Calibration of the yield tables for the main tree species in Hesse, Germany, using the data of the National Forest Inventory

Over the last decades forest growth has increased significantly compared to the past due to the change of environmental conditions. Though not only a large-scale improvement of site indices is observed, but also accelerated volume growth for a given site index. At the same time changed growth conditions and/or enhanced silvicultural treatments as staggered thinnings have caused diameter distributions, which differ significantly from those of the experimental plots used to develop the yield tables. Hence, the yield table based estimates for the periodic annual volume increment (PAIV) as well as the mean quadratic diameter (Dq) deviate increasingly from current measurements, which leads to a misspecification of values being substantial for forest management and valuation. This article presents the results of an expert opinion commissioned by HESSENFORST State Forest Enterprise and prepared by the consulting bureau ARGUS FORSTPLANUNG. It describes generalized linear regressions models (GLM) for Pedunculate and Sessile oak, European beech, Norway spruce, Douglas fir, Scots pine and European larch in Hesse, which provide unbiased predictions of PAIV and Dq (Formula (1)). Because the models use the related estimates of the yield tables as covariates, the yield table values are calibrated to actual conditions. The yield class and stocking degree were integrated as additional covariates if this resulted in a significant improvement of the model fit. In addition, a nonlinear model based on the Chapman-Richards function was developed, which estimates the PAW depending on age, yield class and stocking degree (Formulae (2) to (5)). The model development is based on the data of the so far three National Forest Inventories (NFI) collected in Hesse in the period from 1986 to 2012. The resulting models show estimates that in average exceed the values of the yield tables significantly for all tree species and both target variables. Based on these models changes of the Dq can be found, whose mean value per tree species is between +3.1 cm or rather +13% (oak) and +6 cm or rather +25% (beech) (Table 3). For high diameters of almost all tree species the model estimates converge to the values of the yield tables (Fig. 1), for the best yield class of pine and the better yield classes of oak they even fall below them. As a reason for this, in particular, the girth limit felling and maintenance of a high density in the earlier stages of the currently old stands are discussed. In general the lower the stocking degree the higher the absolute positive deviation of the mean diameter. For oak and pine, it also increases with declining site index, while the opposite is true for beech and spruce (Fig. 1). For the PAIV, the range of the average differences between the predictions of the GLM and the yield tables is between +0.7 Vfm ha(-1) a(-1) or rather 12% (pine) and +2.5 Vfm ha(-1) a(-1) or rather +26% (beech) (Table 4). As expected, the estimated growth of all tree species studied here increases with increasing stocking degree (Fig. 2), whereas the effect of the yield class is only significant for spruce and Douglas fir. The nonlinear models provide stable growth estimates for beech, spruce and pine only. Their overall error (Table 5) is not reduced compared to the GLM, however, the Chapman-Richards function allows a more differentiated description of the influence of age, site index and density (Fig. 3 and Fig. 4). As a result, compared to the GLM the mean difference between the model predictions and the estimates from the yield table decreases for beech by 0.3 Vfm ha(-1) a(-1), whereas it increases by 0.2 Vfm ha(-1) a(-1) for pine and spruce (Table 5). A comparison with the changes in periodical volume growth and mean diameter in Central Europe described in the literature reveals partly deviating values within the tree species (which may also be due to methodological differences), but overall largely similar magnitudes and spans. It is shown how the yield tables, which are still an important tool for forest planning and evaluation, can be calibrated as a whole based on the developed models and thus brought back closer to reality. Finally, the advantages and disadvantages of this approach, the limitations of its application as well as possibilities for further development are discussed. The application of the methodology presented here to NFI data from other Federal States and data from continuous forest inventories on enterprise level is certainly worth considering.