For the estimation of stand volume (V) through the “WZP”, the author proposed a method combined with a single tree volume table in terms of tree diameter and-height i.e. v
i=∅(d
i, h
i), by means of the formula under written.
V=N•∅(d, h)•λ where N denotes the stem number per hectare, d the mean diameter, h the mean height, and λ does the correction factor for the estimation of mean volume E (v) per tree.
The factor λ can be derived by such calcutation as follows.
Taking v
1=α+βd
2h (combined variable formula), v
2=d
2h/(α+βd) (Takata's formula) or v
3=αd
βh
γ (YAMAMOTO-SCHUMACHER'S formula), the expectation of single tree volume E (v) is given respectively as follows, under experimental assumptions that the correlation coefficient between tree basal area (g
i) and -height (h
i) is nearly equal to 2/3, and the coefficient of variation of diameter (C
d) is about two times as large as that of height (C
h) in plantations.
E (v
1)=α+βd
2h•(1+5/3C
2d)
E (v
2)={d
2h/(α-βd)}(1+5/3C5
2d)
E (v
3)=αd
βh
γ•λ
with λ_??_{1+β/2(β-1)C
2d }{1+γ/8(γ-1)C
2d}{l+βγ/3C
2d}, or λR_??_1+5/3C
2d in case β and γ is rounded respectively by 2 and 1.
Thus the stand volume can be estimated by such method more speedily than by a conventional one summing up each tree volume, and the accuracy of this method was warranted by some practical comparisons with the latter case.
In case estimations of tree volume by diameter class are postulated, we have only to divide the total volume estimated at first stage by the above method, proportionally to the basal area by diameter class.
Making use of the range of diameter, σ
d can be easily estimated to calculate the λ. The “WZP” should be used being combined with above method, because factors in the formula: V=N•∅(_??_, _??_)•λλ can be estimated with efficiency by the “WZP” of two kinds and calipering tree diameters as shown below.
Outdoor work: a) Count the relascopic tree at the j-th sample point of size n.
b) Measure diameters of nearest trees of an appropriate size taken secondly around the sample point.
c) Count the conometeric tree at sample points of size n.
Indoor work:
a) Estimate the basal area per hectare (G).
b) Estimate the mean diameter and the variance of diameter to calculate the mean basal area d and λ.
c) Estimate the stem number per nectare (N) through G divided by g; secondly, with the very N just estimated, estimate the mean height h
c from the author's formula: h
c=100_??_B
c/N (tgβ/_??_π), where B
c. denotes the mean of conometeric tree count, β the constant angle in conometer.
When the tree height varies to so high degree that C
2h/2 cannot be neglected, the correction factor i be replaced by λ
c(_??_1+37/24C
2d), smaller than λ to correct the estimate of h
c{=h_??_1+C
2h_??_h(1+C
2h/2)} positively biased.
According to the author's view from some statistical logics, the above method is usually regarded as more precise than other ones on the estimation of stand volume, so long as the stem number per hectare (N) is more than the size of sample point (n).
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