# Assessing Precision in Conventional Field Measurements of Individual Tree Attributes

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## Abstract

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## 1. Introduction

_{obs}), would have an effect on the precision of the measurements.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Workflow for Sampling of the Trees to Be Measured

#### 2.2.1. Sample Plot Measurements

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_{obs}, and height. A Haglöf Mantax Blue calipers and a Haglöf Vertex IV Ultrasonic (Haglöf Sweden AB, Långsele, Sweden) clinometer were used for measuring dbh

_{obs}and height, respectively. The identity of the person doing the measurements was also recorded. The values for dbh

_{obs}were obtained in millimetre scale using cross measurements with calipers. The mensurationist determined the height of 1.3 m above the base of the tree with a standardized 1.3 m long measure and then measured dbh from two directions perpendicular to each other on two sides of the tree (i.e., cross measurement) without any predetermined directions. Before tree height measurements, the clinometer was calibrated to current weather conditions using a measuring tape to measure the distance between the transponder and the clinometer. The clinometer was always calibrated when the mensurationist moved to a new plot or if the weather conditions changed.

_{obs}and height for all the trees on the sample plots was 19.1 cm (range between 5.0 cm and 73.1 cm) and 17.6 m (range between 1.4 m and 37.5 m), respectively.

#### 2.2.2. Sample Trees

_{obs}and height once for all the 9435 trees on 120 field plots, a sub-sample of the 319 trees was selected for re-measurement of the dbh

_{obs}and height and to evaluate variability in the measurements. The sampling of the trees was based on tree species and dbh

_{obs}. These sample trees included 156 Scots pine, 81 Norway spruce and 82 birch (Betula pendula and B. pubescens). The sample trees were measured independently by three other mensurationists to obtain four independent dbh

_{obs}and height measures for each sample tree. Again, dbh

_{obs}was based on cross measurements without any predefined measurement direction. All the mensurationists used measurement devices of same brand and model (i.e., Haglöf Mantax Blue calipers and Haglöf Vertex IV Ultrasonic clinometer) throughout the measurements. The measurement accuracy of the devices was tested with reference measurements and no differences were observed between the measurement devices used. The dbh

_{obs}and height of the sample trees varied between 5.6 cm and 46.6 cm and from 5.0 m to 33.1 m, respectively (Table 1). These trees were located on 12 different field sample plots.

#### 2.3. Evaluation of the Variance in the Field Measurements

_{obs}and height measurements were analyzed by tree species, and dbh- and height-based tree size classes. The sample trees were divided into five classes containing comparably sized trees for analyzing the precision for dbh

_{obs}and height measurements. The aim of this analysis was to investigate whether the variance in measurements changed between differently sized trees. For the dbh, the classes were 5.0–12.9 cm, 13.0–16.9 cm, 17.0–20.9 cm, 21.0–24.9 cm and over 25.0 cm. For the height, the classes were 5.0–14.9 m, 15.0–17.4 m, 17.5–19.9 m, 20.0–22.4 m and over 22.5 m. Classification of a tree into a size class was determined based on mean values of the four measurements. We tested whether the differences between the four measures were statistically significant on 95% level of significance using an analysis of variance (ANOVA). An ANOVA was performed for both dbh

_{obs}and height measurements.

_{n−1}of four dbh

_{obs}and height measurements for every sample tree was calculated using Equation (1).

_{n−1}is the unbiased estimator of standard deviation, n is the number of the measurements, ${x}_{i}$ the measured value and $\overline{x}$ the mean of the measurements. The relative standard deviation s

_{%}was calculated using Equation (2).

_{n−1}is the standard deviation and $\overline{x}$ the mean of the measurements.

_{obs}and height measurements of four separate measurements were calculated for the entire sample, as well as by tree species and for the dbh- and height-based size classes. We also investigated the size of the variation between the minimum and maximum value of the four dbh

_{obs}measurements from each tree. The same investigation was done for the four height measurements. In addition, and to satisfy one of our stated objectives of this study, we investigated how much the standard deviation of dbh measurements varied if only one dbh measurement would have been taken by each mensurationist from all of the trees instead of the dbh

_{obs}(i.e., cross measurements). For this part of the analysis, only the first of the two recorded dbh measurements from each mensurationist was used as the measured dbh value of the tree to simulate a scenario where each mensurationist recorded only one dbh value for each tree.

## 3. Results

_{obs}or height (α = 0.05). For dbh

_{obs}measurements, it was assumed that the means of the dbh

_{obs}measurements by all mensurationists (dbh

_{obsm}) are equal to each other (Equation (3)).

_{obs}-means, the p-values were 0.952, 0.975 and 0.993 for pine, spruce, and birch, respectively.

_{m}) were equal to each other:

_{obs}(i.e., 0.55 cm) was observed for spruce, whereas the largest difference between measured height values was observed for birch (0.82 m), but the differences were not significant (Table 4).

_{obs}and the mean height of all the sample trees were 20.5 cm and 18.8 m, respectively. The means of standard deviations for all dbh

_{obs}and height measurements were 0.3 cm (1.5%) and 0.5 m (2.9%), respectively (Table 5). Analyzed tree-by-tree, the standard deviation in dbh

_{obs}measurements varied from 0 cm to 1.0 cm and in height measurements from 0.1 m to 1.9 m (Figure 2). The relative standard deviation in the dbh

_{obs}and height measurements was smallest for Norway spruce although the absolute standard deviation was smallest for birch in dbh

_{obs}and Scots pine in height (Table 5).

_{obs}values from the same tree among the four measures varied in range from 0 cm to 2.1 cm (Figure 3). For 80.6% of the 319 trees measured, the range in variation remained less than 1.0 cm and for 94.0% less than 1.5 cm. For height, the difference between minimum and maximum values of the four individual measurements from the same tree was from 0.1 m to 4.2 m, respectively (Figure 3). For 73.3% of the trees, the largest difference within the height observations from the same tree was less than 1.5 m.

_{obs}, the standard deviation of the measurements was 0.5 cm (2.2%) (Figure 4). Likewise, the standard deviation was 0.5 cm for all tree species. The difference between the smallest and largest measured dbh value from the same tree varied from 0 cm to 6.6 cm; for 93.4% of the trees, the range of dbh measurements remained less than 2.0 cm.

_{obs}measurements varied between 0.2 cm and 0.4 cm (from 1.4% to 1.9%) in the five dbh-classes and between 0.2 cm and 0.4 cm (from 1.3% to 1.9%) within the five height classes (Table 6 and Table 7). The absolute standard deviation values increased as the dbh increased. The reversed trend was detected with relative standard deviations (Table 6).

_{obs}and height measurements by tree size are plotted in Figure 5.

## 4. Discussion

_{obs}) from the same tree was 2.1 cm. For tree height, the respective difference was 4.2 m. Despite the relatively large maximum differences, it should be noted that for 80.6% of the trees, the range in the dbh

_{obs}measurements was less than 1.0 cm.

_{obs}measurements, there seemed to be very little variation over the entire data set, since the relative standard deviation was only 1.5% which is in line with the results of Hyppönen and Roiko-Jokela [33] who obtained 1.4% standard deviation in dbh measurements. Päivinen et al. [38] have also studied the precision of dbh measurements performed by several mensurationists; the standard deviation for dbh in their study was 0.69 cm (2.8%). In both of the previous studies mentioned, the number of unique trees in the data set was relatively small when compared to this study (n = 319 trees), since the data consisted of only 38 [33] and 64 [38] unique trees. In those studies, the measurements were then repeated several times, to get the total amount of dbh measurements to 540 and 520 measurements, respectively. In our study, spruce had the lowest relative standard deviation in dbh measurements which is supported by the findings of Päivinen et al. [38]. One possible reason for the greater precision found in this study can be related to the nature of spruce bark, since spruce bark is more homogenous than the outer surface of pine or birch trees. In [37], 95% of measured diameters were within 5 cm of the control measurements when the mean dbh was 52.7 cm, whereas Elzinga et al. [32] reported that in dbh measurements, errors greater than 5% may be expected in 5% of measurements. In general, the design of different studies may restrict the comparison of the results to each other if different kinds of measurement devices are used; if the diameter is acquired with single or cross measurement; or if the cardinal directions for caliper measurements are undefined, as it was in this study; or if the height of 1.3 m is marked on the tree or not.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Variation in forest density (Vegetation ratio) and height (Mean canopy height) in the Evo study area. Black dots represent all possible field plots and the red dots describe the 120 field sample plots that were selected.

**Figure 2.**Boxplots demonstrating the variation range of the standard deviation (std) of tree dbh

_{obs}(mean of cross measurements) and height measurements from the sample trees in cm and m, respectively. The standard deviations are presented for all the sample trees as well as separately for the tree species. In the figure, the bottom and the top of the box represent the first and third quartiles and the band inside the box is the median. The ends of the whiskers are within 1.5 interquartile of the lower and upper quartiles. The circles represent outliers.

**Figure 3.**Histograms describing the frequency of largest difference among the sample tree measurements. On left: within the dbh

_{obs}(mean of cross measurements) measurements from the same tree. On right: within the tree height measurements from the same tree.

**Figure 4.**Boxplot describing the standard deviations (std) of sample tree dbh (diameter-at-breast-height) measurements with two different methods. On left, the standard deviation is a result of dbh values acquired using cross-measurements (i.e., dbh

_{obs}), whereas on right, only one dbh measurement per mensurationist was used.

**Figure 5.**Standard deviation of tree dbh (diameter at the breast height) and tree h (height) measurements represented as the function of dbh and h of the sample trees.

**Table 1.**The mean and standard deviation (std) of dbh

_{obs}(diameter-at-breast-height) and height of the sample trees as well as the variation range of dbh and height among the sample trees.

Tree Species | n | mean dbh_{obs} (cm) | std dbh_{obs} (cm) | min dbh_{obs} (cm) | max dbh_{obs} (cm) | mean height (m) | std height (m) | min height (m) | max height (m) |
---|---|---|---|---|---|---|---|---|---|

Scots pine | 156 | 20.1 | 6.9 | 6.2 | 46.6 | 17.7 | 4.3 | 5.0 | 32.1 |

Norway spruce | 81 | 24.8 | 7.8 | 5.6 | 44.5 | 21.7 | 5.7 | 5.2 | 33.1 |

Birch | 82 | 17.0 | 7.1 | 6.2 | 42.7 | 18.0 | 4.4 | 6.9 | 33.1 |

All sample trees | 319 | 20.5 | 7.7 | 5.6 | 46.6 | 18.8 | 5.0 | 5.0 | 33.1 |

**Table 2.**The results of ANOVA analysis for dbh

_{obs}measurements for all sample trees as well as for different tree species with degrees of freedom (Df), sum of squares (Sum Sq), mean squared error (Mean Sq), F-value and p-value.

dbh_{obs} | |||||
---|---|---|---|---|---|

Species | Df | Sum Sq | Mean Sq | F-value | p-value |

All sample trees | 3 | 3194 | 1064.8 | 0.179 | 0.911 |

Scots pine | 3 | 1644 | 548 | 0.114 | 0.952 |

Norway spruce | 3 | 1320 | 440.1 | 0.072 | 0.975 |

Birch | 3 | 459 | 153.1 | 0.031 | 0.993 |

**Table 3.**The results of ANOVA analysis for tree height measurements for all sample trees as well as for different tree species with degrees of freedom (Df), sum of squares (Sum Sq), mean squared error (Mean Sq), F-value and p-value.

Height | |||||
---|---|---|---|---|---|

Species | Df | Sum Sq | Mean Sq | F-value | p-value |

All sample trees | 3 | 13,819 | 4606.3 | 1.832 | 0.140 |

Scots pine | 3 | 6262 | 2087.2 | 1.117 | 0.342 |

Norway spruce | 3 | 4844 | 1614.6 | 0.495 | 0.686 |

Birch | 3 | 3280 | 1093.3 | 0.553 | 0.647 |

**Table 4.**Mean values of dbh

_{obs}(diameter-at-breast-height, cross measurement) and height (h) measurements by different mensurationists.

dbh_{obs} (cm) | ||||
---|---|---|---|---|

Mensurationist 1 | Mensurationist 2 | Mensurationist 3 | Mensurationist 4 | |

Scots pine | 19.95 | 20.03 | 20.09 | 20.38 |

Norway spruce | 24.52 | 24.68 | 24.81 | 25.07 |

Birch | 16.82 | 16.97 | 17.05 | 17.14 |

All sample trees | 20.31 | 20.42 | 20.51 | 20.74 |

h (dm) | ||||

Mensurationist 1 | Mensurationist 2 | Mensurationist 3 | Mensurationist 4 | |

Scots pine | 17.91 | 18.02 | 17.83 | 17.21 |

Norway spruce | 21.77 | 22.12 | 21.69 | 21.05 |

Birch | 18.29 | 18.16 | 18.09 | 17.47 |

All sample trees | 18.99 | 19.10 | 18.88 | 18.25 |

**Table 5.**The species specific means of the standard deviations (std) calculated from the four independent dbh

_{obs}(diameter-at-breast-height) and h (height) observations from each of the sample trees.

Species | n | Std dbh_{obs} (cm) | Std dbh_{obs} (%) | Std h (m) | Std h (%) |
---|---|---|---|---|---|

Scots pine | 156 | 0.3 | 1.6 | 0.5 | 2.7 |

Norway spruce | 81 | 0.3 | 1.3 | 0.6 | 2.6 |

Birch | 82 | 0.3 | 1.5 | 0.7 | 3.6 |

All sample trees | 319 | 0.3 | 1.5 | 0.5 | 2.9 |

**Table 6.**The mean dbh

_{obs}(mean of cross measurements) and h (height) of the five tree size classes that are based on the dbh, as well as the class-wise means of standard deviations (std

_{obs}) calculated from the four observations of dbh

_{obs}and h.

Dbh classes | |||||||
---|---|---|---|---|---|---|---|

dbh_{obs} | h | ||||||

dbh Classes (cm) | n | Mean (cm) | Std_{obs} (cm) | Std_{obs} (%) | Mean (m) | Std_{obs} (m) | Std_{obs} (%) |

5.0–12.9 | 57 | 10.3 | 0.2 | 1.9 | 12.5 | 0.4 | 2.9 |

13.0–16.9 | 61 | 15.1 | 0.2 | 1.5 | 16.4 | 0.5 | 3.0 |

17.0–20.9 | 56 | 19.1 | 0.3 | 1.6 | 18.2 | 0.5 | 2.6 |

21.0–24.9 | 62 | 23.3 | 0.3 | 1.4 | 20.7 | 0.6 | 3.1 |

25.0+ | 83 | 30.3 | 0.4 | 1.4 | 23.9 | 0.7 | 2.8 |

All trees | 319 | 20.5 | 0.3 | 1.5 | 18.8 | 0.5 | 2.9 |

**Table 7.**The mean dbh

_{obs}(mean of cross measurements) and h (height) of five tree size classes that are based on tree height, as well as the class-wise means of standard deviations (std

_{obs}) calculated from the four measurements of dbh

_{obs}and h.

Height classes | |||||||
---|---|---|---|---|---|---|---|

dbh_{obs} | h | ||||||

Height Classes (m) | n | Mean (cm) | Std_{obs} (cm) | Std_{obs} (%) | Mean (m) | Std_{obs} (m) | Std_{obs} (%) |

5.0–14.9 | 63 | 11.6 | 0.2 | 1.9 | 12.0 | 0.4 | 3.0 |

15.0–17.4 | 63 | 17.2 | 0.3 | 1.5 | 16.4 | 0.4 | 2.7 |

17.5–19.9 | 64 | 20.1 | 0.3 | 1.5 | 18.2 | 0.5 | 2.6 |

20.0–22.4 | 44 | 22.2 | 0.3 | 1.3 | 20.8 | 0.7 | 3.4 |

22.5+ | 85 | 29.0 | 0.4 | 1.4 | 25.0 | 0.7 | 2.9 |

All trees | 319 | 20.5 | 0.3 | 1.5 | 18.8 | 0.5 | 2.9 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Luoma, V.; Saarinen, N.; Wulder, M.A.; White, J.C.; Vastaranta, M.; Holopainen, M.; Hyyppä, J. Assessing Precision in Conventional Field Measurements of Individual Tree Attributes. *Forests* **2017**, *8*, 38.
https://doi.org/10.3390/f8020038

**AMA Style**

Luoma V, Saarinen N, Wulder MA, White JC, Vastaranta M, Holopainen M, Hyyppä J. Assessing Precision in Conventional Field Measurements of Individual Tree Attributes. *Forests*. 2017; 8(2):38.
https://doi.org/10.3390/f8020038

**Chicago/Turabian Style**

Luoma, Ville, Ninni Saarinen, Michael A. Wulder, Joanne C. White, Mikko Vastaranta, Markus Holopainen, and Juha Hyyppä. 2017. "Assessing Precision in Conventional Field Measurements of Individual Tree Attributes" *Forests* 8, no. 2: 38.
https://doi.org/10.3390/f8020038