Abstract
The National Forest Inventory in Lithuania has collected Scots pine (Pinus sylvestris) and Norway spruce (Picea abies) trees measurement data across the country. Investigations to determine the suitability of these data for updating stem profile and volume models are required. New models for stem volume and stem profile (taper) were developed using a q-exponential function in the symbolic computational language MAPLE. Work associated with the National Forest Inventory has derived very accurate Scots pine and Norway spruce trees stem profile equations that have an application not only in deriving total tree volume estimates, but as a cost-effective mensuration tool to estimate stem volume at any part of the trunk. Three previously constructed models and a new q-exponential model for stem profile and stem volume were employed to compare predicted values with empirical values of diameter outside bark and stem volume. Performance statistics for the stem volume and stem profile equations included four statistical indices: mean percentage of absolute bias, precision, Acaike’s Information Criteria, and an adjusted coefficient of determination.
Highlights
Foresters have a long history of being aware of the variability in individual tree form and trying to model it so that the overall stem profile can be described more precisely
Compatibility between taper and volume equations is characterized as when the total volume obtained by summation of the sections whose volumes are defined using the taper equation is approximately identical to the volume calculated by the volume equation
For the q-exponential segmented stem profile model defined by equation (9), a joint point was calculated at 0.45 (Norway spruce trees) and 0.52 (Scots pine trees), and for the Burkhart segmented taper model defined by equation (7), a joint points to the both Scots pine and Norway spruce species were calculated at 0.11 and 0.75, as the fit statistics obtained the best values
Summary
Foresters have a long history of being aware of the variability in individual tree form and trying to model it so that the overall stem profile can be described more precisely. Examples of the first approach are the variable-exponent stem profile models by Kozak[1,2,3] In these a single continuous function with a changing exponent from ground to tip describes the neiloid, paraboloid, and several intermediate forms[2]. Numerous equations forms have been developed to predict tree volume Most of these volume equations have been developed by combining predictor variables diameter at breast height and total height in various ways. Our main contribution is to expand stem profile and stem volume models by using q-exponential functions and to compare the taper equations’ performance in predicting the diameter outside the bark at any given height and stem volume for Scots pine and Norway spruce species
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