Height–diameter modeling of tree species in boreal and mixed forests using a mixed-effects approach and stand-level variables
Bibliographic record
Abstract
Forests are ecologically complex, and trees play a structural and functional role in ecosystem dynamics. Tree height–DBH (diameter at breast height) relationships serve as a key indicator of forest productivity, competition, and succession, fundamental to sustainable forest management. This study develops height–DBH models for eight ecologically important tree species in boreal and mixed forests by applying nonlinear mixed-effects modelling approach to improve the predictive accuracy of height estimations. We evaluate height–DBH functions, including the two-parameter power function and Chapman–Richards function, incorporating stand-level variables—stand height based on dominant or co-dominant trees (SHT), basal area (BAH), and tree density (TPH) to refine predictions. Results indicate that mixed-effects models significantly improved model performance, with M4 (Chapman–Richards with mixed-effects) and M5 (Chapman–Richards function with mixed-effects and stand-level variables)–showing lowest AIC (Akaike Information Criterion) across species. Incorporating stand-level variables significantly enhanced performance, though improvements varied by species. The high accuracy of model M5 was further confirmed by validation process. Among stand-level variables, SHT contributed the most to height predictions (25.3 – 53.0%), while BAH (≤ 0.36%) and TPH (≤ 0.01%) had negligible effects. Still M4 can be a reliable alternative when stand-level variables are unavailable. This study highlights the effectiveness of a mixed-effects modelling framework complemented by stand-level variables in improving tree height estimation. Our research improves decision-making in growth and yield estimations of mixed stands and enhances the reliability of forest vegetation simulator outputs, thereby supporting ecological integrity.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".