Comparing the two paradigms for fixed-area sampling in large-scale inventories
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The majority of large-scale forest inventories use some form of fixed-area sampling. In recent books and scientific publications, the estimators for these surveys have been derived using two different paradigms. The first, which will be referred to as the tessellated plane paradigm, relies on the assumption that the area is divided into equal area contiguous blocks which constitutes an area sampling frame. These blocks can be formed using the pixels of a satellite image. Inference for this paradigm is drawn by considering the distribution of the finite number of possible estimates derived from the area frame. The other approach will be referred to as the continuous plane paradigm, which assumes random positioning of the sample plots. Inference for this paradigm can be drawn without relying on an area frame. The necessary assumptions for using either paradigm are compared when current forestry techniques, such as the use of open cluster plots and satellite imagery, are used. The tessellated population paradigm requires many more assumptions, some of which may be difficult to justify. Estimators of both forest area and basal area under these paradigms are contrasted and the strengths and weaknesses of both are compared. The primary advantage of the tessellated population paradigm is that more strata can be used to reduce the variance of the estimators. Both paradigms appear to be reasonable alternatives until some of the practical problems of forest inventories are considered. Examples include the difficulty associated with measuring plots that partially cover water and adjusting for changes in remote sensing technologies over time. In these situations, the tessellated population paradigm may be more difficult to implement because of the difficulty in estimating changes over time and properly accounting for linear and fragmented strata, such as rivers and lakes.