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Functional relationship between diameter at breast height and diameter at the base

To define the functional relationship and its inverse (function) between diameter at breast height and diameter at the base , it is necessary to develop proper aspects of classification: to determine the territorial and species split for which it is practical and rational to define functions. This requires taking into consideration mathematical statistical and forestry related practical aspects both. In terms of mathematics and statistics, one needs to determine the level of hierarchy where the fit between models is appropriate in statistical terms and the functions developed are also appropriate. From a professional point of view, it is important that the functions meet the technical requirements, and are easily manageable and easy to utilise. That includes keeping the number of models low for practical reasons as well as the option to develop the most suitable model for each final group to the greatest possible extent.

Hierarchy levels arising during the studies:

• territorially:
  • Micro region
  • Mezzo region
  • Macro region
  • plain – hill, mountain
  • countrywide
  • other options
• from the perspective of species:
  • tree species
  • tree species groups
  • deciduous /coniferous
  • countrywide
  • other options

Studies found that linear regression is practically the most suitable model for a functional description of the relationship between trunk diameter and diameter at the base.

The output of fundamental data (of 3330 specimens) was used to determine the level in the hierarchy of territories (micro, mezzo and macro regions, mountains, hills, plains and countrywide) and species (tree species, species groups, deciduous /coniferous and countrywide) which is applicable (with a suitable low number of models) and provides statistically reliable models. To ensure the reliability of analysis the study only covered groups where the number of specimens were (at least)10 and above.

Statistical comparisons of the various linear models generated for each hierarchy level rely on the generalised version of the Student t-test, which examines the equivalence of the identical features of two populations at an N-4 degree of freedom. The test was used to determine whether or not two models at (on?) different levels of the hierarchy with identical basis could be considered equivalent. The goodness (accuracy) of the fit between models was described with a scientifically approved determination coefficient..

(During the final classification, both forestry related, practical (limited number of groups) and mathematical, statistical (as accurate and reliable as possible) aspects were taken into consideration) Due to These considerations, certain compromises were made during the decision making..( The data currently available provides us with a model system that works on tree species group and national levels at the same time) Lower level resolutions would have produced incomplete model sets, i.e. it would have been impossible to define a model for several cases due to the lack of data, which would have limited practical application.( In case of a more in-depth breakdown, the set of models would have been inconclusive. That is, in many cases due to lack of data, no model could have been produced and that would have had a negative effect on the application)

In view of the considerations laid out above, Sopp's tree species groups and country-wide models were used on the species and the territorial sides, respectively. (Due to the aforementioned, Sopp’s classification for tree species groups and country-wide models for territorial breakdown were used respectively) Sopp's 28 tree species groups were divided into 5 groups on a statistical basis considering the similarity of models. It is important to note that the established groups are also justifiable professionally from the perspective of forestry. An advantage of this approach involves the complete coverage of all potential cases, that is to say it is possible to provide a statistically reliable ad valuable model for any tree species group (including groups where no or scarce data exist, as it is possible and professionally sound to group them into one of the 5 established groups). We have defined a model for each of the 5 groups established this way depending on whether the need called for modelling base or stem diameter.

Symbols used below(Legend/Abbreviations):

DBH Diameter at Breast Height

Db Diameter at base (approx. 20 cm)

(See separate table for a detailed discussion and identification)

Acacia (tree species group 1 according to Sopp):

DBH=0.66*Db+26.74

Db=1.27*DBH+4.91

Beech, alder (tree species groups 2 and 12 according to Sopp):

DBH=0.66*Db+42.8

Db=1.32*DBH-0.62

Oak (tree species groups 3,5,6,7,8,9,10 and 16 according to Sopp):

DBH=0.7*Db+18.49

Db=1.26*DBH+18.01

Poplar (tree species groups 4,11,13,14,15,17,18,19,20,21 and 22 according to Sopp):

DBH=0.84*Db-6.01

Db=1.09*DBH+34.51

Pine (tree species groups 23-28 according to Sopp):

DBH=0.77*Db+13.4

Db=1.21*DBH+5.32

The practical significance of this task is the ability to estimate diameter at breast height if diameter at the base is known, and by, using the common functions of forestry (such as the Sopp – Király function), to estimate wood mass or wood volume. This may play a major role in estimating the volume of stolen wood when illegal felling occurs. Other potential uses might include cases when volumes need to be estimated for various tree parts, such as biomass above ground level.

It is important to note that further enhancement of the available database, with additional, more in-detail surveying, more refined (e.g. tree species group-macro region) and therefore more exact models could be defined