Estimation of periodic annual increment of tree ring widths by airborne laser scanning

The study was conducted in Karhuvaara (63°16′N, 29°03′E), municipality of Juuka, Finland. A total of 93 circular sample plots of 15 m radius were selected randomly from pine-dominated stands under the restriction that a stand may have only one plot. Plot locations were positioned by means of a global navigation satellite system (GNSS). The GNSS data were corrected afterwards to a sub-meter accuracy by means of a virtual reference station (Trimble VRS). The field work was done in 2015. The forest area includes company-owned, intensively managed boreal forests with Scots pine (Pinus sylvestris L.) as the dominant species. Other species included Norway spruce (Picea abies L. (Karst.)), downy birch (Betula pubescens Ehrh.), and silver birch (Betula pendula Roth). The forest area represents the middle boreal managed pine forests found in the Nordic countries and some parts of Russia.

The species and the diameter at breast height (DBH) were measured for all trees. From each plot, a total of 25 Scots pine trees were randomly selected for height measurement and drillings. For each plot, the Näslund (1937) height curve was fitted by means of sample trees, and the heights of the rest of the trees were predicted. By using information on the species, the DBH, and tree height, the tree volumes were predicted with the functions formulated by Laasasenaho (1982).

The width of the growth rings over the last 10 years and tree age were determined from the drillings. To measure the widths of the 10 outermost growth rings, an electronic micrometer was used. The PAI was calculated at the plot level, i.e., as the average of the mean annual increments of each measured tree. In our case, the modelled PAI was obtained as the diameter-weighted mean of the widths of the tree rings over the past 10 years by using the sample trees only. The most important plot-level stand attributes are presented in Table 1 and some of their distributions in Appendix Fig. A1. The average PAI, for example, was 1.03 mm. The distributions show that the age values, in particular, are skewed towards the lower end of the scale, which is typical for intensively managed forests.

Of the 93 plots, 24 had been thinned during the 10-year PAI estimation period. The soil type was classified as either mineral soil (n = 56) or peatland (n = 37). The site fertility type was classified as grove moderate (Vaccinium-Myrtillus type, MT) (n = 9) or poor (Vaccinium vitis idaea type, VT) (n = 47), following the classification by Cajander (1926). Correspondingly, out of the 37 peatland plots, 4 were type MT, 23 type VT, and 10 very poor (Calluna vulgaris type, CT).

The ALS data were collected on 13 July 2005, i.e., 10 years before the field data. The ALS device used was Optech ALTM 3100 (1064 nm), operated at an altitude of 2000 m above ground level. The pulse density of the data was 0.6·m⁻², and the nominal footprint diameter was 0.6 m. ALS-based predictors for area-based estimation at the plot level were computed separately for the first (f) and the last (l) echoes. The category f contained the original “first of many” and “only” echoes, and the category l contained the “last of many” and “only” echoes. No height threshold was applied. We computed height percentiles (p₅, p₁₀, …, p₉₀, p₉₅) and corresponding density percentiles, i.e., bincentiles, (b₅, b₁₀, …, b₉₀, b₉₅). In addition, we computed the means and the standard deviations of the intensities. The last ALS-based predictor considered here was a proxy for the effective leaf area index (LAI_e), calculated after Korhonen et al. (2011) as follows:where the above-height cover index (ACI) is the percentage of all echo types >1.3 m above ground level.

First, the correlation (r) between ALS metrics and the PAI was analyzed. In the modelling of the PAI, the multiple linear regression (MLR) was used in the following model form:where i = 1, …, n, and n is the number of observations; y_i is the dependent variable, PAI in our case; x_i are explanatory variables; β₀ is the intercept; β₁, …, β_p are coefficients for each explanatory variable; and ε_i is the residual standard error.

The parameters of the MLR models were estimated with the method of ordinary least squares. We also included the logarithmic transformations of the ALS metrics used as candidates for explanatory variables. The models were fitted in the R environment by means of the STATS package (R Development Core Team 2019). The selection of variables was made from a total enumeration of model candidates with three predictors and, alternatively, with additional dummy variables. The idea of the alternative model was to test the possible improvement in model reliability brought by the available field data from stand databases. The tested dummy variables included field-based information on the soil type (mineral soil or peatland), site fertility (fertile (MT) or poor (VT and CT), and the forest operations (thinning or no thinning). For the MLR models, the residual standard error and the coefficient of determination (R²) were reported. The predictive performances associated with the MLR models were assessed by using leave-one-out cross-validation. The accuracy of the full model and cross-validation predictions was evaluated in terms of the root-mean-square error:where n is the number of plots, y_i is the observed PAI for plot i, and is the predicted PAI for plot i.

Subsequently, the RMSE% was calculated by dividing the RMSE by the observed PAI mean, and then multiplying the result by 100. For cross-validation predictions we also calculated bias.

Our analyses showed that the correlations between the PAI and the ALS metrics are not very strong but adequate for predictive modelling (Appendix Table A1). The strongest correlations (r = −0.53 and r = −0.50) were observed with the standard deviation of the last () and the first () echo intensities, respectively. Figure 1 shows that there is a strong correlation between the PAI and the but quite a lot of variation also. The next strongest correlations were found between the PAI and the highest height percentiles of the first echoes. The effective LAI had only a weak correlation with the PAI (r = 0.13).

The models constructed are presented in Table 2. In the model using ALS information only, the logarithm of the metric having the second highest correlation with the PAI was included (). The predictors and are the same metrics but computed from the first and the last echoes, respectively. Together, they describe the difference between the first and the last echoes by using certain weights (estimated coefficients). In conclusion, the smaller the difference, the larger the PAI. The relationship between the observed and the predicted PAI, obtained by using ALS information, is presented in Fig. 2.

In the model using both ALS and stand database data as explanatory variables, the behavior of ALS metrics was logical, i.e., the signs were similar to those in the first models. Two of the dummy variables considered were statistically significant and improved the model reliability. Both dummy variables also had positive signs, i.e., the PAI was larger in plots on mineral soil or where thinnings were planned to be conducted. The dummy variable for site fertility was not statistically significant as an explanatory variable. The relationship between the observed and the predicted PAI in the alternative model is presented in Fig. 3.

The cross-validated RMSEs of the PAI predictions (Table 3) showed that the effect of cross-validation was minor in comparison with the use of full data. The additional stand register information decreased the RMSE% value by 2.7 percentage units. The bias in cross-validation was practically zero. The models’ residual behavior was also examined in relation to observed stand ages and planned thinning operations (Fig. 4). The behavior of both models seems to be logical, without any trends at different stand ages.

This study was an empirical examination of the predicted mean PAI of the width of tree rings at the plot level over a period of 10 years. The requirement for this approach is that ALS data are available at the beginning of the growth period. Field measurements of growth are then conducted, either by drilling at the end of the growth period, as was done in this study, or by measuring the field plots at the beginning and the end of the growth period. Our approach of using ALS data to predict future growth thus requires that ALS data acquisition and field measurements are made at different points in time. Multitemporal ALS data cannot be utilized in an application of this type, in which the aim is to predict future growth. Of course, if the change in ALS metrics is available before the actual growth period, this multitemporal information can also be utilized in the modelling. So far, growth attributes have been examined by means of multitemporal ALS data (Tompalski et al. 2021), but empirical growth modelling based on a single acquisition of remote-sensing data has hardly been done at all.

The error rate in predicting the PAI for the next 10 years by means of ALS data was about 18%–21% at the plot level. This error rate is therefore comparable with a typical volume modelling scenario by means of ALS (e.g., Næsset 2002). For growth attributes, there are no comparable studies as yet (Tompalski et al. 2021). In general, the error rates obtained are also comparable with commonly used forest growth models (Hynynen 1995; Hynynen et al. 2002), but a direct comparison with any growth model based on field information is impossible. Growth modelling always entails a high level of uncertainty. This is because information on the growing conditions (soil, climate, competition, health, genotype) is not available in the applications and because the actual measurement of growth is also prone to errors.

The main result of this study was that the PAI was best modelled in terms of intensities, height percentiles, and variables obtained from stand databases (site and management operations). The role of intensity information was particularly marked in the results, whereas bincentiles were not so useful. To improve model performance, from the RMSE% of 21.2% to 18.5% in this case, information available in stand databases (soil type and management operations in this case) can be used.

The usefulness of the standard deviation of the intensities is probably related to canopy density. Weak intensities typically come from the canopy and strong intensities from the ground echoes, because there was no height threshold in the calculation of the ALS metrics. Thus, plots in mature stands (>50 years) that had undergone thinnings tended to have higher , because both strong single echoes from the ground and weak first-of-many echoes from pulses that were partially intercepted by the canopy were common. Plots with small were typically relatively young (<35 years old) forests with high densities (>1000 stems·ha⁻¹), where most echoes were recorded from the canopy and had smaller intensities. Plots in young stands typically grow quicker than plots in mature stands, and thus had a negative correlation (r = −0.50) with the PAI.

While ALS intensity variables and variables related to the depth of ALS pulse penetration in the canopy correlated strongly with the PAI, our LAI proxy variable had a poor correlation with the PAI and was therefore not included as a predictor variable. This finding suggests that effective LAI estimates based on simple canopy gap frequency observations may not be optimal for prediction of forest growth. This observation is somewhat contradictory, as global biosphere models quantify forest growth through net primary productivity models, which are based on the LAI. A possible explanation is that an uncorrected effective LAI, which we used, may not have a sufficiently high correlation with the true LAI in the forests we studied. We were unable to try clumping or woody area corrections here, for we had no optical LAI measurements from the time of the ALS data acquisition. Therefore, an earlier effective LAI model was transferred from another area located about 280 km away (Korhonen et al. 2011). Our findings also suggest that ALS data may contain other kinds of information that correlate better with forest growth than the effective LAI. For example, the difference between the first and the last echo height percentiles quantifies the depth of the ALS pulse penetration into the canopy, which should be related to foliage density.

We also utilized categorical field information in our PAI modelling. For soil type (mineral soil or peatland) and site fertility (fertile or poor), this information is available in stand databases, for management inventories have collected this information for decades. Soil type information is also publicly available in a database hosted by the Geological Survey of Finland. For information on forest operations, our modelling data includes the thinnings conducted, and when the model is applied to predict future growth, corresponding thinnings are assumed to be carried out in the future, too. However, variables of this type are considered in simulations of forest management plans and are usually applied in conventional growth models (Hynynen et al. 2002). It can thus be concluded that the stand database information used in our study is easily available for applications related to growth prediction in Finland and to improving the model performance. On the other hand, we did not use variables such as basal area or dominant height, which would have required field measurements.

This is the first time that ALS-based PAI models are presented. Such models may be applied in forest management planning. It should be remembered, however, that when the models are applied, up-to-date ALS data are needed for predicting future growth. An alternative to using our models is using ALS-based forest attributes as input to existing growth simulators (Lamb et al. 2018). According to our results, ALS data seem to include enough information to be used in forest growth prediction as such, i.e., the ALS variables describing the canopy structure can be used as predictors of growth similar to conventional field measurements of tree stock. The model behavior was also found to be logical at different stand ages (Fig. 4). We further observed that ALS data may include predictors of growth more effective than the effective LAI.

On closer inspection, our data show a distribution of stand ages that is typical for managed forests in Finland, and the mean volume corresponds to the values obtained in the National Forest Inventory of Finland, though very high values are missing (Korhonen et al. 2017). Our data are thus representative of the pine-dominated areas of the middle boreal zone. However, there are still some shortcomings. As can be seen from the data description (Table 1; Appendix Figs. A1a–A1d), the data lack more fertile spruce-dominated stands, which are usually found in the southern boreal zone. Because of this, the growth rates are rather small. Further studies should therefore use data from more fertile stands with higher growth rates. Also, larger sets of data should be used to avoid the risk of model over-fitting. This study was the first one on the topic, carried out with a limited local data set.

Conventional stand-level growth models are based on field-measured forest attributes, such as tree age, dominant height, stem density, basal area, and site index (Burkhart and Tome 2012). In general, the disadvantage of empirical models currently applied in forest inventories is that they have been constructed by using earlier measurements and are not capable of adapting to changing growth conditions without proper calibration with recent measurements (Eerikäinen 2002). It is evident that the traditional empirical models require major modifications before they can deal with changing circumstances. One modification possibility is to increase the use of up-to-date and local remote-sensing data in the development of new growth modelling applications.