# Reproducibility of Stress Wave and Electrical Resistivity Tomography for Tree Assessment

## Abstract

**:**

## 1. Introduction

_{Loss}) repeated over the course of years. Here, the complete process from the acquisition of raw data (sensor positions, stress wave travel times, electrical resistivities) to the mechanical evaluation of tomograms in terms of loss in section modulus, is analyzed for the first time. This investigation will help risk assessors and tree pathologists alike to evaluate differences between tomograms made by different operators at different times.

## 2. Materials and Methods

#### 2.1. Sites and Trees

#### 2.2. Tomography

^{3}sonic tomograph (argus electronic GmbH, Rostock, Germany), electrical resistivity tomograms were made with either a Picus Treetronic

^{3}(argus electronic GmbH, Rostock, Germany) or a Geotom (GEOLOG2000 System- und Meßtechnik, Starnberg, Germany).

#### 2.3. Treatments

- number of operators: either one, two or three
- installation of nails: either use the same nails, or install new ones
- time between repeated measurement: minutes, weeks, or years
- devices: measurements repeated with the same or a different product

#### 2.4. Statistical Analyses

- Distance between sensors/electrodes, d
- Cross-sectional of the tomogram, A
- Stress wave travel-time, t
- Stress wave velocity, v
- Loss in section modulus, ${Z}_{\mathrm{Loss}}$
- Electrical resistance, Ω
- Electrical resistivity, $\rho $

## 3. Results

#### 3.1. Stress Wave Travel Times, Stress Wave Velocity, and Sensor Positions

#### 3.2. Electrical Resistivity Tomography

## 4. Discussion

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

A | Cross-sectional area, m^{2} |

d | distance |

ERT | Electrical resistivity tomography |

$\rho $ | Electrical resistivity, Ωm |

SoT | Stress wave tomography |

t | Stress wave travel-time, time-of-flight |

v | Stress wave velocity, m s^{−1} |

Z | Section modulus, m^{3} |

${Z}_{\mathrm{Loss}}$ | Loss of section modulus |

## Appendix A

**Table A1.**Statistical analysis of data presented in Figure 2.

CSA 2021 | |
---|---|

Generalized Least Squares | |

CSA 2017 | 0.928 *** (0.907, 0.948) |

Constant | 0.023 *** (0.006, 0.040) |

N | 54 |

**Table A2.**Statistical analysis of data presented in Figure 2.

CSA 2020 | |
---|---|

Generalized Least Squares | |

CSA 2015 | 0.970 *** (0.946, 0.995) |

Constant | 0.015 (−0.011, 0.041) |

N | 29 |

**Table A3.**Statistical analysis of data presented in Figure 2.

Time-of-Flight | |
---|---|

Linear Mixed Effects | |

Year 2019 | 0.0001 *** (0.00004, 0.0001) |

Year 2021 | 0.0001 *** (0.0001, 0.0001) |

d | 0.001 *** (0.001, 0.001) |

Year 2019:d | 0.0002 *** (0.0002, 0.0003) |

Year 2021:d | 0.0002 *** (0.0002, 0.0003) |

Constant | 0.001 *** (0.001, 0.001) |

N | 52,685 |

**Table A4.**Statistical analysis of data presented in Figure 2.

Time-of-Flight | |
---|---|

Linear Mixed Effects | |

Year 2020 | −0.00004 ** (−0.0001, −0.00000) |

d | 0.002 *** (0.001, 0.002) |

Year 2020:d | −0.0004 *** (−0.0005, −0.0003) |

Constant | 0.001 *** (0.001, 0.001) |

N | 15,034 |

**Table A5.**Statistical analysis of data presented in Figure 2.

Velocity | |
---|---|

Linear Mixed Effects | |

Year 2019 | −83.843 *** (−90.023, −77.663) |

Year 2021 | −82.239 *** (−88.714, −75.764) |

d | 385.596 *** (371.721, 399.472) |

Year 2019:d | −116.463 *** (−134.705, −98.221) |

Year 2021:d | −143.544 *** (−162.900, −124.187) |

Constant | 1196.230 *** (1153.759, 1238.701) |

N | 52,685 |

**Table A6.**Statistical analysis of data presented in Figure 2.

Velocity | |
---|---|

Linear Mixed Effects | |

d | −288.695 *** (−308.006, −269.384) |

Year 2020 | −77.531 *** (−104.349, −50.713) |

d:Year 2020 | 61.460 *** (36.516, 86.404) |

Constant | 1178.768 *** (1087.910, 1269.626) |

N | 10,017 |

**Table A7.**Statistical analysis of data presented in Figure 2.

${\mathit{Z}}_{\mathbf{Loss}}$ | |
---|---|

Linear Mixed Effects | |

Constant | 0.344 *** (0.298, 0.389) |

N | 204 |

**Table A8.**Statistical analysis of data presented in Figure 2.

${\mathit{Z}}_{\mathbf{Loss}}$ | |
---|---|

Linear Mixed Effects | |

Year | 0.008 (−0.001, 0.017) |

Constant | −15.038 (−33.223, 3.148) |

N | 51 |

**Table A9.**Statistical analysis of data presented in Figure 3.

Decay in Tomogram | |
---|---|

Linear Mixed Effects | |

Operator 2 | 360.228 (−260.478, 980.935) |

Operator 3 | 45.803 (−574.904, 666.509) |

Site PA | 1042.200 (−236.794, 2321.193) |

Operator 2:Site PA | −1179.744 (−2737.216, 377.729) |

Operator 3:Site PA | −543.753 (−2621.287, 1533.780) |

Constant | 1962.491 ** (159.324, 3765.658) |

N | 33 |

**Table A10.**Statistical analysis of data presented in Figure 4.

Velocity | |
---|---|

Linear Mixed Effects | |

Species Fagus | 101.765 (−27.576, 231.106) |

Species Picea | −6.438 (−212.318, 199.443) |

Species Quercus | 75.431 (−66.245, 217.107) |

d | 5.746 (−42.482, 53.975) |

Species Fagus:d | 254.883 *** (205.903, 303.862) |

Species Picea:d | 188.407 *** (124.049, 252.765) |

Species Quercus:d | −73.114 *** (−123.187, −23.040) |

Constant | 873.880 *** (753.399, 994.362) |

N | 68,451 |

**Table A11.**Statistical analysis of data presented in Figure 4.

R | |
---|---|

Linear Mixed Effects | |

Species Fagus | 30.617 (−106.249, 167.482) |

Species Picea | 702.369 *** (560.373, 844.365) |

Species Quercus | −136.691 * (−292.989, 19.606) |

Section edge | −71.491 (−210.607, 67.624) |

Section middle | −19.997 (−159.113, 119.119) |

Species Fagus:Section edge | 6.014 (−136.829, 148.857) |

Species Picea:Section edge | −560.837 *** (−711.898, −409.776) |

Species Quercus:Section edge | 154.985 * (−11.290, 321.260) |

Species Fagus:Section middle | −41.345 (−184.188, 101.498) |

Species Picea:Section middle | −344.959 *** (−496.020, −193.898) |

Species Quercus:Section middle | 55.538 (−110.737, 221.813) |

Constant | 275.118 *** (144.350, 405.885) |

N | 984 |

**Table A12.**Statistical analysis of data presented in Figure 5.

Velocity | |
---|---|

Linear Mixed Effects | |

Air temperature | −0.678 * (−1.422, 0.066) |

Constant | 900.022 *** (870.669, 929.376) |

N | 215 |

**Table A13.**Statistical analysis of data presented in Figure 5.

R | |
---|---|

Linear Mixed Effects | |

Section middle | 19.333 *** (7.814, 30.851) |

Section edge | 21.844 *** (10.325, 33.364) |

Air temperature | −3.072 *** (−3.741, −2.403) |

Section middle:Air temperature | −0.864 * (−1.764, 0.036) |

Section edge:Air temperature | −1.552 *** (−2.452, −0.652) |

Constant | 248.454 *** (229.677, 267.231) |

N | 648 |

**Table A14.**Statistical analysis of data presented in Figure 7.

R | |
---|---|

Linear Mixed Effects | |

Section middle | 19.333 *** (7.814, 30.851) |

Section edge | 21.844 *** (10.325, 33.364) |

Air temperature | −3.072 *** (−3.741, −2.403) |

Section middle:Air temperature | −0.864 * (−1.764, 0.036) |

Section edge:Air temperature | −1.552 *** (−2.452, −0.652) |

Constant | 248.454 *** (229.677, 267.231) |

N | 648 |

**Table A15.**Statistical analysis of data presented in Figure 8.

R | |
---|---|

Linear Mixed Effects | |

Repetition 2 | −0.066 (−0.211, 0.078) |

Repetition 3 | 0.234 *** (0.089, 0.378) |

Repetition 4 | 0.552 *** (0.408, 0.697) |

Repetition 5 | 0.814 *** (0.670, 0.959) |

Repetition 6 | 1.000 *** (0.855, 1.144) |

Constant | −49.086 *** (−63.570, −34.602) |

N | 5148 |

**Table A16.**Statistical analysis of data presented in Figure 9.

Sap Wood Area | |
---|---|

Linear Mixed Effects | |

Tag | 0.00000 (−0.00000, 0.00000) |

Constant | 0.033 *** (0.026, 0.039) |

N | 96 |

**Table A17.**Statistical analysis of data presented in Figure 11.

Decay in Tomogram | |
---|---|

Linear Mixed Effects | |

Operator 2 | 360.228 (−260.478, 980.935) |

Operator 3 | 45.803 (−574.904, 666.509) |

Site PA | 1042.200 (−236.794, 2321.193) |

Operator 2:Site PA | −1179.744 (−2737.216, 377.729) |

Operator 3:Site PA | −543.753 (−2621.287, 1533.780) |

Constant | 1962.491 ** (159.324, 3765.658) |

N | 33 |

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**Figure 1.**SoT (1. and 3. column) and ERT (2. and 4. column) of two beech trees measured three times by different operators using slightly different sensor positions every time (site KF).

**Figure 2.**Correlation of initial and follow-up measurement of t, A, v and ${Z}_{\mathrm{Loss}}$. Tomography was repeated after 2 and 4 years at site KF and after 5 years at site TG. Dashed line indicates 1:1. Gray: 95% confidence interval.

**Figure 3.**Correlation of defect in tomograms and images of stem cross-sections (

**left**: site PA2, operators used the same nails;

**right**: site AP, operators used different nails at new locations). Dashed line indicates 1:1. Gray: 95% confidence interval.

**Figure 4.**Species differences in stress wave velocity (

**top**) and electrical resistivity (

**bottom**, area-weighted median). “centre” refers to the innermost third of the stem cross-section, “edge” to the outermost third, while “middle” refers to the remainder.

**Figure 5.**Correlation of tangential stress wave velocity (

**top**), electrical resistivity ((

**bottom**), area-weighted median), and air temperature (site KF). “centre” refers to the innermost third of the stem cross-section, “edge” to the outermost third, while “middle” refers to the remainder. Tomography was repeated for 4 years at site KF by different operators placing new sensor positions. Gray: 95% confidence interval.

**Figure 6.**ERT of two spruce trees measured several times in 2021 (

**top**) and on one day in July (

**bottom**), site PA1. Top row: every second measurement with Geotom, all else with Picus Treetronic.

**Figure 7.**Correlation of initial and follow-up measurement of $\rho $. Tomography was repeated after 2 (

**left**), and 4 (

**right**) years at site KF by different operators placing new sensor positions. Here, $\rho $ is the area-weighted median of the outermost 33% of the stem cross-section. Dashed line indicates 1:1. Gray: 95% confidence interval.

**Figure 8.**Course of $\Omega $ from 8 o’clock until noon in four P. abies. Mean and standard error. Site PA1.

**Figure 9.**Sapwood area of 20 spruce trees measured several times in 2021 (site PA1, including only measurements with Picus TreeTronic). Inset shows variation of sapwood area in one individual tree with the largest changes in the sample. Blue: Linear Regression, gray: 95% confidence interval, dashed: 1:1.

**Figure 10.**Effect of variation in length measurements on the standard deviation of ${Z}_{\mathrm{Loss}}$ (blue area). Assumptions: Diameter of cross-section D 1 m, diameter of cavity d 0.7 m. I: Second moment of area (Equation (2)).

**Figure 11.**Correlation of initial ${Z}_{\mathrm{Loss}}$ and its changes at follow-up measurements. Tomography was repeated after 2 (2019), 5 (2020) and 4 (2021) years at sites TG and KF by different operators placing new sensor positions. Gray: 95% confidence interval.

Site | Location ^{1} | Type | Species | n | Operators | Different Nails | Different Devices | Season | Measurements |
---|---|---|---|---|---|---|---|---|---|

KF | Göttingen | open field | Fagus sylvativa L. | 47 | 3 | x | Sep. 2017, Sep.–Dec. 2019, Mar. 2021 | SoT, ERT | |

PA1 | Göttingen | forest | Picea abies (L.) Karst. | 20 | 1 | x | Feb.–Nov. 2021 | ERT | |

TG | Hannover | park | Quercus robur L. | 26 | 2 | x | Oct. 2015, Oct. 2020 | SoT, ERT | |

AP | Heidelberg | roadside | Acer pseudoplatanus L. | 5 | 3 | x | May 2021 | SoT, ERT | |

PA2 | Heidelberg | forest | Picea abies (L.) Karst. | 7 | 3 | Sep. 2014 | SoT |

^{1}All sites in Germany.

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Rust, S.
Reproducibility of Stress Wave and Electrical Resistivity Tomography for Tree Assessment. *Forests* **2022**, *13*, 295.
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**AMA Style**

Rust S.
Reproducibility of Stress Wave and Electrical Resistivity Tomography for Tree Assessment. *Forests*. 2022; 13(2):295.
https://doi.org/10.3390/f13020295

**Chicago/Turabian Style**

Rust, Steffen.
2022. "Reproducibility of Stress Wave and Electrical Resistivity Tomography for Tree Assessment" *Forests* 13, no. 2: 295.
https://doi.org/10.3390/f13020295