294).
The simulation integrated models which are presented here are grouped according to the spatial level to which they refer as there is a close relationship between spatial level of analysis, theoretical background of the model, and level of aggregation used (or, possible). Most models are based on economic theory – either micro- or macro. Microeconomic models are also distinguished according to their adopting a continuous utility maximization framework or a discrete, random utility theory framework. Three groups of models are discussed: (a) urban/metropolitan level simulation models, (b) regional level simulation models, and (c) global level simulation models.
4.6.3A Urban/Metropolitan level simulation models
The first simulation models to be considered are urban/metropolitan level models. The application of, more or less, heuristic techniques to provide answers to land use forecasting questions which arise naturally in the context of planning dates back to the 1950s when elementary, plan-based forecasts were generated by means of such techniques. The Detroit Metropolitan Area Transportation Study and the Chicago Area Transportation Study (CATS) were among the first efforts which had the greatest influence. The former is credited with introducing "what has come to be known as the Urban Transportation Planning (UTP) model … which operationalizes the concept … that urban trip-making is a derived demand depending on land uses and that future travel could be derived from forecasts of future and uses" (Kain 1986, 848). The CATS model (Hamburg 1960 cited in Kain 1986, 848) "devised an ingenious land use forecasting model based on the concept of development capacity" (Kain 1986, 848) utilizing floor area data and historical information on population densities and vacant land. However, (computer) simulation techniques emerged in the early 1960s when more refined modeling techniques started to develop and information technology was making rapid progress. In fact, this latter development is one of the reasons for the flourishing of simulation techniques in the following decades up to the present.
Among the first, large-scale applications of simulation were models of the housing market. Although these are not integrated models of land use change proper as they concentrate on a particular subsystem of the urban spatial system, the housing market, and not on land use, they attempt some kind of integration in the sense that: (a) they examine the demand for housing and the allocation of households in each housing submarket (in a way similar to many gravity-type integrated models discussed previously), (b) they consider the interaction between demand and supply of housing, and (c) they disaggregate the housing market considerably to capture (within the constraints of the models applied, of course) the spatial variability of the housing market. The following models which belong to this category are presented here:
Adopting a broader perspective on integration, other modelers attempted to simulate the relationships among more components of the urban/metropolitan system. The literature calls these models dynamic simulation models. Two examples of this line of integrated modeling are given:
The San Francisco CRP model
The earliest housing market simulation model was the San Francisco CRP model designed by A .D. Little (Rothenberg-Pack 1978, Kain 1986) whose primary focus was less on forecasting than on evaluating various housing and community development programs. It represents a pioneering effort to model the behavior of both housing demanders and suppliers and to relate their decisions in a rudimentary market clearing framework. It was concerned with the central city (and not with the wider metropolitan region) and it did not consider competition between the central city’s housing market and that of the rest of the region. It required exogenous forecasts of population by household types according to demographic characteristics and income. It represented 114 types of households (defined in terms of income, family size, race and age), 27 types of dwelling units (defined in terms of structure type, tenure, number of rooms and conditions), and 106 neighborhoods. It developed housing supply models which assumed profit maximizing housing suppliers and made supply decisions according to projected market rents and estimates of the cost of new construction (Kain 1986). For a variety of reasons whose discussion is beyond the scope of the present project, this model did not become fully operational (for details see Rothenberg-Pack 1978).
The UI, NBER, HUDS urban simulation models
Three other simulation models of the housing market, developed in the 1970s, are widely known: the Urban Institute model (UI), the NBER (National Bureau of Economic Research) Urban Simulation model and the HUDS (Harvard Urban Development Simulation) model (Kain 1986). All three models provide modeling of demand for housing, supply of housing, and a housing market clearing mechanism.
The UI model produces long run equilibrium solutions of housing quantities and prices based on a Walrasian auction mechanism for a 10-year simulation period (Kain 1986). Housing demand is modeled on the basis of utility theory. Households seek to maximize their utility subject to a budget constraint; the housing services demanded depend on quantity of housing services consumed, quantities of other goods consumed, employment accessibility, average journey-to-work travel time for each zone of the study area, relative wealth of the zone, racial composition of the zone. The utility functions assume that the optimum quantity of housing services demanded is independent of neighborhood characteristics.
Housing supply is modeled similarly following the economic theory for producers; i.e. assuming profit maximization. The housing production functions express current level of housing services in terms of initial level of services and a quantity of newly added capital inputs (including housing depreciation). These housing supply functions are calibrated from historical data. The UI model provides for less spatial (six zones) and household detail compared to the NBER-HUDS models which are discussed next.
The NBER-HUDS models is essentially a family of three models starting from the Detroit Prototype moving to a second version used to study the market effects of housing allowances as part of the Experimental Housing Allowance Program (EHAP) and ending with HUDS which was designed and used to evaluate the impacts of spatially concentrated housing improvement programs (Kain 1986). The structure of the basic NBER model is presented below based on Chapin and Kaiser (1979) and Kain (1986). The characteristics of the housing and demand models of NBER and HUDS are discussed together (following Kain 1986) as both belong to the same family.
The NBER-HUDS models provide annual housing market clearing solutions in contrast to the UI model which assumed a 10-year simulation period. They employ a disequilibrium framework for clearing the housing market which is modeled by means of linear programming. Housing is modeled in great detail as a multidimensional bundle of housing services described in terms of structure type, neighborhood quality, and quantity of structure services households must consume as an indivisible package at a particular location. The structure of the prototype NBER model is presented in 4.2d. The description which follows reflects the characteristics of the two versions of this original prototype. Six submodels are included corresponding to the demand and the supply side of the housing market. The first submodel is a supply-oriented dwelling unit-filtering submodel which estimates changes in housing quality either downward due to aging or upward due to renovations on the basis of expected housing prices in the zone and exogenous maintenance costs. The output of this submodel is a distribution of expected housing prices by dwelling type and zone and an aged and renovated housing stock.
The second submodel is a demand-oriented employment location model which receives as input exogenously determined revisions of employment levels and composition (by industry) at each workplace. It translates these changes into changes in employee household characteristics – age of the head of the household, family size, income, education, race – for each of 96 household types. The third submodel is called a movers’ submodel which generates mover households that enter the housing market as demanders of housing. It introduces new household formation as well. The moving households generate vacancies that enter the supply side as available housing units.
The fourth submodel is a demand allocation submodel which allocates housing demanders (the 96 household types) at each workplace to one of 50 housing submarkets defined as 50 housing bundles based on five neighborhood quality levels and 10 structure types. The allocation is operationalized by means of econometrically estimated multinomial logit demand functions and takes into account the relative minimum gross prices of the 50 housing bundles. The demand function expresses the probability that a worker employed at workplace j will live in residence zone i and the conditional probability that he will commute by mode m, given the choice of residence i so as to minimize travel costs which include both time and money costs. Note that this is not a spatial allocation but an allocation to housing type.
The fifth submodel is a supply submodel which estimates demolitions, conversions, and new construction for each zone. The housing supply functions are similar to the UI’s supply functions but are more elaborate and detailed reflecting, among others, expectations of the housing suppliers of future changes in prices, investments, etc. The last submodel is the market clearing assignment model. After each housing market participant has been assigned to a housing submarket, a linear programming algorithm is used to assign them to residence zones. The same algorithm produces estimates of location rents which are used as price signals and, in combination with other information, are used to calculate market prices for each of the 50 housing bundles in each of the 200 residence zones (of the Chicago area application of HUDS). Taking into account the distributions of both housing and household characteristics at the start of the simulation period, the output of this model is the distribution of these characteristics at the end of the period (a year).
The NBER-HUDS models are more detailed spatially and in terms of household types than the UI model. All three models are restricted to urban areas and to housing, employ economic theory of profit and utility maximization to estimate housing supply and demand, and they are suited to analyzing impacts of housing policies. The analysis of land use change with these models is constrained by the above features and lacks a host of other explanatory factors (environmental, social, cultural, political, institutional). In fact, these models are not explanatory models as they are fitted with historical data and start with a predetermined theoretical schema, that of utility maximization. Interactions with other types of land use are implicit at best. The emphasis of these models on accessibility as one of the explanatory factors of household housing choice behavior is characteristic of the functionalism of modeling activity in the 1960s and 1970s.
The CUFM model
The California Urban Futures Model (CUFM) developed by Landis (1994, 1995) is a more recent modeling effort to provide a model of the housing market which could be used in a planning context for the analysis of alternative plans. It has a diverse heritage as its designer notes (Landis 1995) of which the Lowry and the NBER pieces are of interest here. It has several innovative features with respect to both past and contemporary models of the housing market. First, it focuses on private land developers as the most influential agents in the context of urban development. These are assumed to be profit maximizing individuals who decide to develop a site if it has a high development potential. Second, CUFM models the supply side of the housing market explicitly by adopting a spatial system of reference based on the notion of Developable Land Units (DLUs) which may be individual sites or groups of sites with similar characteristics (with respect to residential development). DLUs are stored and manipulated in a GIS environment. The solutions generated by the model are, thus, depicted in greater spatial detail on a site by site or DLU basis in contrast to zone-based integrated models. Third, the purpose of CUFM was to simulate the development effects of locally-based land use and development policies, the latter constituting an important input to the operation of the model.
CUFM consists of four linked submodels: (a) the Bottom-Up Population Growth Submodel, (b) the Spatial Database, (c) the Spatial Allocation Submodel, and (d) The Annexation-Incorporation Submodel. The Bottom-Up Population Growth Submodel represents the demand side of the whole model. It generates five-year population growth forecasts for every city and county as a function of city size and growth history, outward expansion potential, and the adoption of specific policies intended to promote or retard growth. It consists of two linear regression equations one for cities and one for counties (Landis 1994). The Spatial Database represents the supply side of the whole model and includes the geometry, location and attributes of each DLU. It consists of a series of map layers that describe the environmental, land use, zoning, current density, and accessibility attributes of all sites in the study region. The Spatial Allocation Submodel allocates the projected population growth to the DLUs of the study area with the use of certain rules and procedures. Its main function is to "clear the market" by matching the demand for developable sites to the supply of such sites. DLUs are developed in decreasing order of their expected profitability (to private developers). Finally, the Annexation-Incorporation Submodel consists of a series of procedures for annexing newly developed DLUs to existing cities or incorporating clusters of DLUs into new cities.
The profit potential of a DLU, measured as per acre residential development profit (i, j, k) is calculated as the difference between the net home sales price (i, j, k) and the following cost items:
The subscripts used denote:
| i | the size and quality level of a typical new home in each community |
| j | the slope, environmental characteristics, and specific location of the home site (or DLU) |
| k | the jurisdiction in which the home is located |
Although CUFM provides a spatially explicit integrated model of the housing market which can be used to analyze various policies as well as to incorporate the environmental variability of a study area, it has several shortcomings in the view of more holistic integrated models. First, although it rests on the assumption of profit maximizing land developers, it lacks a firm theoretical grounding on economic as well as on sociological or other theories on land development. Second, it does not take into account the interaction of land use with the transportation network which has proven to be very important in metropolitan areas at least. Third, it does not include feedbacks from development or excess demand on housing prices. Fourth, it does not deal with the allocation of other uses such as industrial, commercial, etc. In fact, it ignores the important, "driving" influence of the location decisions of various types of employment on the subsequent development (including housing) of an urban region; i.e. it does not model the jobs-housing balance. Finally, the "journey-to-work" variable (i.e. accessibility) which is central in several past and contemporary integrated models is of secondary importance and does not affect directly the allocation of development. This is not necessarily a negative feature of the model as, in fact, the emphasis of several models on accessibility as a determining driver of urban development has been criticized frequently as it downplays the importance of other determinants of urban spatial structure and growth (namely, the location decisions of producers or, equivalently, of capital).
Dynamic simulation models
Simulation techniques have found important applications in modeling dynamic urban and regional systems given the complexities of modeling these systems as well as the tremendous (if not infeasible) data requirements. Among the first widely known urban dynamic models are J. Forrester’s (1969) simulation modeling exercises which, however, were aspatial and, hence, did not deal with land use at all. Several dynamic urban and regional models have been proposed and the interested reader is referred, among others, to Andersson and Kuenne (1986), Bennett and Hordijk (1986), and Miyao (1986). Wegener (1994) reviewed and compared briefly 12 operational urban models built in the 1980s and 1990s of which several account for land use such as POLIS (Prastacos 1986), CUFM (Landis 1992), ITLUP (Putman 1983, 1991), TRANUS (de la Barra 1989), LILT (Mackett 1983), MEPLAN (Echenique et al. 1990), IRPUD (Wegener 1982, 1985, 1986a). The presentation of all these elaborate models is beyond the scope of this contribution. The reader is referred to recent reviews for further information (Southworth 1995, Wegener 1994). In this section, only a few selected models are presented which relate closely to the analysis of land use change and they are representative of the modeling tradition in this area. These are:
The Dortmund Model
Wegener (1980, 1982) developed a multilevel dynamic simulation model of the economic and demographic development of the Dortmund region, Germany, to capture urban growth and decline processes. Its purpose is to simulate the location decisions of industry, residential developers and households, the resulting migration and commuting patterns, land use development, and the impacts of public programs and policies in the areas of industrial development, housing and infrastructure. The model is operational for the city of Dortmund (consisting of 30 zones and 40 subregions).
The general subject of the model is the study of the endogenous adaptation of urban regions to changing exogenous conditions through public and private decisions. It starts from the observation that several national and multiregional models (of the late 70s-early 80s when the model was designed) cannot capture the essential causes of urban decline because they lack the spatial resolution necessary to take into account agglomeration diseconomies and scarcity of resources, most notably of land. Most models of urban spatial development have been built to allocate growth and have failed to address the issue of urban decline. Only a few of them consider some causes of urban decline such as an aging population, economic recession, outdated infrastructure, and scarcity of buildable land. One of the reasons Wegener advances for this drawback of urban models is the lack of a theory of spatial decision behavior of urban actors such as enterprises, households, individuals and considers his model an attempt to contribute to such a theory.
The Dortmund model is organized at three spatial levels: (a) state, (b) urban region, and (c) city. The first-level model is a multiregional, demo-economic (i.e. demographic-economic) model of the state. Its regions are functionally defined as labor markets. It predicts how regions compete to attract industries and migrants under exogenous preconditions. State policies are taken into account such as public subsidies for industrial development, housing programs, infrastructure investment in specific regions, large scale location or relocation decisions by major industrial corporations. The model yields forecasts of employment by industry and population by age, sex, and nationality in each of the 34 labor market regions as well as migration flows between them.
The second-level model subdivides the urban region into 30 zones. It predicts intraregional location decisions of industry, residential developers and households, resulting migration and commuting patterns, land use development, and impacts of public programs and policies in the areas of industrial development, housing and infrastructure. The outputs of the model are employment by industry, population by age, sex and nationality, households by income, size, age and nationality, dwellings by size, quality, tenure, and building type, and land use by land use category for each of the 30 zones plus the volume of migration and commuting between them. Finally, the third-level model receives as input the output of the second-level model to allocate further the projected activities within each of the 30 zones of the second level. The rest of the presentation of Wegener’s model refers to the second-level model - the urban region – which concerns the modeling of the spatial distribution of activities in the urban region.
The basic structure of the model is shown in Figure 4.2e. It is a recursive, spatially disaggregated simulation model of the urban region. It operates at 2-year increments up to a time horizon of 20 years. It receives as input from the first-level model zonal data on employment (40 industrial sectors), population (20 5-year cohorts), 30 categories of households (characterized by nationality, age of head, income, size), 30 types of housing (characterized by type of building, tenure, quality and number of rooms), industrial and commercial buildings, public facilities, 30 land use categories 10 of which relate to built-up areas), and transportation networks. Urban growth and decline are modeled in terms of the spatial distribution or redistribution of three major urban activities: employment, housing and population.
The employment model simulates the effects of major economic and technological developments such as recession, sectoral changes, productivity increases which cause changes in demand for industrial and commercial floorspace and eventually buildings and land affecting, thus, the spatial structure of the region. This model treats each of the 40 sectors as separate submarkets and makes no distinction between basic and non-basic sectors. At the beginning o the simulation period, it starts with employment in sector s at time t in zone i, Esi(t). This employment can change in six ways as follows:
(a) sectoral decline calculated by the following equation:
rsEsi(t, t+1) = Esi(t)[1 - Es(t+1)/Es(t)] (4.82)
where,
| rs | stands for redundant sectoral workers |
| Es | denotes total employment |
(b) lack of building space is calculated by the following equation:
rbEsi(t,t+1) = [Esi(t) - rsEsi(t,t+1)][1-bsi(t)/bsi(t+1)] (4.83)
| rs | stands for jobs to be relocated because of lack of space |
| bsi(t) | is existing floorspace per workplace at time t |
| bsi(t+1) | is the projected floorspace per workplace at time t+1 |
(c) closing down of large plants which is considered as a "historical event" for which there is no model and, hence, it is exogenously determined (as number of workers and vacated space)
(d) new jobs in vacant buildings which is estimated by a pro rata rule
(e) new jobs in new buildings modeled as extra demand accommodated in new buildings through an allocation function
(f) demolition where the last two steps are reiterated to account for the relocation of jobs caused by demolition.
The housing model assesses changes in housing stock in three different ways:
(a) filtering, where the housing stock filters down in quality each simulation period expressed by the following equation:
R (t+1) = h (t, t+1) R(t) d(t, t+1) (4.84)
where,
| R | an MXK occupancy matrix (M number of household groups, K number of housing types) |
| h | an MXM matrix of transition rated of households |
| d | an KXK matrix of transition rates of housing types |
(b) public housing which is exogenously determined (as a form of policy)
(c) new housing construction which considers additions to the housing stock usually in a subset of the 30 housing types (submarkets).
The demand for new housing is estimated as a function of price changes in a given submarket compared with other investment alternatives (i.e. as a function of relative profitability). This demand is allocated to vacant residential land through an allocation function which accounts for the capacity and attractiveness of a zone.
The population model consists of two distinct but interrelated parts. The first projects existing population of each zone by age, sex, and nationality. The second projects the same population in terms of households by size, income, age of head, and nationality. The relationships between population aging, household formation, migration of households, and migration of persons are modeled as a sequential probabilistic process. For population aging, standard cohort-survival population projection techniques are used. A portion of foreign population is transferred to the native population. Household formation is calculated by using transitions between household states as in the case of transition between age groups. They are aggregated to 30 household types and matrix h(t, t+1) used in equation (4.84) is formed. Consistency checks between aging and household formation are performed also. The migration of households is modeled by an elaborate housing market submodel which represents the interaction between supply of housing (by landlords) and housing demand (by households). A micro-simulation probabilistic approach using the Monte Carlo technique is employed to simulate the housing market as a sequence of search processes of households looking for a house and landlords looking for a tenant. Finally, the migration of persons translates the results of household migration into numbers of persons by taking into account the age distribution of households by type.
Integrated land use/transportation models
An important class of urban/metropolitan models, known as integrated land use/ transportation models, were built in the decades of the 1970s and 1980s and their development continues up to the present. Their common purpose is to model the simultaneous nature of land use and transportation interactions and decisions in urban/metropolitan areas and, thus, be used to analyze the spatial (land use) impacts of changes in the transportation system and/or the location of activities. The land use- transportation connection remains always important because, even in the present information age, the transportation system provides the physical links between the various land markets of the urban system. Before discussing particular representative models, the main features of the integrated land use/ transportation models are briefly presented first.
Until the time research on integrated land use/ transportation models began, transportation and land use modeling and planning moved on separate tracks. A transportation study would assume as given a future land use pattern consisting, mainly of the spatial distribution of residences and workplaces, to design a system of transportation facilities that would serve adequately this pattern. The spatial distribution of activities offered input to procedures for estimating: (a) the total number of trips from and to each zone or subarea of a region and (b) the origin-destination (OD) trip matrices between pairs of zones (split by transport mode if possible). Given the various sets of OD trip matrices, the trips would be "loaded" on the transportation network to test whether the configuration of the transportation system could serve adequately the given spatial pattern of activities.
In the same vein, forecasting the future spatial distribution of activities in an urban area would assume the transportation network as given. Other inputs necessary in this context included: (a) description of the base year spatial distribution of activities (mainly, residences and workplaces) and (b) regionwide population and economic forecasts. Some kind of simulation model was (or is) used to produce the future spatial distribution of activities served by the given transportation network. These future land use patters were evaluated against various planning goals.
As it may have become evident from the above, the main shortcoming of the separate modeling of the land use and the transportation systems is that it ignores the feedbacks between them. The transport system may induce the spatial redistribution of activities – rearrangements of population and employment in space. In their turn, the changed patterns of activities impact on the transportation system (causing, e.g., congestion). In this way, a "chain reaction" is set in motion within an urban area. As Gordon and Moore (1989) put it: "both approaches to urban model building (the activity location and the transportation modeling) though clearly complementary, are equally deficient…. Congestion costs are determined within the process of land use allocation and, in turn, affect this allocation. It is intellectually inconsistent to accept either transportation costs or land uses as fixed" (Gordon and Moore 1989, 1196). This shortcoming attempts to alleviate an integrated land use/transportation model.
The first line of development of integrated land use/transportation models grew out of the gravity or spatial interaction models as recast by Wilson (1967) as entropy maximization models. These models can be used either as transport models which predict transport flows between origin and destinations or as allocation models which allocate population and employment to zones. Coupling these two aspects of the spatial interaction models provides a means to model in an integrated fashion the linkages between two or more sub-systems of the urban or regional spatial system. According to Wegener (1986b): "The general idea is to formulate the relationship between two subsystems as constraints of one process on the other and then solve the spatial interaction system under these constraints. Examples of this kind of integration effort are models linking transport and location (Boyce 1977, Los 1978), or models linking two or more urban activities (Brotchie 1978, Coelho and Williams 1978, Sharpe and Karlqvist 1980, Leonardi 1981)" (Wegener 1986b,18). The resulting models are usually non-linear constrained optimization models (see Batten and Boyce 1986 for an exposition of the evolution and mathematical formulation of these models).
Another line of integrated land use/transportation models consist of coupling an activity allocation with a transportation model for the simultaneous modeling of the land use-transport connection. Of the several integrated land use/transportation models built since the mid-70s along this line, three are presented briefly below: (a) ITLUP, (b) TRANUS, and (c) CATLAS. ITLUP employs location and transport models of the spatial interaction variety while the other two employ models based on the framework of random utility (or, discrete choice) theory. The recent trends and developments in integrated land use/transportation modeling are presented at the end of this section.
ITLUP – Integrated Transportation Land Use Package
Among the first and most celebrated of those models which have been built upon the Lowry modeling formulation is Putman’s Integrated Transportation and Land Use Package – ITLUP (Putman 1983). ITLUP grew out of a research project which was commissioned by the U.S. Department of Transportation for the study of the interrelationships of transportation development and land development. Based on the description provided by its developer, a schematic representation of ITLUP is shown in Figure 4.2f. Inputs to the model are: (a) base year descriptions of the spatial distribution of employment and residences and (b) the characteristics of the unloaded base year transportation network. These data are used to generate a preliminary estimate of trips in the metropolitan area. These estimated trips are loaded on the future transportation network so that its characteristics (travel time and cost) reflect the traffic volumes that would be on the network if the base year spatial distribution of activities had not changed. These characteristics of the network together with the base year spatial distribution data and the forecast regionwide control totals are used to produce a trial estimate of the spatial distribution of activities in the projection year. These are, then, loaded on the future transportation network whose modified characteristics can be used to reallocate the projected spatial distribution of activities. This is compared to the first trial estimate. If there are no differences, an equilibrium has been reached and the model run is ended. If there are differences, new trips are generated and loaded on the network and the procedure is repeated. Evidently, this type of land use/transport modeling takes into account the feedbacks among the two components of the urban system – land use and transport. In the following, the land use and the transportation models employed in the context of the integrated model are presented first followed by a discussion of their integration.
The land use model which was originally selected for ITLUP was the Projective Land Use Model (PLUM), a derivative of the Lowry model (see section 4.6.2.). PLUM accepts as given the spatial distribution of basic employment and then produces the spatial distribution of the population (residences) and nonbasic (basically retail) employment. The general form of the residential location model employed is given by the following equation:
(4.85)
where,
| Ni | is the number of persons living in zone i |
| Ej | is the number of employees working in zone j |
| pij | is the probability that a person who works in zone j will live in zone I, and |
| g | is a scaling adjustment factor |
The probability pij is the central element of this equation and it is considered as having two components: a trip function and an attractiveness measure. In the earliest versions of PLUM there was no attractiveness term. The trip function used in all versions of PLUM had the following form:
(4.86)
where,
pc is the probability of a trip of length (i.e. travel time
or travel cost) c and 
and
empirically derived
parameters.
In a later version of PLUM, two modifications were introduced in the calculation of the travel probabilities. The first was to modify the original calculation of the probability of traveling to a zone; instead of dividing the probability of traveling to an isochronal annulus by the number of zones in the annulus , the probability of traveling to an annulus was divided by travel cost to the annulus . The second modification was to include a measure of attractiveness the residence-zone end of a work trip, essentially a residential holding capacity or, a measure of "opportunities", as it was called, given by the following expression:
(4.87)
where,
| Ui | is a measure of opportunities for new residential development in zone i |
| Lvi and Lri | are, respectively, residential land acreage and vacant (nonindustrial) acreage in zone i, and |
| Hi | is the number of housing units in zone i |
Modifications of the above measure of attractiveness were introduced later to better reflect the state of existing infrastructure which influences the development potential of a zone.
To better estimate the trips generated in the zones of the urban system, a disaggregated residential allocation model (DRAM) was developed after the first version of ITLUP had been completed which accounted for the following types of trips: (a) work-to-home, (b) work-to-shop, and (c) home-to-shop (Putman 1983). By normalizing trip probabilities (i.e. dividing each pij by the sum of trips from all origin to a destination zone), the residential location model that resulted is basically a singly-constrained spatial interaction model (see section 4.4). Further improvements of this model resulted in the final formulation of the DRAM model which combined a multivariate attractiveness measure of a zone to residential locators (by type of locator) and a two-parameter trip function (for details, see Putman 1983).
To account for the location of non-basic (or, population-serving) employment, a singly-constrained spatial interaction model was formulated also of the form:
(4.88)
where,
(4.89)
| Sij | is the number of persons living in zone i and shopping in zone j |
| Yi | is the purchasing power of consumers living in zone i |
| WRj | is the retail "attractiveness" of zone j |
| f(cij) | is the generalized cost function of a trip between i and j |
The reader is referred to Putman (1983) for details on the treatment of the projections of the location of basic employment in ITLUP (which in the Lowry-type models is assumed to be exogenously given).
Turning now to the transport models used in ITLUP, the transportation model package which had been developed by the Planning Sciences Group of the University of Pennsylvania was used. This package contained procedures for network coding, tree tracing, and several traffic assignment procedures. The typical transportation analysis includes four steps: trip generation, trip distribution, trip assignment and modal split. The trip assignment procedure involves taking an exogenously calculated origin-destination trip matrix and determining the paths these trips take over the transportation network. The trip assignment procedure used in ITLUP was more sophisticated employing alternative algorithms for trip assignment and allowing for modal split (different modes of transport).
The critical aspect of the integrated model is the integration of the land use model with the transportation model. In ITLUP this is done via trip generation. More specifically, the land use models produced the distribution of residences and nonbasic employment to the zones of the urban system. From these distributions, a set of trips – the origin-destination (OD) matrix – was produced for input to the transport network model. The person-trip matrices thus generated are then converted by means of some procedure to vehicle-trips to be loaded on the transportation network. To illustrate the linkage between the land use and the transportation models, the simple, original form of the land use model shown in equation 4.85 is used. This is as follows:
where,
| Tij | is the number of trips from zone i to zone j |
Because the trip probabilities, pij, used in the final form of the land use models are normalized – leading to a singly-constrained spatial interaction model form (equation 4.88), it is assured that the sum of trips thus generated equals exogenously estimated future totals of population and employment. The joint calculation process employed in ITLUP results in a trip matrix consistent with the spatial distribution of trip makers, their trip origins, and trip destinations.
ITLUP has been used in a series of policy analyses which are discussed in Putman (1983). These include analysis of the impacts of: (a) redistribution of basic employment, (b) high-speed road links, (c) land use controls, (d) regional growth or decline, (e), regionwide changes in transportation costs. Additional procedures were developed also which used the results of ITLUP to assess the impacts of transportation, location, and land use policies on air quality. ITLUP has been used by several planning agencies in the United States as an aid in making land use and transportation decisions (Putman 1983). A similar, Lowry-type model like ITLUP is LILT (Leeds Integrated Land Use/Transport) developed by Mackett (1983) for the Leeds Metropolitan Area which was then applied to several other British and foreign cities.
TRANUS (Transportation and Land Use System) and CATLAS
(Chicago Area
Transportation Land use Analysis System)
Sharing the common purpose of all integrated land use/transportation models, the models discussed below differ from the previous ones in that the land use and transport models they employ are discrete choice models drawing from the random utility theory instead of the classical gravity or spatial interaction theoretical framework. Random utility theory (McFadden 1978) aims "to explain and forecast the behavior of urban actors such as investors, households, firms, or travelers. Random utility models predict choices between alternatives as a function of attributes of the alternatives, subject to stochastic dispersion constraints that take account of unobserved attributes of the alternatives, differences in tastes between the decision makers, or uncertainty or lack of information" (Wegener 1994, 24). It is a more suitable approach to modeling phenomena where the variables under consideration are not continuous (like residential choice, land use, shopping behavior); hence, marginal analysis (characteristic of the classical continuous utility maximization models) cannot handle them satisfactorily. For example, in the Muth-Mills equilibrium models, housing prices reflect marginal productivity conditions consistent with long-run competitive equilibrium (Straszheim 1986, 746), which may not be the case in the short run or when the capital stock is durable as it is the case with housing. Discrete choice models drawing on random utility theory model utility maximizing choices as a problem in random utility functions (Straszheim 1986, 746). A brief exposition of the basic characteristics of discrete choice models is offered below followed by the presentation of the TRANUS and the CATLAS models.
Starting with the individual case, the perceived utility an individual s associates with the choice of option k, usk, in a decision situation, is defined as:
usk = Us(Xk, Ss) (4.91)
where,
| Xk | represent the measurable attributes of option k |
| Ss | the socio-economic characteristics of the individual s |
Even in this individual case, the utility function is not deterministic because individuals behave differently each time in choice situations. In the aggregate case of a group of individuals, the variations in the utility functions become even larger as aggregation introduces many sources of variability. Thus, for the group as a whole, a distribution of perceived utilities.
An aggregated utility function of the utility, usk, for a population s (of the same socio-economic characteristics) as regards a choice option k is given by the following expression:
usk = Us (Xk,
)
(4.92)
where,
| Xk | represents the measurable properties of option k, and |
|
the random variation in the utility function |
The utility function shown in equation (4.92) is divided into two
components, a deterministic and a stochastic component. The deterministic
component represents the fixed and measurable aspects of utility,
Vk, or, the strict utility of an
option. The stochastic component,
, reflects the
probabilistic nature of the utility within the population. The probability that
population group s will choose option k, psk, is defined as the integral of the cumulative joint
probability function, 
expressing the variation within the population with respect
to option k:
(4.93)
Depending on the particular mathematical
function chosen for equation (4.93) produces alternative mathematical
expressions. A common expression is the multinomial logit model:
(4.94)
This model form has been already presented in the section on the statistical models of land use change. It is used in several other applications of random utility theory as shown below. At this point, it is important to note that Anas (1983b) showed the convergence of the random utility and the entropy maximizing theory. More specifically, the above multinomial logit model resulting from random utility maximization is, at equal levels of aggregation, equivalent to the entropy maximizing (gravity) model.
TRANUS is an integrated model employing the random utility theory framework for the land use and transportation models of which it is comprised. The following discussion borrows heavily from the description offered by its developer, Tomas de la Barra (1989). A schematic description of the model structure is shown in Figure 4.2g. The upper part of the Figure depicts the dynamic interactions of the land use with the transport models for time periods t1, t2, …. tn. The bottom part of the Figure shows the working of TRANUS within a single time period. In the following, the land use, or activity location/allocation, model, the transport model and their integration are discussed.
The activity location procedure requires the following inputs:
The procedure starts with the determination of totals of induced employment and population given an exogenously determined level of total basic employment. The increments of basic employment and floorspace forecast for the current period are allocated to the zones of the urban system. The location of the increments of basic employment can be estimated by means of a simple probabilistic model or can be set by the user (reflecting, e.g. the location of new major plant). The location of the increments of floorspace is more elaborate as it takes into account the amount of floorspace in the previous period, land values, and potential floorspace. The user can predetermine the location of floorspace in the zones also.
The location of induced activities and floorspace in the zones of the system is the next step. The following equation is used for the allocation procedure as well as for the estimation of flows between pairs of activities:
(4.95)
where,
 |
is the number of activities (e.g. jobs) of sector n in zone j generated by activities in sector m in zone i; r denotes iteration number |
 |
is level of activity of sector m in zone i |
 |
is the utility function associated with activity of sector n |
 |
is an empirically estimated parameter |
The utility function takes the form:
(4.96)
where,
 |
is the composite cost of transport for activity n between zone i and zone j |
 |
is a parameter regulating the effect of land values on
the location of activity n which combines with
 for the effect of the composite
cost of transport |
| rj | is the value of land in zone j |
Once all activities have been allocated to zones, appropriate floorspace demand functions are used to estimate total demand for floorspace in each zone. This is, then, compared to the current fixed supply of floorspace. Land values in each zone are adjusted appropriately to produce an equilibrium between supply and demand of floorspace.
The main outputs of the activity allocation model described above are:
(a) the location of activities in each zone, (b) the supply of floorspace, (c)
(equilibrium) land values, and a set of
matrices which represent the
functional relationships between zones and sectors. These are input to the
transportation model.
The transportation model adopts the random utility theoretical
approach also. The interested reader is referred to de la Barra (1989) for the
details of this model. Basically, it follows the structure of a typical
transportation package consisting of the following sequence of procedures: trip
generation, modal split, and network assignment. The important link between the
land use and the transport component of the integrated model is trip generation
(as it was the case also with ITLUP). The demand function for transport, which
converts the flows between sectors and zones calculated by the activity
allocation model above, to number of trips from zone i to zone j by sector n,
, is
given by the following equation:
(4.97)
where,
 |
is the total activity level of sector n between zone i
and zone j; it is found by summing
 over all m sectors |
| n |
is the minimum number of trips sector n must perform
and n+n is the maximum |
 |
is the generalized composite cost of travel |
The number of trips by sector are then distributed to different transport modes by means of a multinomial logit model of the form shown in equation (4.97). Trips by transport mode are distributed over the paths of the transportation network by means of another multinomial logit model where the utility function takes account the cost of transport on the particular path. By applying vehicle occupancy rates, trips are transformed into number of vehicles in each link of the network.
At the end of the iterative process, travel speeds and waiting times change as a function of demand/capacity ratios. This leads to an adjustment of travel and waiting times and, then, to a new estimation of travel cost in each link. The new travel costs affect trip generation, modal split and assignment as well as the location of activities in a future time period.
TRANUS has been used in several applications such as: (a) the design of an urban development plan for the island of Curacao, (b) the design of a land use plan for La Victoria (Venezuela), (c) a study for the extension of the Caracas metro system, (d) the design of the Caracas-La Guaira motorway, (e) the design of the central railway system in Venezuela, (f) the evaluation of motorway projects in Venezuela, and (g) the evaluation of alternative energy scenarios in urban regions (de la Barra 1989). Several other integrated models sharing the structure of TRANUS and employing the random utility theoretic framework have been developed such as MEPLAN (Echenique et al. 1990; see also, Wegener 1994, Southworth 1995) and they have been used in various applications (see, for example, SPARTACUS 1999). It is interesting to note that most integrated land use/transport models of the 1990s, either new models or developments of past models, adopt the random utility theoretic framework
CATLAS (Anas 1982, 1983) is another model in the category of integrated land use/ transport models which is restricted to the housing market as opposed to TRANUS which was a more general model for any type and number of activities in an urban or a regional system. Its purpose is to model the joint choice of housing, residential location and mode of travel. Anas utilizes also the theoretical framework of random utility theory as housing and travel mode choice are not continuous but discrete choices.
The model developed by Anas (1982) is called CATLAS (Chicago Area Transportation Land use Analysis System). It is a dynamic simulation model which employs a nested multinomial logit model, consistent with utility or profit maximization, where choices are represented as a sequential choice probability structure (i.e. the probability of a household choosing a house type and location is represented as a product of conditional probabilities – i.e. as the product of the conditional probability of choosing a house type given the choice of location times the marginal probability of choosing a location) (Straszheim 1986). CATLAS consists of four behavioral submodels: (a) a demand submodel, (b) an occupancy submodel, (c) a new construction submodel, and (d) a demolition submodel.
The demand submodel is a sequential choice model which computes the probability that a worker employed at workplace j will live in residence zone i and the conditional probability he will commute by mode m, given the choice of residence zone i. A single equation is estimated for all households. The occupancy or existing housing stock submodel estimates the probability that the average dwelling in each zone will be offered for rent in a particular year as a function of the average rents in that zone and various zonal attributes. It simulates changes in the housing stock and the rent of each zone as well as changes in the age distribution of the housing stock by zone. Market clearing is achieved by solving for each year’s clearing rent vector, assuming the number of households assigned to each residence zone must equal the number of units supplied in each year (Kain 1986, 859-860).
Recent developments in the area of integrated land use-transportation modeling (or, integrated urban modeling as it is called also) follow particular directions based on an experience of more than two decades with this type of models. In particular, emphasis is placed on the behavioral aspects of the land use-transport (or, activity-travel) system. Activity-based travel analysis recognizes that travel demand is derived from the needs of people to engage in out-of-home activities. Hence, activity-based travel analysis is most appropriate for modeling the land use-transportation interactions. In this context, the appropriate unit of analysis is the individual (or, the household) and, at this disaggregate level, modeling attempts to capture the variability and diversity (and causality) of human mobility. Relevant aspects of activity-travel patterns on which research is focusing include:
At the same time, more appropriate mathematical tools are being developed to provide for more satisfactory modeling of individual behavior. Microsimulation, in particular, is considered, the principal tool for behavioral modeling. As Miller (1996) defines it, microsimulation is an approach to modeling systems that are both dynamic – i.e. evolving over time – and complex. Recent development in computer programming – more specifically, from structured to object-oriented programming (Booch 1994, Booch et al. 1999) – has led to the development of object-oriented microsimulation. This modeling approach permits a one-to-one mapping between objects in the real world and objects in the simulated world (Miller and Salvini 1998, Kanaroglou 2000). Overall, the trend is towards developing models which are more sensitive to reality and towards modeling techniques capable of representing this reality.
The preceding brief presentation of the dynamic urban simulation models does not permit a complete and documented assessment of the strengths and weaknesses of this class of integrated models of land use. The interested reader will find such evaluations in the references provided. However, from the particular perspective of the analysis of land use change which is the present focus, certain observations can be made as regards the most notable characteristics of these models. Firstly, they embed the study of land use change in the broader context of changes in population and employment in urban/ metropolitan areas which are assumed to be the important determinants of land use change in these contexts. Not all of these models are really comprehensive as they emphasize selected (and not all) aspects of the urban system modeled (Wegener 1994). This characteristic carries on the particular types of land uses they consider which, with a few exceptions, are usually residential and commercial uses.
In terms of theoretical underpinnings, all models rely on some version of micro-economic theory (Alonso’s urban land market theory mainly) and/or random utility theory. In other words, they are deductive , functionalist models moving in the same theoretical tradition as the earlier urban economic models. This means that, as regards the quality of explanation of the urban phenomena – including land use change – they offer, the same criticisms as those directed to urban modeling of the 1960s and 1970s potentially apply (Sayer 1976, 1979a, 1979b). More generally, in view of the diversity of the theories of land use change which have been presented in Chapter 3, which reveal many more determinants and processes of change in addition to the economic ones, the theoretical basis of these models appears to be rather limited. On the other hand, several of them adopt the random utility theoretical framework which appears to be more flexible and capable of accommodating and handling a variety of behavioral/ theoretical assumptions compared to the continuous utility maximization frameworks which governed certain of the earlier microeconomic urban models. In particular, the operational forms of discrete choice models provide for the inclusion of many factors which theory suggests as being important determinants of individual choice behavior and, consequently, of potential spatial change. Several of these factors are discrete (e.g. cultural values, environmental conditions, institutional regimes) which makes the random utility theoretical framework particularly suitable for including them in land use change models. Future research and analysis of these models will reveal their ability to include many more aspects of land use change than their current versions.
4.6.3B Regional level simulation models
Turning now to regional level integrated simulation models, a greater diversity of simulation approaches and model applications is encountered. Even the expression "regional level" is somewhat misleading in terms of the actual spatial coverage of the relevant models as it may refer to an assembly of urban regions, to a collection of contiguous subdivisions of a large nation, or the nation itself considered as a collection of regions (variously defined), or to a group of nations. The most characteristic differences of the regional level from the urban level simulation models are rooted in "the difference that space makes" (note: title of an essay by A. Sayer 1985). The change from the lower to the higher level of the spatial scale implies: (a) changes in the nature of the spatial entities under study and the related processes of change; other land use types are included – mainly agriculture and forestry – which were not very relevant at the urban level; other types of agents are involved and other decision making are relevant, (b) other determinants of land use change obtain importance at higher levels such as environmental (climate, geomorphology), political, macro-economic, etc., (c) the complexity of the system to be modeled increases as both the numbers of the interacting entities increase as well as their variations, and (d) other patterns of spatial structure and change are visible and are amenable to modeling (mainly, coarser and less detailed). The models which are presented below have been selected, first, because they are representative of a more contemporary genre of models of the economy-environment-society interactions and, second, because their direct purpose is modeling of land use change. This latter feature reflects the recent interest on the critical role of land use and its change in triggering larger scale environmental change.
Several reviews of integrated modeling efforts of the economy-environment-society interactions as well as of those factors with land use have been undertaken. Most of them conclude that the number of models in which land use change is adequately modeled is very small (see, for example, Turner et al. 1995, Fischer et al. 1996a, Lonergan and Prudham 1994). One of the possible explanations is that the purpose of most modeling exercises was not modeling of land use change until recently. For example, Fischer et al. (1996a) cite a model built to study the effects of global climate change on U.S. agriculture (Adams et al. 1993 cited in Fischer et al. 1996a, 5). It is a combined bio-physical and economic spatial optimization model which represents production and consumption of 30 primary agricultural products including crop and livestock commodities. It consists of a set of micro- or farm level models integrated with a national sector model. Production behavior is described in terms of the physical and economic environment of some 63 production regions of the United States. Regional level supply curves determine the availability and use of land, labor and irrigation water. However, except for the direct effects of climate change on U.S. agriculture, the model "did not investigate other driving forces such as urbanization nor possible implications and feedbacks of land use change on the dynamics of the resource base such as the potential for competing demand for water (Ficher et al. 1996a, 6).
Four integrated models – or, better, modeling approaches or frameworks – which can be classified as regional level simulation models are presented below which address the analysis of land use change directly:
The CLUE modeling framework
The CLUE modeling framework (Conversion of Land Use and its Effects) is being developed at the Wageningen Agricultural University in the Netherlands to model land use changes as a function of their driving factors (Veldkamp and Fresco 1996a, 1996b, 1998, Verburg et al. 1997, de Koning et al. 1998, Verburg et al. 1999). It has been applied to analyze land use/cover changes in several countries such as Ecuador, Costa Rica, Java, and China. A basic outline of this framework follows based on the several publications of the CLUE research group.
The CLUE modeling framework is a spatially explicit modeling framework for the analysis of land use/cover dynamics at various spatial scales. Its most recent versions incorporate also dynamic analysis of feedbacks of land use changes on the local environment, the population, etc. as it is the case, for example, of agricultural over-use or unsuitable use in sensitive areas. In other words, the CLUE framework can be described as an integrated, spatially explicit, multi-scale, dynamic, economy-environment-society-land use model. According to members of the CLUE group, it is a cross-disciplinary model as it integrates environmental modeling and a geographic information system (Veldkamp and Fresco 1996b).
The modeling procedure consists of two consecutive steps. First, past and present land use patterns are analyzed at various levels of spatial aggregation using multiple regression analysis to determine the most important bio-physical and socio-economic determinants of land use at each level of aggregation as well as the quantitative relationships between them and the area of various land use types (the linear regression models used in module CHANGE to perform these analyses were presented in section 4.3.2.). The second step uses the results of the analysis of the first step to explore possible future land use changes within a spatially explicit framework using scenarios of future socio-economic development (de Koning et al. 1998). The CLUE modeling framework has a modular structure as shown in Figure 4.2h. Modeling of the supply side is taken up by the Yield Module while modeling of the demand side is taken up by the Demand Module. The Population Module provides input to the Demand Module as changes in population modify the demand for different commodities. The Allocation Module allocates the projected needs (demands) for land use of various types to the grid cells in which the study area is subdivided to produce the actual patterns of future land use which will result from the projected changes in its drivers.
The Demand Module calculates the demand for various types of land use based on the national level demand for various commodities. National level demand consists of domestic consumption and exports. Exports are assessed exogenously and they are related to international prices and national subsidies. Domestic consumption is assessed as a function of population size, composition (urban and rural) and consumption patterns. The Population Module provides the necessary demographic input to the Demand Module. Consumption patterns may be related to macro-economic indicators like GNP, purchasing power and price levels. Demand functions for separate commodities are estimated based on historical data. To account for difficult-to-predict changes in demand, alternative scenarios are formulated which take into account various population projections and changes in diet patterns. The production volumes demanded for the separate commodities are translated into areas of the corresponding land use/cover types using crop specific yield coefficients (for animal products, production per animal and stocking densities are used). The areas calculated for separate crops are aggregated to broader land use/cover types to obtain the demand for land at the level of these aggregate types.
The Yield Module assesses the yield of each of the main land use/cover types as a function of their surface area (in each cell of the study area), bio-physical conditions, technology level, management level and their general intrinsic cover value. The bio-physical conditions considered are: slope, altitude, soil drainage, and climate. The technology level is simulated by using urban population as a proxy. The management level is simulated by using rural population as a proxy (Veldkamp and Fresco 1996b). Finally, the intrinsic cover value is a dimensionless indicator (a numerical value for each land use/cover type) which reflects the relative value of a land use/cover type (which may be affected by changes in market demand and supply of the associated commodities).
The Allocation Module provides for the actual allocation of the demand for land by land use/cover type generated by the Demand Module to the cells of the study area in accordance with the ability of land in each cell to support the actual demand as assessed by the Yield Module. The CLUE modeling framework applies a nested scale approach for this allocation drawing on the idea that local land use change is the product of changes in both the drivers of land use at higher scales as well as of changes in local bio-physical and socio-economic conditions. The basic allocation procedure is as follows. The national demand for each land use type is allocated first to the cells at the higher spatial aggregation level to establish the comparative advantages between higher level regions of meeting the demand. Within these higher level cells, then, local changes in all land use types in the lower level of aggregation cells are calculated based on their bio-physical and socio-economic conditions (obtained from the Yield Module) taking into account also the conditions of the larger level cells. The actual calculation of the land use changes at each spatial level are made by using the regression equations estimated from the first step of the modeling procedure. If a cell has less area than that demanded for a certain land use type, then an increase in the area of this land use type is considered within the limits sets by the supply side. The actual fraction of land use change assigned to each cell is determined iteratively and simultaneously for all land use types taking into account competition among land use types within each cell (de Koning et al. 1998). This allocation procedure attempts to integrate top-down with bottom-up demands and constraints to simulate the effects of future changes in the drivers of land use.
The CLUE model version applied to the case of Costa Rica (CLUE-CR) has a structure similar to the basic one described above but it incorporates more detail and feedbacks as shown in Figure 4.2i. This version is characterized by the authors as a discrete finite state model written in PASCAL (Veldkamp and Fresco 1996b, 233). It simulates the following (exhaustive) land use/cover types: arable land, permanent crops, pastures and range lands, natural vegetation and a residual group (secondary vegetation, towns, roads, bare rock, etc.). It makes a number of assumptions the most important of which are: (a) a dynamic equilibrium exists between population and agricultural production; trade is not ruled out but assumes a minor role, (b) agriculture is the main employment and income generator in the rural areas of Costa Rica, (c) the smallest unit of analysis is a grid-cell which, despite its biophysical and socio-economic uniformity, may accommodate all five land use types, (d) land use change occurs only when bio-physical and human demands cannot be met by existing uses of land (note: the authors mean probably quantitative land use change), (e) food and money reserves incorporated in the model for a two-year period imply that seasonal and annual yield fluctuations do not have a direct effect on land use changes.
The modules of the CLUE-CR are similar to those of the CLUE model shown in Figure 4.2h. In particular, CRNEED corresponds to the demand and yield modules and the CHANGE module corresponds to the allocation module in Figure 4.2h. AUTODEV is a module which accounts for autonomous land use change (independent of national demand) in the case national demands do not give rise to land use change as well as in the case certain cells are not selected by the allocation procedure described above. In the next time step, the autonomous land use change calculated is fed back to CRNEED and CHANGE to simulate bottom up effects of local to the regional and national levels. BIOPHEED is an optional module which simulates feedback effects of agricultural overuse or unsuitable use in sensitive areas (e.g. erosion-prone arable land). DISPEST is another optional module designed to simulate the spatial and temporal effects of pests and diseases on land use/cover dynamics. The model’s input data as well as its output are geo-referenced and managed in a GIS system.
According to the CLUE research group, the modeling framework they propose requires further elaboration to become a reliable policy support instrument. These include high spatial resolution data, linkages to farming systems analysis, land evaluation systems (e.g. FAO’s system already mentioned in this contribution), and optimization planning models. To assist in the assessment of climate change impacts, CLUE has to be linked to GMCs (General Circulation Models) with the application of proper upscaling procedures.
The CLUE modeling framework is a worthwhile attempt to address the land use change issues as it is sensitive to the requirements of integration along all dimensions with a special emphasis on the critical spatial dimension. It adopts a macro-, aggregate approach to the analysis of land use change and it is intended primarily to serve as a predictive tool in analyzing the land use impacts of future development scenarios at large scales – regional and national. It is relatively simple to comprehend and functional to use but its explanatory capability is seriously limited exactly because of these characteristics. Several points should be made about this. First, the application of statistical procedures to identify the most important drivers of land use change is questionable for three reasons at least: (a) statistical associations do not imply causal relationships which is what the search for the drivers of land use change is about; (b) statistical analysis – at least of the sort applied in CLUE – cannot capture the qualitative aspects and determinants of land use change (notably the institutional, the political, and the cultural) which are the most important and critical for future developments especially in the context of developing countries, and (c) the statistical significance/importance of explanatory variables does not necessarily assure their theoretical importance (see Achen 1982). Additional problems associated with statistical modes of land use change can be found in the relevant section of this contribution. The statistical analyses which constitute the first step of the CLUE modeling framework may be considered as exploratory steps which should be complemented by thorough analysis using other, mostly qualitative, techniques. Second, the analysis of spatial data in the context of CLUE does not seem to have been performed by means of the appropriate spatial statistical procedures. This can be fixed rather easily, however, given the wide dissemination of the related packages (Levine 1996, LeSage 1999) and expertise as well as the recent integration of spatial analysis techniques and GIS (Fischer and Nijkamp 1993, Longley and Batty 1996, Fischer et al. 1996). The most important point, however, which should be stressed is the absence of a rigorous theoretical basis supporting the whole modeling effort. For the moment, the CLUE models yield crude statistical pictures of past and future land use patterns produced mechanistically. The incorporation of at least certain behavioral assumptions and theoretical arguments in the relationships studied will enhance a tool which has already a well-designed structure.
The Cellular Automata Modeling Framework
Another integrated simulation modeling approach draws from the theoretical framework of Social Physics discussed in chapter 3 and more specifically from the theory of fractals to model the structure and evolution of land use patterns. It applies cellular automata concepts to model a variety of complex, dynamic, socio-economic and environmental phenomena (see, for example, Tobler 1979, Couclelis 1985, 1988, 1989, Engelen 1988, White and Engelen 1992). The approach – henceforth called cellular automata approach – to be presented below is considered to be "quite general in terms of the situations to which it can be usefully applied" (Engelen et al. 1995, 203). It has been shown to apply to both the urban and larger geographical scales for the comprehensive, integrated analysis of land use change.
Before presenting this modeling approach, the concept of the cellular automaton is defined and the justification for using this concept in modeling is briefly sketched. "Cellular automata are mathematical objects that have been studied extensively in mathematics, physics, computer science and artificial intelligence (Gutowitz 1991)…. Tobler (1979) defined them as geographical models but they have only rarely been applied in human geography in the years since he proposed them…. A cellular automaton consists of an array of cells in which each cell can assume one of k discrete states at any one time. Time progresses in discrete steps, and all cells change state simultaneously as a function of their own state, together with the state of the cells in their neighborhood, in accordance with a specified set of transition rules. Transition rules can be either quantitative or qualitative or both" (Engelen et al. 1995, 207). A cellular automata model consists of: "(a) a cellular space, normally two dimensional, (b) a definition of the neighborhood of a cell, (c) a set of possible cell states, and (d) a set of transition rules" (White and Engelen 1994, 240).
Spurred by the need to account for the important role of spatial detail in many real world systems, "in recent years there has been an explosion of interest in what may be referred to collectively as connectionist models … abstract Boolean algebra, neural networks and cellular automata. Much of the research in this domain is aimed at uncovering general principles for the organization and evolution of dynamical systems" (White and Engelen 1994, 239). The application of cellular automata concepts to the integrated analysis of socio-economic and environmental phenomena seems to fare better than conventional modeling approaches (such as spatial interaction models and GIS-based models) for a variety of reasons. First, they make possible the integration of macro- with micro-scale temporal processes. Similarly, they make possible the integration of macro- and micro- spatial phenomena and the related decisions. In this way, they can make the maximum possible use of available spatial and temporal detail, in contrast to conventional approaches which operate either at the macro- or at the micro- level and cannot integrate both. Lastly, they offer a flexible platform to cope with complex real world systems; i.e. to represent meaningfully a variety of interactions among the various components of a spatial system – social, economic, environmental . This is because cellular automata approaches "can represent the generation of complex patterns by simple rules" (White and Engelen 1994, 238). As the rules can be specified by the users, alternative theoretical assumptions may be tested against reality and their validity assessed in particular socio-economic and environmental contexts. This will be demonstrated in the following presentation.
Drawing on White and Engelen (1994) and Engelen et al. (1995), two examples – an urban and a regional level – of the cellular automata approach are offered to present its application to the analysis of land use change in two different contexts and with different degrees of detail. The urban example assumes a cellular city divided into a number of cells each of which can be in any one of four possible hierarchically ordered states (uses of land) – vacant, residential, industrial, and commercial. During the city’s evolution, cells are converted from one state (use of land) to another in the order shown above; i.e. only from a lower to a higher state. The hierarchy is imposed to simplify the model and, in fact, it can be dropped easily. In this example, the net number of cells to be converted to each non-vacant state is determined exogenously. The gross number of cells to be converted is larger, however, as some cells will change state and more vacant cells are needed to compensate for these conversions. The neighborhood of each cell has a radius of six units (a unit is one cell width). Each cell in the neighborhood falls into one of 18 discrete distance categories (as the grid is regular). The transition rules are specified in terms of transition potentials for all allowable transformations from a given state to other states. A deterministic rule is as follows:
(4.98)
where,
| Phj | the transition potential from state h to state j |
| mkd | the weighting parameter applied to cells with state k in distance zone d |
| i | the index of cells within a given distance zone |
| Iid | 1 if the state of cell i = k |
| Iid | 0 if the state of cell i ¹ k |
Note that according to this equation, the transition potential has a value greater than one which means that each cell has a non-zero chance of transition.
It is possible to introduce weighting functions that have distance decay properties similar to those of the traditional spatial interaction models but it is also possible to create any other sort of distance relationship which appears meaningful. The deterministic transition potentials calculated by equation (4.98) are multiplied by a stochastic disturbance factor to account for such factors as differences in tastes and values among decision makers in the system as well as imperfect information. At each iteration up to three potentials are calculated for each cell in the array. Starting from the lower state and given the number of cells to be converted to this use ( exogenous ), the cells with the highest potential for this use are converted first. The same procedure is repeated for the other uses. In this example, the number of cells to be converted in each iteration is assumed to grow at a constant rate which represents the urban growth rate. In this way, the land use patterns obtained following these conversion rules are produced and can be observed to change over time at each iteration. This procedure was applied to a large number of cities by White and Engelen (1992) who concluded that despite differences in initial conditions and other stochastic variations, at a deeper level, urban form is quite robust. For example, these authors show that, with four land use types considered, the city has a tendency towards concentric land use zones (White and Engelen 1994).
The regional level example adopts a more comprehensive approach to account for the dynamic mechanisms and geographical features which become important determinants of the organization of higher level spatial systems. Its description reflects its application to the case of a Caribbean island with the purpose of studying the effects of sea level rise caused by climatic change (Engelen et al. 1995; White and Engelen 1997; see, also, MODULUS, 1999). The model operates at two spatial levels – an upper and a lower level – which interact with one another as follows: (a) at each time step, the basic geographic data needed by the upper level model are retrieved from the database. These are aggregated to the regions used in the upper level model and passed to it; (b) the upper level model calculates the values of the variables in each region and passes them to the lower level, the cellular model; (c) the cellular model allocates these values on a micro level and in doing that it may use more information from the database; and (d) the results from the previous step are used to update the database and, thus, be used as input at the next iteration as the model returns to the first step (White and Engelen 1994).
The upper or macro-level model integrates the natural, social and the economic subsystems which are linked to each other in a network of mutual, reciprocal influence as shown in Figure 4.2j. The natural subsystem represents the relationships between sea level rise and temperature change with precipitation, storm frequency, suitable land area, and external demands for services and products. In the social subsystem, the demographic conditions of the system are modeled. The economic subsystem is modeled by means of an input-output model (of, theoretically, any degree of aggregation) solved at each iteration given exogenous changes in demand (due to exports or to domestic final demand caused by population growth). The economic subsystem is linked to the natural subsystem through climate-induced changes in export demands; to the social subsystem through household demands and to the micro-level model via a land productivity expression which translates activity levels to land use demands. This latter expression takes into consideration the scarcity of land, as measured by prices, and land productivity for particular activities.
The lower level model is a cellular automata model which is developed on a cellular array of 500X500m cells and calculates land use changes on the basis of transition rules as it was the case with the urban model. The differences from the previous case are that: (a) the neighborhood of each cell is now larger, (b) 13 land use types (states of each cell) are considered, (c) at each iteration cells are converted to the use for which they have the highest potential, and (d) interactions between pairs of land uses (or activities) are modeled in greater detail by means of attraction-versus-distance functions to represent the effects of push and pull factors on each cell and for each activity. The aggregate, distance-weighted push and pull effects of all the cells in the neighborhood together determine the locational suitability of the cell for each possible land use type. To determine the cells’ potential for transition from one type to another, the cell’s intrinsic suitability in terms of its own physical, environmental and institutional characteristics is calculated as an aggregate measure from a number of geographical attributes such as soil quality, elevation or land use regulations stored in a geographical database. A cell’s suitability can change during a simulation either by the user or due to changes in environmental or other conditions produced by previous iterations (Engelen et al. 1995).
It is interesting to discuss the land allocation process simulated in this model. As said before, cells are converted to the use for which they have the highest potential. The conversion process starts with the cells having the highest potential and proceeds until a sufficient number of cells have been converted to satisfy the demands established by the upper level model. A land rent is calculated also for each economic sector based on the existing level of demand for land use by that sector, relative to the quantity and suitability of available land. The rents are returned to the upper level model where they affect the land productivity coefficients translating output into demand for land. Similarly, the suitability factor for all cells actually occupied by a particular activity is monitored and changes in average suitability for the activity are passed back to the upper level and result in further changes in productivity parameters. In this way, the model captures the interactions between the micro-scale geography and the global dynamics directly and continuously (White and Engelen 1994).
The approach described above has been applied to both urban and regional level cases for the analysis of land use change (the island of St. Lucia in Eastern Caribbean and the metropolitan region of St. John’s Newfoundland, Canada). Further developments include, among other, the design of an interface between this approach and GIS and its incorporation into broader decision making support tools. In this latter application, cellular automata models are linked to models of the economic, environmental and social subsystems of a spatial system for integrated analysis and decision support. Such a spatial decision support tool is MODULUS developed in the European Union for the integrated analysis of land degradation, desertification and water management in the Northern Mediterranean (MODULUS 1999). For other applications of the cellular automata modeling approach in urban and regional contexts which allow for greater complexity in land use conversion and the resulting patterns to be modeled the reader is referred to Clarke et al. (1997), White et al. (1997), Wu and Webster (1998).
Before moving to the next integrated simulation model, some comments on the cellular automata approach are in order. First, it is a discrete modeling approach and serves as an additional indication that discrete approaches may be better suited to modeling spatial change phenomena than continuous approaches. The cellular automata approach makes no direct claim to economic theory as it is the case with the discrete choice models referred to in the previous group of urban simulation models. It can accept various specifications of the rules governing the conversion of land uses in the cells of the study area. This means that economic or any other theory can be used to guide the particular rules used. In addition, it has the added flexibility of incorporating environmental and other considerations in the assessment of the potentials for change as well as of being linked to higher level models as well as to GIS for more efficient use and manipulation of input and output spatial information. The concept of the transition rules in cellular automata modeling and the estimation of transition probabilities are similar to the corresponding concepts and estimation in discrete choice modeling and in Markov modeling which will be discussed in the section on other modeling approaches. It is noted that cellular automata modeling does not consider the transportation system explicitly (at least) which may be a shortcoming in view of the important feedbacks between land use and transportation as well as the environmental impacts caused by the development of transportation systems. Finally, as regards its apparent lack of firm theoretical grounding, the cellular automata approach is arguably designed to provide a testing ground for a variety of theoretical propositions as reflected in the specification of the transition rules. The question which arises, however, is whether the spatial subdivision assumed by the model (the cellular array and the magnitude of the cells) is congruent with the actual spatial formations which emerge under the complex interplay of the forces which drive land use change.
IIASA LUC (Land Use Change) Model
The last regional level modeling framework to be discussed is perhaps the most ambitious effort to build one of the most comprehensive, integrated models for the analysis of land use change. The International Institutes for Applied Systems Analysis (IIASA) Land Use Change (LUC) project has developed a modeling framework for "the analysis of spatial and intertemporal interactions among various socio-economic and biogeophysical factors that drive land use and land cover change (Fischer et al. 1996a, 74). The modeling framework is intended for use in various policy and decision making settings where land use change is directly or indirectly implicated. The overall modeling framework is depicted in Figure 4.2k (see, also, the IIASA/LUC web page). The theoretical and methodological basis of this modeling endeavor is provided by welfare theory and the related analytical methods. As shown in Figure 4.2k, the whole modeling exercise is embedded within a GIS framework which provides both the necessary spatial databases as well as stores and generates the resulting land use maps. LUC has been developed for modeling land use changes and related policy issues in China and Northeast Asia but its structure and methodology is applicable to several other regional contexts. A brief presentation of the main features of the complex LUC modeling framework is given here drawing on Fischer et al. (1996a); the reader is referred to related publications for full information (found at the IIASA web-site listed in Appendix 1.B). The conceptual framework of welfare analysis adopted is discussed first and then the treatment of the spatial and temporal aspects of modeling land use and land cover change in LUC is described. The analysis of land resources is outlined with an emphasis on the specification of land-based production sector models (agriculture and forestry).
In welfare analysis a number of commodities are assumed to exist in the study area. These include both goods and factors of production (e.g. food, fiber, energy, labor, capital, services) indexed k = 1,… K. Each commodity is exchanged at a price pk. Demand is generated by a number of consumers indexed i = 1,…. I. Supply is provided by a number of producers indexed j = 1,…. J. The net production of a number of commodities by producer j is denoted by yjk. Producers sell their products (y) at the market at market prices p. Consumers own commodity endowments, wi, which they offer for exchange and, at given prices p, they demand commodity bundles xik. An excess demand vector can be formed:
(4.99)
Naturally, for the market to be in equilibrium, prices should adjust so that no commodity is in excess demand; i.e. z(p) £ 0.
Each producer operates within certain technology options which can be
represented by a set of possible production plans Yi. If a
competitive equilibrium situation is assumed, then producers choose production
levels yj that maximize their profits,
:
(4.100)
The resulting maximum profit function is:
j(p) = max
{[p, yi]
½ yj Î Yj}
(4.101)
Similarly, consumers consume commodity bundles, xi, so as to
maximize their utility subject to their budget constraint determined by
available consumer income hi which consists of two elements: the
proceeds of selling the endowments wi
and the consumer’s share in profit
j. It
is assumed that consumers own a non-negative share
ij in
firm j and that they receive dividends
ij j(p). The utility maximization
relationship is:
max ui (xi) (4.102)
subject to:
[p, xi] £ hi (4.103)
In this context, an optimal welfare program refers to the choice of the
levels of commodities to be produced by producers so that the welfare of
consumers is maximized subject to commodity balances. The welfare of consumers
is assumed to be the sum of their individual utilities properly weighted by
socially defined weights, i . In mathematical notation this
problem is written as:
(4.104)
subject to:
(4.105)
The solution to this welfare maximization problem produces Pareto-optimal solutions . The above problem can be modified to take into account trade as well as policy measures adopted by the state to correct for market imperfections in the allocation of resources. In LUC, as in several similar applications of this welfare theoretic framework, there are three types of economic agents – consumers, producers and the government – which are represented by means of homogenous groups in each type.
The spatial representation of the economic system as specified above incorporates several other characteristics of the natural and social environment within which the activities of these economic agents and the interactions among them take place. The study region is divided into compartments, i.e. subregions. In each compartment, the economic system is modeled in the way specified above. A compartment may be a collection of farms, a watershed, a zone within a country or a group of provinces. Compartments reflect structured entities – i.e. subsystems of the larger system being modeled. Because they may change over time, the designers of LUC contend that the compartments must avoid being geographically static. Hence, they propose the organization of all relevant spatial data on rectangular grids with compartments being defined as collections of grid cells which can vary possibly over time. Areas where no human intervention takes place – as in wilderness areas – form separate compartments.
A compartment is not necessarily internally homogeneous; in fact, it can be further subdivided into smaller homogeneous land management units to facilitate meaningful biogeophysical evaluation (see, the FAO AEZ procedure mentioned in Chapter 1). Compartments are organized hierarchically so that the particular characteristics and land use driving forces at each level of the hierarchy can be described as well as decision making at various levels of hierarchy can be modeled. All spatial data are stored in and manipulated by a GIS. Each compartment is described in terms of its physical, geographic and environmental characteristics and the characteristics of the endowments of the economic agents it includes. The description refers also to applicable economic and physical balance equations (e.g. budget constraints, commodity demand and supply balances, consistency between resource use and availability) as well as to the identification of "immobile" (e.g. soil, climate) and "mobile" (e.g. labor, capital, water, minerals) resources. In the LUC modeling framework, the economic agents within the compartments interact through commodity trade and financial markets, and flows of mobile resources. They compete for the allocation of limited public resources and they are jointly affected by policies and other constraints. Compartments interact also through human migration, materials transport and flows of pollution.
To model the flows of commodities and resources among compartments at various levels of the spatial hierarchy, certain approaches are adopted to simplify the onerous modeling of several thousands of commodities produced and transported through the compartments of the spatial system. In particular, the trade-pool approach is adopted which assumes a trade pool into which all exports flow and from which all imports originate. In addition, commodity balances are constructed which constitute fundamental relationships in general equilibrium models.
Temporally, the LUC model is specified in discrete, five-year, time steps. A distinction is made between exogenous and endogenous dynamics. Exogenous dynamics is caused by factors which are specified outside of the model and they are built into the model by means of time-dependent functions defined by the user (such as shifts in technology, consumer preferences and life styles, etc.). Endogenous dynamics refers to the allocation decisions of consumers and of producers and they are modeled via a T-period competitive equilibrium model which ensures – within its assumptions and other limitations – intertemporal Pareto-efficiency of the allocation produced over time (covering T periods). Population dynamics is modeled also in accordance with the temporal framework mentioned above and taking into account natural increase (births minus deaths) and net migration.
The centerpiece of the LUC model is a welfare program. This program has the form of an optimization problem that maximizes the weighted sum of the utilities of the consumers (see equations 4.104 and 4.105). The program includes four types of constraints: (a) the utility constraint which specifies how the utility of a given consumer group depends on its consumption in the current and in the next time period – i.e. it reflects group preferences intertemporally; (b) the transformation constraints which reflect the technology of the economy – i.e. describes net supplies in period t and resources in the next period which are feasible at the given level of resources in the current period; (c) the commodity balance which ensures that demand for commodities does not exceed feasible supplies; (d) the stock consistency constraint which ensures that the level of a resource used in a given period does not exceed the level carried over from the previous period.
The above welfare program and the decentralized competitive equilibrium operating context which is assumed are normative with respect to institutions; i.e. they assume perfect market economies, an assumption which may not be true and realistic for several countries or groups of countries. The LUC research team anticipates input from experts to specify how the basic model structure can be "distorted" to accommodate real world institutional and political systems which do not comply with the general equilibrium welfare model assumed above (Fischer et al. 1996a).
Modeling the dynamics of resource stocks in the LUC model takes into account processes of both resources accumulation as well as resource degradation associated with production activities. The production component of the LUC model purports to analyze the spatial and temporal allocation of land and its resources to various regional activities such as crop agriculture, livestock grazing, forestry, energy production, mining, settlements and infrastructure, manufacturing, recreation and natural reserves. Under natural conditions, land cover (not land use) changes can be estimated from vegetation models under various assumptions about biogeochemical and climate conditions. The task of modeling land use change (or, transformation) in systems managed by human agents is much more difficult as these changes are constrained by natural conditions and they are determined by the level of technology, economic conditions and demographic trends. These supply-side factors are taken into account in the LUC model.
The production component of the model assumes capital and environmental stocks which are available at the beginning of the current period as inputs to the production process. Pollution is represented as use of resources. The effects of production processes on human welfare (e.g. health) are taken into account either as arguments in the utility functions or as constraints on production. One of the main tasks in the LUC modeling framework is the specific
