A Divide-Consistent, Seamless QGIS Workflow for SOTA Prominence (150 m) in Austria with Post-Computation Review Layers

Abstract

Summits on the Air (SOTA) certification in Austria requires a minimum topographic prominence of 150 m. This work presents an automated, reproducible workflow that computes national prominence directly on a raster digital terrain model, together with the post-computation review layers needed to reconcile the computed result against an existing authoritative summit database. Abstract We present an automated, reproducible workflow that computes national prominence directly on a raster digital terrain model. Its core is PixelMinimax, a pixel-level descending Union-Find: DEM pixels are processed from highest to lowest elevation, and the key col of each summit is assigned at the moment its component first merges with a higher-elevation component. This descending sweep is the union-find solution of the bottleneck (widest-path) problem on the pixel graph and is known in the literature as the water-sweep formulation; the contribution here is its seamless, out-of-core application to a national DEM together with a proof that the first merge occurs exactly at the key-col elevation (Theorem 1), so that no intermediate basin-saddle graph, no tiling and no parameter tuning are required and mountain-to-plain transition zones are handled correctly. The O(n log n) computation runs at 10 m resolution and is followed by a dual 1 m refinement of summit and key-col elevations for candidates within an empirically conservative ±20 m band around the threshold. Applied to the national Austrian ALS-derived DEM (2 450 224 128 pixels), the workflow identifies 2433 qualifying summits and agrees with 95.4 % of the official SOTA Austria database in a cross-comparison. We analyse the remaining discrepancies — 362 newly computed candidates and 100 uncomputed database entries — and attribute them to identifiable geometric and data-coverage causes. Contributions PixelMinimax, a seamless, out-of-core formulation of the descending Union-Find (water-sweep) prominence computation that operates directly on a national raster DEM of 2 450 224 128 pixels without tiling and without an intermediate basin-saddle or divide-tree graph. A proof (Theorem 1) that a summit's component first merges with higher terrain exactly at its key col, together with the NaN-guard invariant that enforces this during the descending scan, and its placement in the bottleneck-path and persistence literature. An O(n log n) characterisation of the external-sort variant and the identification of the drainage-outlet failure mode of basin-graph formulations, which the pixel-level processing order avoids by construction. A dual-resolution (10 m → 1 m) refinement scheme with a ±20 m decision band (130 m ≤ ρ < 170 m) around the 150 m threshold that is empirically conservative for the Austrian production run. A national-scale cross-comparison against the official SOTA Austria database, including a structured analysis of the observed discrepancies. Relation to prior work In graph-theoretic terms the key col is the bottleneck (widest-path) value from the summit to higher terrain on the vertex-weighted 8-connected grid graph of the DEM (Pollack 1960; Hu 1961). Divide-tree methods (Kirmse & de Ferranti 2017) materialise the maximum spanning tree of the peak–saddle graph and answer pairwise queries on it. The descending union-find sweep computes the same quantity without the tree; it is the dynamics of a maximum in mathematical morphology (Grimaud 1992), the death value in 0-dimensional persistence (Edelsbrunner et al. 2002), and has been described as the "water sweep" base algorithm of a tiled global prominence computation (Dumitrescu & Diac 2024). This work does not claim the sweep as such. Why a pixel-level method Local-window and fixed-radius approaches (TPI, geomorphons, r.param.scale) cannot locate key cols lying outside their search radius and therefore systematically underestimate prominence. Basin-saddle graph approaches fail differently: in mountain-to-plain transition zones, basin boundaries cross valley floors at drainage outlets, so the boundary minimum is a near-valley elevation rather than a ridge saddle. PixelMinimax resolves this by processing order — the ridge saddle is reached first because it is higher, and the NaN-guard prevents any later, lower connection from overwriting the assigned key col. No parameter tuning is required. National production run — key figures 2 450 224 128 valid DEM pixels processed (10 m, 40 km cross-border padding, EPSG:25833); the padding terrain takes part in the sweep, prominence is written only for peaks inside Austria 2433 qualifying summits with refined prominence ρ ≥ 150 m 2053 MATCH_OK, 18 MATCH_ELEV, 362 NEW_CALC, 100 DB_NO_PEAK, plus 1298 FOREIGN_PEAK context rows 95.4 % agreement with the official SOTA Austria database (2071 of 2171 Austrian entries) 92.4 % authoritative BEV name coverage (2247 of 2433 summits) Step 2 wall-clock runtime 10 h 29 m 42 s on a 64 GB Apple Silicon workstation with NVMe scratch storage; 95.8 GB scratch footprint Beyond prominence: auditing an existing database The post-computation review chain (Steps 5b–5e) turns the comparison into a structured audit rather than a pass/fail test. It exposes a systematic coordinate-quality pattern in the existing database: Step 5c flags 911 rows for coordinate, name or identity review, and 849 of the 2171 Austrian database entries (39.1 %) carry a displaced coordinate; for most of these an independent BEV reference point confirms the shift. The resulting priority-ranked Reviewer Concentrate (1401 rows) is distributed to human reviewers and re-joined to the working database in QGIS. Software and reproducibility The production pipeline — the driver script and all QGIS Processing scripts implementing Steps 1–5d — is available at github.com/Erwin60/sota_prominence and archived on Zenodo (see related identifiers). The results reported here were produced with software release 5.2.2; the code is unchanged in releases 5.2.3 and 5.3.1, which update only the bundled article and the repository metadata. The repository includes a full parameter reference and worked usage examples. The three BEV base datasets used here — the ALS-derived DGM 1 m height raster, the Verwaltungsgrenzen (VGD) boundaries, and the DLM Geonamen layer — are provided free of charge by the Austrian Federal Office of Metrology and Surveying (BEV) under its open-data terms and can be downloaded directly from the cited product pages, so the full input stack is publicly reproducible. The input geodata and the SOTA Austria database are not redistributed with this record and remain subject to their respective providers' terms. Environment: QGIS 3.34+, GRASS GIS 8.x, GDAL 3.8+, SAGA GIS 9.x on Apple Silicon macOS. Version history 5.3.1 (October 2026): consistency corrections after a check against the v5.1 GeoPackages and the published scripts. Großglockner key col at the Brenner Pass on the Austrian–Italian border, about 91 km west of the summit (the 34.4 km given before is the summit's distance to the border); Step 2b routing targets searched among Austrian peaks only; refinement band stated as 130 m ≤ ρ < 170 m with explicit bases for its statistics; FOREIGN_PEAK listed as fifth status; NEW_CALC and DB_NO_PEAK fully broken down; coordinate-shift counts, N1 name-source definition, flag compositions and Step 5c/5d naming corrected; national table column “P1” renamed “F-Rev”. No figure, table value or numerical result changed. 5.3 (September 2026): adds the related work on bottleneck-path, persistence and water-sweep formulations and restates the contributions accordingly (the descending union-find sweep is prior art; the contribution lies in its seamless national application, the first-merge proof, the dual 1 m refinement and the review chain). No figure, table value or numerical result changed. 5.2.2 (July 2026): corrects the Zenodo identifiers of the accompanying software record. 5.2.1: first archived version of the v5.1 data freeze. Publication status This is a self-archived, author-produced preprint, version 5.3.1. It has not been peer-reviewed by a journal. The document is typeset in the IEEE journal template (IEEEtran) for formatting consistency only; it has not been submitted to, reviewed by, or published by the IEEE. Reported results correspond to the v5.1 national data freeze. Citation Grabler, E. (2026). A Divide-Consistent, Seamless QGIS Workflow for SOTA Prominence (150 m) in Austria with Post-Computation Review Layers (version 5.3.1). Zenodo. https://doi.org/10.5281/zenodo.21279805(concept DOI, resolves to the latest version)