A new method for estimating the soil-water diffusivity of unsaturated soils based on the Boltzmann transform and the principle of stationary action

Accurately measuring the nonlinear soil–water diffusivity remains a complex and time-consuming task. This study extended a simple method for estimating the soil–water diffusivity of unsaturated soils based on the Boltzmann transform and the principle of stationary action. The power relationship between the Boltzmann transform variable and diffusivity is explicitly expressed, with the corresponding power exponent commonly assigned a value between 1 and 3. By comparing the analytical and numerical results, it was found that the predictions are consistent when the power exponent is taken as 2. The proposed method in this study is more concise and convenient for computation when compared to the existing methods. It directly describes the relationship between the soil–water diffusivity and the water content distribution profiles. The proposed theoretical model has limited predictive ability for certain soil types, such as loam and clay. To improve the methodology, more data from different soil types should be collected in the future to better predict soil–water diffusivity. In conclusion, the method proposed in this paper provides a concise and effective method that will have a wide range of applications in future practice in the fields of soil science, agricultural engineering, and environmental research.