Age-independent diameter increment models for mixed mountain forests

Abstract

Mixed mountain forests with an uneven-aged structure are characterized by a high tree-growth variability making traditional age-dependent growth models inapplicable. Estimating site productivity is yet another impediment for modelling tree growth in such forests. Uneven-aged mixed-stand forests are known for their high resilience, resistance and productivity, and are being promoted as a suitable alternative to even-aged, pure plantations for climate change adaptation and mitigation. However, their growth must be accurately measured and predicted, but diameter at the breast height (dbh) increment models specifically designed for uneven-aged mixed mountain forests are still rare. Using permanent sampling network data and 465 increment cores, we built two age-independent dbh increment ({i}_{d}) models for the main species of the study area, namely Norway spruce (Picea abies (L.) Karst.), silver fir (Abies alba Mill.) and European beech (Fagus sylvatica L.). Mixed effects models and the algebraic difference approach were employed to develop {i}_{d} models based on empirical and commonly used theoretical growth functions. A past growth index was further developed and introduced in the model in order to explain the {i}_{d} variability. Several mixed effects calibration strategies were assessed in order to obtain the most accurate localized curve for new plots. Tree size, competition and biogeoclimatic variables were found to explain the {i}_{d} through the empirical growth function, while the growth index significantly improved the theoretical growth function for Norway spruce. The optimization of the calibration strategy for the mixed effects modelling framework enables the growth index implementation in forest practice as an accurate method for estimating site productivity. The accuracy of the two {i}_{d} models was similar: the root mean squared error of the empirical growth function varied between 0.940 and 1.042 cm for spruce, beech and fir, while the root mean squared error obtained through the theoretical growth function for spruce only was 1.105 cm. The basal area increment prediction at the plot level based on the theoretical growth function reached a root mean squared error of 0.043 m2 while using the empirical growth function the root mean squared error is 0.047 m2. The high accuracy obtained using age-independent models underlines their suitability for predicting growth in mixed uneven-aged forests. The developed models can be easily integrated into forest practice to accurately obtain {i}_{d} estimates.