# Predicting Tree Diameter Distributions from Airborne Laser Scanning, SPOT 5 Satellite, and Field Sample Data in the Perm Region, Russia

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## Abstract

**:**

## 1. Introduction

- Relatively even-aged stands: The diameter distributions are unimodal and near normal.
- Absolutely uneven-aged stands: The diameter distributions are “negative-exponential” or “reverse J-shaped”.
- Relatively uneven-aged stands: The tree diameter distributions are multimodal, i.e., with several peaks.

## 2. Materials and Methods

_{k}and V

_{k}, for the set of dependent variables Y and independent variables X, which maximize the correlations between them:

_{k}are the canonical coefficients of dependent variables and γ

_{k}are the canonical coefficients of the independent variables (k = 1, …, s). The most similar neighbors (MSN) distance metric between plot u and plot j derived from canonical correlation analysis is described, as follows [30]:

_{u}is the vector of independent variables from target observation, X

_{j}is the vector of independent variables from the reference observation, Γ is the matrix of canonical coefficients of the independent variables, and Ʌ is the diagonal matrix of squared canonical correlations.

## 3. Results

#### 3.1. Validation within Reference Data

#### 3.2. Validation within Independent Test Data

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Location of the Perm region (

**a**), and magnification of the Perm region, showing the study area inside the Solikamsk forest district (

**b**).

**Figure 2.**Plot-level root-mean-squared error (RMSE) values relative to mean with k-MSN (k most similar neighbor) and sparse Bayesian (SB). V = total stem volume; G = basal area; N = number of stems; H = basal area weighted mean height; and, D = basal area weighted mean diameter.

**Figure 3.**Example of estimated (blue line) and measured (gray histogram) functional group diameter distributions in the test plot, elected as “the best goodness-of-fit” based on Reynolds error indices. The error index values are 17.99, 8.75, 19.77, and 2.07 for (

**a**) Total, (

**b**) Spruce/Fir, (

**c**) Pines, and (

**d**) Broadleaf Group, respectively. For trees with a minimum diameter of 22 cm the error index values are 8.33, 3.77, 8.17, and 0.45 for Total, Spruce/Fir, Pines, and Broadleaf Group, respectively. DBH = diameter at breast height.

**Figure 4.**Example of estimated (blue line) and measured (gray histogram) functional group diameter distributions in the test plot, elected as “the average goodness-of-fit” based on Reynolds error indices. The error index values are 44.64, 58.57, 31.19 and 3.90 for (

**a**) Total, (

**b**) Spruce/Fir, (

**c**) Pines, and (

**d**) Broadleaf Group, respectively. For trees with a minimum diameter of 22 cm the error index values are 8.68, 11.3, 16.47, and 0.80 for Total, Spruce/Fir, Pines, and Broadleaf Group, respectively.

**Figure 5.**Example of estimated (blue line) and measured (gray histogram) species group diameter distributions in the test plot, elected as “the worst goodness-of-fit” based on Reynolds error indices. The error index values are 122.94, 73.89, 41.75 and 24.1 for (

**a**) Total, (

**b**) Spruce/Fir, (

**c**) Pines, and (

**d**) Broadleaf Group, respectively. For trees with a minimum diameter of 22 cm the error index values are 27.13, 13.51, 24.91, and 5.49 for Total, Spruce/Fir, Pines, and Broadleaf Group, respectively.

**Table 1.**Field reference plot statistics and mean values, with standard deviations in parentheses. n = 281.

Variable | Pines | Spruce/Fir | Broadleaf Group | Total |
---|---|---|---|---|

Total stem volume (m^{3} ha^{−1}) | 151.1 (159.6) | 142.7 (141.1) | 68.0 (113.0) | 361.7 (163.3) |

Basal area (m^{2} ha^{−1}) | 14.4 (14.6) | 15.0 (13.1) | 6.9 (10.6) | 36.3 (14.0) |

Number of stems (n ha^{−1}) | 317.0 (409.7) | 618.5 (428.7) | 244.1 (380.7) | 1180.0 (533.0) |

Basal area weighted mean height (m) | 21.7 (4.3) | 16.6 (5.6) | 18.4 (5.2) | 20.4 (3.6) |

Basal area weighted mean diameter (cm) | 28.9 (8.2) | 21.2 (8.8) | 21.5 (8.8) | 26.2 (6.1) |

**Table 2.**Field test data statistics and mean values, with standard deviations in parentheses. n = 18.

Variable | Pines | Spruce/Fir | Broadleaf Group | Total |
---|---|---|---|---|

Total stem volume (m^{3} ha^{−1}) | 276.4 (159.0) | 147.3 (143.2) | 35.7 (130.5) | 459.4 (131.7) |

Basal area (m^{2} ha^{−1}) | 23.1 (12.6) | 13.5 (11.8) | 2.9 (10.3) | 39.5 (9.8) |

Number of stems (n ha^{−1}) | 419.8 (267.3) | 407.6 (253.0) | 34.1 (104.9) | 861.5 (252.1) |

**Table 3.**The RMSE (relative root-mean-squared errors) values and biases relative to mean of test plots (n = 18).

Variable | Pines | Spruce/Fir | Broadleaf Group | Total | ||||
---|---|---|---|---|---|---|---|---|

RMSE | Bias | RMSE | Bias | RMSE | Bias | RMSE | Bias | |

Total stem volume | 0.32 | 0.13 | 0.59 | 0.03 | 1.19 | 0.09 | 0.17 | 0.09 * |

Basal area | 0.30 | 0.02 | 0.53 | −0.10 | 0.97 | −0.09 | 0.14 | −0.03 |

Number of stems | 0.41 | −0.02 | 0.72 | −0.52 ** | 2.33 | −1.73 ** | 0.45 | −0.32 ** |

**Table 4.**The RMSE values and biases relative to mean of test plots considering only trees with a minimum value of diameter at breast height (DBH) of 22 cm (n = 18).

Variable | Pines | Spruce/Fir | Broadleaf Group | Total | ||||
---|---|---|---|---|---|---|---|---|

RMSE | Bias | RMSE | Bias | RMSE | Bias | RMSE | Bias | |

Basal area | 0.31 | 0.03 | 0.62 | 0.03 | 1.33 | 0.17 | 0.15 | 0.04 |

Number of stems | 0.32 | 0.05 | 0.60 | 0.07 | 0.40 | −0.22 * | 0.13 | 0.04 |

**Table 5.**The mean, minimum and maximum Reynolds error index values of test plots for diameter distributions including all diameter classes and diameter classes with a minimum DBH value of 22 cm.

Statistics | Pines | Spruce/Fir | Broadleaf Group | Total | ||||
---|---|---|---|---|---|---|---|---|

All | Min 22 | All | Min 22 | All | Min 22 | All | Min 22 | |

Mean | 28.20 | 15.17 | 48.91 | 10.74 | 10.15 | 2.67 | 66.57 | 15.71 |

Minimum | 8.15 | 5.06 | 8.75 | 1.26 | 1.60 | 0.00 | 17.99 | 8.33 |

Maximum | 46.74 | 28.91 | 97.96 | 26.95 | 52.34 | 24.95 | 122.94 | 27.13 |

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## Share and Cite

**MDPI and ACS Style**

Peuhkurinen, J.; Tokola, T.; Plevak, K.; Sirparanta, S.; Kedrov, A.; Pyankov, S.
Predicting Tree Diameter Distributions from Airborne Laser Scanning, SPOT 5 Satellite, and Field Sample Data in the Perm Region, Russia. *Forests* **2018**, *9*, 639.
https://doi.org/10.3390/f9100639

**AMA Style**

Peuhkurinen J, Tokola T, Plevak K, Sirparanta S, Kedrov A, Pyankov S.
Predicting Tree Diameter Distributions from Airborne Laser Scanning, SPOT 5 Satellite, and Field Sample Data in the Perm Region, Russia. *Forests*. 2018; 9(10):639.
https://doi.org/10.3390/f9100639

**Chicago/Turabian Style**

Peuhkurinen, Jussi, Timo Tokola, Kseniia Plevak, Sanna Sirparanta, Alexander Kedrov, and Sergey Pyankov.
2018. "Predicting Tree Diameter Distributions from Airborne Laser Scanning, SPOT 5 Satellite, and Field Sample Data in the Perm Region, Russia" *Forests* 9, no. 10: 639.
https://doi.org/10.3390/f9100639