# Accuracy of Double Bark Thickness Estimation Methods Used in Spruce—(Picea abies L. Karst) Timber Production in Czechia

^{*}

## Abstract

**:**

## 1. Introduction

_{0}, p

_{1}, and p

_{2}are parameters of the polynomial function for Norway spruce, which are as follows: p

_{0}= 0.57723, p

_{1}= 0.006897, and p

_{2}= 1.3123; α is the intercept of the linear function; β is the parameter of the univariate linear function; DOB is diameter over bark (mm); V

_{UB}is volume under bark (m

^{3}); l is log length (m).

## 2. Materials and Methods

^{3}per hectare of forest. According to the internal data of the UEF, the use of CTL harvesting technologies has increased over the years, reaching roughly half of the total harvests in 2022. The remainder of the timber was harvested by the tree-length harvesting method, using motor-manual felling and skidding. Both short and long timber of higher grades were trucked to the conversion depot, where they were processed further and fed into the sawmill operated by the UEF.

## 3. Results

^{2}= 0.98, and a significant p-value of 0.0000. The relationship was represented by a regression Equation (5):

## 4. Discussion

^{2}of 0.76. Sonmez et al. [59] observed the effects of various factors on double bark thickness and derived prediction models for Picea orientalis (L.). Diameter over bark at breast height explain 50% of the double bark thickness variability at breast height on shady aspects and 68% of the variations in double bark thickness on sun-exposed aspects. According to Sonmez et al. [59], in addition to age and diameter, the aspect of tree growth should be taken into account to estimate the amount of merchantable timber and bark. Several factors, therefore, need to be considered when constructing accurate double bark thickness estimation models.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Regression and correlation analysis between diameter over bark (mm) and diameter under bark (mm).

**Figure 3.**Scatterplot representing the relationship between the diameter over bark and double bark thickness. The scatterplot includes the estimates provided by the polynomial and linear models from measured over-bark diameter data (DBT ED: measured diameter data; DBT LB: linear function; DBT P: polynomial function).

**Figure 4.**Scatterplot representing the relationship between the diameter over bark and double bark thickness. The scatterplot includes the estimates provided by the polynomial and linear models from rounded-down over-bark diameter data. (DBT RD: rounded down diameter data; DBT LB RD: linear estimation based on rounded down data; DBT P RD: polynomial estimation based on rounded down data).

**Figure 5.**Box plots for comparisons of rounded-down (DBT RD) and non-rounded-down (DBT ED) data with relevant polynomial (DBT P or DBT P RD) and linear (DBT LB and DBT LB RD) estimates.

Variable | Descriptive Statistics | ||||||
---|---|---|---|---|---|---|---|

Valid N | Mean | Median | Minimum | Maximum | Std. Dev. | Coef. Var. | |

DOB (mm) | 438 | 294.8 | 290.5 | 163.0 | 492.0 | 60.7 | 20.6 |

DUB (mm) | 438 | 280.8 | 278.2 | 155.0 | 476.0 | 59.3 | 21.1 |

DBT ED (mm) | 438 | 13.9 | 13.0 | 1.5 | 38.0 | 6.1 | 43.6 |

DBT LB (mm) | 438 | 12.1 | 12.0 | 8.6 | 17.4 | 1.6 | 13.4 |

DBT P (mm) | 438 | 11.6 | 11.5 | 8.4 | 17.2 | 1.6 | 13.7 |

DBT RD (mm) | 438 | 8.8 | 8.5 | −6.5 * | 37.5 | 6.8 | 77.9 |

DBT RD LB (mm) | 438 | 11.6 | 12 | 8 | 17 | 1.6 | 14.1 |

DBT RD P (mm) | 438 | 11.2 | 11 | 8 | 17 | 1.6 | 14.7 |

N = 438 | Regression Summary of Dependent Variable: DBT ED (mm) R = 0.28 R ^{2} = 0.08; F(1436) = 39.715; p < 0.00000; Std. Error of Estimate: 5.8179 | |||||
---|---|---|---|---|---|---|

b* | Std. Err. of b* | b | Std. Err. of b | t(436) | p-Value | |

Intercept | 5.404130 | 1.379508 | 3.917432 | 0.000104 | ||

DOB (mm) | 0.288937 | 0.045849 | 0.028884 | 0.004583 | 6.301970 | 0.000000 |

^{2}= coefficient of determination; p-value = serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected; b* = parameter estimates from the model in which we would standardize all regressors so that their mean is equal to zero.

**Table 3.**Results of the regression and correlation analysis between DBT RD (mm) and DOB RD (mm), bold type = statistical significance.

N = 438 | Regression Summary for Dependent Variable: DBT RD (mm) R = 0.30 R ^{2} = 0.09; F(1436) = 44.440; p < 0.00000; Std. Error of Estimate: 6.5675 | |||||
---|---|---|---|---|---|---|

b* | Std. Err. of b* | b | Std. Err. of b | t(436) | p-Value | |

Intercept | −1.11161 | 1.525205 | −0.728829 | 0.466498 | ||

DOB RD (mm) | 0.304135 | 0.045623 | 0.03434 | 0.005152 | 6.666316 | 0.000000 |

^{2}= coefficient of determination; p-value = serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected; b* = parameter estimates from the model in which we would standardize all regressors so that their mean is equal to zero.

**Table 4.**Paired-samples T-test outcomes for the comparisons between the measured and rounded-down double bark thickness (DBT ED and DBT RD, respectively); DBT ED and the linear model (DBT LB), DBT ED and the polynomial model (DBT P) estimates; DBT RD and DBT LB RD and DBT RD and DBT P RD, i.e., the rounded-down data and model estimates.

Paired-Samples t-Test Differences Are Significant on a Level of p < 0.05000 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Variables | Mean | SD | N | Difference | SD Differences | t | SV | p | CI −95.0% | CI +95% |

DBT ED (mm) | 13.919 | 6.070 | ||||||||

DBT RD (mm) | 8.838 | 6.886 | 438 | 5.081 | 2.883 | 36.87 | 438 | 0.00 | 4.810 | 5.351 |

Paired-Samples t-TestFifferences Are Significant on a Level of p < 0.05000 | ||||||||||

Variables | Mean | SD | N | Difference | SD Differences | t | SV | p | CI−95.0% | CI+95% |

DBT ED (mm) | 13.919 | 6.070 | ||||||||

DBT LB (mm) | 12.160 | 1.633 | 438 | 1.759 | 5.812 | 6.33 | 437 | 0.00 | 1.213 | 2.304 |

DBT ED (mm) | 13.919 | 6.070 | ||||||||

DBT P (mm) | 11.672 | 1.599 | 438 | 2.247 | 5.810 | 8.09 | 437 | 0.00 | 1.701 | 2.792 |

Paired-Samples t-TestDifferences Are Significant on a Level of p < 0.05000 | ||||||||||

Variables | Mean | SD | N | Difference | SD Differences | t | SV | p | CI−95.0% | CI+95% |

DBT RD (mm) | 8.838 | 6.886 | ||||||||

DBT LB RD (mm) | 12.023 | 1.640 | 438 | −3.185 | 6.575 | −10.13 | 437 | 0.000 | −3.802 | −2.567 |

DBT RD (mm) | 8.838 | 6.886 | ||||||||

DBT P RD (mm) | 11.541 | 1.597 | 438 | −2.703 | 6.578 | −8.59 | 437 | 0.00 | −3.320 | −2.085 |

Dataset | Error Metric | DBT P (mm) | DBT LB (mm) |
---|---|---|---|

DBT ED (mm) | MAE^{(a)} | 4.835932 | 4.777381 |

MBE^{(b)} | −2.24719 | −1.7591 | |

MAPE^{(c)} | 46.13819 | 47.04241 | |

RMSE^{(d)} | 6.223826 | 6.066472 | |

Dataset | Error metric | DBT P RD (mm) | DBT LB RD (mm) |

DBT RD (mm) | MAE^{(a)} | 5.720047 | 5.89026484 |

MBE^{(b)} | 2.702997 | 3.185274 | |

MAPE^{(c)} | 65.19454385 | 68.8024884 | |

RMSE^{(d)} | 7.105576 | 7.29973099 |

^{(a)}= mean absolute error; MBE

^{(b)}= mean bias error; MAPE

^{(c)}= mean absolute percentage error; RMSE

^{(d)}= root mean square error).

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**MDPI and ACS Style**

Jankovský, M.; Dudáková, Z.; Allman, M.; Dvořák, J.; Peseu, P.O.; Jácome, S.P.G.
Accuracy of Double Bark Thickness Estimation Methods Used in Spruce—(*Picea abies* L. Karst) Timber Production in Czechia. *Forests* **2023**, *14*, 1026.
https://doi.org/10.3390/f14051026

**AMA Style**

Jankovský M, Dudáková Z, Allman M, Dvořák J, Peseu PO, Jácome SPG.
Accuracy of Double Bark Thickness Estimation Methods Used in Spruce—(*Picea abies* L. Karst) Timber Production in Czechia. *Forests*. 2023; 14(5):1026.
https://doi.org/10.3390/f14051026

**Chicago/Turabian Style**

Jankovský, Martin, Zuzana Dudáková, Michal Allman, Jiří Dvořák, Prince Opoku Peseu, and Sandra Paola García Jácome.
2023. "Accuracy of Double Bark Thickness Estimation Methods Used in Spruce—(*Picea abies* L. Karst) Timber Production in Czechia" *Forests* 14, no. 5: 1026.
https://doi.org/10.3390/f14051026