Some Observations on the Movement of Water to Plant Roots<sup>1</sup>

Gardner, W. R.; Ehlig, C. F.

doi:10.2134/agronj1962.00021962005400050024x

Cited by 77 publications

(36 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However, as a simpler alternative we can use the zero flux or full saturation boundary condition at the bottom of the growing box. Both of these boundary conditions are motivated by experimental conditions: (a) zero flux corresponds to the plant growth pot that is sealed at the bottom so that no water leaks in or out from the pot [44]; (b) full saturation boundary condition corresponds to an experiment where the growing pot is seated in the water reservoir which is constantly topped up so that the soil at a given level is always fully saturated [45].…”

Section: Boundary Conditionmentioning

confidence: 99%

See 1 more Smart Citation

A mathematical model of plant nutrient uptake

Koebernick¹,

Fowler²,

Darrah

2001

Journal of Mathematical Biology

113

159

View full text Add to dashboard Cite

This thesis deals with the mathematical modelling of nutrient uptake by plant roots. It starts with the Nye-Tinker-Barber model for nutrient uptake by a single bare cylindrical root. The model is treated using matched asymptotic expansion and an analytic formula for the rate of nutrient uptake is derived for the first time. The basic model is then extended to include root hairs and mycorrhizae, which have been found experimentally to be very important for the uptake of immobile nutrients. Again, analytic expressions for nutrient uptake are derived. The simplicity and clarity of the analytical formulae for the solution of the single root models allows the extension of these models to more realistic branched roots. These models clearly show that the "volume averaging of branching structure" technique commonly used to extend the Nye-Tinker-Barber with experiments can lead to large errors. The same models also indicate that in the absence of large-scale water movement, due to rainfall, fertiliser fails to penetrate into the soil. This motivates us to build a model for water movement and uptake by branched root structures. This model considers the simultaneous flow of water in the soil, uptake by the roots, and flow within the root branching network to the stems of the plant. The water uptake model shows that the water saturation can develop pseudo-steadystate wet and dry zones in the rooting region of the soil. The dry zone is shown to stop the movement of nutrient from the top of the soil to the groundwater. Finally we present a model for the simultaneous movement and uptake of both nutrients and water. This is discussed as a new tool for interpreting available experimental results and designing future experiments. The parallels between evolution and mathematical optimisation are also discussed.

show abstract

Section: Boundary Conditionmentioning

confidence: 99%

“…The zero flux boundary condition at the bottom boundary of the growing box [44] is given by 37) and constant saturation at the bottom of the growing box [45] or in the field [134], is given by…”

Section: Boundary Conditionmentioning

confidence: 99%

A mathematical model of plant nutrient uptake

Koebernick¹,

Fowler²,

Darrah

2001

Journal of Mathematical Biology

113

159

View full text Add to dashboard Cite

show abstract

“…Soil water matric head distributions around the idealized root were calculated. This concept was extended in later papers [Gardner, 1964[Gardner, , 1965Gardner and Ehlig, 1962] and proved to be very insightful but lacked practical applicability since the detailed geometry of the rooting system is difficult to measure and is time dependent. Consequently, most root water extraction terms have been developed using a macroscopic rather than a microscopic approach.…”

Section: Introductionmentioning

confidence: 99%

One‐, two‐, and three‐dimensional root water uptake functions for transient modeling

Vrugt¹,

Wijk²,

Hopmans³

et al. 2001

Water Resources Research

299

236

View full text Add to dashboard Cite

Abstract. Although solutions of multidimensional transient water flow can be obtained by numerical modeling, their application may be limited as root water uptake is generally considered to be one-or two-dimensional only. This is especially the case for trees. The first objective of this paper is to test the suitability of a three-dimensional root water uptake model for the simultaneous simulation of transient soil water flow around an almond tree. The soil hydraulic and root water uptake parameters were optimized by minimizing the residuals between measured and simulated water content data. Water content was measured in a three-dimensional grid around a sprinkler-irrigated almond tree for a 16 day period, following irrigation. A second objective was to compare the performance and results of the three-dimensional flow model with one-and twodimensional root water uptake models. For this purpose, measured water contents were aggregated in the x and y direction in the one-dimensional case and in the radial direction for the two-dimensional uptake model. For the estimation of root water uptake model parameters a genetic algorithm was used to estimate the approximate global minimum of the parameter space, whereas final parameters were determined using the Simplex optimization algorithm. With the optimized root water uptake parameters, simulated and measured water contents during the 16-day period were in excellent agreement for all root water uptake models. Most significantly, the spatial variation in flux density below the rooting zone decreased when reducing multidimensional root water uptake to fewer dimensions, thereby justifying the proposed multidimensional approach.

show abstract

“…Obviously, the soil constituted the major resistance in the pathway of the water from the soil to the plant leaves. This confir.ms the early flndings of Gardner and Ehlig (1962), and indicates that at low soil water potentials the unsaturated permeability is the most important factor controlling the rate of water uptake by plant roots.…”

Section: Yang and De Jong-water Uptake Patterns And Flow Resistancementioning

confidence: 73%

“…The resistance to water flow in both the soil and the plant was calculated from the equation proposed by Gardner and Ehlig (1962). Assurning that the root system varies only vertically, the root zone is divided into a number of layers and the water uptake for nth layer written as:…”

Section: Methodsmentioning

confidence: 99%