5.2.2 Continuous Spatial Representation of Urban Land Value

5.2.2 Continuous Spatial Representation of Urban Land Value

One of the fundamental principles of the Urban Land Value Field (ULVF) is that urban land value is represented as a continuous spatial field rather than a collection of isolated parcel values.

Conventional land valuation methods assign values only to locations where land parcels or market transactions exist. Consequently, urban value is represented as a discrete set of observations separated by administrative boundaries or cadastral parcels. While appropriate for property appraisal, such representations do not capture the continuous spatial processes governing value formation throughout the urban system.

In reality, urban value changes gradually across space. Transportation infrastructure, accessibility, commercial centers, public facilities, environmental quality, and socioeconomic activities generate spatial influences that extend beyond individual parcel boundaries. These influences interact continuously, creating value gradients and transition zones rather than abrupt discontinuities.

Within the ULVF framework, urban land value is therefore represented as a continuous scalar field,

where:

• denote geographic coordinates,

• represents time,

• denotes the urban land value at every location and every moment.

This formulation enables value to be estimated not only at observed parcels but throughout the entire urban space. Every geographic location possesses a potential value determined by the combined influence of surrounding urban processes.

Continuous spatial representation provides several important advantages:

• It eliminates artificial discontinuities created by parcel boundaries.

• It allows spatial gradients of urban value to be quantified.

• It supports interpolation between observed market transactions.

• It enables multi-scale spatial analysis from neighborhoods to metropolitan regions.

• It provides a mathematical basis for integrating GIS, remote sensing, and artificial intelligence.

Rather than viewing urban land as isolated economic units, ULVF treats the city as a continuous spatial system in which value emerges from interconnected physical, economic, social, institutional, and environmental processes. This representation forms the mathematical foundation for subsequent analyses of spatial interaction, temporal evolution, and urban value prediction.

Key References

The discussions presented in Section 5.2.2 are primarily based on the following references:

[21] Longley, P. A., Goodchild, M. F., Maguire, D. J., & Rhind, D. W. Geographic Information Systems and Science.

[22] Burrough, P. A., & McDonnell, R. A. Principles of Geographical Information Systems.

[23] Batty, M. The New Science of Cities