4.2. Relationships between Indicator and Scenic Beauty Value
Except for crown width/crown height ratio (CRD), correlations between the rest parameter and SBE value were all found to be significant at the level of
p < 0.01 (
Table 5). In this study, only those parameters have extremely significant correlations (
p < 0.01) with SBE value were involved in factor analysis. In this sense, parameters of crown width/ crown height ratio (CRD) were eliminated as indicators of scenic beauty.
The absolute value of the correlation coefficient can be used as a standard to measure the influence of indicators on SBE value. From large effects to small effects, the indicators are ordered as follows: Annual average increment of diameter (AID) > dead crown/crown ratio (RDCL) > annual average increment of crown (AIC) > crown volume (CV) > crown width/tree height ratio (CED) > crown height/tree height ratio (CR) > stem straight degree (SSD) > diameter/tree height ratio (RDH) > annual average increment of tree height (AIH).
There were various correlations between different indices for isolated trees (
Table 4). Firstly, there was a positive correlation between crown volume (CV) and crown height/tree height ratio (CR), while a negative correlation was observed between dead crown/crown ratio (RDCL) and both crown volume (CV) and crown height/tree height ratio (CR). This might be caused by the increasing canopy area; with the development of live branches, the proportion of dead branches decreases. Secondly, annual average increment of tree height (AIH) has a negative correlation with crown width/tree height ratio (CED) and diameter/tree height ratio (RDH). The value of crown width/tree height ratio and diameter/tree height ratio was obtained from the crown and diameter at breast height (DBH) compared with tree height, thus the values of crown width/tree height ratio and diameter/tree height ratio (RDH) were affected by tree height. Thirdly, a positive correlation was also observed for annual average increment of diameter (AID) and annual average increment of crown (AIC), which means that the crown shows a positive linear trend with changing tree diameter. No more correlations between stem straight degree (SSD) and other indices are observed. There was no evidence to show that bending trees were influenced by the crown size or tree diameter. High correlations suggest that there may be overlap between indicators and one may be redundant for analysis. Hence, factor analysis was used to integrate them into a comprehensive index in order to decrease the amount of variables in the model.
Table 5.
Significance correlations between indicators of individual trees.
Table 5.
Significance correlations between indicators of individual trees.
| SBE | CV | CED | RDH | AIH | AID | AIC | CR | SSD | RDCL | CRD |
---|
SBE | | | | | | | | | | | |
CV | 0.237 ** | | | | | | | | | | |
CED | 0.227 ** | 0.429 ** | | | | | | | | | |
RDH | −0.121 ** | 0.100 * | 0.607 ** | | | | | | | | |
AIH | −0.11 ** | 0.068 | −0.576 ** | −0.816 ** | | | | | | | |
AID | 0.900 ** | 0.195 ** | 0.206 ** | 0.214 ** | 0.099 * | | | | | | |
AIC | 0.267 ** | 0.120 ** | 0.068 | 0.095 * | 0.004 | 0.334 ** | | | | | |
CR | 0.182 ** | 0.622 ** | 0.390 ** | 0.156 ** | −0.073 | 0.143 ** | 0.095 | | | | |
SSD | −0.134 ** | 0.022 | 0.013 | 0.040 | −0.020 | −0.070 | −0.068 | −0.028 | | | |
RDCL | −0.343 ** | −0.358 ** | −0.383 ** | −0.198 ** | 0.151 ** | −0.295 ** | −0.107 * | −0.565 ** | −0.002 | | |
CRD | 0.090 * | −0.051 | 0.034 | −0.032 | −0.064 | 0.121 ** | 0.021 | 0.043 | −0.034 | −0.071 | |
4.3. Established Quality Traits of Isolated Trees with an Index Equation
Results from factor analysis showed that the contribution rates for 4 factors were 25.7%, 25%, 15%, and 11.84%, respectively. Together, the four factors account for 77.54% of the total variance (
Table 6). The results from the rotated component matrix showed that there was a positive correlation between Factor 1 and diameter/tree height ratio (
r = 0.93) and crown width/tree height ratio (
r = 0.72), but the correlation was negative between Factor 1 and annual average increment of tree height (
r = −0.94). Factor 1 reflected the coordination degree between the canopy and the trunk; hence it was defined as the stem-crown harmony index, and expressed as U
1. The relationship between Factor 2 and parameters crown volume (
r = 0.83) and crown height/tree height ratio (
r = 0.89) presented positive correlations, while Factor 2 and dead crown/crown ratio (
r = −0.70) showed a negative correlation. Factor 2 was defined as the crown shape index and is expressed as U
2. The relationship between Factor 3 and annual average increment of diameter (
r = 0.76) and annual average increment of crown (
r = 0.85) showed positive correlations. Because Factor 3 described tree growth, it was defined as growth index, expressed as U
3. The relationship between Factor 4 and stem straight degree (
r = 0.96) presented a positive correlation. Because Factor 4 quantified trunk straightness, it was defined as the stem shape index and expressed as U
4.
Table 6.
Rotated component matrix of 4 factors for 9 indices.
Table 6.
Rotated component matrix of 4 factors for 9 indices.
Index | Factor 1 | Factor 2 | Factor 3 | Factor 4 |
---|
diameter/tree height ratio | 0.93 | 0.09 | 0.12 | −0.02 |
annual average increment of tree height | −0.94 | 0.06 | 0.01 | 0.05 |
annual average increment of diameter | 0.13 | 0.18 | 0.76 | 0.18 |
annual average increment of crown | −0.01 | 0.04 | 0.85 | 0.11 |
stem straight degree | 0.03 | −0.04 | −0.03 | 0.96 |
dead crown/crown ratio | 0.16 | −0.70 | −0.15 | 0.29 |
crown volume | −0.01 | 0.83 | 0.11 | 0.11 |
crown width/tree height ratio | 0.72 | 0.49 | 0.05 | 0.01 |
crown height/tree height ratio | 0.09 | 0.89 | 0.03 | 0.01 |
Cumulative factor contribution (%) | 25.71 | 50.07 | 65.70 | 77.54 |
According to the simplified factor calculation method in this paper, the index Equations are (4)–(7) as follows:
Where CV is crown volume; CED is crown width/ tree height ratio; RDH is diameter/tree height ratio; AIH is annual average increment of tree height; AID is annual average increment of diameter; AIC is annual average increment of crown; CR is crown height/tree height ratio; SSD is stem straight degree; RDCL is dead crown / crown ratio.
4.4 Model of Quality Traits of Individual Trees
The model and all explanatory variables were significant or very significant at the 0.05 level (
Table 7). Based on comparison of
R2 from these models, the precision in the nonlinear model is higher than that of the linear model.
R2 value in multiple linear stepwise regression (0.63) is higher than it in multiple linear regression (0.60). The highest
R2 value (0.66, same in quadratic polynomial regression and quadratic polynomial stepwise regression) were obtained in the nonlinear model.
Table 7.
Regression descriptions of independent variable number, model formula regression, and formula fitting status for quality traits of individual tree indices.
Table 7.
Regression descriptions of independent variable number, model formula regression, and formula fitting status for quality traits of individual tree indices.
Model Type | Model Formula | R2 | F | p |
---|
Multiple linear regression | SBE = 27.47 + 18U1 + 27.95U2 + 150.39U3 − 4.06U4 | 0.60 | 180.25 | 0.001 |
Multiple linear stepwise regression | SBE = 26.98 + 18.02U1 + 27.71U2 + 150.8 U3 | 0.63 | 240.21 | <0.001 |
Quadratic polynomial regression | SBE = 19.45 + 40.41U1 + 9.21U2 + 206.56U3 − 3.18U4 − 68.U12 − 108.45U22 − 88.58U32 − 3.12U42 + 126.73U1U2 − 5.01U1U3 + 22.97U1U4 + 67.57U2U3 − 11.09U2U4 − 13.66U3U4 | 0.66 | 58.29 | <0.001 |
Quadratic polynomial stepwise regression | SBE = 19.84 + 42.98U1 + 206.43U3 − 72.22U12 − 103.48U22 − 93.63U32 + 76.81U2U3 − 14.94U3U4 + 133.22 U1U2 | 0.66 | 103.13 | 0.001 |
The theoretical values of model in theory are values for growth index, crown shape index, stem-crown harmony index and stem shape index, which were equivalent to the maximum SBE value (
Figure 1). The relationship between one comprehensive index and the SBE value can be obtained through setting the other three comprehensive indices to be their theoretical values. Results showed that: (1) with the increasing of stem-crown harmony index, crown shape index, and growth index, SBE increased rapidly; (2) while these three comprehensive indices reached their theoretical values of 0.85, 0.7, 0.96, SBE reached the optimum value of 196.22 in theory; (3) while stem-crown harmony index and crown shape index were more than their theoretical value, SBE decreased dramatically; (4) while growth index was over its theoretical value, SBE decreased slowly; (5) while stem shape index was equal to 0, SBE reached its optimum value, with the increasing value of this index, SBE decreased linearly.
Figure 1.
The relationship between four indices and SBE value change trend.
Figure 1.
The relationship between four indices and SBE value change trend.
This means that in a stand forest, if enough space is available for a single tree, with its continuous growth, the quality of this tree usually develop well. However, for a single tree located in a stand forest, the effects from surrounding trees are unavoidable. There is a competitive relationship between individual tree and trees around it, for example, its crown might be overlapped by surrounding trees—this may easily lead to a disproportional ratio of tree body, and hence cause a decrease in scenic quality. The relationship between SBE value and U4 suggests that trees with straight trunks have high quality.
In addition, the quadratic polynomial could reflect the effect of interaction of indices with SBE grade. In this study, there is a positive correlation between SBE and the interaction of stem-crown harmony index and crown shape index, a positive correlation between SBE and crown shape index and growth index, and a negative correlation between SBE and growth index and stem shape index.
Due to the interaction between growth index and stem shape index was not significant, only one index to be set as its theoretical optimum value was necessary in making clear the influence of the interaction of other two indices on single tree’s beauty quality among stem-crown harmony index, crown shape index and growth index. It can be seen from the chart of interaction between crown shape index and stem-crown harmony index (
Figure 2a), while crown shape index kept stable, with the increasing of harmony index, SBE was increased. While stem-crown harmony index kept stable, with the increasing of crown shape index, SBE increased at first followed by a decrease. While these two both increased, SBE also increased.
In the chart of interaction between crown shape index and growth index (
Figure 2b), while crown shape index kept stable with the increasing of growth index, SBE increased. While growth index kept stable with the increasing of crown shape index, SBE first increased and then decreased. While these two both increased, SBE also increased.
Figure 2.
Effect of interaction between different indices on SBE.
Figure 2.
Effect of interaction between different indices on SBE.