A Variogram Model Comparison for Predicting Forest Changes

Abstract

Changes in forest lands can be assessed by comparison between real images taken on different dates. However, the main forest features (e.g., basal area, stand height and aerial biomass volume) are better estimated by indirect methods related to the forest canopy. Variogram models have been used to measure forest stand structure; however, they have a known dependence on image parameters such as pixel size, contrast and sensor type. In addition, variogram methods allow us to select among different mathematical fitting functions that have different characteristics for estimating forest stands. Consequently, the above factors should be considered and corrected for when analysing forest changes from different images. The study focuses on the problem of choosing a mathematical function to fit the experimental semivariograms of high-spatial-resolution images of forest stands and the relationships between the semivariogram parameters and forest-stand features of a cluster of pine trees (Pinus pinaster Ait.) in a Mediterranean region (Madrid, Central Spain). The work compares the characteristics of spherical and exponential functions. In particular, the following issues were studied: (i) which model best fits the experimental semivariogram; (ii) how semivariogram models perform according to image spatial resolution; and (iii) the relationships between different models fitted to a particular experimental semivariogram. All of the analyses were carried out using five series of real images, including 2 aerial photographs from 1990, 2 orthophotographs from 2000 and an IKONOS image from 2003. The analysis considered up to 4 semivariogram features, namely range, sill, gradient and slope. The obtained results show that there is no optimum unique model and that the best mathematical function for fitting depends on the pixel size and on the forest variable that to be predicted. In particular, spherical models performed better for large pixels and exponential models performed better for small ones. According to the results, equalisation and normalisation image procedures improved forest prediction in comparison over analyses of raw images. As a general rule, exponential models obtained better forest-diameter predictions than did spherical models, while spherical models obtained better forest-stand height estimations. As a consequence, predicting forest changes using semivariogram models would require the use of normalised images and two different fitting functions for two different pixel sizes.