Submitted:
06 July 2026
Posted:
08 July 2026
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Abstract
Keywords:
1. Introduction
2. Materials and Methods
2.1. Implementation of Timber Harvesting
2.2. Timber Harvesting Measurements
2.3. Modeling Rut Formation and Rut Depth
3. Results
3.1. Analysis of Rut Formation
3.2. Analysis of Stand and Timber Harvesting Variables
3.3. Modeling


4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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| Observations | Mean | Minimum | Maximum | Total | Plots |
|---|---|---|---|---|---|
| AU | 4.7 | 1 | 14 | 169 | 36 |
| AL | 2.9 | 1 | 8 | 57 | 20 |
| BU | 1.2 | 1 | 2 | 16 | 13 |
| BL | 2 | 1 | 5 | 74 | 37 |
| CU | 1.4 | 1 | 3 | 10 | 7 |
| CL | 1.5 | 1 | 3 | 24 | 16 |
| Load Class | N | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|---|
| t | n | n | m | n | cm | m | m | t |
| 100 | 22 | 3.1 | 5.5 | 1.1 | 10.3 | 2.7 | 1.4 | 63 |
| 200 | 26 | 6.7 | 5.1 | 1.6 | 11.6 | 3.3 | 1.9 | 140 |
| 400 | 9 | 21.3 | 5.2 | 3.2 | 18.0 | 6.5 | 3.0 | 442 |
| All | 57 | 7.6 | 5.2 | 1.7 | 12.2 | 3.6 | 1.9 | 158 |
| Variables | Unit | A | B | p–value |
|---|---|---|---|---|
| Thickness of peat layer | cm | 33.8 | 49.2 | 0.000*** |
| Depth of ground water table | cm | 38.1 | 30.8 | 0.066 |
| Number of ruts | n | 2.6 | 1.3 | 0.006** |
| Total length of the rut | m | 5.3 | 2.9 | 0.009** |
| The rut length when rut depth > 20 | cm | 2.4 | 1.7 | 0.094 |
| Number of passes | n | 15.6 | 4.5 | 0.000*** |
| Number of loaded passes | n | 6.7 | 2.1 | 0.000*** |
| Cumulative load | t | 325 | 93 | 0.000*** |
| Average load | t | 25 | 22.5 | 0.000*** |
| Stand volume | m3ha−1 | 140 | 122 | 0.022* |
| Removal of timber harvesting | m3ha−1 | 69.7 | 67.8 | 0.790 |
| Crown mass | dm3m−2 | 3.7 | 3.8 | 0.382 |
| • Crown mass of pine | dm3m−2 | 0.96 | 1.74 | 0.012* |
| • Crown mass of spruce | dm3m−2 | 1.38 | 0.80 | 0.034* |
| • Crown mass of birch | dm3m−2 | 1.33 | 1.21 | 0.569 |
| Variable | Estimate | Stand. error | df | t-/chi-squared value |
p-value | VIF |
|---|---|---|---|---|---|---|
| Model 1, ROC = 0.63 | ||||||
| Fixed effects | ||||||
| (Intercept) | −1.838E+00 | 5.581E-01 | 376 | −3.293 | 0.001 | – |
| Number of passes | 3.558E-01 | 1.029E-01 | 376 | 3.458 | 0.001** | – |
| Random effects | ||||||
| Sample plot variance | 7.616E-08 | |||||
| Phi | 7.540E-01 | |||||
| Dispersion | 2.457E+00 | |||||
| Model 2, ROC = 0.60 | ||||||
| Fixed effects | ||||||
| (Intercept) | −2.727E+01 | 2.991E+00 | 376 | −9.117 | < 0.001 | – |
| Cumulative total weight load, tons | 2.978E-01 | 1.073E-03 | 376 | 277.570 | 0.000** | – |
| Random effects | ||||||
| Sample plot variance | 5.070E+02 | |||||
| Phi | −6.074E-01 | |||||
| Dispersion | 1.210E-03 | |||||
| Model 3, ROC = 0.67 | ||||||
| Fixed effects | ||||||
| (Intercept) | 6.614E+00 | 2.159E+01 | 372 | 0.306 | 0.760 | – |
| Stand volume, m3ha−1 (ref. V120 m3ha−1) | 2 | 1.836 | 0.399 | 1.14 | ||
|
5.048E+00 | 1.100E+01 | 52 | 0.459 | 0.648 | |
|
−1.156E+01 | 1.285E+01 | 52 | −0.900 | 0.373 | |
| Depth of ground water level, cm | −1.018E+00 | 3.969E-01 | 52 | −2.566 | 0.013* | 1.31 |
| Number of passes | 1.312E+01 | 1.630E-02 | 372 | 804.559 | < 0.001** | 1.00 |
| Number of tree stems ha−1 | −1.339E-02 | 8.152E-03 | 52 | −1.642 | 0.107 | 1.27 |
| Depth of ground water level: Number of passes | −8.447E-02 | 2.910E-04 | 372 | −290.634 | < 0.001 | |
| Number of passes: Number of tree stems | 3.170E-04 | 7.000E-06 | 372 | 44.993 | < 0.001 | |
| Stand volume: Number of passes | 2 | 110370.000 | < 0.001 | |||
|
2.739E+00 | 1.021E-02 | 372 | 268.170 | < 0.001 | |
|
−1.465E-01 | 8.145E-03 | 372 | −17.980 | < 0.001 | |
| Random effects | ||||||
| Sample plot variance | 1.201E+03 | |||||
| Phi | −6.707E-01 | |||||
| Dispersion | 2.079E-06 |
| Variable Fixed effects |
Estimate | Standard error | df | t–/value | p–value | VIF |
|---|---|---|---|---|---|---|
| (Intercept) | 2.46E+00 | 2.69E-01 | 177 | 9.159 | < 0.001 | – |
| Depth of ground water, cm | −6.64E-03 | 3.27E-03 | 34 | −2.029 | 0.050* | 1.56 |
| Depth of peat layer, cm | 5.55E-03 | 2.63E-03 | 34 | 2.105 | 0.043* | 1.54 |
| Number of passes | 6.91E-02 | 2.17E-02 | 177 | 3.181 | 0.002** | 3.03 |
| Total cumulative load, tons | 3.09E-04 | 4.40E-04 | 34 | 0.703 | 0.487 | 3.07 |
| Number of ruts | 7.54E-02 | 2.26E-02 | 177 | 3.335 | 0.001** | 1.23 |
| Number of tree stems ha−1 | −1.21E-04 | 6.14E-05 | 34 | −1.975 | 0.056 | 1.19 |
| Number of passes: Total load | −1.25E-04 | 4.79E-05 | 177 | −2.597 | 0.010 | – |
| Random effects | ||||||
| Random part | ||||||
| Sample plot variance | 1.730E-02 | |||||
| Residual | 5.573E-02 | |||||
| Phi | 0.698 |
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