Mathematical modelling of land use and landscape complexity with ultrametric topology

Abstract

Three new measures of functional/hierarchical landscape complexity are proposed in this article, based on ultrametric distances, and they are applicable to both raster and vector landscape maps: (a) C = the sum of ultrametric distances (and the associated measure C1 = the normalized sum of ultrametric distances), (b) Cd = the sum of degrees of land use functions and (c) Cy = the cyclomatic complexity of the graph of the ultrametric distances of the model. Each one of these measures provides different assessments of functional landscape complexity. With the measures C and Cd, we can also assess the relative significance of each landscape function for the overall landscape functional complexity. Assessing the 'decomposability' of the landscape system is also possible, allowing us to decide which landscape functions are more important than others. All these measures can be calculated for any landscape. Example applications are made on a landscape from the area of Messogia, Attica (Greece). © 2013 Copyright Taylor and Francis Group, LLC.