A method for estimating tree ring density by coupling CT scanning and ring width measurements: application to the analysis of the ring width–ring density relationship in Picea abies trees

Abstract

Key Message

The original method proposed provides useful data for the analysis of ring density variations in stems, highlighting the particular behaviour observed at the base of the tree.

Abstract

Tree growth in volume and wood density are the two factors that determine tree biomass. They are important for assessing wood quality and resource availability. Analysing and modelling the relationships between these two factors are important for improving silvicultural practices of softwoods like Norway spruce, for which a negative relationship is generally observed between ring width and ring density. We describe an original method for obtaining ring density data (RD) by coupling conventional ring width measurements (RW) and air-dry density measurements obtained with X-ray computer tomography at high-speed but with lower resolution than the RW data. The method was applied to 200 discs of Norway spruce trees sampled in a plantation to assess its relevance. The RW–RD relationship was analysed as a function of cambial age and disc height in the stem. Descriptive statistical models were developed and compared to models in the literature. These models made it possible to analyse the variations of RD as a function of height in the tree at a given cambial age or for a given calendar year and also to observe a shift in the juvenile wood–mature wood boundary between the bottom of the tree and the rest of the stem. The RD– RW relationship was observed in the juvenile wood at the base of the stem but not in the juvenile wood higher up. Furthermore, the juvenile wood formed at the base of the tree was denser than the juvenile wood formed higher up and the mature wood formed at the same height. In conclusion, the proposed method was found to be relevant, especially when wood discs are readily available, and the results obtained highlighted the importance of distinguishing juvenile wood formed at the base of the tree from that formed higher up.

Appendices

Appendix A: Variation of the ring width–ring density relationship with height in the stem

See Fig. 10.

Fig. 10

Air-dry density as a function of ring width for the different estimated heights in the stem (0, 4.5, 9 and 13.5 m). Trend curves for each height level are plotted

Appendix B: Comparison of average air-dry densities between juvenile and mature wood

See Table 5.

Table 5 Average air-dry densities in juvenile and mature wood at each height level and significance of the differences obtained by performing t-tests. Rings less than 10 years old were assumed to belong to juvenile wood. The statistical significance is indicated by: ns: $p\ge 0.05$; *$0.05>p\ge 0.01$; **:$0.01>p\ge 0.001$; ***$p<0.001$

Appendix C: Ring width and density versus calendar year

See Fig. 11.

Fig. 11

Plot of ring width (RW) and density (RD) as a function of calendar year

Appendix D: Variations in the correlation between ring density and ring width as a function of calendar year

See Fig. 12.

Fig. 12

Pearson correlation coefficient between air-dry ring density (RD) and ring width (RW) as a function of calendar year, including all height levels. The coefficients are computed for each year (dashed blue line) and then using a five-year moving window for the computation to obtain a smoothed curve (red line). A 95% confidence band is plotted for the smoothed curve (dashed red line)

Appendix E: Number of annual rings versus height in the stem

See Fig. 13.

Fig. 13

Total number of annual rings measured at each height level in the stem (black circles) and extrapolation (red curve) up to 20 m using the splinefun function of R

Appendix F: Preliminary three-segment model

Ring width and density both decrease over the last years of growth of the sampled trees (Fig. C). The decline seems to occur around year 2010, whatever the height level. For assessing more precisely, the year of decline and verify if it depends on the height a three-segment linear model were fitted. The boundary between segments 1 and 2, supposed to correspond to the juvenile–mature transition, was assumed to depend only on cambial age, whereas the boundary between segments 2 and 3 was assumed to depend on growth year. Eq. F.1 was used to predict density to guarantee the continuity between the 3 segments:

$$\begin{aligned} \begin{array}{ll} d &{}= (a-c) \cdot x_0 + b\\ x_1 &{}= CA - GY + y_1\\ f &{}= (c-e) \cdot x_1 + d\\ \end{array} \qquad WD = \left\{ \begin{array}{ll} a \cdot CA + b, &{} \hbox { if}\ CA \le x_0, \\ c \cdot CA + d, &{} \hbox { if}\ x_0 < CA \le x_1, \\ e \cdot CA + f, &{} \text {otherwise.} \end{array} \right. \end{aligned}$$

(F.1)

where WD is the density, CA the cambial age and GY the growth year of the considered ring. a, b, c, e, $x_0$ and $y_1$ are the fixed parameters to be adjusted. x0 is the cambial age of the juvenile–mature transition and $y_1$ the beginning year of the final decline.

The model was first fitted on the whole data-set, including rings from all 111 selected discs (see “Preliminary data processing”), except ring #1 of each disc. Since the residuals of the general model were strongly dependent on disc height, mainly for the bottom disc, mixed models with random height effects were used to find exponential relations of most of the parameters with height. We finally arrived to the following relations:

$$\begin{aligned} \begin{aligned} x_0&= x_{01} \cdot \exp (H)^{-1} + x_{02} \\ b&= b_1 \cdot \exp (H)^{-1} + b_2 \\ c&= c_1 \cdot \exp (H)^{-0.5}+ c_2 \\ e&= 1 + e_1 \cdot c\\ \end{aligned} \end{aligned}$$

(F.2)

where H is the disc height. $x_{01}$, $x_{02}$, $c_1$, $c_2$, $b_1$, $b_2$ and $e_1$ are fixed parameters to be fitted together with a and $y_1$ of Eq. F.1.

To verify that $y_1$ was not depending of height a mixed model based on Eqs. F.1 and F.2 was adjusted with a random height effect on $y_1$ (Table 6). The anova test from the stats package of R showed that both models were equivalent with $y_1 = 2009.47$ whatever the height level. This suggests that the WD and RW decline begun just after 2009. Figure 14 shows the WD values predicted by this model. Since the CA corresponding to 2009 depends on the disc, the intersect point between segments 2 and 3 also depends on the disc. The RMSE of the model is 45.4 $kg.m^{-3}$ on the full dataset and 45.1 $kg.m^{-3}$ when considering only the rings with $GY \le 2009$.

Fig. 14

Measured values of WD (points) and predicted values by the three-segment model of Eqs. F.1 and F.2 (lines) in relation with CA (left) and GY (right) for each height level

Table 6 Fitted fixed parameters (estimates and standard errors in brackets) of the three-segment model of Eqs. F.1 and F.2

Appendix G: Model #1 taking as input cambial age (CA) and height in the tree (H)

Mixed models including a random effect corresponding to the height level on the parameters of the model of Eq. 1 were fitted one after the other to output the variations with height shown in Fig. 15.

The exponential relations of Eq. 2 were used in model #1 to account for these variations. The parameter a was let constant because the increase of a with the height in the tree led to too erroneous results in extrapolation (i.e., for heights above 13.5 m) with positive values of a, whereas the slope of the first segment must remain negative.

The plot of residuals of model #1 versus ring width (Fig. 16) shows a negative trend, especially for the smallest ring widths, which leads to model #2 including ring width.

Fig. 15

Variation of parameters a, b, c and $x_0$ according to the height in the tree (H) for the piecewise model of Eq. 1 taking as input cambial age (CA) only. The fitted models on plots for b, c and $x_0$ are of the same form as the set of equations given in Eq. 2

Fig. 16

Residuals of the final model #1 as a function of ring width (RW). The trend curve is in red.In green, a model of the form $residuals = f \cdot \exp (RW)^{-1} + g \cdot RW$

Appendix H: Model #2 taking as input cambial age (CA), ring width (RW) and height in the tree (H)

See Fig. 17.

Fig. 17

Residuals of the final model #2 as a function of ring width (RW). The trend curve is in red