Spatial correlation analysis between topographic parameters for defining the geomorphometric diversity index: application in the environmental protection area of the Serra da Esperanca (state of Parana, Brazil)

The present work, by focusing on geomorphological modeling within the context of geodiversity, addresses the definition of a diversity index based on the evaluation of the association between topographic variables corresponding to the North district of the Environmental Protection Area of the Serra da Esperanca, state of Parana, Brazil. In light of resources provided by digital modeling of the relief as well as by spatial statistics, the study consisted in submitting geomorphometric parameters to Shannon's diversity index and evaluating the resulting data by means of spatial correlation analysis, which in its turn was guided by the Bivariate Moran's index. Association of the variables in different crosstab phases resulted in the identification of those with positive spatial correlation, presenting high diversity mainly over and around escarpments, in consonance with the initial assumption of this study. In the same vein, we confirmed the hypothesis that a limited amount of topographic features does enable measurement of topographic variations, which justifies the introduction of the term geomorphometric diversity index. Since the study has a methodological character, comparative analyses between quantitative resources are necessary for addressing specific objectives within distinct themes and areas of interest.