{
  "abstract": "Canopy cover is normally reported as a fraction of a horizontal map plane. When the domain of inference is the land surface, the appropriate target is the fraction of terrain surface area under canopy. We define this estimand on a C1 graph surface and show that it differs from vertical-projection cover by the planimetric covariance of cover with the area density, divided by the mean area density; the rumple index is a different quantity. A LiDAR pulse is recorded as a canopy return only when detection succeeds, so the naive return fraction estimates cover multiplied by the canopy detection probability. We study an inverse-probability-weighted estimator that uses that probability as the inclusion probability, and a weighted corner-averaged Cramér-von Mises lack-of-fit statistic for constant mean surface-area cover under independent canopy returns, calibrated by a parametric bootstrap. Synthetic validation on the flat plane and the Gaussian hill gives a naive bias near -0.40 and a weighted bias near 0.00; at 5000 pulses the test holds size at 0.02-0.06 across the simulated null cells and reaches power 0.79 under surface-uniform and 0.85 under plane-uniform sampling against broad slope-dependent cover, but only 0.12-0.13 against a compact hotspot. The definitions and their exact reductions are machine-checked in Lean 4. No field data yet.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04103",
  "author_total": 1,
  "authors": [
    {
      "name": "Marco Mandap"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bkqgdkc4mert8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04103",
  "fulltext_url": null,
  "id": "bkqgdkc4mert8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04103",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bkqgdkc4mert8.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:34Z",
      "native_id": "2611.04103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Terrain-Surface-Area Cover from LiDAR: Inverse-Probability-Weighted Estimation and a Global Cramér-von Mises Lack-of-Fit Test",
  "title_text": "Terrain-Surface-Area Cover from LiDAR: Inverse-Probability-Weighted Estimation and a Global Cramér-von Mises Lack-of-Fit Test",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:10Z",
  "url": "https://research.draconitic.com/paper/bkqgdkc4mert8",
  "venue": "arXiv",
  "versions": []
}