Vol. 2 (2026): Continuous Publication
Special Section: Mathematical and Computational Modelling of Agricultural and Natural Resource Systems

Multiyear Validation and Mass-Balance Auditing of Richards Simulations on Uniform and Graded Finite-Volume Meshes Using USDA SCAN Observations

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  • José D. Zúniga-Varela,
  • Marlon M. López-Flores,
  • William Campillay-Llanos
José D. Zúniga-Varela Escuela de Matemática y Ciencias de la Computación, Universidad Nacional Autónoma de Honduras, Tegucigalpa, Honduras
Marlon M. López-Flores Laboratório de Inteligência Artificial, Robótica e Cibernética (LIARC), Instituto Militar de Engenharia (IME-RJ), Rio de Janeiro, Brazil
William Campillay-Llanos Departamento de Ciencias Matemáticas y Físicas; Núcleo de Investigación en Producción Alimentaria (NIPA), Universidad Católica de Temuco, Temuco, Chile
https://doi.org/10.7770/jonraf-v2-art2907

Published 2026-09-22

Keywords

  • Richards equation,
  • Temporal validation,
  • Soil moisture,
  • Finite-volume method,
  • Mesh grading,
  • Mass-balance audit
    • ...More
    Less

Copyright (c) 2026 José D. Zúniga-Varela, Marlon M. López-Flores, William Campillay-Llanos (Autor/a)

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Abstract

Purpose: We tested whether surface-focused mesh grading reduced spatial discretization error in a finite-volume Richards model, whether grid rankings persisted across seasons, and whether hourly water-balance residuals decreased under temporal refinement. Methods: Hourly observations from the U.S. Department of Agriculture (USDA) Soil Climate Analysis Network (SCAN) at Mahantango Creek, Pennsylvania, were quality controlled and aggregated daily for June–September 2023–2025. Effective parameters were selected from 2023; 2024–2025 were held out. Uniform, logarithmic, and algebraic grids were compared with a 40–640-cell reference sequence. An hourly audit compared 32- and 64-substep predictor–corrector configurations. Results: The combined held-out root mean square error (RMSE) was 0.0292 m3 m-3, and depth-specific Nash–Sutcliffe efficiency (NSE) values were 0.603, 0.777, and 0.875 at 5.1, 10.2, and 20.3 cm. At 40 cells, logarithmic grading reduced mean profile error by 47.9% in calibration and 62.1–71.8% in validation; algebraic grading had the lowest error in all three events. Grid errors were below 0.19% of held-out model–observation RMSE. Doubling boundary substeps reduced the maximum substep residual from 1.41×10-9 to 8.48×10-10 m but increased the maximum hourly residual from 1.26×10-8 to 2.13×10-8 m and the cumulative residual from 2.46×10-7 to 3.74×10-7 m. Conclusions: Surface-focused grading proved transferable across seasons, but its field-scale effect was secondary to forcing, structural, and observational uncertainty. The accounting was internally consistent, but strict temporal convergence was not demonstrated; the benchmark is mass-balance audited, not asymptotically mass-conservative.

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