# Scaling Approach for Estimating Stand Sapwood Area from Leaf Area Index in Five Boreal species

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{sp}) versus sapwood area (SA

_{sp}) to estimate a single tree’s leaf area (where the tree’s sapwood area is the predictor). Linear models for about 20 conifers, such as Scots pine (Pinus sylvestris L.) [2]; Ponderosa pine (Pinus ponderosa Douglas ex Lawson) [3]; Loblolly pine (Pinus taeda L.) [4]; Douglas fir (Pseudotsuga menziesii (Mirbel) Franco) [3,5,6]; Lodgepole pine (Pinus contorta) [7,8,9,10]; Engelmann spruce and Subalpine fir (Picea engelmanni Parry ex Engelmann and Abies lasiocarpa (Hooker) Nuttall) [10]; Pinyon pine (Pinus edulis Engelmann) and One-seeded Juniper (Juniperus monosperma (Engelmann) Sargent) [11]; and Balsam fir (Abies balsamea (L.) Mill.) [12,13], were reported. While deciduous species haven’t been studied as greatly as coniferous species, there are some published works for Mountain ash (Eucalyptus regnans F. Muell.) [14]; Trembling aspen (Populus tremuloides) [10]; and Cherry bark oak (Quercus falcate Q.Pagoda) and Green ash (Fraxinus pensylvanica Marshall) [15]. In this last work, the model for predicting leaf area was improved by not only having sapwood area as a predictor, but by adding total height and live crown ratio to the model [15].

_{sp}:SA

_{sp}regression models (linear and non-linear). The discrepancy between results have helped to understand that the LA

_{sp}:SA

_{sp}relationship is driven by site conditions such as stand density [16,17,18], climatic factors [19], and physical characteristics [20]. Naturally, it is expected that the LA

_{sp}:SA

_{sp}relationship is species-specific [20], but this has not always been observed. For example, the Lodgepole pine (Pinus contorta) LA

_{sp}:SA

_{sp}allometric relationship is linear [21] but in another study, a nonlinear regression better explained this relationship [10]. Thus, while in theory the LA

_{sp}:SA

_{sp}relationship is positioned as linear, this could change due to site conditions.

_{sp}:SA

_{sp}relationship. More recent studies attempted to model Eucaliptus regnans’ stand sapwood area-basal area ratios by scaling up individual stumps’ visual heartwood-sapwood differentiation and using digital photography. They obtained a linear model with a coefficient of determination of 0.85 [27]). Modeled sapwood area at the stand level using LIDAR images and individual tree detection algorithms were used to predict sapwood area/basal area relationships at the stand level [28]. Their predicted values drew correlation coefficients that varied from 0.5 to 0.84, where the most adequate fit was with a regression model that combined LIDAR derived data and observed basal area. A mathematical model of a catchment’s basal area-sapwood area was created by indirect estimates through LIDAR imaging [29].

_{sp}:SA

_{sp}relationship and therefore, the calculation of the error propagated to the final estimate will determine the quality of an allometric model and help detect if the model contributes to over- or under-estimates. A thorough statistical analysis to determine the normality of each dataset, will help to determine if a regression model fits the dataset or whether other statistical/mathematical models should be considered. Hence, the objectives of this paper are: (1) To create reliable regression models—if adequate for each dataset—to estimate sapwood area at the breast height for Populus tremuloides, Pinus banksiana, Pinus contorta, Picea glauca, and Picea mariana; (2) to develop appropriate scaling LA-SA relationships for forest stands comprised of a mixture of these species; and (3) to determine the absolute error propagated while scaling sapwood depth from an individual tree up to the stand level.

## 2. Materials and Methods

#### 2.1. Model Approach and Sampling Design

_{plot}equal to the summation of all the individual trees’ sapwood cross-sectional area (SA

_{i}) inside the stand.

_{i}is species specific for each tree i in the stand containing n trees of different species. Similarly, the single tree’s leaf area (LA

_{plot}) will be the summation of all trees’ leaf area inside the stand.

_{OB}) data so that Equation (3) below could be used to estimate SA

_{i}:

^{th}tree’s average sapwood depth and ${D}_{O{B}_{i}}$ is the i

^{th}tree’s diameter at breast height. Equation (3) calculates SA

_{i}as the region lying between two concentric circles within a tree’s cross-section. The outermost circle borders the bark and vascular cambium, while the innermost one bounds the heartwood. These circles are naturally irregular but tree trunks are treated as having a cylindrical shape. The models obtained were used to estimate every tree’s sapwood area SA

_{i}inside the delimited stand. Equation (1) is then used to estimate the stand level sapwood area (SA

_{plot}) of that single tree representing the whole stand. The correlation between species specific leaf area and sapwood area (LA

_{sp}:SA

_{sp}) and a mathematical scaling approach detailed in Section 3 were used to estimate LA

_{plot}:SA

_{plot}.

_{plot}, was obtained by measuring the Leaf Area Index (LAI) by light transmission, and the surface ground area of interest. Stands of four different sizes are used to validate the LA

_{sp}:SA

_{sp}relationship. Four stands were 60 × 60 m, and nine were 10 × 10 m. These stands were located in the Sibbald Areas of Kananaskis Country, Alberta, Canada. The species composition of these stands was either dominated by deciduous trees (mainly Populus tremulolides), or coniferous trees (Pinus contorta and Picea glauca). Figure 1 and Figure 2 show the location and delimitation of these stands. Two more stands were delimited at Whitecourt, in northern Alberta: One was dominated by Pinus banksiana individuals (20 × 20 m) and one was dominated by Picea mariana (15 × 15 m) individuals. The stands whose species composition was dominated by a conifer tree were labelled as “coniferous”, and for those whose species composition was dominated by a deciduous tree were labeled as “deciduous”. The 10 × 10 m stands were distinguished from the larger ones ($\ge 300\mathrm{m}$

^{2}) by adding a prime symbol in front of their assigned number. Field data collected at each stand included: (a) Number of trees per stand, (b) species identification, and outer bark diameter at breast height for every tree inside the stand, and (c) Leaf Area Index for the stand. LAI was measured in the 60 × 60 m stands using the Tracing Radiation and Architecture Canopies (TRAC, 3rd Wave Engineering Co.; Nepean, Ontario, Canada) device. The Canopy Analyzer LAI-2000 (LI-COR Incorporated; Lincoln, Nebraska, US) was used to measure LAI in the stands of 20 × 20 m and 15 × 15 m, located in Whitecourt.

#### 2.2. Treatment of Saplings

_{OB}and $\overline{sd}$, or between D

_{OB}and cross-sectional area per species (SA

_{sp}) will be different than for mature trees and thus, were treated separately. Furthermore, due to their size and composition, saplings were considered part of the understory, and this study focused on scaling allometric correlations of the overstory. Saplings were considered those trees with D

_{OB}ranging between 2.41 cm and 10.2 cm, and heights between 38.1 cm and 76.2 cm. Trees found inside of the stands with a D

_{OB}≤ 10cm were considered saplings, and were excluded from all allometric correlations.

#### 2.3. Statistical Analysis

_{plot}and LAI, and between SA

_{plot}and LA

_{plot}). The pairwise comparison consisted of comparing the parameters’ C.I.s to see if they overlapped or not. This was another way to test if there was correlation between the variables. Because they are different parameters and the units differ, it was not suitable to use mean values or standard deviations to test the similarity between the two sample populations [39,40,41].

_{1}= ${\chi}_{\nu ,1-\alpha /2}^{2}$ and u

_{2}= ${\chi}_{\nu ,\alpha /2}^{2}$. Therefore, K is a function of the sample standard deviation (S), and the sample mean ($\overline{X}$).

## 3. Model Implementation and Data Results

_{OB}results obtained for each species sampled to create the tree-level allometric correlations reported in [31].

#### 3.1. Tree-Level Allometric Correlations

_{OB}[31]. This was also true of Picea mariana. Picea glauca and Populous tremuloides did however, show significant, positive linear correlations between $\overline{sd}$ and D

_{OB}. For Picea glauca, the relationship from [31] and used here was:

_{OB}(that is, whether there is no relationship or a significant linear relationship like those shown in Equations (6) and (7)), the methods for scaling up to the stand level using D

_{OB}required a species-based approach. Thus, for Picea glauca and Populous tremuloides, Equations (6) and (7) were used to determine stand level $\overline{sd}$ estimates from stand level estimates of D

_{OB}, respectively. For those species without a strong tree-level linear correlation, a simple stand average, i.e., $\overline{sd}$, was proposed.

#### 3.2. Stand-Level Allometric Correlations

#### 3.2.1. Scaling Up Sapwood Area from the Tree to the Stand Level

_{plot}was performed by fusing two approaches. To estimate the sapwood area at every stand, if Picea glauca and/or Populus tremuloides trees were present, their respective linear model was applied—this was the first scaling approach. But under the presence of Pinus banksiana and/or Pinus contorta and/or Picea mariana, their respective average sapwood area was applied, which is the second scaling approach. Therefore,

_{sp,j}is the total number of trees inside the stand of species j; ${D}_{O{B}_{i,j}}$ is the i

^{th}individual’s D

_{OB}of species j; and ${\overline{sd}}_{i,j}^{\prime}\text{}$ is the i

^{th}individual’s estimated sapwood depth for species j, and estimated for trees of species Picea glauca with Equation (6), or Populus tremuloides with Equation (7). The second term on the right-hand side of Equation (8a) pertains to those species that did not produce a significantly linear model. Thus, M is the number of species k present in the stand with k being Pinus banksiana, Pinus contorta, or Picea mariana. M = 0, 1, 2 or 3; and N

_{sp,k}is the number of trees in the stand of each of these species. Based on previous results [31], it was assumed that the sapwood cross-sectional area for each of these three species remained relatively constant as the tree grew. Therefore, for each of these species k, the average sapwood area was calculated based on results from [31] with important details given in the next paragraph for ${\overline{SA}}_{k}$.

_{OB}. Microscopically differentiated average sapwood depth (averaged over the four cardinal directions) from wood cores obtained for the fives species was correlated with D

_{OB}for each tree in that study. Average sapwood area for each species that did not have a linear relationship between $\overline{sd}$ and D

_{OB}was computed using Equation (9):

_{k}was the number of cored trees in the sample sets of [31]. Values of ${\overline{SA}}_{k}$ and t

_{k}for all five species are reported in Table 1 and [31] provides greater details not contained here.

_{plot}calculated for each 60 × 60 m and 10 × 10 m stand, including tree species, tree quantity, stand D

_{OB}statistics and the error associated with SA

_{plot}, are given in Table 2 and Table 3, respectively. The conifer sites were those sites containing Picea glauca, Pinus contorta, Pinus banksiana, and Picea mariana. The deciduous sites were mainly composed of Populus tremuloides. If deciduous individuals were present in the coniferous stands, their numbers counted for less than 10% of the total tree quantity or were mainly saplings. Such was the case of the site Conifer-5, with a Populus tremuloides tree quantity of 114; however, 92 individuals were saplings. Thus, the count of deciduous trees inside the stand was a small portion of the total in terms of sapwood area contribution. Most of the deciduous sites were 100% pure stands, and if any other tree was present, it counted for less than 5% of the total stand’s tree quantity (e.g., Deciduous-6). Most of the coniferous sites (60 × 60 m and 10 × 10 m) were composed of Picea glauca and Pinus contorta trees. The two pure coniferous sites were Conifer-11 and Conifer-12.

#### 3.2.2. Leaf Area Estimates at the Stand-Level

_{eff}, was measured with the Canopy Analyzer LAI-2000 (LI-COR Incorporated; Lincoln Nebraska, US. To convert LAI

_{eff}to Leaf Area Index (LAI), we applied Chen’s equation [43]:

_{eff}with typical values reported in [45]. The LAI

_{eff}of the Pinus banksiana stand was similar to an intermediate/medium productivity stand (LAI

_{eff}= 2.20) with ${\alpha}_{l}$ of 0.05 and ${\gamma}_{E}$ of 1.35. The Picea mariana stand LAI

_{eff}value was similar to a mature medium/high productivity stand (LAI

_{eff}= 2.78), thus, ${\alpha}_{l}$ is assumed as 0.14 and ${\gamma}_{E}$ as 1.35. Finally, ${\mathsf{\Omega}}_{E}$ was derived from typical values reported by [45] as well; thus, the ${\mathsf{\Omega}}_{E}$ values for Picea mariana and Pinus banksiana were respectively set as 0.65 and 0.75. The fifteen stands estimated LAI (LAI

_{plot}) concur with the previous reported values by [43,45,46].

_{plot}was estimated based on the definition of Leaf Area Index: “The total one-sided (or one half of the total all-sided) green leaf area per unit ground surface area”:

_{plot}. The coniferous 10 × 10 m stands’ areas were adjusted and reported as 150 m

^{2}in order to take into account what is known as the “TRAC footprint”. The TRAC footprint was created by trees with shadows large enough to fall into the delimited stand influencing the TRAC measurements. Thus, the LAI measured in the field belonged to a larger area than the delimited one. This effect was not evident in the 10 × 10 m deciduous stands. Furthermore, the TRAC footprint was influenced by tree height and solar zenith angle (θ) [44]. Therefore, the TRAC footprint was adjusted by assuming that in Kananaskis Country, the coniferous trees’ average height was approximately 15 m, and the solar noon zenith angle was about 45.21$\xb0$ on the date when LAI was measured (day 238 of the year). Therefore, the extent of the footprint (tree height × tanθ) was 15 m. This extent would occur in only one side of the stand giving an LAI for a stand area of 10 × 15 m.

#### 3.2.3. Stand Level Leaf Area Sapwood Area Allometric Correlations

_{plot}and LA

_{plot}(ρ ≈ 0.999), and the p-value that equaled zero gave sufficient evidence to conclude that the correlation was not zero (α = 0.05). Results of the regression analysis supported the decision of fitting a linear model to the data, showing that LA

_{plot}resulted in a significant predictor of SA

_{plot}with a p-value < 0.0001 (α = 0.05). The ANOVA results determined that LA

_{plot}contributes significantly to the model (α = 0.05). The first fitted model (Figure 3) had a high coefficient of determination (R

^{2}= 99.8%) that supported the theory of SA

_{plot}being fairly well explained by a linear model. The R

^{2}

_{adj}(99.8%) was close in value to the R

^{2}. The R

^{2}

_{pred}(57.77%) was weak with a large difference from R

^{2}

_{adj}. Thus, there was a slight indication of one value inflating the prediction, and thus, this model might not be suitable for other stands. The list of unusual observations draws attention to the large influence that the Deciduous-6 site gives to the model, considering it was an unusual observation. Even if the observation was not considered an outlier, it was removed from the sample set, and the regression model was fitted with only the four observations. In the second regression attempt (Figure 4), all the coefficients of determination values were lower than the ones of the first model. The R

^{2}was high (99.2%), and the R

^{2}

_{pred}(79.5%) was in reasonable agreement with the R

^{2}

_{adj}(98.78%). Thus, the second model was proposed for practical use.

_{plot}and LA

_{plot}estimates for the 10 × 10 m and 60 × 60 m stands are given in Table 5. For all coniferous sites, there was a strong linear correlation between the SA

_{plot}and the LA

_{plot}, and the p-value supports that the correlation is not zero. However, if a regression model was derived by using both sample sets (10 × 10 m and 60 × 60 m stands), the lack-of-fit test is significant at a p-value of 0.019. The lack-of-fit test suggested a possible curvature in the model and that some other type of model should be fitted. It was assumed that the mismatch between the two data sets was due to the overestimation of LAI due to the influence of the footprint at the 10 × 10 m scale. Therefore, the sapwood area for the 10 × 10 m stands were underestimated between 20% and 29.6%. Hence, in the case of the coniferous sites, the obtained values for the 10 × 10 m stands were not suitable for combination with the 60 × 60 m stands because of the footprint caused by the canopy type (which was not randomly distributed, that is, it was clumped, and had large open areas that allow trees outside of the stand to reflect their shadows inside of it).

_{plot}is a significant predictor of the SA

_{plot}(α = 0.05). However, the model’s R

^{2}

_{pred}for the 10 × 10 m stands denote inadequacy for future predictions, and the R

^{2}

_{pred}(38.37%) significantly differs from the R

^{2}

_{adj}. The regression model for the 60 × 60 m stands, however, show a better agreement between its coefficients of determination (Figure 6). Still the difference between R

^{2}

_{adj}and the R

^{2}

_{pred}was large (68.60%), but the model adequacy check gave enough evidence to support the decision for fitting a linear model to the 60 × 60 m data set. Both models have similar slopes that differ by just about 0.37 cm

^{2}.

#### 3.2.4. COV Confidence Intervals

_{plot}, LAI, and LA

_{plot}.

_{plot}, SA

_{plot}, and LAI confidence intervals were not significantly different; therefore, this suggested that there may be correlations amongst these scaling factors. For the deciduous data set, the LA

_{plot}and SA

_{plot}confidence intervals were not significantly different, while the LAI confidence interval was significantly different from the LA

_{plot}and SA

_{plot}confidence intervals. Therefore, this may be an indication of a correlation between LA

_{plot}and SA

_{plot}but there should be no correlation between SA

_{plot}and LAI in the deciduous data set. These results were in reasonable agreement with the results obtained with the Pearson’s correlation hypothesis test and the regression analysis.

#### 3.3. Estimates of Error Propagation

_{plot}estimates (ΔSA

_{plot}) was calculated based on the rules of error propagation that are derived from a Taylor series [47]. Equation (8a) describes SA

_{plot}as the summation of each tree’s SA, thus, ΔSA

_{plot}will be given by the summation of each tree’s error contribution to SA:

^{th}tree’s D

_{OB}and estimated $\overline{s{d}_{i}}$, respectively. The measurement of D

_{OB}were carefully verified by measuring the circumference of the trees at breast height on the same tree, 50 times. Two trees were measured in this exercise. The average error calculated was $\pm $0.0024 m.

_{plot}is:

_{plot}was estimated by the following equation:

^{2}; $\Delta {\overline{SA}}_{sp}$ for the Picea mariana sample set was also 0.0002 m

^{2}. Table 2 and Table 3 report ΔSA

_{plot}for the coniferous and deciduous sites, respectively.

_{plot}(ΔLA

_{plot}):

_{plot}was given by:

_{plot}was ±334.80 m

^{2}and ±138.26 m

^{2}for the 415 m

^{2}stand. A coniferous stand of 60 × 60 m had a ΔA

_{plot}of ±152.40 m

^{2}. Notice that ΔA

_{plot}of the stands named Conifer-11 and Conifer-12 (from Whitecourt) were ±50.8 m

^{2}and ±44.45 m

^{2}, respectively (because they had a smaller surface area). For the 10 × 10 m deciduous stands, ΔA

_{plot}equaled ±1.00 m. The errors on LA

_{plot}estimates are given in Table 4. Notice that the ΔLA

_{plot}became larger as the stand size increased, being more notorious in the larger stands. In addition, the contribution of ΔLAI to ΔA

_{plot}was small, but still the size of the stand influenced the first term of the Equation (21); however, if LAI increased in large stands, then ΔA

_{plot}became large (e.g., Conifer-4, Deciduous-6).

_{plot}for deciduous and coniferous stands using the obtained linear models, establishes that SA

_{plot}= f(LA

_{plot}). Thus, the error propagation on the linear models follows:

_{plot}produced the following:

_{plot}= 0.00127ΔLA

_{plot}

_{plot}was:

_{plot}= 0.000312ΔLA

_{plot}

## 4. Discussion and Conclusions

_{plot}will influence transpiration values if used to scale tree sap flow measurements. Since the accuracy of water balance components is crucial in this area of work, the authors believe that determining SA, SA

_{plot}, LA and LA

_{plot}propagated errors are fundamental to any such research and modelling. A number of studies have already highlighted the relevance of creating reliable allometric models, and have analyzed the error associated with their allometric correlations in order to support their reliability [26,49,50,51].

_{OB}. In this study, D

_{OB}was not an adequate sapwood area predictor of Pinus banksiana, Pinus contorta and Picea mariana species. As a result, scaling cross-sectional sapwood area to the stand-level was approached by combining the estimates of SA obtained with the regression models for Picea glauca and Populus tremuloides, and by using an average of the sapwood area of the remaining three species in a combined approach that scaled up sapwood area from a single tree to the stand scale. To the authors’ knowledge, the use of average sapwood area has not been previously studied as an option for scaling key, characteristic dimensions of trees. This combined approach gives reliable SA

_{plot}estimates that were significantly correlated to LA

_{plot}estimates derived from measurements of LAI. The final relationship (for both groups conifers and deciduous) allowed the development of linear models for predicting SA

_{plot}as function of LA

_{plot}. We attribute the reliability of the average sapwood area values to the careful and detailed methods that were used to measure a single tree’s sapwood depth, and that contributed to an error that was almost negligible [31]. This statement was supported by a more recent research study that reached similar conclusions regarding accurate measures of sapwood depth [52].

_{plot}estimates were mainly influenced by the size of the stand that in turn influenced the LA

_{plot}values—the larger the plot, the more the associated error with LA

_{plot}. This error (ΔLA

_{plot}) had an impact on the estimates of SA

_{plot}having LA

_{plot}as predictor, and prevented stronger regression models by combining the 10 × 10 m and the 60 × 60 m coniferous stands. On the contrary, in the case of the Populus tremuloides, the addition of stands of a size in between 10 × 10 m and 60 × 60 m would improve the model even further and may allow it to be applicable for use on other data sets; and perhaps even allow the addition of the stand Deciduous-6 to the model. Another important point is that the reduction of error on leaf area estimates depends on accurate delimitation of the stands, and as the stand’s size increases, it is more complicated to retain accurate stand delimitation. Still, stands larger than 10 × 10 m are needed in order to limit discrepancies associated with the footprint on LAI. Even though small stands give the smallest errors, there are large discrepancies between estimates of LA

_{plot}and SA

_{plot}due to the footprint influence. Consequently, we consider the analysis of the regression model for the 10 × 10 m stands helps to support the reliability of the 60 × 60 m linear models (since both follow the same linear pattern and the slope is practically the same). For future modelling, it might be suitable to add the slope as another predictor of sapwood area to the stand level, as suggested by [53] who determined that it is the slope that determines the correlation between stand-level leaf area and sapwood area. The authors recommend that at least for conifer trees, it is preferred to use stands that are bigger than 100 m

^{2}, and by trying to reduce the footprint influence on LAI derived from optical measurements. Furthermore, attention to the accuracy in the relationship between D

_{OB}and sd cannot be understated. In a simple computation to determine SA in the plots when simply using an average sapwood area (Equation (9)) for all species as opposed to Equation (9) only for Pinus contorta, Pinus banksiana and Picea mariana and the appropriate linear form of Equation (8) for Populus and Picea glauca, significant overestimates of SA were found (results not shown here). This in turn created an overestimate of the slope in the LA:SA models (as in Figure 3, Figure 4, Figure 5 and Figure 6) for each set of plots.

_{OB}and LA allometries. Thus, any attempt to use the reported correlations in this paper for other estimates should do so for similar site conditions, topographic and climatic characteristics. In this study, it was possible to aggregate cross-sectional sapwood area from the tree to the stand level in a mixed forest by differentiating between deciduous and coniferous groups of trees, and by combining two different approaches, with an error that is considered negligible.

_{plot}and LA

_{plot}relationship is maintained at larger scales in this particular area and for the five studied species. There is still some variation that is not explained by the models. Thus, it is recommended that allometric characteristics of the trees, such as crown class, soil moisture or even vapor pressure deficit and maximum summer temperature as suggested by [56], could be introduced in the allometry by season, in order to observe what other factors influences SA

_{plot}.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Geographical location of coniferous plots. The plots are in the Sibbald area, Kananaskis Country.

**Figure 2.**Geographical location of deciduous plots. The plots are in the Sibbald areas, south-east of Barrier Lake (Kananaskis Country).

**Figure 3.**Fitted linear regression model for Populus tremuloides predicted SA

_{plot}in relation to its LA

_{plot}. This model includes all 60 × 60 m and 10 × 10 m stands.

**Figure 4.**Fitted linear regression model for Populus tremuloides predicted SA

_{plot}in relation to its LA

_{plot}. This model does not include the stand Deciduous-6.

**Figure 5.**Fitted linear regression model for the 10 × 10 m stands of conifers, SA

_{plot}in relation to its LA

_{plot}.

**Figure 6.**Fitted linear regression model for the 60 × 60 m stands of conifers, SA

_{plot}in relation to its LA

_{plot}.

**Table 1.**Values of average tree-level sapwood area for each species computed with data from [31]. Only for the first three species on the list, ${\overline{SA}}_{k}$ was used to estimate stand level (SA) in Equation (8b).

Species (k) | ${\mathit{t}}_{\mathit{k}}$ | $\overline{\mathit{S}{\mathit{A}}_{\mathit{k}}}$ (cm^{2}) |
---|---|---|

Pinus banksiana and Pinus contorta | 33 | 176.47 |

Picea mariana | 21 | 213.57 |

Populus tremuloides | 26 | 277.13 |

Picea glauca | 17 | 277.52 |

**Table 2.**Descriptive statistics of the 60 × 60 m stands located in the Sibbald areas of Kananaskis Country, Alberta, and Whitecourt, Alberta. Tree quantity is either N

_{sp,k}or N

_{sp,j}depending on the species; SA

_{sp}is either SA

_{j}or SA

_{k}in Equation (8b), depending on the species, ΔSA

_{plot}is the absolute error associated with SA

_{plot}. D

_{OB}units are in cm, and all areas are in units of m

^{2}.

Plot | Tree species | No. of Trees | Max. D_{OB} | Min. D_{OB} | Avg. D_{OB} | SA_{sp} | SA_{plot} | ∆SA_{plot} |
---|---|---|---|---|---|---|---|---|

Conifer-4 ^{1} | Picea glauca | 434 | 43.3 | 2.2 | 13.14 | 2.92 | ||

Pinus contorta | 276 | 33.42 | 5.73 | 20.15 | 4.87 | 7.79 | ± 0.03 | |

Conifer-5 ^{1} | Picea glauca | 164 | 48.38 | 2.86 | 18.31 | 2.29 | ||

Pinus contorta | 48 | 26.1 | 1.59 | 14.09 | 0.85 | |||

Populus tremuloides | 114 | 19.42 | 2.86 | 7.23 | 0.14 | 3.28 | ± 0.03 | |

Conifer-11 ^{2} | Pinus banksiana | 129 | 25.15 | 6.37 | 16.57 | 2.28 | 2.28 | ± 0.03 |

Conifer-12 ^{2} | Picea mariana | 60 | 23.55 | 5.09 | 15.69 | 1.28 | 1.28 | ± 0.01 |

Deciduous-1 ^{1} | Populus tremuloides | 83 | 25.46 | 9.55 | 18.57 | 1.45 | 1.45 | ± 0.01 |

Deciduous-6 ^{1} | Populus tremuloides | 498 | 31.19 | 8.91 | 19.1 | 9.37 | ||

Picea glauca | 14 | 48.38 | 7 | 23.4 | 0.18 | 9.55 | ± 0.08 |

^{1}Indicates Sibbald region of Kananaskis Country and

^{2}indicates Whitecourt region.

**Table 3.**Descriptive statistics of the 10 × 10 m stands (indicated with a prime symbol) located in the Sibbald areas of Kananaskis Country, Alberta. Note, ΔSA

_{plot}is the absolute error associated with SA

_{plot}. The error propagation estimation is detailed in Section 3.3. D

_{OB}units are in cm, and all areas are in units of m

^{2}.

Plot | Tree Species | No. of Trees | Max. D_{OB} | Min. D_{OB} | Avg. D_{OB} | SA_{sp} | SA_{plot} | ∆SA_{plot} |
---|---|---|---|---|---|---|---|---|

Conifer-1’ | Picea glauca | 29 | 24.51 | 5.091 | 6.53 | 0.16 | ||

Pinus contorta | 12 | 26.74 | 14.01 | 19.89 | 0.21 | 0.37 | ± 0.001 | |

Conifer-2’ | Pice glauca | 15 | 27.06 | 7.641 | 14.88 | 0.21 | ||

Pinus contorta | 9 | 27.37 | 16.23 | 20.23 | 0.16 | 0.37 | ± 0.001 | |

Conifer-3’ | Picea glauca | 19 | 25.78 | 4.461 | 12.48 | 0.19 | ||

Pinus contorta | 13 | 29.6 | 10.82 | 19.98 | 0.23 | 0.42 | ± 0.0007 | |

Conifer-4’ | Picea glauca | 9 | 21.33 | 3.501 | 12.59 | 0.04 | ||

Pinus contorta | 14 | 27.06 | 11.78 | 20.35 | 0.25 | 0.29 | ± 0.0003 | |

Conifer-5’ | Picea glauca | 4 | 28.33 | 12.41 | 18.94 | 0.05 | ||

Pinus contorta | 13 | 32.79 | 15.92 | 22.33 | 0.23 | 0.28 | ± 0.0002 | |

Conifer-10’ | Picea glauca | 5 | 33.74 | 5.091 | 16.87 | 0.19 | ||

Pinus contorta | 14 | 34.7 | 12.73 | 21.99 | 0.11 | |||

Populus tremuloides | 1 | 21.01 | 0.02 | 0.32 | ± 0.0005 | |||

Deciduous-7’ | Populus tremuloides | 31 | 32.79 | 9.871 | 17.15 | 0.34 | 0.34 | ± 0.004 |

Deciduous-8’ | Populus tremuloides | 28 | 28.01 | 14.01 | 20.29 | 0.59 | 0.59 | ± 0.005 |

Deciduous-9’ | Populus tremuloides | 22 | 23.24 | 14.64 | 19.92 | 0.43 | 0.43 | ± 0.004 |

**Table 4.**Leaf Area Index (LAI) and estimated LA

_{plot}according to stand size where ΔLA

_{plot}is the absolute error associated with LA

_{plot}. The error propagation estimation is detailed in Section 3.3. Prime symbol indicates 10 × 10 m stands. No prime symbol indicates 60 × 60 m stands.

Site | LAI | Plot Size (m^{2}) | LA_{plot} (m^{2}) | ∆LA_{plot} (m^{2}) |
---|---|---|---|---|

Conifer-1’ | 6.90 | 150 | 1035.00 | ± 19.90 |

Conifer-2’ | 6.04 | 150 | 906 | ± 19.04 |

Conifer-3’ | 6.57 | 150 | 985 | ± 19.57 |

Conifer-4’ | 5.34 | 150 | 801 | ± 18.34 |

Conifer-5’ | 4.51 | 150 | 676.5 | ± 17.51 |

Conifer-10’ | 6.12 | 150 | 918 | ± 19.12 |

Conifer-4 | 5.71 | 3600.00 | 20,556.00 | ± 1338.20 |

Conifer-5 | 2.54 | 3600.00 | 9144.00 | ± 855.10 |

Conifer-11 | 3.76 | 400 | 1502.52 | ± 259.32 |

Conifer-12 | 4.96 | 300 | 1486.97 | ± 242.82 |

Deciduous-1 | 2.64 | 415 | 1093.53 | ± 405.85 |

Deciduous-6 | 3.14 | 3600,00 | 11,304.00 | ± 1144.27 |

Deciduous-7’ | 2.30 | 100 | 230 | ± 12.30 |

Deciduous-8’ | 3.57 | 100 | 357 | ± 13.57 |

Deciduous-9’ | 3.22 | 100 | 322 | ± 13.22 |

**Table 5.**Estimated sapwood area and their respective leaf area per stand, conifer sites. The first six sites are of size 10 × 10 m while the last four are of 60 × 60 m.

Site | SA_{plot} (m^{2}) | LA_{plot} (m^{2}) | Pearson’s Correlation Coefficient, (p-Value) |
---|---|---|---|

Conifer-1’ | 0.37 | 1035 | |

Conifer-2’ | 0.37 | 906 | |

Conifer-3’ | 0.42 | 985.5 | |

Conifer-4’ | 0.29 | 801 | |

Conifer-5’ | 0.28 | 676.5 | |

Conifer-10’ | 0.33 | 918 | |

0.85 ^{1}, (0.033) | |||

Conifer-4 | 7.79 | 20,556.00 | |

Conifer-5 | 3.28 | 9144.00 | |

Conifer-11 | 2.28 | 1502.52 | |

Conifer-12 | 1.28 | 1486.97 | |

0.98 ^{2}, (0.022) | |||

0.97 ^{3}, (<0.001) |

^{1}Correlation between 10 × 10 m stands,

^{2}correlation between 60 × 60 m stands,

^{3}correlation includes all stands.

**Table 6.**Coefficient of variation (COV) results for the coniferous and deciduous stands’ SA

_{plot}, LA

_{plot}and LAI with their 95% confidence intervals (95% C.I.s).

Site Type | Variable | COV | 95% C.L. |
---|---|---|---|

Coniferous | SA_{plot} | 0.72 | 0.4963–1.6222 |

LA_{plot} | 0.79 | 0.5943–1.9426 | |

LAI | 0.32 | 0.2438–0.7976 | |

Deciduous | SA_{plot} | 1.46 | 0.6614–1.7885 |

LA_{plot} | 1.82 | 0.7026–1.8999 | |

LAI | 0.17 | 0.1344–0.3633 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Quiñonez-Piñón, M.R.; Valeo, C.
Scaling Approach for Estimating Stand Sapwood Area from Leaf Area Index in Five Boreal species. *Forests* **2019**, *10*, 829.
https://doi.org/10.3390/f10100829

**AMA Style**

Quiñonez-Piñón MR, Valeo C.
Scaling Approach for Estimating Stand Sapwood Area from Leaf Area Index in Five Boreal species. *Forests*. 2019; 10(10):829.
https://doi.org/10.3390/f10100829

**Chicago/Turabian Style**

Quiñonez-Piñón, M. Rebeca, and Caterina Valeo.
2019. "Scaling Approach for Estimating Stand Sapwood Area from Leaf Area Index in Five Boreal species" *Forests* 10, no. 10: 829.
https://doi.org/10.3390/f10100829