Manual for the reproducible geometric and computational implementation of Bührig-type metrics in submarine canyons

Technical Description of the Manual This record corresponds to the technical and methodological manual that formalizes the reproducible geometric implementation of Bührig-type transverse metrics in submarine canyons, constituting the conceptual and operational foundation of the software SAC_Buhrig_Metrics_V1 (Viveros Velásquez, 2026, v1.0.6. Zenodo. https://doi.org/10.5281/zenodo.18618759). The document explicitly develops the geometric and computational translation of the conceptual framework presented by Bührig et al. (2022) in their global analysis of controls on submarine canyon geomorphology: Bührig, L. H., Colombera, L., Patacci, M., Mountney, N. P. & McCaffrey, W. D. (2022). A global analysis of controls on submarine-canyon geomorphology. Earth-Science Reviews, 233, 104150. https://doi.org/10.1016/j.earscirev.2022.104150 While Bührig et al. (2022) establish the global comparative framework and conceptual use of the Wmax, Dmax, and SWmax metrics, the present manual addresses the explicit geometric formalization required for their reproducible implementation on real transverse profiles derived from bathymetric Digital Elevation Models (DEMs). Methodological Scope The manual rigorously develops: The operational definition of key points P1–P4 on real transverse profiles The explicit vector-based geometric construction of the transverse system Trigonometric resolution using the law of cosines in non-ideal triangles Formalization of Wmax as the Euclidean distance between effective canyon margins Definition of Dmax relative to the thalweg and the line connecting real canyon edges Derivation of SWmax as the maximum geometric flank slope The complete reproducible implementation pipeline Individual and batch geometric validation procedures Formal separation between observational data and geometric processing The document establishes a deterministic architecture in which: Input data → Explicit geometric construction → Mathematical resolution → Final morphometric metrics Observed geomorphological asymmetry is explicitly preserved, and no assumption of ideal orthogonality or geometric symmetry is imposed. Correspondence with the Software This manual constitutes the official methodological specification supporting the computational implementation archived as: Viveros Velásquez, M. A. (2026). SAC_Buhrig_Metrics_V1 (v1.0.6). Zenodo.https://doi.org/10.5281/zenodo.18618759 It guarantees formal correspondence between: The conceptual framework of Bührig et al. (2022) Explicit geometric formalization Reproducible algorithmic implementation Traceable morphometric outputs The manual does not present new scientific results nor test geomorphological hypotheses. Its function is strictly technical: to ensure mathematical coherence, geometric traceability, and computational reproducibility under standards compatible with Q1-level scientific publishing. Transferability Although the initial application was conducted on the San Antonio Submarine Canyon (Chile), the methodological architecture is regionally independent and can be implemented in any submarine canyon system provided that: A bathymetric DEM of sufficient resolution is available The thalweg is mapped Canyon edges are properly delineated Nature of the Record This record constitutes the formal methodological documentation supporting the reproducible pipeline and ensuring the technical auditability of the system. The associated file is under restricted access and is available upon formal request or under licensing agreement.