A GIS-Based Shape Index for Land Parcels Demetris Demetriou* a,b John Stillwell a and Linda See c,d a School of Geography, University of Leeds, Leeds LS2 9JT, UK b District Land Consolidation Department of Larnaca and Famagusta, 18 Stratigou Timagia, 6051 Larnaca, Cyprus c International Institute of Applied Systems Analysis (IIASA), Schlossplatz 1, A-2361 Laxenburg, Austria d Centre for Advanced Spatial Analysis (CASA), University College London (UCL), London WC1E 6BT, UK ABSTRACT Shape analysis is of interest in many fields of spatial science and planning including land management in rural areas. In particular, evaluating the shape of existing land parcels is critical when implementing rural development schemes such as land consolidation. However, existing land parcel shape indices have major deficiencies: completely different shapes of parcels may have the same index value or similar parcel shapes may have different index scores. Thus, there is a clear requirement for a more accurate and reliable measurement method. This paper therefore presents a new parcel shape index (PSI) which integrates a geographical information system (GIS) with a multi-attribute decision-making (MADM) method. It involves the amalgamated outcome of six geometric measures represented by value functions involving a mathematical representation of judgements by experts that compare each geometric measure with that of an optimum parcel shape defined for land consolidation projects. The optimum shape has a PSI value of 1 while the worst shape has a value close to 0. The shape measures used in the model include length of sides, acute angles, reflex angles, boundary points, compactness and regularity. The paper uses data for two case study areas in Cyprus to demonstrate the superiority of the new PSI over three existing shape indices employed in other studies. The methodology utilized here can be implemented in other disciplines dealing with the assessment of objects that can be compared to an optimum. Keywords: Shape analysis, parcel shape index (PSI), multi-attribute decision making, land consolidation, ArcGIS, Cyprus 1. INTRODUCTION Shape measurement has been a focus of geographical study for many years. However, despite several authors attempting to develop generic methods for measuring shape in the past 1,2,3 , there is still no satisfactory method for measuring shape in a standard and explicit manner because of the variety of factors involved for each specific spatial context. Wentz 4 reflects upon the complexity of the task and emphasizes that a single numerical representation of shape is difficult to achieve through mathematical or statistical formulations. Moreover, indices developed in the context of solving one problem may not be applicable to others and hence efforts for developing a new method should be focused on analysing shapes in the context of each particular problem 5 and satisfying a set of basic requirements 2 . For example, a number of researchers have focused on indices for use in urban areas 6,7 , ecology 8,9,10 and remote sensing 11 . In the case of land management, the analysis of land parcel shapes is a key issue when considering the implementation of appropriate measures for ameliorating agricultural land fragmentation, such as land consolidation that involves restructuring the land tenure system (including the shape of parcels) and the provision of appropriate access and irrigation/drainage infrastructure. In particular, the aim is to evaluate the shape of existing land parcels in terms of their appropriateness for agricultural development. Thus, a number of studies have appeared that have involved either developing a new shape index for land parcels 12 or using existing indices for this purpose 13,14,15,16,17,18 . However, these indices are problematic when it comes to the interpretation of the similarities and differences in the values of the index in relation to parcel shape 3,19,20 . In particular, situations may arise in which a rectangle may have the same index value as a very irregular shape; or completely different shapes may have the same index value; or similar shapes may have different index scores. These weaknesses occur mainly due to the fact that none of the current indices provide an overall definition of shape 20 , i.e. only some of the geometric parameters of shape are taken into account. *demdeme@cytanet.com.cy; phone 357 99428462; fax 357 24304357