Table 5-4: Comparison of the Theoretical Values of Measured DBH and Canopy Area of Larch Plantations
Breast Diameter (cm) | Crown Area (m²) | Measured Value | Class Value | Difference | Real Side Value | Class Value | Difference
----------------------|------------------|----------------|-------------|------------|------------------|-------------|------------
6 | 2.516 | 2.5675 | +0.0515 | 14 | 5.147 | 5.684 | 0.501
7 | 3.237 | 2.9856 | -0.2514 | 15 | 5.853 | 6.042 | 0.187
8 | 3.644 | 3.3257 | -0.338 | 16 | 6.202 | 6.438 | 0.236
9 | 4.199 | 3.8077 | -0.312 | 17 | 6.514 | 6.836 | 0.322
10 | 4.199 | 4.0918 | -0.0272 | 18 | 7.306 | 7.236 | -0.07
11 | 4.227 | 4.4781 | 0.2511 | 19 | 7.645 | 7.6379 | -0.0071
12 | 4.600 | 4.8659 | 0.2659 | 20 | 8.093 | 8.0425 | -0.0515
13 | 5.147 | 5.2559 | 0.1086 | 21 | 8.973 | 8.4478 | -0.525
Using this empirical equation, it is possible to calculate the maximum density index for larch plantations at different growth stages. This index naturally exceeds the density of standing trees under normal stand growth conditions. However, it is recommended to determine the reasonable management and density levels for larch plantations. Further studies are needed to obtain more accurate data. Based on data from the Hebei Academy of Forestry Science, and considering the correlation between breast diameter growth and stand density, initial guidelines for operating density indices at various DBH growth stages have been proposed in Table 5-5 for tending purposes.
Table 5-5: Management Index of Larch Plantation Density
Breast Diameter (cm) | Maximum Density (1.0) (trees/ha) | Operating Density (0.7–0.8) (trees/ha)
----------------------|----------------------------------|---------------------------------------
6 | 3940 | 2758–3152
7 | 3392 | 2374–2714
8 | 2980 | 2086–2384
9 | 2670 | 1869–2136
10 | 2404 | 1683–1923
11 | 2195 | 1537–1756
12 | 2020 | 1414–1616
13 | 1873 | 1311–1498
14 | 1746 | 1222–1397
15 | 1636 | 1145–1309
16 | 1540 | 1078–1232
17 | 1456 | 1019–1165
18 | 1380 | 966–1104
19 | 1311 | 901–1050
20 | 1252 | 876–1002
21 | 1198 | 839–958
22 | 1148 | 804–918
23 | 1102 | 771–882
24 | 1060 | 742–848
25 | 1022 | 715–818
For example, in the Mengzi Forest Management Bureau's Longtoushan Forest Farm, after investigation, the existing stand density was found to be 2170 trees/ha with an average DBH of 11.6 cm. Using the management density table, when the average DBH reaches 12 cm, the corresponding stand density should be 1616 trees/ha. Since the current density is higher than this, thinning is required, removing 554 to 756 trees per hectare, which corresponds to a defoliation rate of 20% to 30%. This helps ensure the stand grows normally. After thinning, when the DBH increases to 15–17 cm, another round of thinning will be conducted.
When using the management density index, if the forest was densely planted initially and thinning was delayed, it is important to avoid over-thinning during the first cut. This can lead to short-term issues such as "pulling the bow." Therefore, it is advisable to leave a few extra trees so that the stand can gradually transition to a more reasonable density.
The Longtoushan Forest Farm has summarized its experience in thinning larch plantations and established a reference table for tending and thinning based on the relationship between DBH, forest age, and the number of reserved trees (Table 5-6).
Table 5-6: Criteria for Thinning
Stand Diameter (cm) | Age (years) | Reserve Number (trees/ha) | Thinning Intensity (%) | Interval (years)
--------------------|-------------|---------------------------|------------------------|-----------------
5–6 | 10–12 | 3500–4000 | 35–40 | 4–5
8–10 | 15–18 | 2000–2500 | 30–35 | 4–5
12–16 | 20–25 | 1200–1600 | 30–35 | 5–6
18–24 | 28–36 | 800–1000 | 25–30 | 5–6
To determine the number of retained trees after cutting, the Udaot empirical formula is commonly used:
$$ N = \frac{10000}{(0.164d)^2} $$
Where:
- $ N $: Number of retained trees after harvesting
- $ d $: Average diameter of retained trees
- 0.164: A coefficient
This formula is considered applicable in most cases. To use it for determining thinning intensity, the average diameter of the retained trees must be estimated beforehand. According to surveys and calculations for 16-year-old larch plantations, the number of remaining trees can be calculated using the Udaot formula before applying lower layer thinning:
$$ N = \frac{10000}{(0.164 \times 9 \times 9)} = 2258 $$
This result aligns with other calculation methods, which suggest an appropriate range of 1750 to 2250 trees per hectare.
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