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

Abstract

& Key message Using the three characteristic points of a forest stand, dg (mean quadratic diameter), d min (diameter of the smallest tree) and d max (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, d min and d max ) 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).

From small forest samples to generalised uni‐ and bimodal stand descriptions

“…Thereby, the stand attributes are usually calculated based on entirely measured stands. However, Schütz and Rosset (2020) recently showed that a few simple stand attributes are informative enough to accurately determine the parameters of the diameter distribution at the stand scale using a PPM approach. By forming one single log‐likelihood function over the characteristics of different stands, Cao (2004) developed a method (equation 13 in his paper) to generalise the parameter estimation in one likelihood function that enables proper estimation of uncertainty associated with the regression parameters.…”

Combining Weibull distribution and k-nearest neighbor imputation method to predict wall-to-wall tree lists for the entire forest region of Northeast China

“…With the increasing need for detailed forest attributes (e.g., tree lists) to answer regional questions, including understanding the current structure and succession status of a forest, formulating targeted forest management strategies for different forest regions, or predicting tree species distribution shifts under climate change (Ferraz et al 2020;Wang et al 2019), the development of efficient and accurate methods to obtain such regional tree list information has attracted significant research interest. Although previous studies have applied both parametric diameter distribution modeling (e.g., Weibull function) and nonparametric imputation (e.g., kNN model) to predict tree lists (Packalén and Maltamo 2008;Schütz and Rosset 2020;Shang et al 2017), the integration of these two methods proposed in our study is novel for generating wall-to-wall tree lists over large areas with limited forest inventory data. The Weibull function, especially the two-parameter Weibull function, is extensively used to describe the diameter distributions of single-and mixed-species stands (Hao et al 2022;Liu et al 2014;Schmidt et al 2020;Zhang et al 2018b).…”

“…This approach usually uses a probability density function (PDF) (e.g., gamma, beta, exponential, log-normal, Johnson's SB, Weibull) to fit the diameter distribution for each stand and then predicts the PDF parameters using stand attributes (Liu et al 2009;Temesgen et al 2003). The two-parameter Weibull function has been reported to be the simplest and most accurate PDF for diameter distribution modeling for tree species worldwide, owing to its flexibility in describing different shapes of diameter distributions and fewer parameters (Diamantopoulou et al 2015;Schmidt et al 2020;Schütz and Rosset 2020). Schmidt et al (2020) modeled the diameter distributions of clonal eucalyptus stands in Brazil using a Weibull function and re-measured information from 56 permanent sample plots as predictor variables.…”

“…Schmidt et al (2020) modeled the diameter distributions of clonal eucalyptus stands in Brazil using a Weibull function and re-measured information from 56 permanent sample plots as predictor variables. Schütz and Rosset (2020) compared different methods of predicting Weibull distribution parameters to better describe the diameter distributions of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) in monospecific, regular temperate European forests.…”

Bayesian Evaluation of Smartphone Applications for Forest Inventories in Small Forest Holdings

“…It has proven to be a valuable replacement for the Spiegel Relaskop in rapid stand parameter estimations, with excellent accuracy in stands similar to ours (e.g., [17,18]). MOTI has been considered as a standard private forest stand inventory tool by several private forest enterprises in Switzerland [19], providing inexpensive stand parameter estimates needed for further simulations [20].…”