1. Introduction
Forest stands often develop a diversity of canopy structures across space and time. The diversity may result from the natural dynamics in stands through time (e.g., growth, mortality, succession, stand composition), the variability of biophysical factors (e.g., soil, climate, elevation) or human activities [
1,
2]. Boucher et al. [
1] for example, stated that disturbance regimes and climate have an effect on canopy structures. Laflèche et al. [
3] showed that site characteristics, species composition, and climate influence site productivity.
Canopy structures can be described through forest attributes measured during field inventories (e.g., canopy cover, height, diameter, stand volume) or through remote sensing tools such as the light detection and ranging (lidar) [
4]. Lidar is an active sensor which uses pulses of laser light to measure the distance to a target and record the strength of light backscattering from this target. It generates a point cloud which is a three-dimensional representation of the volumetric interaction between pulse photons and the target. It has been extensively used in forestry to describe the vertical structure of stands [
5,
6,
7]. Metrics can be calculated from the point clouds to statistically describe them (e.g., height metrics, canopy cover metrics). They are often used as explanatory variables to model forest attributes such as basal area, timber merchantable volume, biomass, etc. [
8,
9,
10,
11].
Spatially extensive acquisitions of lidar datasets are now possible, making this tool attractive for large-scale inventories [
12,
13]. Such inventories often require several lidar surveys. Combining the resulting datasets is challenging, especially when there is variability amongst the sites distributed across a given survey area, or when time has elapsed between the field inventory and the lidar survey (temporal discrepancy). In this situation, it is difficult to transfer a site-specific model to another location and therein obtain the same prediction accuracy.
Recent research has ways to accurately predict forest attributes from lidar over large-scale areas. Hansen et al. [
2] for example, included biophysical variables (climate, topography, and soil) in their model when predicting lidar canopy height and canopy cover for five ecoregions located along a 4000 km transect. Næsset and Gobakken [
14] and Nilsson et al. [
15] calibrated site-specific models to predict forest attributes from lidar and combined the models’ outputs to make predictions at a large-scale. Their approach allowed for accurate predictions locally but required several models for working at the large-scale level. and opted for a general mixed-effect model to predict timber volume, biomass or dominant height of multiple sites. Both authors obtained an overall goodness comparable to the site-specific (local) models. This approach offered the advantage of building a single predictive model which could be adapted to the specific conditions found in the different sites.
Several questions remain when predicting forest attributes of different sites in an operational context, including the following: (1) Does the combination of multiple lidar datasets in a generalized predictive model increase the bias at each site? (2) Does accounting for the variability in sites limit the model biases at each site? (3) How should forest attributes be predicted outside the range of the studied sites? and (4) Do temporal discrepancies between field and lidar acquisitions have an effect on the model prediction accuracy? This study, therefore, aims at analyzing the effects of variability amongst sites and temporal discrepancies on the prediction accuracy of timber merchantable volume of sites located along a bioclimatic gradient.
4. Discussion
Our study aimed at building a generalized lidar-based model to predict the timber merchantable volume of various study sites located along a gradient of bioclimatic factors. The field and the lidar data were acquired at different dates. We opted for a nonlinear random coefficient model to predict the MV as several studies have shown that mixed-effect models can accurately predict forest attributes both at small and large-scale levels [
32,
33,
34]. The model needed to be adjusted given the variability amongst study sites and the temporal discrepancies.
A crucial step in building the MV models was the search of optimal explanatory variables. The combination of havgf, p2f and hstdf provided the best subset of variables. The addition of a growth adjustment function improved the model significantly (
p-value < 0.0001). This function accounted for the MV growth that occurred during the temporal discrepancy. It also enabled us to accurately combine the different lidar datasets. It included a height variable (havgf) as the effect of time on merchantable volume varies with the stand development stage. This result confirms the need to adjust predictive models when temporal discrepancies occur [
35].
Models 4 and 6b were the best candidate models. Model 4 contained a site random coefficient (
) accounting for the variability amongst sites. The model performed as efficiently as Model 3, which contained several coefficient adjustments (
p-value = 0.9913). This result showed that a local adjustment of canopy height was therefore enough to account for the variability amongst sites. This can be explained by the fact that the correlation between the MV and havgf was high compared to the other explanatory variables (
Figure 2). It was of 0.87 versus 0.41 for p2f and hstdf. Modifying havgf only would, therefore, have a comparable effect to modifying all the model parameters.
Model 4 random coefficients varied with the characteristics of the study sites: they were positive at the Mauricie_south, Mauricie_north and SLSJ_south sites and negative at the Montmorency and the SLSJ_north sites. The Mauricie_south, Mauricie_north and SLSJ_south sites also had higher H–D ratios (H–D = 0.99, 0.98, 0.96;
Table 1) compared to the Montmorency and the SLSJ_north sites (H–D = 0.94 and 0.88). Thinner stems are characterized by higher H–D ratios and have lower merchantable volumes. For a given height, trees were therefore possibly thinner at the Mauricie_south, Mauricie_north and SLSJ_south sites compared to the Montmorency and the SLSJ_north sites. For a given average height, canopy density and canopy structural heterogeneity, havgf needed to be decreased at the Mauricie_south, Mauricie_north and SLSJ_south sites and increased at the Montmorency, SLSJ_north sites when predicting the MV with the same equation.
Table 1 shows a gradient of bioclimatic factors amongst study sites: higher temperatures and gdds were observed at the Mauricie_south, Mauricie_north and SLSJ_south sites compared to the Montmorency and SLSJ_north sites. The random coefficient values (Models 5a and 5b) decreased substantially when a bioclimatic variable was added to the canopy height parameter. This result suggests a correlation between the site variability and the bioclimatic gradient in this case study. The fixed-effect Model 6b which included the elevation variable had a similar prediction accuracy to Model 4 but a lower AIC value. The relationship between the environmental conditions of a study area and the canopy structure variability has also been assessed in other studies [
2,
36]. Gdd is an indicator of accumulated heat and can be correlated with tree growth [
37]. Warmer temperatures and longer growing seasons have a positive effect on tree height growth [
38] as well as lower elevations [
39]. Trees will, therefore, have a higher H–D ratio and a lower merchantable volume for a given height. Conversely, lower gdds or higher elevations have a negative effect on tree height growth. Trees will have a lower H–D ratio and a higher merchantable volume for a given height. The H–D ratio was smallest at the SLSJ_north site and Montmorency sites.
The canopy variability may be due to other factors such as tree mortality, fire disturbance, site species composition, lidar sensor settings, return density, etc. Sites were composed of similar species, predominantly balsam fir and spruce (
Table 1). We tested Models 4 and 6b on a sample of field plots where the proportion of balsam fir was > 60% (256 plots). We obtained similar MV predictions (pseudo-R
2 = 0.87 and 0.86; RSD = 24.4 m
3 ha
−1 and 24.5 m
3 ha
−1 respectively). We, therefore, considered that the species composition had little effect on the MV predictions in this case study.
Several studies have also demonstrated that the lidar settings can have an effect on the precision of derived forest attributes [
40,
41,
42]. The lidar data were acquired separately and with variable acquisition settings in this case study (
Table 2). We could not analyze the settings’ effects on the MV models as we did not have enough datasets to draw conclusions. However, their effects would likely be minor compared to the bioclimatic gradient, which had a direct effect on the MV. Further research should be done on this issue.
Our study has several practical uses in an operational context. It suggests flexible models to predict the merchantable volume in study sites where spatial and temporal variabilities are observed. The proposed models are adaptable enough to combine lidar datasets acquired at different time periods. They can accurately predict the merchantable volume both at local (site-specific) and large-scale levels (multiple sites). Using a random coefficient model, such as Model 4, is more advantageous than building several local lidar-based models when predicting forest attributes at a large-scale level. When the variability amongst sites is related to a bioclimatic gradient, a simpler fixed-effect model, such as Model 6b, could then be used with a similar prediction accuracy. The fixed-effect models offer the advantage to be generalizable to other sites of known gdd/elevation, even when field inventory has not been done. As lidar data will be available for the entire province of Quebec by 2021, new lidar study sites could be tested to confirm the relationship between the bioclimatic gradient and the MV variation. The data could also be combined with satellite data to predict the MV at large scale [
43,
44].