Accurate Prediction of Soil Moisture Distribution in Root Zone Using Meshless LRBF Methods

Core Concepts

The proposed numerical model accurately predicts soil moisture dynamics in the root zone by solving the Richards equation with different formulations of the root water uptake sink term using an efficient meshless LRBF method.

Abstract

This study presents a coupled numerical model that accounts for both unsaturated soil flow and plant root water uptake. The Richards equation is used as the governing equation, and different formulations are considered for the root water uptake sink term.
The key highlights and insights are:

Two macroscopic models are used to represent the root water uptake: the stepwise and exponential forms proposed by Yuan and Lu, and the nonlinear form proposed by Broadbridge et al.
The Kirchhoff transformation is employed to linearize the highly nonlinear Richards equation, and Picard's iterations are used to further linearize the problem.
A meshless method based on localized radial basis functions (LRBF) is proposed to solve the resulting system of equations efficiently. The LRBF approach avoids the need for mesh generation and produces a sparse matrix system, which helps overcome ill-conditioning issues.
Numerical experiments are performed in 1D, 2D, and 3D to validate the proposed model against analytical solutions and experimental data. The results demonstrate the accuracy and efficiency of the LRBF method in predicting soil moisture dynamics in the root zone under various scenarios, including evaporation, irrigation, and root water uptake.
The numerical results show that the impact of root water uptake on soil moisture distribution can be significant, depending on the soil and plant parameters. The proposed model can be a useful tool for studying soil-water-plant interactions and designing efficient water management practices.

Stats

The numerical results demonstrate root mean squared errors (RMSE) of the water content in the range of 10^-8 to 10^-4, indicating the high accuracy of the proposed LRBF method.

Quotes

"The LRBF meshless approach is an accurate and computationally efficient method that eliminates the need for mesh generation and is flexible in addressing high-dimensional problems with complex geometries."
"The localized approach leads to inverting a sparse matrix, which avoids ill-conditioning problems that occur in the full matrix generated using the global method."

Key Insights Distilled From

LRBF meshless methods for predicting soil moisture distribution in root zone

by Mohamed Bouj... at arxiv.org 04-22-2024

https://arxiv.org/pdf/2404.12453.pdf

Deeper Inquiries

How can the proposed numerical model be extended to account for other complex processes, such as solute transport, heat transfer, or soil-atmosphere interactions

The proposed numerical model can be extended to account for other complex processes by incorporating additional governing equations that describe solute transport, heat transfer, or soil-atmosphere interactions. For solute transport, an advection-diffusion equation can be coupled with the Richards equation to simulate the movement of solutes in the soil-water system. This would involve introducing additional parameters such as the dispersion coefficient and initial solute concentration profiles.
To incorporate heat transfer, the energy balance equation can be included in the model to study the thermal dynamics of the soil. This would involve considering heat conduction, convection, and possibly radiation within the soil domain. Parameters such as thermal conductivity, specific heat capacity, and boundary conditions related to heat flux would need to be defined.
For soil-atmosphere interactions, boundary conditions at the soil surface can be modified to account for atmospheric influences such as evaporation, precipitation, and air temperature. This would require coupling the soil model with atmospheric models to capture the exchange of moisture and energy between the soil and the atmosphere.
By integrating these additional processes into the existing numerical model, a more comprehensive understanding of soil dynamics can be achieved, allowing for the simulation of coupled phenomena that occur in real-world soil systems.

What are the potential limitations of the macroscopic root water uptake models used in this study, and how could they be improved to better capture the underlying physical processes

The macroscopic root water uptake models used in this study have certain limitations that could be addressed to better capture the underlying physical processes. One limitation is the empirical nature of these models, which may not fully capture the complex interactions between plants and soil. To improve these models, more detailed and mechanistic approaches could be developed based on physiological principles governing plant water uptake.
Another limitation is the assumption of uniform root distribution and constant root water uptake rates, which may not reflect the actual variability in root architecture and activity. Incorporating spatial variability in root distribution and dynamic changes in root water uptake rates based on plant physiological responses to environmental conditions could enhance the accuracy of the models.
Furthermore, the linear and exponential formulations used for root water uptake may oversimplify the actual processes occurring in the soil-plant system. Developing more sophisticated models that consider non-linear relationships between soil moisture, root water uptake, and plant physiological responses could lead to more realistic predictions of soil moisture dynamics in the root zone.
Overall, improving the macroscopic root water uptake models by incorporating more mechanistic and dynamic representations of plant-soil interactions could enhance their predictive capabilities and provide a more accurate representation of the complex processes involved.

Could the LRBF meshless method be combined with other numerical techniques, such as adaptive mesh refinement or domain decomposition, to further enhance the computational efficiency and accuracy of the model

The LRBF meshless method can be combined with other numerical techniques, such as adaptive mesh refinement or domain decomposition, to further enhance the computational efficiency and accuracy of the model.

Adaptive Mesh Refinement (AMR): By integrating LRBF with AMR, the computational domain can be dynamically refined in regions of interest, such as areas with high gradients or complex geometries. This adaptive approach allows for a more efficient allocation of computational resources and improved resolution where it is most needed, leading to more accurate results with reduced computational cost.

Domain Decomposition: Domain decomposition techniques can be used to divide the computational domain into subdomains that can be solved independently and then combined to obtain the overall solution. By combining LRBF with domain decomposition, parallel computing can be utilized to solve large-scale problems more efficiently. This approach can lead to faster computation times and improved scalability for complex simulations.

Coupling with other Meshless Methods: LRBF can also be coupled with other meshless methods, such as the method of fundamental solutions or radial point interpolation methods, to leverage the strengths of different techniques and improve the overall accuracy and efficiency of the numerical model. This hybrid approach can provide a more robust and versatile framework for solving a wide range of soil dynamics problems.

By integrating LRBF meshless method with these advanced numerical techniques, the computational capabilities of the model can be significantly enhanced, allowing for more accurate and efficient simulations of soil moisture distribution in the root zone and other complex soil processes.