In geosciences, soil-water interactions are defined by soil water potential, which provides a quantitative estimate of the soil water thermodynamic state. Due to the interactions between water and soil particles, soil water has different physical properties than free water; hence, analyzing soil water may require different methods and approaches. Typically, soil water potential is defined as the sum of three independent functions: gravitational, osmotic, and matric. However, there is a problem with this definition because the osmotic and matric potentials exhibit coupling effects. Moreover, due to its high values, the matric potential dominates the total potential, whereas the gravitational potential may appear negligible. However, gravity may lead to different flow mechanisms altering the soil's mechanical behavior. As a result, it may not be valid to calculate the total water potential as the algebraic sum of the different potentials. There are also mathematical challenges in the common use of water potential; as soil saturation decreases, water potential can reach thousands of kPa, which requires mathematical balancing in the equations by multiplying it by a variable with a value near zero. However, multiples of numbers of different magnitudes are problematic from a mathematical perspective, especially when applied to numerical analysis. This paper discusses the strengths and limitations of the definitions and mathematical formulations of this variable.
