Analysis of the nutrient uptake by roots in fixed volume of soil as predicted by fixed boundary, moving boundary and architectural models

TL;DR

This study compares fixed and moving boundary models for nutrient uptake by roots, showing the moving boundary model generally predicts low-concentration uptake more accurately and offers a computationally efficient alternative.

Contribution

The paper introduces an improved moving boundary model for nutrient uptake that outperforms fixed boundary models at low concentrations and is computationally efficient.

Findings

Moving boundary model predicts low-concentration nutrient uptake more accurately.

Fixed boundary model overestimates uptake at low concentrations.

The new model offers a simpler, low-cost alternative to 3D-architectural models.

Abstract

This work examines the relevance of the one-dimensional models used to study the influx and the cumulative uptake of nutrient by roots. The physical models studied are the fixed boundary model (Barber and Cushman 1981) and an improved version of our moving boundary model (Reginato et al. 2000). A weight averaged expression to compute influx on root surface and a generalized formula to estimate the cumulative nutrient uptake are used. The moving boundary model problem is solved by the adaptive finite element method. For comparison of simulations of influx and cumulative uptake versus observed results six set of data extracted from literature are used. For ions without limitations of availability fixed and moving boundary models produces similar results with small errors. Instead, to low concentrations, the fixed boundary model over predicts while the moving boundary model always produces better results mainly for K. For the P uptake the moving boundary model produces better results only when the concentrations are very low and their predictions are comparable to the obtained by a 3D-architectural model. The obtained improvements would explain any failures of previous models for ions of low availability. Therefore, our model could be a simpler alternative due to its low computational burden.