Smoothing Earth's surface: The complexity of soil texture class transitions

Area of Science:

• Soil Science
• Geostatistics
• Computational Soil Science

Background:

• Soil depth functions are crucial for soil analysis and modeling.
• Existing methods struggle to interpolate discrete soil texture classes with depth.

Purpose of the Study:

• To introduce phySplines, a novel physics-informed spline for interpolating categorical soil texture data with depth.
• To develop a method that overcomes limitations of discrete soil class representation in continuous soil profiles.

Main Methods:

• phySplines maps soil texture classes to a numerical space for continuous interpolation.
• Minimizes depth-weighted Dirichlet energy using an Euler's cumulative mass process.
• Incorporates pedological theory for physically consistent class transitions and mass continuity.

Main Results:

• Achieved high accuracy with kappa values of 0.96, 0.94, and 0.96 at global, provincial, and local scales.
• Successfully captured transitional soil states and mitigated class representation bias.
• Generalized across missing soil layers and maintained mass and energy continuity.

Conclusions:

• phySplines provides a robust, continuous framework for soil texture interpolation.
• Enables more accurate soil profile analysis, modeling, and visualization.
• Facilitates future research in numerical soil classification and multifunctionality assessment.