General considerations about the use of allometric equations for biomass estimation on the example of Norway spruce in central Europe

Allometric relations for tree growth modelling have been subject to research for decades, partly as empirical models, and partly as process models such as the pipe model, hydraulic architecture, mechanical approaches or the fractal-like nature of plant architecture. Unlike empirical studies, process models aim at explaining the scaling within tree architecture as a function of biological, physical or mechanical factors and at modelling their effect on functionality and growth of different parts of an individual tree. The goal of the underlying study is to link theoretical explanation to empirical approaches of tree biomass estimation by the example of Norway spruce (Picea abies [L.] Karst.). Decisively, this article tries to take allometry out of the purely curve-fitting exercise common in literature and derives implications for the use of allometric biomass functions.Our results demonstrate that the dbh as independent variable might be misleading for the comparison of universal scaling laws with empirical studies. We were able to show, that the use of a recalculated diameter in relative stem height by means of a taper form model confirms general biological implications better than the dbh measured at a fixed tree height. We used a compiled dataset of altogether 245 trees that were measured on different sites in central Europe to proof our consideration. As one result we estimated a scaling factor b of 2.65 for the allometric relation (agb = a  D0.1b) between a diameter in relative stem height (D0.1) and aboveground biomass (agb), which is close to scaling relations predicted by process models. The standard error of a linear regression model based on the log-transformed variables could be slightly reduced to 0.21 (R2 = 0.98) when we used the diameter in relative tree height.