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Analysis of Land Use Change: Theoretical and Modeling Approaches
Helen Briassoulis, Ph.D.
4.6 Integrated models (link to Table 4.1c)
4.6.1. Econometric-type integrated models
4.6.2. Gravity/Spatial Interaction-Type Integrated Models
4.6.2A The Lowry Model and Garin’s versions
4.6.2B TOMM (Time Oriented Metropolitan Model)
4.6.2C PLUM (Projective Land Use Model)
4.6.2D Activity Allocation and Stocks-Activities Models

4.6. Integrated models

Integrated models of land use change are diverse as integration takes on different meanings in different contexts. They are called also comprehensive or general models although the term "integrated" has come to dominate the literature since the 1980s. In the present context, integrated models are those models which consider in some way the interactions, relationships, and linkages between two or more components of a spatial system – be they sectors of economic activity, regions, society and economy, environment and economy, and so on – and relate them to land use and its changes either directly or indirectly (see, Wegener 1986b, on the feature of integration of integrated models). The emphasis here will be mostly on those integrated models which contain an explicit land use component or treat land use directly as it was the case with the previous model categories. However, several other integrated models which relate to land use indirectly will be mentioned where appropriate. It is noted that, to this author’s knowledge, the purpose of model building in most of the integrated models presented in this section, was not modeling of land use change but modeling of some other aspect of a spatial system of interest. Integrated models whose direct purpose is the analysis of land use change are of a very recent origin as discussed below.

Integrated models, in general, appeared in the 1960s during the "quantitative revolution" in urban, regional and geographic analysis. The first efforts included land use explicitly and integrated models which continue in this modeling tradition keep this feature or have improved upon it. Several integrated models have been developed starting from the decade of the 1960s onwards which are aspatial; i.e. they consider interactions between several aspects of a spatial system but without an explicit spatial frame of reference (for example, demographic-economic, energy-economic, environmental-economic, etc.). One instance in which these integrated models include the spatial dimension is when they are formulated in an interregional or multi-regional context (see, for example, Issaev et al. 1982). Aspatial integrated models do not account for land use change in most cases.

A common characteristic of integrated models, in addition to their emphasis on integration, is that they are mostly large-scale models. In fact, an inspection of the literature on large-scale models reveals that, most of the time, these are integrated models (see, for example, Batten and Boyce 1986, Boyce 1988, Wegener 1994). The range of spatial levels covered starts from the urban/metropolitan and reaches the global. The spatial coverage of integrated models is closely related to their purpose, focus, and other structural and design characteristics as shown in the following presentation. As regards the latter aspect of model structure, a broad distinction can be drawn between "compact" or "unified" and "modular" or "composite" model forms (see, for example, Briassoulis 1986, Wegener 1994). The first form refers to integrated models which are described by a single operational expression which contains all the arguments whose integration is represented; for example, a single equation, an input-output model, etc. The second form refers to integrated models which combine several separate models of the components of the spatial system which are being modeled. The second form is more common in recent versions of integrated models.

The meaning of integration varies with the model purpose and is reflected in the structure of the integrated model. Five dimensions of integration can be distinguished broadly:

  1. spatial integration – where the horizontal and/or vertical interactions among spatial levels are emphasized with respect to a phenomenon being modeled
  2. sectoral integration – where the model represents the linkages and relationships between two or more economic sectors of the spatial system of interest such as retail, housing, transportation, industry, agriculture, etc.
  3. land use integration – in which the model accounts for the interactions between more than two types of land use such as residential, commercial, manufacturing, transportation, etc.; this dimension of integration may be equivalent at times with the sectoral integration
  4. economy-society-environment integration – where the model represents the linkages between at least two of the several components of the spatial system such as economy-environment, economy-society (e.g. population), economy-energy, etc.
  5. sub-markets integration – where models show how different sub-markets of the whole economy relate to one another; a related type of integration may be considered that between supply and demand. In this latter case, the related economic models are distinguished into partial equilibrium (referring to either demand or supply) and general equilibrium models.

The temporal dimension is not considered as one of the dimensions of integration. Models which incorporate the time dimension are called dynamic, in general, and may concern either simple or integrated models although the latter case is less frequent given the many difficulties associated with building conceptual and operational dynamic integrated models.

The five main dimensions of integration are not mutually exclusive; in fact, any integrated model may combine more than one of these dimensions. The modern trend in integrated model building is to account for several dimensions with a special emphasis on the spatial dimension – especially in modeling land use or environmental characteristics and issues. This latter feature has been greatly facilitated by the rapid developments in information and spatial data management technology. Note, however, that the higher the degree of integration, the greater are the difficulties, on the one hand, to conceptualize and support theoretically the relationships of interest and, on the other, to operationalize and use the respective models.

The integrated models which are presented in the following have been grouped on the basis of their most characteristic feature which is the main modeling tradition in which they belong (Table 4.1c). More specifically, the model groups are: (a) econometric-type integrated models, (b) gravity/spatial interaction-type integrated models, (c) simulation models, and (d) Input-Output-type integrated models. In all these models, land use is either accounted for directly by the model or the land use implications of the models’ results can be assessed outside the model.


4.6.1. Econometric-type integrated models

The most well known econometric-type integrated model which accounts explicitly for various types of land use is the Penn-Jersey model (Seidman 1969, Wilson 1974, Romanos 1976). It is a modular model which adopts an aggregate, macro- approach to modeling the components of a metropolitan economic system. It consists of seven main sub-models as shown in Figure 4.2b which is Wilson’s (1974) interpretation of the model’s structure. It operates sequentially through a series of 5-year periods. A brief description of the model is offered below following Wilson (1974) where the reader is referred for a complete and concise description of the model’s basic equations (the econometric model) and operation.

The model assumes a study region subdivided into zones. A regional demographic model "drives" the rest of the sub-models. It applies cohort-survival analysis to produce population projections by age, sex and race. The output of the demographic model is fed into two models separately: a regional employment and a regional income distribution model. The regional employment model calculates the total labor force by multiplying the population projections by age-sex specific activity rates and assumes a constant (6%) unemployment rate. The total labor force is allocated to different employment sectors using a linear regression model.

The regional income distribution model is based on the results of an income projection model whose task is to predict future median income and the new income-class boundaries based on historical evidence which had shown that the distribution of income among different income quartiles had remained reasonably constant over time. The population projections from the regional demographic model are fed into the income distribution model which produces the allocation of the total population to income groups (which are assumed to each have different locational behavior).

In the residential location model, the population projection for each income group is allocated among the zones of the study region. Original allocations may be amended later when the constraints are checked. The allocation formula by income group used is an accounting equation which calculates the population of a zone (for a given income group) as the sum of the population of the previous period plus the projected change. The projected population change is the sum of net migration to the zone plus the zone’s share of total population growth. Migration from a zone is assumed to be proportional to the population of the zone, its residential desirability, and the zone’s "effective area". The latter is calculated as the minimum of residential land plus available land and prevents a zone from doubling its residential area in a single projection period. As the population projections allocated are expressed as number of households, these are converted into actual number of people by multiplying the number of households by the average household size for the zone.

The residential land use model assesses the amount of residential land in each zone by income group. This is expressed as the product of the projected population (by income group) of the zone (the output of the residential location model) times the amount of residential land consumed by household in the zone. This quantity is estimated from an econometric equation as a function of the zone’s median income, expenditures on transport, and accessibility to opportunities of type l (the connection with Alonso’s model). This model estimates also the price of a household plot of land in each zone as a function of the same variables as above using an econometric equation.

The manufacturing employment location model employs the same mathematical framework as the residential location model. The amount of manufacturing (by sector) and retail employment in a zone is assessed as the sum of employment in the previous period plus change in employment. The change in employment is calculated as a function of the employment of the zone in the beginning of the projection period and net migration to the zone. The latter is assessed as a function of the initial employment, the desirability for manufacturing and retail location of the zone, and the zone’s effective area which is calculated as in the residential location model.

The manufacturing land use model employs simple trend projection formulae as good econometric equations were difficult to identify. A distinction is made between zones where manufacturing employment is declining and those where it is increasing. For the latter case, all zones are divided into five concentric rings and the rate of increase in manufacturing land use is taken to be proportional to the change in employment in all zones of the ring of which a particular zone is a member.

The service employment location model is a cross-sectional model which employs a mixture of intervening opportunities and gravity model concepts. The main variables are: (a) service activity generated in a zone in a given sector from the households in this zone and (b) service activity generated from workplaces. Conversion coefficients are used which convert activity measures, such as turnover, to employment for each of the above types of service activity. Retail activity is assessed from a spatial interaction (gravity) model which, however, takes into account the ordering of zones so as to account for jobs which remain in a zone or pass from a zone to another. In other words, an intervening opportunities model form is employed. According to Wilson (1974), this was an extremely ambitious model whose successful development, calibration, and use was a substantial achievement of the Penn-Jersey model.

The service land use model employs simple trend projection formulae for the same reasons as it was the case with the manufacturing land use model. Zones where service employment is increasing or decreasing are distinguished as in the case of manufacturing. Finally, the street land use model employs a simple linear regression model to assess the amount of land for streets in the projection period after the land consumed by residential, manufacturing, and service activity has been estimated.

All the estimates provided by the above sub-models are provisional and they are subject to feasibility checks. These checks include: (a) avoiding negative values of obviously positive quantities and (b) observing the maximum values of rate of growth or decline in individual ones or groups of zones. Excess amounts of activity are re-allocated through rather complex procedures as Seidman himself had admitted (Wilson 1974). Finally, it is noted that the model described here was used to allocate land use and activity to the zones of the study area. These were used subsequently in a transportation model which was the original purpose of the Penn-Jersey Transportation Study.

Econometric-type integrated models of land use such as the Penn-Jersey model presented above provide elaborate, although mechanistic, tools to assess land use change as a function of change in the independent variables they take into account: population growth, income changes, employment changes, etc. However, in order to cope with the complexity of the system being modeled, they need to rely frequently on mechanistic calculations which are not supported by a theory of land use change. In addition, the econometric estimates they produce through the systems of equations they employ use, inevitably, historical data. This means that the coefficients reflect the past state of affairs of the urban system modeled which may not be congruent with a future system where several changes, among which, land use change, have taken place. The linear operational forms used present another drawback of these models as several of the changes may be nonlinear such as changes in service employment and changes in the area occupied by the various land use types. The lack of rigorous theoretical backing of these models contributes to these weaknesses. Moreover, they do receive several exogenous inputs which would be better assessed endogenously in a comprehensive treatment of land use change.


4.6.2. Gravity/Spatial Interaction Type Integrated Models

The gravity model, or the family of spatial interaction models in Wilson’s (1974) more comprehensive terminology, has offered a less mechanistic framework to build integrated models of land use compared to the econometric models. Given that it is based on certain, however controversial, theoretical principles and it has been shown to be in agreement with the welfare economic concept of utility maximization (see section 4.4), it has been used as a central modeling device in integrated models of land use allocation.

4.6.2A The Lowry Model and Garin’s versions

The landmark model in this group is the Lowry model designed by Ira Lowry in 1964 for the Pittsburgh metropolitan region and revised several times later on. The model describes the structure of the urban spatial system in terms of activities and corresponding land uses as follows: population-residential land, service employment-service land use, and basic (manufacturing and primary) employment-industrial land use. The model assesses the levels of activities which are then translated into area of land uses by means of land use/activity ratios . It assumes that the study area is subdivided into a number of zones. The basic structure of the model is shown in Figure 4.2c. The exogenous information provided to the model consists of total land, unusable land, "basic" land (for the location of "basic" activities to be defined below), "basic" employment (to be defined below), and characteristics of the transport network. The constraints included in the model concern: (a) allowable amount of land use to be accommodated in each zone, (b) population density per zone, and (c) minimum size of service employment for one of three categories – neighborhood, local or district, metropolitan. Using this information, the model performs two separate sets of calculations: one for the characteristics of the residential sector and one for the retail sector of the urban region. The location of basic activities is assumed to be independent of the location of population and service employment. After allocating the predicted levels of activities to zones, the model performs also consistency checks of the predicted distribution of population against the distribution used to compute potentials to find out if they coincide. In case they do not, the model re-iterates the whole allocation procedure until the two distributions coincide (Batty 1976). A simple presentation of the basic mathematical expression of the Lowry model is given below following Wilson (1974) and Batty (1976).

First, the calculation of the population of the urban region is shown given the magnitude of basic employment which is provided to the model exogenously. The Lowry model borrows from the economic base model in order to perform this calculation (see, for example, Wilson 1974, Hoover and Giarratani 1984, 1999). Total employment in an area is considered to be the sum of basic and service (or, population-serving or local) employment. Basic employment is associated with the production of goods (and services) which are exported out of the region while service (or, population-serving or local) employment is associated with the production of goods (and services) destined to be consumed locally, within the region. The identity expressing the relationship between total, basic and service employment is:

      (4.72)

where,

EB the exogenously given basic employment
ERk service employment in the kth service (retail) sector (summed over all k service sectors)
E total employment

It is assumed that total population, P, is proportional to total employment as follows:

P = f E      (4.73)

where,

f is an inverse activity rate (persons per employee in the basic sector)

It assumed also that total employment in the kth service (retail) sector is proportional to the population as follows:

ERk = ak P      (4.74)

where,

ak is a constant (one for each of the k retail sectors)

Solving equations (4.72)-(4.74) gives the magnitudes of total employment, population and retail employment:

      (4.75)

      (4.76)

      (4.77)

Given these calculations, the rest of the model solution procedure is as follows:

The amount of land available for residential use in each zone j, AjH , is given by:

      (4.78)

where,

total land of zone j

unused land in zone j

land for basic industries in zone j

land for services in zone j

Given the estimate of the total population, this is allocated to the zones of the study region according to a potential model (see section 4.4.) which can be considered as a simple spatial interaction model with only one "mass" term. More specifically:

     (4.79)

where subscript i denotes the destination zone (where employment is located) and f1(cij) is a generalized travel cost function from origin (residential) to destination (employment) zones.

Equation (4.79) ensures that the sum of the population of all zones equals total population. Moreover, for each zone, a check is performed to find whether the maximum population density constraint is exceeded:

      (4.80)

where, zH is the population density of the zone

As mentioned above, in equation (4.74), total employment in retail sector k, ERk, is assumed to be proportional to total population. This is allocated to the zones using a potential model similar to that used for the household sector:

      (4.81)

where,

gk and qk are empirically determined coefficients which express the relative importance of population and employment in the index of market potential
f2(cij) is a generalized travel cost function for the retail sector.

Residential, industrial and retail land use in each zone is calculated using land conversion ratios for population, eP, basic employment, eB, and retail employment, eR, using the following simple, general formula:

Li = el Xil      (4.82)

where,

el is eP or eB or eR
Xil is P, or EiB or EiR

Consistency checks on the calculated amount of land by land use type are performed to ensure that the constraints on each land use type are met.

The Lowry model is solved by iteration for a single period. Both Wilson (1974) and Batty (1976) provide an exposition of the iterative formulation of the model which shows how the equations are executed. The iterative process stops when the predicted distribution of population coincides with the distribution used to compute potentials in the beginning of the solution procedure.

The original version of the Lowry model has been subjected to several improvements and its variants have served as core land use forecasting models in a large number of land use and transportation studies in several countries (mostly the U.S., Canada and the U.K.). Batty (1976) credits Garin (1966) as having reinterpreted the Lowry model in two important ways: "first, the potential models have been replaced by production-constrained gravity models and second, the expanded form of the economic base mechanism has been substituted for the analytic form" (Batty 1976, 63). With respect to the first point, Wilson (1974) shows also how the inclusion of an "attractiveness" term converts the simple gravity-type models of the original Lowry model into gravity models proper. Garin offered also a matrix formulation of the Lowry model (Garin 1966 cited in Wilson 1974) leading to several methodological and solution insights.

4.6.2B TOMM (Time Oriented Metropolitan Model)

The first use of the Lowry model framework was made by Crecine (1964 cited in Batty 1976, 62 and Batten and Boyce 1986, 851) who designed TOMM (Time Oriented Metropolitan Model) for the Pittsburgh Community Renewal Program. This model kept the basic Lowry model structure but provided for: (a) incremental, and not single-year, solutions introducing, thus, the time element in forecasting which accounts for the fact that all changes predicted by the model do not take place in the forecast year but a certain proportion of activity remains stable and (b) disaggregated population into different socio-economic groups in the hope of improving the explanatory power of the model. Another version designed also by Crecine for East Lansing, Michigan (Crecine 1969 cited in Batty 1976, 62) is used as an educational device in the METRO gaming simulation exercise at the University of Michigan (Batty 1976).

4.6.2C PLUM (Projective Land Use Model)

Another application of the Lowry framework is PLUM (Projective Land Use Model) designed by Goldner (1968 cited in Batty 1976, 63 and Batten and Boyce 1986, 851-852) for the San Francisco region. The modifications and improvements made include programming changes to incorporate zones of different sizes, the use of an intervening opportunities model to allocate population and employment, disaggregation of the model’s parameters by spatial unit (the nine countries of the Bay Area), use of zone-specific activity rates and population-serving ratios. For further description and discussion of this model’s use, the reader is referred to Rothenberg-Pack (1978). PLUM has been used by Putman (1983) in building ITLUP -- an integrated land use/transportation model – which is discussed later in this section.

4.6.2D Activity Allocation and Stocks-Activities Models

From the other side of the Atlantic, Echenique and his colleagues at the University of Cambridge in the U.K. (see, Wilson 1974, Batty 1976) developed the Urban Stocks and Activities model, an adaptation of the Garin formulation of the Lowry model framework, which operates at the town scale. They have fitted this model to several British towns and a version has been applied to Santiago Metropolitan area (Echenique et al. 1969 cited in Wilson 1974, 242, Batty 1976, 75-79). One of the important changes this model introduced was the use of floorspace as a measure of location attraction on each iteration of the model. As floorspace is reduced so is the measure of location attraction. The use of floorspace introduces, however crudely, the supply-side mechanism of the urban land market which is not present in the original Lowry formulation. The stocks of floorspace serve as constraints on the demand for space by various activities seeking to locate in a zone (Wilson 1974, Batty 1976). More recent integrated land use-transport models designed by Echenique and his colleagues use also floorspace as a measure of location attraction (Echenique et al. 1990; see also, SPARTACUS 1999).

A more general family of urban models originating from the parent Lowry model have been built by various modelers in the 1970s which Batty (1976) calls Activity Allocation and Stocks-Activities Models. These models are variations of the spatial interaction model which are used to allocate population and employment to the zones of an urban/metropolitan region while the Stocks-Activities models operate at the town scale where they translate the activity allocations to land uses. Batty (1976) describes the operational forms and technical details of these models and provides information on their applications in the U.K. as well as intermodel comparisons.

To close the discussion of the Lowry model, a brief evaluation of the first generation of Lowry-type models is in order. The main purpose of these models is to forecast (or, predict) future changes in the distribution of the population, employment and land uses in urban (mostly) areas given exogenous changes in basic employment. In other words, they are basically demand-driven models in which the supply side of land is under-represented in the best case. From the analysis of land use change point of view, this is an important drawback as various aspects of the supply of land (economic, environmental, institutional, etc.) play a crucial role in determining the direction and amount of change which comes about with changes in the demand for land by space-consuming activities (among others). This drawback is further reinforced by the static nature of all these models (despite efforts to produce dynamic versions – see, Crecine 1968, Batty 1976) which does not capture the dynamics of land use change which may be either demand-, or supply-related or, most possibly, may result from their interaction. In addition, from a policy impact analysis viewpoint, these models do not include many policy variables so that they can be used as decision and policy support tools for the large variety of policy interventions through which land use change is effected (see, also, Rothenberg-Pack 1978).

Another drawback relates to their theoretical foundations which borrow from the economic base theory (and model) and the gravity theory (and model). Both have been heavily criticized for their positivist orientation, their many omissions of critical factors related to urban growth (especially the supply side), the mechanistic view of real world phenomena they advance (see, section 4.4), and their poor explanatory power all of which bear importantly on the issue of land use change. Overall, both pieces of theory emphasize, in a rather rudimentary way, the economic determinants of land use change while, as it is being repeatedly stressed, land use change results from much more involved processes even in the economic markets. Besides these deficiencies, the Lowry-type integrated models miss many other aspects of integration, important among which is the impact of the transportation network, a theme which was addressed in the decade of the 1980s by the development of integrated land use-transportation models.

Finally, and most importantly in the perspective of the present project, the treatment of land use is rather simplistic. The land conversion ratios are crude measures (quick and dirty techniques) of the amount of land demanded when changes in economic or population activity take place. They do not account directly for technological variations (low-, vs. high-rise buildings, land use intensification through space-saving technologies), socio-economic and cultural differences (especially when the models are transferred to other cultural settings) in the use of space, non-linearities in the use of space especially those arising out of the interactions among adjacent land uses (demand for space may not be proportional to changes in the space-demanding activities). Moreover, their uniform application over space disregards the supply-side of land use change; i.e. the constraints which the natural and built environment may impose on future changes. The supply side is taken into account by imposing allowable space limits on land use types but the adjustment process the models apply when these limits are exceeded is mechanistic. Evidently, the use of these linear land conversion ratios masks all potential variations in the use of space and makes the assessment of land use change by these models a mechanistic (and mostly self-fulfilling) process.