1. Introduction
Tree height and diameter at breast height (DBH) are two of the more fundamental measurements in forest inventories and provide the basis for many other computations (e.g., basal area, volume, biomass, carbon stock, stand growth,
etc.) [
1,
2]. While tree height may be directly estimated from various remote sensing data (e.g., aerial or satellite images, airborne laser scanning,
etc.), direct estimation of e.g., DBH, tree volume and tree biomass in most cases is not possible. Hence, the determination of these variables using remote sensing methods is usually done by estimation models (allometric equations) in which one or more variables (e.g., tree height, crown diameter or crown area) that may be easily estimated from remote sensing data are the most commonly used independent variables (predictors) [
3].
Research on tree allometry,
i.e., on relationships between dependent and independent variables used in estimation models has been therefore the object of numerous studies. Crown diameter, crown area and tree height are the most commonly used variables in modeling of DBH [
4,
5,
6], stem volume [
6,
7,
8,
9,
10] or tree aboveground biomass [
7,
11] for remote sensing-based inventory. However, in some cases, inclusion of additional variables (e.g., stand density, stand age, soil type, elevation,
etc.) may considerably improve the estimates [
12,
13,
14]. For example, Prieditis
et al. [
14] built a model with tree height as the only independent variable which provides reasonably accurate estimates of DBH (
R2 = 0.792), but when the crown diameter and information about tree age and soil type obtained from existing forest database were added to the model, the accuracy of DBH increases (
R2 = 0.872). Furthermore, according to Maltamo
et al. [
12], besides above-mentioned variables, the allometric relationship between main tree parameters (DBH, crown dimensions and tree height) could also be affected by other variables, such as stand silvicultural history, genetic factors of tree seed, tree position in a stand, site fertility, stand development class,
etc. Therefore, which and how many independent variables should be used in allometric equations are very important issues in modeling of tree characteristics.
Estimation models may be built using field measurement [
4,
5,
6,
13,
14] or combination of field and remote sensing measurement [
8,
9]. In that case positions of trees in the field have to be measured with high precision and determined on remote sensing data which often is not easy [
10].
European black pine (
Pinus nigra Arn.) is an important tree species of the Mediterranean and Sub-Mediterranean regions, occurring in the discontinuous area which includes Southern Europe (from Spain to Turkey), Minor Asia, and North-Western Africa [
15,
16]. Due to its discontinuous and wide distribution, black pine is a very variable species in regards of its morphological, anatomical and physiological characteristics and therefore occurs in a large number of subspecies, varieties and forms [
17]. In the Mediterranean and Sub-Mediterranean parts of Croatia, European black pine occurs mostly in pure even-aged stands or in forest cultures, but could also form small groups in Sub-Mediterranean deciduous forests and scrubs [
17].
Due to lower commercial values of timber stocks, high costs of classical forest inventory make the management and inventory of Mediterranean forests difficult. Using data from remote sensing could help in reducing the forest inventory costs. Although tree and stand characteristics of European black pine has been widely researched e.g., [
18,
19,
20], to the best of our knowledge there are no adequate allometric equations that may be used for estimation of DBH, tree volume and aboveground biomass of black pine trees using remote sensing data. Therefore, the main aim of this research was to develop models for predicting DBH, merchantable tree volume (V), and aboveground biomass (AGB) of individual black pine trees grown in Sub-Mediterranean Croatian forests which will be suitable for remote sensing-based forest inventories. The purpose of new models is not only to add knowledge about tree allometry of black pine and to help in local forest inventories, but also to facilitate data collection for national reports on biomass and carbon stocks.
2. Materials and Methods
2.1. Research Area
The research was conducted in the state-owned forests of the management unit Borovača, which is located in the Sub-Mediterranean part of Croatia, 30 km north of Split (
Figure 1). Covering the total area of 3804.32 ha, the management unit extends from 43°41′18″ to 43°44′57″ north latitude and from 16°23′38″ to 16°34′11″ east longitude (Transverse Mercator projection, GRS 1980 ellipsoid, Croatian Terrestrial Reference System datum). The research area included 23 subcompartments of pure even-aged stands of European black pine covering all age classes with the exception of the first age class (<20 years). The basic stand structural elements of 23 subcompartments grouped in age classes obtained from valid Forest management plan are shown in
Table 1. Those stands have never been intensively harvested as may be seen from the high values of stand densities.
Figure 1.
The location of the research area. Gray shaded subcompartments were selected for data collection.
Figure 1.
The location of the research area. Gray shaded subcompartments were selected for data collection.
Table 1.
The average values and ranges (in brackets) of basic stand structural parameters of 23 stands (subcompartments) grouped in age classes obtained from valid Forest management plan.
Table 1.
The average values and ranges (in brackets) of basic stand structural parameters of 23 stands (subcompartments) grouped in age classes obtained from valid Forest management plan.
Age Class | Age (years) | Number of Stands | Site Class | Stand Density (Trees·ha−1) | Basal Area (m2·ha−1) | Volume (m3·ha−1) | Annual Increment (m3·ha−1) |
---|
II | 21–40 | 6 | II | 944 | 17.8 | 80.7 | 4.7 |
(794–1186) | (15.5–22.6) | (70.9–105.1) | (3.7–6.2) |
III | 41–60 | 3 | II | 1246 | 34.9 | 278.7 | 6.7 |
(981–1401) | (28.9–38.2) | (298.8–304.1) | (5.5–7.3) |
IV | 61–80 | 6 | II | 876 | 26.7 | 224.2 | 4.2 |
(496–1221) | (17.0–34.2) | (144.6–285.1) | (2.5–5.1) |
V | 81–100 | 6 | II | 493 | 25 | 237.9 | 3.5 |
(348–859) | (21.5–35.4) | (182.8–308.3) | (2.8–5.0) |
VI | 101–120 | 2 | II | 700 | 36.3 | 330.7 | 5.2 |
(681–719) | (34.7–37.9) | (283.7–377.7) | (5.1–5.3) |
The altitude of the selected part of the research area ranges from 460 to 695 m and slopes from 5° to 35° although slopes can locally reach up to 85°. According to Köppen classification, the climate is typical temperate mesothermal with warm and dry summers. The Adriatic Sea is the main factor influencing the climate of the area. Based on the data from 1981 to 2000, the average annual rainfall is 1123 mm with the most precipitation in November (163 mm), and with the lowest precipitation in July (39 mm) and August (56 mm). The annual average temperature is 12.8 °C, with the lowest monthly average of 3.5 °C recorded in January (the coldest month) and the highest monthly average of 23.1°C recorded in July (the warmest month). The meteorological data were obtained from the meteorological station Sinj located about 12 km east of the management unit Borovača. The pine stands in the research area occur on the following soil types: rendzina on dolomite, rendzina on carbonate, and silicate-carbonate regosol [
21].
2.2. Data Collection
Field measurement of tree variables (DBH, tree height, crown diameter) was conducted on the sample of 501 randomly selected black pine trees distributed throughout the research area (23 subcompartments). An attempt was made to achieve an equal distribution of sampled trees within all age classes and regular spatial distribution throughout the research area as well as proportional participation of the diameter degrees over the sample DBH distribution. From each age class approximately 100 trees were sampled. The following variables were measured for all trees in the sample: (i) DBH, by using a calliper with a centimeter graduation; (ii) tree height (H); and (iii) two mutually perpendicular projections of crown diameter (CD) on the ground, both (H and CD) using a Vertex III hypsometer with a precision of 0.1 m. The edges of the visible light part of the crown (the part of the crown that is not overlapped by the crown of another tree and for which may be assumed that is visible on the aerial or satellite images) were projected on the ground in two mutually perpendicular directions. The lengths of both projections were measured from edge to edge through the crown center. The CD was calculated as the average of two measured projections.
The position (x, y coordinates) of each tree was recorded with a GPS receiver. The positional (horizontal) accuracy quoted by the manufacturer of the MobileMapper 6 GPS receiver (Magellan Navigation Inc., Santa Clara, CA, USA) is 2–5 m for ideal conditions (e.g., open sky, a substantial number of available satellites and their geometry, etc.).
Additional stand parameters, namely distance to the closest tree (DCT) and number of the trees in the circle of 5 m radius, were detected for each tree in the sample. Detected number of trees in the circle of 5 m radius was then used to calculate stand density (N) in terms of number of trees per ha (trees·ha−1) for each tree. Stand age (SA) was obtained from the Forest management plan.
Furthermore, additional site variables (altitude, slope, aspect) were derived for each tree based on GPS recorded tree’s coordinates overlaid upon generated digital terrain model (DTM). The DTM, that is a regular grid (raster) with 1 m cell size was generated from triangulated irregular network (TIN) created from digital terrain data (breaklines and mass points) using software QGIS 2.4.0. The digital terrain data used for TIN creation were obtained from the Croatian State Geodetic Administration (Product Specification 301D150).
The merchantable tree volume (V), comprising of stemwood and branchwood up to 7 cm overbark diameter measured on thinner end, was calculated for each tree from field-measured DBH and H using the Schumacher-Hall function [
22] and parameters from Croatian black pine volume tables [
23] (Equation (1)). The black pine tables were built using a destructive sampling of 843 trees from forest cultures and pure even-aged stands of black pine, mainly located in the Mediterranean and Sub-Mediterranean parts of Croatia. The DBH of sampled trees ranged from 5 cm to 79 cm and heights from 5 m to 39 m.
where V is the merchantable tree volume up to a diameter of 7 cm overbark in m
3,
b0 (0.00004935),
b1 (1.913996) and
b2 (1.021436) are parameters of black pine volume tables,
f (1.003441) is Meyer’s correction factor, DBH is field measured diameter at breast height in cm, and H is field measured tree height in m.
To calculate the aboveground biomass (AGB) of each tree field-measured DBH and equation (Equation 2) applied from the results of research conducted by Zečić and Vusić [
24] were used. Based on 16 randomly selected and destructively sampled black pine trees in the management unit Borovača, with DBH ranging from 11 cm to 30 cm, Zečić and Vusić [
24] determined the relationships between the measured values of individual tree components (merchantable tree volume including bark, branchwood, and smallwood) and the DBH. Branchwood includes branch sections with overbark diameter ranging from 7 cm to 3 cm measured on thinner end, whereas smallwood includes branches and twigs thinner than 3 cm. In order to express biomass in kg for the purpose of this study, both merchantable tree volume including bark and branchwood were multiplied with fresh wood density (WD = 1020 kg·m
−3) of black pine taken from domestic Croatian literature [
25]. Finally, oven-dry aboveground biomass of each tree was obtained by multiplying the biomass sum of all tree components with 0.5. Namely, according to Zečić
et al. [
26] oven-dry biomass of black pine approximately weighs 50% less than its biomass in fresh (green) condition.
where AGB is the oven-dry aboveground biomass in kg, DBH is field measured diameter at breast height in cm, and WD is wood density of black pine in kg·m
−3.
Description and descriptive statistics of variables considered for modeling of DBH, V and AGB are summarized in
Table 2.
Table 2.
Description and descriptive statistics (Mean, SD—standard deviation), Min—minimum), Max—maximum) of variables considered for modeling of diameter at breast height (DBH), merchantable tree volume (V) and aboveground biomass (AGB) of individual black pine trees.
Table 2.
Description and descriptive statistics (Mean, SD—standard deviation), Min—minimum), Max—maximum) of variables considered for modeling of diameter at breast height (DBH), merchantable tree volume (V) and aboveground biomass (AGB) of individual black pine trees.
Group | Variable | Description | Type | Units | Mean | SD | Min | Max |
---|
Tree variables | DBH | Diameter at breast height | Dependent | cm | 22.2 | 7.7 | 10.2 | 55.0 |
V | Merchantable tree volume | Dependent | m3 | 0.32 | 0.28 | 0.02 | 1.97 |
AGB | Aboveground biomass | Dependent | kg | 215.46 | 179.19 | 32.72 | 1467.85 |
H | Tree height | Independent | m | 13.5 | 3.8 | 4.6 | 25.9 |
CD | Crown diameter | Independent | m | 2.88 | 1.41 | 0.42 | 8.35 |
Stand variables | DCT | Distance to the closest tree | Independent | m | 2.05 | 1.05 | 0.30 | 8.82 |
N | Stand density | Independent | trees·ha−1 | 1038 | 580 | 127 | 891 |
SA | Stand age | Independent | years | 70 | 25 | 33 | 102 |
Site variables | Z | Terrain altitude | Independent | m | 564.3 | 45.8 | 467.4 | 694.7 |
S | Terrain slope | Independent | | 21.5 | 17.3 | 0 | 84.8 |
A | Terrain aspect (0–360°) | Independent | | 190.2 | 93.9 | 0 | 357.9 |
2.3. Statistical Analysis
Modeling of DBH, merchantable tree volume (V) and aboveground biomass (AGB) of individual black pine trees was based on linear regression analysis (univariate or multiple) using the program SAS 9.3 [
27] with a 5% significance level considered statistically significant.
Prior to the modeling, normality of dependent variables (DBH, V, AGB) was checked using Shapiro-Wilk test [
28,
29]. To meet the normality condition necessary for further statistical analysis, dependent variables were transformed into appropriate forms.
Potential models of DBH, V and AGB estimation were initially selected using R2 selection method. All combinations of independent variables and their contribution to model goodness expressed through coefficient of determination (R2) were evaluated, and the following criteria for selection of potential models were adopted and used: (i) models with one independent variable were selected if R2 of the model is higher than 0.60; (ii) models with two or more independent variables were selected if inclusion of second or each subsequent variable increases the R2 of the model for more than 0.05.
The selected potential models were then built using univariate or multiple linear regressions depending on a number of independent variables used in modeling. Models were evaluated and compared based on statistical significance of models and theirs parameters, coefficient of determination (R2), root mean square error (RMSEsqrt or RMSEln) calculated from the transformed predicted and observed values of dependent variables, back-transformed root mean square error (RMSEbt), and graphical analysis of the predicted vs. observed values. The RMSEbt was calculated from the predicted and observed dependent variables back-transformed to their original values. For the final recommendation between observed models, practical applicability of the models was also considered.
4. Discussion
The objective of this research was to develop models for predicting three characteristics of individual black pine trees grown in Sub-Mediterranean Croatian forests suitable for remote sensing-based inventory. Models for predicting diameter at breast height (DBH), merchantable tree volume (V) and aboveground biomass (AGB) were developed based on data collected from field measurement, existing database, and DTM using regression analysis, the most commonly used statistical method in forest modeling [
30]. Research by Prieditis
et al. [
14] showed that inclusion of extra variables in addition to H and CD may considerably improve the DBH estimation accuracy. Therefore, within this research, besides H and CD, additional stand and site variables were also considered as potential predictors of DBH, V and AGB of individual black pine trees. The first condition while selecting the potential predictors was that variables should be easy obtainable from remote sensing data. In total, eight variables (H, CD, N, DCT, SA, Z, S, A) were candidates for independent variables (
Table 2).
A preliminary evaluation indicated a non-normality of all dependent variables (DBH, V, AGB). Therefore, prior to modeling, DBH data were transformed into a square root form, while V and AGB data were transformed into a logarithm form. Similar transformations of dependent variables may be observed in other research as well [
4,
6,
9,
10,
14]. However, unlike these researches, the independent variables in this research were not transformed because the relationships between transformed dependent and non-transformed independent variables were linear.
Of all eight independent variables evaluated by
R2 selection method, the three variables (CD, H, SA) have proved to be potentially good predictors of DBH and AGB, whereas four variables (H, CD, N, DCT) were selected as potential predictors of V. According to established criteria, site variables (Z, S, A) were excluded from further analysis in all three cases due to low
R2 value (
R2 < 0.05) and their small contribution to model goodness. The main reason for that may lie in the fact that trees were sampled in only one management unit (locality) where a variation in, e.g., elevation (465–695 m) of location of the sampled trees, is not so high to have great influence on tree characteristics. It may be assumed that site variables could have greater influence in large-scale models (e.g., on national or regional level) for which trees are usually sampled from various locations with various site characteristics. In that case, additional stand (e.g., stand index, site class) or site variables (e.g., soil type) should also be observed and their contribution to model goodness evaluated. Based on the conducted
R2 selection method, the set of three models with identical combination of independent variables was selected as the most appropriate to fit DBH (
Table 3) and AGB (
Table 5) data by regression analysis, whereas for fitting V data the set of four models was selected (
Table 4). Although all models (
Pr > F < 0.001), as well as their parameters (
Pr > |t| < 0.001) were highly significant (
Table 3,
Table 4 and
Table 5), there was a considerable variation among models’ performance (
R2, RMSE
sqrt, RMSE
ln, RMSE
bt) in all three cases.
Results of regression analysis indicated the CD as the most important predictor of both DBH and AGB, and H as the most important V predictor of individual black pine trees. However, according to evaluation statistics (
Table 3,
Table 4 and
Table 5) and graphical analysis (
Figure 2,
Figure 3 and
Figure 4) it seems that neither CD nor H as only predictors are capable to produce highly accurate estimates of DBH, V or AGB. Namely, coefficients of determination (
R2) provided by these models amounted to 0.63, 0.68, and 0.60 for DBH, V, and AGB, respectively. The inclusion of stand variables, namely the inclusion of SA in addition to CD in DBH and AGB models (D2, B2, B3), as well as inclusion of N or DCT in addition to H in V model (V2) improved considerably the models’ performance. The addition of stand variables increased
R2 values in these models to 0.71 (DBH model D2), 0.74 (V model V2), 0.75 (V model V3), and 0.69 (AGB model B2). Therefore, it may be assumed that these models (D2, V2, B2, B3) could provide reasonably accurate estimates of tree DBH, V and AGB. However, among all tested models, the best performance in all three cases (predicting DBH, V and AGB) had the models with both CD and H as individual variables (models D3, V4, B3) producing the highest prediction accuracy (
R2) and the least errors (RMSE
sqrt or RMSE
ln, and RMSE
bt). By using these models the coefficients of determination (
R2) for DBH, V and AGB amounted to 0.83, 0.89 and 0.82, respectively. According to the results of
R2 selection method, the inclusion of any third variable to the models, in addition to CD and H, only slightly improved the models increasing
R2 value of the models for less than 0.02. Therefore, models with tree variables were not included in the regression analysis.
The results of this research are in accordance with numerous other studies on modeling tree variables for remote sensing-based inventory [
4,
5,
6,
10,
31], which also showed that models with H and CD as independent variables are the most suitable for predicting DBH, V or AGB biomass of individual trees. Moreover, similar to this research, some of the mentioned studies [
4,
6] revealed that inclusion of stand or site variables in addition to CD and H brought only small improvements to the model performance, whether for predicting DBH or V. Therefore, inclusion of the third variable in models for predicting DBH, V or AGB in most cases is not necessary, especially for local-scale models. In this research, the addition of stand variables (SA, N, DCT) had greater influence on models’ performance only when they were added as a secondary variable.
Among various remote sensing methods, the developed models could be primarily used for inventories based on measurements from high-resolution digital aerial stereo-images or from airborne laser scanning data (ALS) [
4,
6]. Currently, both methods (digital stereo-photogrammetry and ALS) are suitable and enable estimation of H and CD at tree level [
6,
32]. Research on applicability of high-spatial resolution stereo-images [
33,
34,
35,
36] or high-density ALS data [
14,
37,
38] for H estimation showed that H could be estimated with both methods with high accuracy and with no statistically significant difference compared to field measurements. Unlike H, it is more time-consuming and more difficult to accurately estimate crown size (area or diameter) of individual trees from remote sensing data, especially in densely canopied stands where overlapping of the crowns of the adjacent trees is common and complicates crowns measurement of individual trees [
4,
7,
33,
38,
39]. Besides stand structure, estimated results of crown dimensions could be influenced by the pulse density of airborne laser scanning or spatial resolution of aerial images, but also by the computer algorithm used for crown delineation in cases when automatic method of delineation was used. Namely, visibility and detection of small branches and irregular crown parts are dependent upon resolution of aerial images or density of ALS data [
3,
38]. However, despite potential obstacles in estimating crown dimensions by remote sensing methods, in our case CD should not be omitted from the models, since it was revealed that it is a very strong predictor of all tree dependent variables.
Results of this research are promising and suggest that the use of developed models with H and CD as predictors (models D3, V4, B3), estimated from high-resolution aerial stereo-images or high-density ALS data, could provide reasonably accurate predictions of DBH, V and AGB of individual black pine trees, at least for the forest management unit for which they were developed. This assumption relies on the following reasons: (i) results of regression analysis showed good performance of the proposed models in terms of high prediction accuracy (
R2) and reasonably small errors (RMSE
sqrt or RMSE
ln, and RMSE
bt), and (ii) homogeneous structure of the researched pure even-aged black pine stands may facilitated detection and estimation of H and CD of individual trees. However, this assumption should be further validated by conducting remote sensing-based inventory and by comparing the obtained results with field measurement results. In the case that differences between field- and remote sensing-based estimates of predictor (independent) variables will be detected, it may be necessary to develop calibration functions to adjust any biases in the remote sensing-based estimates [
13]. To examine wider applicability of the proposed models, validation should also be conducted on another Mediterranean and Sub-Mediterranean areas of black pine stands. It should be noted that models developed in this research may not be appropriate in mixed or open forest stands, because the research was conducted in pure, densely canopied stands.