Comparison of formulae for estimating tree bole volumes of Pinus sylvestris

Abstract

Tree bole volumes of 103 Scots pine (Pinus sylvestris L.) were estimated using nine methods (paracone, centroid, control-variate with one and two measurement points, Huber's formula, antithetic method using importance sampling, standard volume table, local volume table, importance sampling using one and two measurement points, and a taper equation). These estimates were compared with “true” volume of each tree bole which was determined by aggregating the volumes of measured short sections (average 1m) using Smalian's formula. The antithetic method performed well in terms of mean square error and tolerance intervals, which indicate the precision of the estimates. For both importance and control-variate sampling, better precision of the estimate may be achieved by taking measurements at two positions along a stem. The results showed that the antithetic method, importance sampling and control-variate method with two measurement points, paracone and centroid methods are useful alternatives to local volume tables and other standard formulae and are recommended for tree bole volume estimations of Scots pine in Turkey. However, in practice, convenience and economics play an important a role in the decision whether to use given estimation methods. On that basic, the paracone or centroid method may be recommended for use in tree volume estimating, as these are the easiest methods to apply, are less time consuming than other methods and show very acceptable statistical performance.