Manual for the Reproducible Geometric and Computational Implementation of Bührig-Type Metrics (Wmax, Dmax, SWmax, L, Δz, SIav, thGav): Application to the Head of the San Antonio Submarine Canyon System

Description This manual presents a complete geometric and computational framework for the reproducible implementation of Bührig-type morphometric metrics in submarine canyon systems, with specific application to the head sector of the San Antonio Submarine Canyon (SAC), Chile. The document provides a rigorously structured methodology for extracting and computing transverse and longitudinal geometric parameters from high-resolution bathymetric Digital Elevation Models (DEMs). The bathymetric surface used in this study was generated from point-based hydrographic data provided by the Chilean Hydrographic and Oceanographic Service (SHOA), originally distributed in CSV format with geographic coordinates referenced to WGS84 and associated depth values. These data were interpolated using ordinary kriging to construct a continuous submarine elevation surface, subsequently reprojected to WGS 1984 UTM Zone 18 South (EPSG: 32718), and exported as a single-band 32-bit floating-point GeoTIFF. This DEM constitutes the three-dimensional foundation of the morphometric analysis. The workflow is implemented in Python 3. 12. 5 and integrates expert geomorphological curation in ArcGIS 10. 5, ensuring spatial coherence, deterministic processing, and full traceability of results. The transverse framework is based on the explicit geometric formalization of four control points (P1–P4) per cross-sectional profile, enabling reproducible computation of Bührig metrics, including maximum width (Wmax), maximum depth (Dmax), maximum canyon wall slope (SWmax), lateral internal angles (B1, B2), and the derived aspect ratio (Wmax/Dmax). The method avoids assumptions of symmetry or orthogonality and preserves the natural scalene geometry characteristic of real submarine canyon profiles, allowing rigorous treatment of asymmetric or rotated sections. In addition to transverse metrics, the manual incorporates longitudinal thalweg analysis, including true channel length (L), total vertical difference (Δz), average sinuosity index (SIav), mean longitudinal gradient (thGav), and maximum gradient estimation derived from numerical differentiation of the depth–distance profile. Together, these parameters provide an integrated geometric characterization of submarine canyon morphology across both cross-sectional and axial dimensions. The project architecture follows a deterministic raw → processed → outputs logic, with clearly defined data structures, modular directory organization, sequentially numbered scripts, and standardized geospatial formats (GeoTIFF, Shapefile, CSV). Each computational stage is explicitly documented, including geometric construction of auxiliary points, vector-based projection methods, law-of-cosines angle computation, and systematic graphical validation at both individual and batch levels. This design ensures interoperability, scalability, and methodological transferability to other submarine canyon systems and geomorphological case studies. Software Architecture Available At Viveros Velásquez, M. A. (2026). SACHeadBuhrigMetrics (v1. 0. 1). Zenodo. https: //doi. org/10. 5281/zenodo. 18645491 GitHub repository: https: //github. com/MAVIVEROSVELASQUEZ/SACHeadBuhrigMetrics The methodology adheres to Q1-level reproducibility standards in geomorphology and Earth sciences and aligns with open science principles. All computational stages, geometric constructions, input datasets, and validation procedures are transparently documented to allow independent replication. Individual and batch graphical validations demonstrate that derived metrics represent a faithful geometric abstraction of real canyon morphology rather than computational artifacts. Although the case study focuses on the San Antonio Submarine Canyon, the geometric framework is fully generalizable to other submarine incision systems, provided that adequate bathymetric DEMs and reliable thalweg and canyon-edge cartography are available. The pipeline therefore provides a robust and transferable methodological foundation for regional and global comparative analyses, continental margin morphodynamic studies, sediment transfer investigations, and applications in submarine geohazard assessment. This manual serves both as a technical reference and as a scalable methodological template for quantitative submarine geomorphology conducted under rigorous reproducibility and open-science standards.