For the analyses of papers I and IV, SI was estimated for 42 validation plots with areas of ∼3700 m2. The models were first applied to each individual subplot to predict the SI, and validation plot level SI was subsequently estimated as the mean of SI predictions made for subplots within the validation plot. Field data on the age and height of site trees allowed for a comparison of the laser-estimated SI with ground reference values of SI. To evaluate the accuracy of the indirect method in paper I, ground reference values of height-differential SI, calculated from ground reference Hdom from the two points in time, were compared with the correspond-ing values of SI estimated from bitemporal ALS data.
Cross validation was used for the evaluation of the classification accuracies in paper II. Single plots were removed iteratively, and the kNN classifiers were fitted with data from the remaining plots. For each iteration, the out-of-sample plot was classified, and the procedure was repeated until each plot obtained a class label.
The accuracies of the classifications were then assessed using the overall accuracy and kappa.
In paper III, cross validation was used to assess the accuracy of disturbance clas-sifications and SI predictions at the level of the 250 m2sample plots. In addition, the models for predicting SI were applied to the circular validation plots of 1000 m2located in districts B and C. The validation plots were divided into four quad-rants, and SI was estimated for each validation plot as the mean of predictions made for quadrants classified as undisturbed.
The accuracy of SI predictions in paper I was assessed by computing the mean differences (MD) and root mean square error (RMSE). The RMSE is a collective expression of the magnitude of the random and systematic deviations between the true and the estimated value. In paper III, the RMSE relative to the ground reference mean (RMSE%) was additionally computed, and in paper IV, the MD relative to the ground reference mean (MD%) was also used in the assessment.
5. Results and discussion
5.1 Methods of SI estimation
Overall, the direct method was slightly more accurate than the indirect method (Table 4), which may be expected because direct estimates only contain a single set of errors as opposed to errors occurring for both points in time (McRoberts et al., 2014). Systematic errors were, however, greater for estimates obtained by the direct method than those obtained by the indirect method. The direct method provided better accuracy in pine-dominated forest than in spruce-dominated forest, while the indirect method worked equally well in either species groups.
Table 4. Mean differences (MD) and root mean square errors (RMSE) between ground reference and laser-estimated H40 site index obtained for validation plots in district A.
Method Dominant species MD RMSE
Direct Spruce -0.67 1.78
Direct Pine 0.53 1.08
Indirect Spruce -0.13 1.82
Indirect Pine -0.04 1.82
There were strong correlations between ground reference values of SI and bitem-poral ALS metrics, which is a logical result; larger values of ALS metrics that reflect initial canopy height and canopy height increment suggest a high SI. How-ever, no previous study had modelled SI directly from bitemporal ALS data and applied the models in an area-based inventory approach. Although several studies had used bitemporal ALS data for predicting SI at the level of individual trees (Hollaus et al., 2015; Kvaalen et al., 2015; Solberg, 2010), such methods have less potential for use in repeated forest management inventories. Firstly because in-dividual tree analyses require point densities> 5-10 m-2 (Yu et al., 2010), which is higher than what is commonly available from previous inventories carried out 10-15 years earlier. Secondly, the area-based method is the most common method for ALS-based forest inventory (White et al., 2013a), and the direct and indirect methods proposed in paper I can thus more easily be incorporated in operational forest management inventories.
Although less accurate, the indirect method provided a practical alternative be-cause it is age-independent. In a previous study, V´ega and St-Onge (2009) esti-mated SI indirectly from a time series of canopy height models constructed from historical DAP data and an ALS-derived digital terrain model. Using a similar ap-proach, Persson and Fransson (2016) used two canopy height models constructed from bitemporal ALS data. The two studies differed from paper I, however, in that the temporal resolutions were 58 and 3 years, respectively, and because they used canopy height models as opposed to area-based estimates of Hdom. The temporal resolution of 15 years in paper I is a more likely scenario in repeated ALS-based forest inventories, and the results may therefore be more relevant from an operational perspective.
Two main advantages of indirect SI estimation are that no additional field work is required, as SI is estimated from Hdom at two points in time, and that the obtained SI estimates reflect recent growing conditions. However, being based on Hdom development over a much shorter window of time than the more common age-height approach, also makes the indirect method more sensitive to errors. Ac-curate and precise Hdom estimates are required at both points in time, as small deviations at either point in time will have great impact on the obtained SI es-timates. Particularly systematic errors occuring at both points in time and in oppsite directions will have considerable negative impact on the accuracy of the obtained SI estimates. The direct method, on the other hand, has the advan-tage that it can easily be incorporated in repeated ALS-based forest inventories, in which models are already commonly applied for direct prediction of forest at-tributes. Another advantage of the direct approach is that field data from only a single point in time are needed.