Optimising the Yield of Energy from Biomass by Analytical Models of the Rate of Growth

In the reported study of growth-rates of grey alder (Alnus incana) stands at different quality sites the authors, as a continuation of an earlier study, propose and use analytical models to approximate experimental data of mean annual increments of standing stock. The model equations of growth-rate functions are further used to optimise the cutting age by minimising the total area of stands for sustainable annual supply of biomass. The growth-rate behaviour with the age of natural grey alder stands is described by an exponential function of three parameters defining the initial and the maximum growth-rates, and the age at which the growth-rate maximum is reached. None of the parameters is known from experiment, and they are found by least-square fit of the available experimental mean values appraised at the chosen time intervals into the model. A high correlation between the experimental data and the model function is found. The optimum cutting age of 18 years determined in the earlier study is confirmed. In farmed stands the growth-rate is made to continue increasing at a lower speed, and is well approximated by a linear function, in which case it is shown that the cutting age cannot be optimised with respect to the area minimum existing under the condition of a decreasing growth-rate after passing a maximum. In the case of a constant or slowly growing annual increment the authors suggest considering the ratio between the increment of stock per unit of the total area to the increase in the area. The overall efficiency of using the product of photosynthesis for a 20-year-old grey alder stand is roughly estimated to be 0.3%.