### Calculation of stem parameters in the software PraleStat

### Basal area

Basal area is to be calculated from the breast height diameter or from the calculated stem diameter at breast height according to the formula for the calculation of basal area.

### Top diameter or calculated breast height diameter

Diameter of the breakage or stub top determines the stem diameter

- at adjusted height of breakage or stub from the pair [stub or breakage, lying stem], or
- at a height of isolated breakage or stub.

The calculated breast height diameter of lying stem from the pair [stub or breakage, lying stem] determines the stem diameter at 1.3 m of stem length.

These parameters are calculated by using the formula for the calculation of tree stem diameter at a desired height. The formula is further introduced the breast height diameter and the fitted height of breakage or stub.

The calculated breast height diameter is used to calculate the basal area.

### Fitted height

Fitted height is to be determined in all stems with a non-zero diameter at breast height according to Näslund’s regression function

,
**h = d^2 * (a + b*d)^(-2) + 1,3
**

where

h is fitted height,

d diameter at breast height, and

a, b are regression parameters.

Regression parameters are determined for each tree species by linear regression using the least square method of the function

,
**H = a + b*d
**

where

,
**H = d * (h - 1,3)^(-1/2)
**

h being the measured height of healthy stem [S;X;*;0] and d being the corresponding breast height diameter.

### Volume

Volume
*healthy stem
* [(S);(X,O);*;*] is determined from the volumetables of tree species according to breast height diameter and fitted height.

Should a stem have a diameter larger than the largest diameter stem of givenheight in the volume table, the volume is to be calculated as a product ofthe stem basal area and the form height of the stem of corresponding height.

Should a stem have a greater fitted height than the tallest stem of givendiameter in the volume table, its volume is to be calculated as a product ofits fitted height and the ratio of the tallest stem volume of correspondingdiameter from the volume table to its height.

Should a stem have a greater fitted height and at the same time a largerdiameter than the tallest stem of the largest-diameter in the volume table,the volume is to be calculated as a product of stem basal area, stem fittedheight and stem form factor. Stem form factor is to be calculated as a formheight to height ratio of the tallest stem.

Volume of
*isolated lying stem
* [(L);(X,V);*;*] is determined similarlyas in the healthy stem with measured length to be used instead of fitted height.

Should the volume table not include the value for height at a value of the measured length of isolated lying stem and the corresponding diameter, and should this not be the case of a taller or larger-diameter stem than presentedin the volume table, the volume is to be determined as a sum of the volumes ofblunted cones of identical height of max. 0.5 m, approximating the stem body.For the calculation of approximation cone base diameters the relevant form function is to be introduced breast height diameter, fitted height and lyingstem length.

Volume of
*isolated breakage or stub
* is to be calculated as a sumof the volumes of approximation cones with using breast height diameter andthe height of stub or breakage.

Should the height of isolated breakage or stub be zero, the volume is tobe calculated as for the healthy stem with the corresponding fitted height.

Volume of
*breakage or stub from the pair
* [stub or breakage, lyingstem] is calculated similarly as the volume of isolated breakage or stub exceptfor cases in which the volume is established to be zero.

Volume of
*lying stem from the pair
* [stub or breakage, lying stem] iscalculated as a difference between the stem volume with a breast height diameterof the concerned breakage or stub and the height equal to a sum of the breakageor stub height and the length of the lying part, and the volume of the concernedbreakage or stub from the pair [stub or breakage, lying stem].

Should this difference come out as a zero or negative, the volume is determinedat 0.05 m^{3}.

Should the volume table not include the value for height corresponding to the sum of breakage or stub height and length of the lying part and the corresponding diameter, and at the same time the case in question is not thatof a stem taller or with a larger diameter than presented in the volume table,the volume is to be determined by means of approximation cones with the use ofbreakage or stub breast height diameter and a sum of the breakage or stub heightand the length of the lying part.

Authors: Martin AMBROŽ & David Janík