Stem Volume and Taper Functions

Abstract

Direct measurement of the wood volume in a tree stem is a difficult and time-consuming process, particularly if the tree is standing. For many forest species around the world, functions have been developed that allow estimation of the volume in all of the stem or that much of it which is large enough to be merchantable. These 'volume' functions require measurement only of the diameter at breast height over bark and total height of the tree and, sometimes also, the degree of taper of the stem determined by diameter measurement at two heights. More recently, functions have been developed widely across the world that allow estimation of the stem diameter at any height up a tree stem, again, usually from measurement only of diameter at breast height over bark and total height of the tree. Whilst rather more complex mathematically than volume functions, these 'taper' functions allow estimation both of the total wood volume in a tree stem and of the dimensions of the individual logs that might be cut from the stem as required by the market that the forest is supplying. This chapter describes these functions and their application. The FunctionsAs discussed in Chap. 5, stem volume measurement is a laborious and timeconsuming task even for felled trees. In modern forestry practice, one of the most common reasons for taking such measurements is to develop stem volume functions or taper functions for a particular tree species in a particular forest region.Volume functions allow estimation of the total stem volume of a standing tree from simple measurements, usually its diameter at breast height over bark and its total height. Sometimes also they allow estimation of the volume of parts of the stem that are large enough to be sold as logs, that is, the merchantable volume of wood available from the tree.Taper functions estimate how the diameter of a tree stem varies along its length. As with volume functions, they generally require that only the diameter at breast height and total height of the tree be measured. Furthermore, they can be used to estimate both merchantable and total stem wood volumes. In particular, they can estimate in much greater detail than volume functions the dimensions of individual

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“…where d i is the diameter in position i (cm), DBH is the diameter taken at 1.3 m from the soil (cm), h i is the height in position i (m), h is the total height (m), and b j represents model parameters [21]. Usable wood is optimized for logs with the longest length and the highest commercial value, with the remaining logs classified in lower quality classes, typically with shorter lengths.…”