Performances of different methods of estimating the diameter distribution based on simple stand structure variables in monospecific regular temperate European forests

Key message
Using the three characteristic points of a forest stand, dg (mean quadratic diameter), dmin (diameter of the smallest tree) and dmax (diameter of the largest tree), appears informative enough to determine the parameters of the whole diameter distribution and, hence, the standing volume, with an accuracy of 2–3%. This is related principally with a particular feature of the Weibull distribution function, and the empirical dependency of the main scale parameter α + β from the mean quadratic diameter (dg): This allows the prediction of the parameter β with an unexpectedly high likelihood. This feature could be used for growth modelling as well as inventory purposes, at least for monospecific and even-aged stands and, maybe more, because this feature is proper to the function itself.
Context
One of the most appealing applications of diameter distribution functions is to predict compliant stand diameters without needing to tally all stems, but in determining the function parameters only on the base of simple stand characteristics. This can be applied for yield model construction or inventory purposes.
Aims
The aim of this paper is to compare different methods of estimating the Weibull distribution parameters, partly based on parameter recovery method (PRM). They use a remarkable, empiric property of the Weibull function. Their performances are assessed in comparison to real distributions from a wide database of permanent Swiss yield plots repeatedly measured (time series) for Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.).
Methods
The Weibull distribution offers the advantage of simple but reliable estimation procedures. One of these is the main (scale) parameter β being given at a remarkable point of the function free, i.e. independent from the shape parameter γ. Because dg lies very close to this point, it correlates empirically very tightly with this parameter and thus allows for a trustful simple estimation. We compare, with appropriate statistic tests, real distribution with such obtained with the usual maximum likelihood estimation (MLE) of the Weibull parameters and those obtained with these new procedures.
Results
The results obtained from a set of 800 yield plots of regular spruce stands and 596 of beech in Switzerland illustrate the good performances of the two much simpler procedures. The accuracy of estimating the standing volume is about 1.4% for beech and 2.8% for spruce when the site index (SI) is known.
Conclusion
The three considered characteristic stand attributes (dg, dmin and dmax) appear robust enough for determining the diameter distribution with a respectable accuracy. This is enough reason for a revival of the old, but very ingenious, method of angle count sampling of Walter Bitterlich (1947).