The choice of window size in approximating topographic surfaces from Digital Elevation Models
Bibliographic record
Abstract
Quantitative surface analysis through quadratic modelling of Digital Elevation Models (DEMs) is a promising tool for automatically describing the physical environment in ecological studies of terrestrial landscapes. Fundamental topographic variables such as slope, aspect, plan and profile curvature can be simply calculated from the parameters of a conic equation fitted to a DEM window through the least-squares method. The scale of the analysis, defined by the size of the DEM window used to fit the conic equation, affects both the estimated value of the topographic variables and the propagation of elevation errors to derived topographic variables. The least-squares method is amenable to the analytical treatment of the propagation of elevation errors to the derived topographical variables. A general analytical model of error propagation is presented that accounts for the effects of window size and of spatial autocorrelation in elevation errors. The method is based on the Taylor approximation of the least-square fitting equation and allows for the presence of stationary autocorrelation in the elevation errors. In numerical simulations with DEMs from British Columbia, Canada, it is shown that increasing the size of evaluation windows effectively reduces the propagation of elevation errors to the derived topographic variables. However, this was obtained at the expense of topographic detail. A methodology is proposed to evaluate quantitatively the loss of topographic detail through a χ 2-test of the corrected residuals in the immediate neighbourhood of the evaluation point. This methodology, in combination with the analytical model of error propagation, can be used to select the scale or range of scales at which to calculate topographic variables from a DEM.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".