Relationships between the mean trees by basal area and by volume: reconciling form factors in the classic Bavarian yield and volume tables for Norway spruce

The Norway spruce forests of southern Germany and Austria have been at the forefront of forestry research for well over 100 years. The 1960s were a particularly productive period that saw the development of the yield tables of Ernst Assmann and Friedrich Franz, and the form and volume tables of Reinhard Kennel. Both of these works (or the equations that underpin them) are still in common use today. Even though both sets of tables were developed concurrently in the Institute for Growth and Yield at the Munich Forest Research Institute, a cursory examination suggests they are mutually incompatible, as they appear to use different values of form factor. The discrepancy can be explained by examining the differences between the mean tree by basal area (the tree with the quadratic mean diameter) and the mean tree by volume. This difference is shown to be predictable from data contained in the yield tables, and a conversion equation is developed and tested. The results show that the two sets of tables can be considered fully compatible if we accept that the volumetric mean tree is not identical to the mean tree described in the yield tables