Optimizing height measurement for the long-term forest experiments in Sweden

Information on tree height is useful for volume estimation and site productivity assessment and as such, remains one of the most important variables often measured in forest inventories. Measuring a sufficient number of sample trees requires considerable sampling effort and cost. In this study, we developed height functions for optimizing tree height measurement in the Swedish long-term forest experiments (LTFEs). Two large datasets from the LTFE databases: fitting data (from thinning, fertilisation and mixed species experiments) and validation data (tree species and spacing experiments) collected over several decades were used. The fitting and validation data comprise 133,788 and 68,440 observations, respectively, each covering a large range of growth and environmental conditions across Sweden. A multilevel nonlinear mixed-effects modelling approach was used to build the generalised height functions for Scots pine, Norway spruce, birch (Silver and Downy birch united), other conifers and other broadleaves, considering variations in heights and other stand characteristics at sample plot-level and revision-level. The response calibration of the functions was first carried out with all measured heights of the validation data, and second, using heights of one to six sample trees obtained from different tree selection strategies (diameter extremes, largest diameters, and smallest diameters). The mixed-effects height functions explained most of the height variations in the fitting dataset (pseudo R2: 0.938 - 0.970; RMSE: 0.957 - 1.363 m) without any residual trends. The validation showed that the functions accounted for 95 - 98 % of the height variation in the validation dataset, with RMSE ranging between 0.770 and 1.040 m, confirming the functions' high accuracy. We recommend the measurement of four sample tree heights based on diameter ex-tremes as the ideal threshold for response calibration. These functions and the suggested sampling technique would reduce sampling effort and inventory cost of height measurements for subsequent inventories of the LTFEs.