Diameter Distribution Modeling in Forest Ecosystems

Diameter distribution modelling seeks to characterise the frequency of tree stem diameters within forest stands, forming a fundamental basis for forest inventory, growth prediction and sustainable management. By representing the structural composition of a stand, these models inform estimates of timber yield, carbon sequestration and biodiversity potential. Approaches range from classical parametric functions—such as the Weibull, gamma and beta distributions—to non-parametric percentile and kernel density methods. Recent advances integrate stochastic processes and mixed-effects frameworks to capture temporal dynamics, while remote sensing and machine learning techniques enable parameter recovery and spatial scaling from limited field samples. The global application of these models spans boreal to tropical forests, supporting decision-making under changing climatic and management regimes.

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Recent work in northeastern China evaluated parameter prediction for the Weibull distribution across major coniferous species, comparing ordinary least squares, maximum likelihood and cumulative distribution function regression. The study demonstrated that cumulative distribution regression yields superior fit statistics and lower prediction errors across age classes, guiding improved plantation management. In Switzerland, researchers assessed seven methods for deriving stand-level diameter distributions from small national forest inventory plots. A simultaneous three-step parameter prediction model delivered the lowest generalised prediction errors in even-aged stands, while simple pooling proved more accurate for uneven structures; a Random Forest approach excelled in predicting species composition. In Spain, low-density airborne LiDAR data were combined with parameter recovery models to reconstruct diameter distributions in Pinus halepensis plantations. Six probability density functions were tested, revealing that beta and generalized beta functions offered the most accurate fits when moments were predicted from LiDAR metrics, thus validating non-destructive, large-scale assessment methods.

Diameter Distribution Modeling in Forest Ecosystems publication trend

The graph below shows the total number of articles in diameter distribution modeling in forest ecosystems across all publications each year (not limited to Nature Index journals).

Technical terms

Parametric distribution: A mathematical function defined by a small set of parameters used to describe the probability of diameters in a stand.

Weibull function: A flexible two- or three-parameter distribution widely applied to model diameter frequencies due to its ability to represent skewed data.

Percentile method: A non-parametric approach that uses empirical diameter percentiles to reconstruct the distribution without assuming a functional form.

Parameter recovery model: A statistical technique that estimates distribution parameters from summary statistics (e.g., mean, variance) or remotely sensed predictors.

Random Forest: A machine learning ensemble method employing multiple decision trees to predict complex stand attributes such as species composition.

LiDAR metrics: Quantitative variables derived from laser scanning data, used to infer canopy structure and estimate diameter distribution moments over large areas.

References

1. Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province, China. Journal of Forestry Research (2023).
2. Deriving forest stand information from small sample plots: An evaluation of statistical methods. Forest Ecology and Management (2023).
3. Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain). Remote Sensing (2021).