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In the common methods of forest mensuration, including stem volume  models and Bitterlich sampling, stem cross-sections are assumed to be  circular. In nature this assumption is never exactly fulfilled. Errors  due to non-circularity have been presumed to be small and unimportant  but studied little: theoretical and empirical studies exist on  cross-section area estimation, but errors in stem volume estimation have  not been investigated at all, and errors in Bitterlich sampling are  theoretically known only for stand basal area estimation. In the  theoretical part of this study, we developed methods for quantifying the  systematic and sampling errors that 22 common ways of selecting  diameter within non-circular cross-sections induce (i) in area estimates  by the circle area formula, (ii) in stand total estimates by Bitterlich  sampling, and (iii) in stem volume estimates by a volume equation, by a  cubic-spline-interpolated stem curve, and by a generalised volume  estimator. In the empirical part, based on the digital images of 709  discs taken at 6â10 heights in 81 Scots pine stems from different parts  of Finland, we investigated the variation in cross-section shape, and  demonstrated the magnitude of the errors presented in the theoretical  part. We found that non-circularity causes systematic overestimation of  area and volume, and inflicts potentially systematic error on stand  total estimates by Bitterlich sampling. In our data these effects were  small, but the finding is not generalisable due the skewed size  distribution and poor geographical representativeness of the data. We  recommend using diameter derived from girth for both tree and stand  level estimation, as it involves no sampling error and produces clearly  the most stable systematic errors.

silva fennica

On non-circularity of tree stem cross-sections: effect of diameter selection on cross-section area estimation, Bitterlich sampling and stem volume estimation in Scots pine