In this study, we studied the effects of climatic factors (temperature, precipitation, solar radiation, relative humidity and wind speed) on the anatomical characteristics of the wood of two eucalyptus clones, GC (Eucalyptus grandis × camuldulensis) and GU (Eucalyptus grandis × urophylla). The first set of data was eleven anatomical characteristics of wood, which were formed daily over a period of five years. The fibers are used for the strength and support of the tree, and the veins are used for nutrition.
To account for the physical characteristics of trees, we included the effect of diameter on breast height, stem radius, daily radial growth, and tree suppression or dominance in the model.
Introduction
For the experiment, two important Sappi hybrids (Eucalyptus grandis × urophylla (GU) and Eucalyptus grandis × camuldulensis (GC)) were established. The Sappi experiment is designed to run over at least 8 years in separate phases. Furthermore, these selected trees were used to investigate the physiological and morphological variables throughout the life of the stand. Graphical assessment of the data was used to identify factors other than climatic variables that could explain the variability of tree anatomical characteristics (i.e. tree age, tree effect).
ARIMA modeling of wood anatomical features was used to find a linear relationship between wood properties and climate variables (to assess lag effects).
Preliminary Data Analysis
Data Reduction Using Principal Component Analysis
- Theory of principal component analysis
- Application of principal component analysis for wood anatomy
All principal component analyzes were based on the correlation matrix R of 11 fiber and vessel characteristics to ensure that the 11 variables contribute equally to PC. This justified the use of principal component analysis to reduce the dimensionality of the data on the original 11 fiber and vessel features. 13 Similarly, principal component analysis of phase II to phase IV data on fiber and vessel properties was performed for both GC and GU clones.
The results show that for both clones the first four PCs explain more than 94% of the total variation in the data.
Graphical assessment
- Graphical assessment of the tree and age of tree effects on the wood anatomical
- Graphical assessment of the climatic variable effects on the wood anatomical
Similar to phase I, FD appears to neither increase nor decrease with tree age, suggesting the absence of a linear age effect on FD. However, for stages III and IV, FW appears to be neither increasing nor decreasing with tree age, suggesting the absence of linear age effect on FW. Similar to phase I, VD appears to neither increase nor decrease with tree age, suggesting the absence of a linear age effect on VD.
Furthermore, VF appears to neither increase nor decrease with tree age, indicating the absence of a linear effect of age on VF.
ARIMA Modelling for wood anatomical properties
Theory of ARIMA models
- Definitions and notation
- ARIMA models and modelling
- Model estimation and diagnostics
In model (3.9), the current value Xt of the time series is regressed on the current and past random errors q (Vandaele 1983). According to (Wei 1990), the linear model for Yt as a function of the explanatory series {Xt} is given by. Then the cross-correlation function and the transfer function are contaminated by the autocorrelation structure of the explanatory series {Xt}.
27 One of the formal tests of the null hypothesis that the time series is white noise is the portmanteau test (Box and Jenkins 1970).
Results of the ARIMA modelling approach
- The effects of lagged temperature on fibre and vessel characteristics
- The effects of lagged rainfall on fibre and vessel measurements
- The effects of lagged solar radiation on fibre and vessel measurements
- The effects of lagged relative humidity on fibre and vessel measurements
- The effects of lagged wind speed on fibre and vessel measurements
This means that there was a linear relationship between the fiber dimension series and the lagged temperature series for Stage III GC. This means that there was a linear relationship between the vessel dimension series and the lagged temperature series for Phase III GU. This means that there was a linear relationship between the ship frequency series and the lagged temperature series for Phase I GU.
This result indicates that there was no linear relationship between the fiber wall array and the.
Assessment of climatic factors affecting the wood anatomy
Linear Mixed model
- Estimation of the fixed effects and the variance components
- Covariance structures
- Model reduction
- Assessing the goodness-of-fit of the model
Before estimating the fixed effects β, it is necessary to assume that the vector of the variance components α = (i°,i, i, … , i)′ is known. The vector of the fixed effects β can be estimated using the method of maximum likelihood (Davis 2002). Therefore it is important to estimate the variance components i° and the i explicitly taking into account the loss of the degrees of freedom involved in the estimation of the fixed effects (Verbeke and Molenberghs 2000).
To use the maximum likelihood (ML) estimation method, it is necessary to assume the probability distribution of the data. The ML estimates of the variance components are values of the components that maximize the marginal likelihood function. Fixed effects estimation can be done using the ML method and not using the REML method.
Furthermore, when the data are balanced, the ANOVA and the REML estimates of the variance components are identical. When fitting linear mixed models to the data, the choice of the covariance structures for both the random errors and the random effects is important. Therefore, for the VN structure, there are no mathematical restrictions imposed on the elements of the covariance matrix.
In most cases, histograms and distribution plots of random components and residuals are often used for diagnostic purposes. However, histograms of residuals can be used to check for normality of random effects and error terms.
Application of the linear mixed model to the wood anatomy data
- The effect of categorized climatic variables on the wood anatomy
- The assessment of the continuous climatic variables on the wood anatomy
- Comparison of the analysis of the categorical and continuous climatic variables
This means that the mean difference between FW for GC and GU depends on the level combination. That is, the mean difference between FW for GC and GU depends on the combination of levels by season, holding other effects constant. This means that the mean difference between FW for GC depends on the combination of season level and precipitation, holding other effects constant.
Therefore, the average difference between the FWs for GC and GU depends on the combination of the seasonal solar radiation levels, keeping the other effects constant. This means that the average difference between the FWs for GC depends on the combination of the seasonal levels and the wind speed, keeping the other effects constant. Therefore, the average difference between the FWs for GC depends on the combination of the seasonal levels per temperature at lag 13, keeping other effects constant.
This means the average difference between the FW for GU depends on the combination of the levels of season by solar radiation at lag 28 holding the other effects constant. This means the average difference between the FW for GC depends on the combination of the levels of temperature and rainfall holding the other effects constant. This means the average difference between the FW for GC depends on the combination of the levels of solar radiation and wind speed holding the other effects constant.
Similarly, the combined effect of day 5 temperature and season was significant for Phase II. Furthermore, the combined effect of day 7 temperature and season was found to be significant only for Stage III.
Assessment of tree height, daily increment, radius and climatic factors on wood anatomy
The effect of the dominance/suppression of the tree
Finally, for Phase IV, four trees were dominant for each clone and three trees for GC and four trees for GU were suppressed. Therefore, the information on dominance and suppressed trees will be added to the longitudinal linear mixed model obtained from Chapter 4.
The effect of daily increment, radius and diameter at breast height for wood anatomical
- Using categorical climatic variables
- Using continuous climatic variables
On the other hand, the combined effect of 23rd relative humidity and season was found to be significant for both Phase II clones. On the other hand, the combined effect of season and wind speed was found to be significant for Stage III GC. On the other hand, the results for the random effects for Phases II to IV are shown in Table 5.5.
On the other hand, for phase II GC there was variability for the combined effect of wood and age. On the other hand, the combined effect of season and rainfall was found to be significant for phase II and phase III. On the other hand, the combined effect of seasonal and solar radiation was found to be significant only for phase III GU.
The combined effect of square root of age and season was found to be significant for Phase II and III. Furthermore, the combined effect of rainfall and season was found to be significant only for Phase II. On the other hand, the results for the random effects for Phases II to IV are presented in Table 5.9.
The combined effect of season and relative humidity was found to be significant only for Stage III GU. In addition, the combined effect of solar radiation and season was found to be significant only for Phase II GC.
Comparison of the analysis of the categorical and continuous climatic variables
113 four PCs were found as the square root of age by season interaction and DBH. In summary, as we have seen in the previous sections, it was found that for fiber and vessel characteristics of Eucalyptus tree (FW, FD, VD and VF) the number of significant two-way climate interaction effects decreases as phase increases. Therefore, as we have seen in this chapter, it was found that for fiber and vessel characteristics of eucalyptus (FW, FD, VD and VF) the number of significant two-way climate interaction effects decreases as phase increases.
This result shows that each stage and each clone has different patterns for each variable (FW, FD, VD and VF).
Summary, conclusions and recommendation
Graphic evaluations of wood anatomical characteristics show that trees neither increase nor decrease with age. From the analysis, the lag order of climate variables was found, which is significantly related to FW, FD, VD and VF. We assessed the influence of climate variables by classifying daily climate measures into high, normal and low.
118 From the fitted model analysis, the only joint effect for FW, FD, VD and VF was found to be the joint effect of the square root of age and season. The results of the random effects in the mixed model show that there was significant tree-to-tree FW variability for phase I, phase II GU and phase III GU. In general, summer and autumn are found to be the best seasons to produce greater fiber and vessel characteristics for the two Eucalyptus clones.
But when the tree matures, it can withstand all the climatic conditions of Zululand. The non-significance of climate effects could indicate that climate variables and fiber/vein characteristics of the two Eucalyptus clones are complex non-linear relationships.
