Evaluation of nonlinear equations for predicting diameter from tree height
Bibliographic record
Abstract
With the emergence and advancement of airborne laser scanning technology over the past decade, individual tree height can be easily measured over a large area of forests with a comparable degree of accuracy to conventional ground-based methods. In laser scanning based large-scale forest inventories, the need to predict diameter from remotely sensed tree height calls for a systematic evaluation of equation forms as the first step towards a well-developed approach to developing diameter–height equations. This study evaluated more than 30 height–diameter equations in the forest biometrics literature to select candidates for deriving equation forms for diameter–height equations. The evaluation was based on four criteria: (i) the height–diameter function is inversable; (ii) the inverse function is continuous and monotonically increasing over a specified working range of total tree height; (iii) diameter at breast height is equal to zero when tree height equals breast height in the inverse function; and preferably, (iv) the inverse function has an inflection point that is consistent with biological expectations. A total of 12 candidate equation forms were derived, which included five two-parameter and seven three-parameter equations. The estimation properties and predictive performance of these 12 equation forms were further evaluated and compared through repeated sampling and fitting using data from 3581 trees destructively sampled for taper measurements from Pinus radiata D. Don plantations across New South Wales, Australia. Three equation forms, including the constrained Richards, Weibull, and the combined power and exponential function, displayed superior prediction accuracy and estimation properties and so were recommended as the primary equation forms for developing diameter–height equations. The remaining equation forms were marred by either lower prediction accuracy or poorer estimation properties or both. The three recommended equation forms should only serve as basic deterministic specifications upon which other tree and stand variables should be incorporated as predictors to further improve their predictive performance.
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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 | 0.007 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".