A one-dimensional model of water flow in soil-plant systems based on plant architecture

The estimation of root water uptake and water flow in plants is crucial to quantify transpiration and hence the water exchange between land surface and atmosphere. In particular the soil water extraction by plant roots which provides the water supply of plants is a highly dynamic and non-linear process interacting with soil transport processes that are mainly determined by the natural soil variability at different scales. To better consider this root-soil interaction we extended and further developed a finite element tree hydro-dynamics model based on the one-dimensional (1D) porous media equation. This is achieved by including in addition to the explicit three-dimensional (3D) architectural representation of the tree crown a corresponding 3D characterisation of the root system. This 1D xylem water flow model was then coupled to a soil water flow model derived also from the 1D porous media equation. We apply the new model to conduct sensitivity analysis of root water uptake and transpiration dynamics and compare the results to simulation results obtained by using a 3D model of soil water flow and root water uptake. Based on data from lysimeter experiments with young European beech trees (Fagus silvatica L.) is shown, that the model is able to correctly describe transpiration and soil water flow. In conclusion, compared to a fully 3D model the 1D porous media approach provides a computationally efficient alternative, able to reproduce the main mechanisms of plant hydro-dynamics including root water uptake from soil.     

The effect of a constant efflux on solute movement to a root

This paper presents two analytical solutions to solute uptake and release by a root (the root exhibits efflux) when both mass and diffusive flows are considered and the water content of the soil is maintained constant. The first solution is for a constant solute concentration at some finite distance from the root, while the second is when there is no solute recharge from the soil outside a cylinder coaxle with the root.Several examples are presented to show the effect of the effluxive term. It is shown that the point where the ratio of efflux to initial ion concentration in solution is equal to the difference between root absorbing power and water flux at the root, is critical to nutrient depletion or buildup at the root surface. It is also shown for the case of no recharge that the concentration profiles when efflux is considered are markedly different than where efflux is not considered.Contribution from the Purdue Agric. Exp. Stn., West Lafayette, IN, 47907. Journal Paper Number7458.     

Use of the root contact concept,an empirical leaf conductance model and pressure-volume curves in simulating crop water relations

A simulation model “DanStress” was developed for studying the integrated effects of soil, crop and climatic conditions on water relations and water use of field grown cereal crops. The root zone was separated into 0.1 m deep layers of topsoil and subsoil. For each layer the water potential at the root surface was calculated by a single root model, and the uptake of water across the root was calculated by a root contact model. Crop transpiration was calculated by Monteith's combination equation for vapour flow. Crop conductance to water vapour transfer for use in Monteith's combination equation was scaled up from an empirical stomatal conductance model used on sunlit and shaded crop surfaces of different crop layers. In the model, transpirational water loss originates from root water uptake and changes in crop water storage. Crop water capacitance, used for describing the water storage, was derived from the slope of pressure-volume (PV) curves of the leaves. PV curves were also used for deriving crop water potential, osmotic potential, and turgor pressure. The model could simulate detailed diurnal soil-crop water relations during a 23-day-drying cycle with time steps of one hour. During the grain filling period in spring barley (Hordeum distichum L.), grown in a sandy soil in the field, measured and predicted values of leaf water and osmotic potential, RWC, and leaf stomatal conductance were compared. Good agreement was obtained between measured and predicted values at different soil water deficits and climatic conditions. In the field, measured and predicted volumetric soil water contents (θ) of topsoil and subsoil layers were also compared during a drying cycle. Predicted and measured θ-values as a function of soil water deficits were similar suggesting that the root contact model approach was valid. From the investigation we concluded: (I) a model, which takes the degree of contact between root surface and soil water into account, can be used in sandy soil for calculation of root water uptake, so that the root conductance during soil water depletion only varies by the degree of contact; (II) crop conductance, used for calculation of crop transpiration, can be scaled up from an empirical single leaf stomatal conductance model controlled by the level of leaf water potential and micrometeorological conditions; (III) PV curves are usable for describing crop water status including crop water storage.     

Modeling soil water movement with water uptake by roots

Soil water movement with root water uptake is a key process for plant growth and transport of water and chemicals in the soil-plant system. In this study, a root water extraction model was developed to incorporate the effect of soil water deficit and plant root distributions on plant transpiration of annual crops. For several annual crops, normalized root density distribution functions were established to characterize the relative distributions of root density at different growth stages. The ratio of actual to potential cumulative transpiration was used to determine plant leaf area index under water stress from measurements of plant leaf area index at optimal soil water condition. The root water uptake model was implemented in a numerical model. The numerical model was applied to simulate soil water movement with root water uptake and simulation results were compared with field experimental data. The simulated soil matric potential, soil water content and cumulative evapotranspiration had reasonable agreement with the measured data. Potentially the numerical model implemented with the root water extraction model is a useful tool to study various problems related to flow transport with plant water uptake in variably saturated soils. This revised version was published online in June 2006 with corrections to the Cover Date.     

Sampling, defining, characterising and modeling the rhizosphere—the soil science tool box

We review methods and models that help to assess how root activity changes soil properties and affects the fluxes of matter in the soil. Subsections discuss (1) experimental systems including plant treatments in artificial media, studying the interaction of model root and microbial exudates with soil constituents, and microcosms to distinguish between soil compartments differing in root influence, (2) the sampling and characterization of rhizosphere soil and solution, focusing on the separation of soil at different distances from roots and the spatially resolved sampling of soil solution, (3) cutting-edge methodologies to study chemical effects in soil, including the estimation of bioavailable element or ion contents (biosensors, diffusive gradients in thin-films), studying the ultrastructure of soil components, localizing elements and determining their chemical form (microscopy, diffractometry, spectroscopy), tracing the compartmentalization of substances in soils (isotope probing, autoradiography), and imaging gradients in-situ with micro electrodes or gels or filter papers containing dye indicators, (4) spectroscopic and geophysical methods to study the plants influence on the distribution of water in soils, and (5) the modeling of rhizosphere processes. Macroscopic models with a rudimentary depiction of rhizosphere processes are used to predict water or nutrient requirements by crops and forests, to estimate biogeochemical element cycles, to calculate soil water transport on a profile scale, or to simulate the development of root systems. Microscopic or explanatory models are based on mechanistic or empirical relations that describe processes on a single root or root system scale and/or chemical reactions in soil solution. We conclude that in general we have the tools at hand to assess individual processes on the microscale under rather artificial conditions. Microscopic, spectroscopic and tracer methods to look at processes in small “aliquots” of naturally structured soil seem to step out of their infancy and have become promising tools to better understand the complex interactions between plant roots, soil and microorganisms. On the field scale, while there are promising first results on using non-invasive geophysical methods to assess the plant’s influence on soil moisture, there are no such tools in the pipeline to assess the spatial heterogeneity of chemical properties and processes in the field. Here, macroscopic models have to be used, or model results on the microscopic level have to be scaled up to the whole plant or plot scale. Upscaling is recognized as a major challenge.     

Transient three-dimensional modeling of soil water and solute transport with simultaneous root growth,root water and nutrient uptake

A three-dimensional solute transport model was developed and linked to a three-dimensional transient model for soil water flow and root growth. The simulation domain is discretized into a grid of finite elements by which the soil physical properties are spatially distributed. Solute transport modeling includes passive and active nutrient uptake by roots as well as zero- and first-order source/sink terms. Root water uptake modeling accounts for matric and osmotic potential effects on water and passive nutrient uptake. Root age effects on root water and nutrient uptake activity have been included, as well as the influence of nutrient deficiency and ion toxicity on root growth. Examples illustrate simulations with different levels of model complexity, depending on the amount of information available to the user. At the simplest level, root growth is simulated as a function of mechanical soil strength only. Application of the intermediate level with root water and nutrient uptake simulates the influence of timing and amount of NO3 application on leaching. The most comprehensive level includes simulation of root and shoot growth as influenced by soil water and nutrient status, temperature, and dynamic allocation of assimilate to root and shoot.     

Root zone solute dynamics under drip irrigation: A review

Infiltration and subsequent distribution of water and solutes under cropped conditions is strongly dependent on the irrigation method, soil type, crop root distribution, and uptake patterns and rates of water and solutes. This review discusses aspects of soil water and solute dynamics as affected by the irrigation and fertigation methods, in the presence of active plant uptake of water and solutes. Fertigation with poor quality water can lead to accumulation of salts in the root zone to toxic levels, potentially causing deterioration of soil hydraulic and physical properties. The high frequency of application under drip irrigation enables maintenance of salts at tolerable levels within the rooting zone. Plant roots play a major role in soil water and solute dynamics by modifying the water and solute uptake patterns in the rooting zone. Modeling of root uptake of water and solutes is commonly based on incorporating spatial root distribution and root length or density. Other models attempt to construct root architecture. Corn uptake rate and pattern of nitrate nitrogen was determined from field studies of nitrate dynamics under drip irrigation using TDR monitoring. The determined nitrate nitrogen uptake rates are within literature values for corn. This revised version was published online in June 2006 with corrections to the Cover Date.     

Modelling the impact of heterogeneous rootzone water distribution on the regulation of transpiration by hormone transport and/or hydraulic pressures

Aims

A simulation model to demonstrate that soil water potential can regulate transpiration, by influencing leaf water potential and/or inducing root production of chemical signals that are transported to the leaves.

Methods

Signalling impacts on the relationship between soil water potential and transpiration were simulated by coupling a 3D model for water flow in soil, into and through roots (Javaux et al. 2008) with a model for xylem transport of chemicals (produced as a function of local root water potential). Stomatal conductance was regulated by simulated leaf water potential (H) and/or foliar chemical signal concentrations (C; H?+?C). Split-root experiments were simulated by varying transpiration demands and irrigation placement.

Results

While regulation of stomatal conductance by chemical transport was unstable and oscillatory, simulated transpiration over time and root water uptake from the two soil compartments were similar for both H and H?+?C regulation. Increased stomatal sensitivity more strongly decreased transpiration, and decreased threshold root water potential (below which a chemical signal is produced) delayed transpiration reduction.

Conclusions

Although simulations with H?+?C regulation qualitatively reproduced transpiration of plants exposed to partial rootzone drying (PRD), long-term effects seemed negligible. Moreover, most transpiration responses to PRD could be explained by hydraulic signalling alone.     

A soil-plant model applied to phytoremediation of metals

This study reports a phytoremediation pot experiment using an open-source program. Unsaturated water flow was described by the Richards' equation and solute transport by the advection-dispersion equation. Sink terms in the governing flow and transport equations accounted for root water and solute uptake, respectively. Experimental data were related to application of Vetiver grass to soil contaminated by metal ions. Sensitivity analysis revealed that due to the specific experimental set-up (bottom flux not allowed), hydraulic model parameters did not influence root water (and contaminant) uptake. In contrast, the results were highly correlated with plant solar radiation interception efficiency (leaf area index). The amounts of metals accumulated in the plant tissue were compared to numerical values of cumulative uptake. Pb²⁺ and Zn²⁺ uptake was satisfactorily described using a passive model. However, for Ni²⁺ and Cd²⁺, a specific calibration of the active uptake model was necessary. Calibrated MM parameters for Ni²⁺, Cd²⁺, and Pb²⁺ were compared to values in the literature, generally suggesting lower rates and saturation advance. A parameter (saturation ratio) was introduced to assess the efficiency of contaminant uptake. Numerical analysis, applying actual field conditions, showed the limitation of the active model for being independent of the transpiration rate.     

Quantification of root water uptake in soil using X‐ray computed tomography and image‐based modelling

Spatially averaged models of root–soil interactions are often used to calculate plant water uptake. Using a combination of X‐ray computed tomography (CT) and image‐based modelling, we tested the accuracy of this spatial averaging by directly calculating plant water uptake for young wheat plants in two soil types. The root system was imaged using X‐ray CT at 2, 4, 6, 8 and 12 d after transplanting. The roots were segmented using semi‐automated root tracking for speed and reproducibility. The segmented geometries were converted to a mesh suitable for the numerical solution of Richards' equation. Richards' equation was parameterized using existing pore scale studies of soil hydraulic properties in the rhizosphere of wheat plants. Image‐based modelling allows the spatial distribution of water around the root to be visualized and the fluxes into the root to be calculated. By comparing the results obtained through image‐based modelling to spatially averaged models, the impact of root architecture and geometry in water uptake was quantified. We observed that the spatially averaged models performed well in comparison to the image‐based models with <2% difference in uptake. However, the spatial averaging loses important information regarding the spatial distribution of water near the root system.     

Water use and sodium chloride uptake by apple trees

Summary Apple trees grown with their root systems split into halves were used to study the effects of non-uniform salinity stress within a root system upon salt and water uptake. Water uptake declined rapidly when sodium chloride solution (90 meq l⁻¹) was added to any root zone but uptake increased correspondingly in the non-saline root zone of each tree. This changed pattern of water uptake with partial salinization did not change the total water use by the trees compared with their water use when neither root zone was salt stressed. After a‘steady-state’ condition of water uptake had been reached 80 to 85% of the water was taken up in the non-saline root zone. Irrigation at three soil matric potential intervals of −6.6, −33 and −66 kPa allowed to develop in the non-saline root zone of each tree did not affect water use responses. Leaf concentrations of Ca, Mg and K were unaffected by treatments. Chloride and Na concentrations increased in leaves with exposure to salinity stress in half root zones and with increasing soil matric potential stress. Some evidence was obtained using tritium enriched water that water was transferred from a non-saline root zone into a saline root zone but the volume involved was unmeasurable.     

Effect of water stress on leaf and root growth,and water uptake ofGmelina arborea ROXB. seedlings

Young seedlings ofGmelina arborea Roxb. were subjected to 2 weeks of drought. Despite the gradual reduction in stomatal conductance, leaf and root growth was not affected until the later part of the stress period. This was attributed to solute adjustment in the roots of the plants. As the severity of water stress increased, root growth was prolific in all the soil segments. As a result, water in the lowest soil segment was used to maintain plant turgor, which in turn sustains the leaf and root growth during the water-stress treatment. The influence of soil water content and soil water potential upon soil water uptake rate was also evaluated on soil profile basis. Rates of extraction began to decline in all soil segments as soon as soil water potential fell below -0.06 MPa, presumably as a result of vapour gaps between the root and soil (root: soil interface resistance). It is suggested that the growth of roots ofGmelina plants away from drying soil will minimize the resistance to water uptake.     

Tracing root permeability: comparison of tracer methods

Root epidermis and apoplastic barriers (endodermis and exodermis) are the critical root structures involved in setting up plant-soil interface by regulating free apoplastic movement of solutes within root tissues. Probing root apoplast permeability with “apoplastic tracers” presents one of scarce tools available for detection of “apoplastic leakage” sites and evaluation of their role in overall root uptake of water, nutrients, or pollutants. Although the tracers are used for many decades, there is still not an ideal apoplastic tracer and flawless procedure with straightforward interpretation. In this article, we present our experience with the most frequently used tracers representing various types of chemicals with different characteristics. We examine their behaviour, characteristics, and limitations. Here, we show that results gained with an apoplastic tracer assay technique are reliable but depend on many parameters–chemical properties of a selected tracer, plant species, cell wall properties, exposure time, or sample processing.     

Leaching requirement conceptual models for reactive salt

Accurate prediction of the leaching requirements (Lr) of crops and striving to attain them is essential for efficient irrigation water use. Solute modeling was extended to develop four Lr conceptual models that do not neglect solute reactions in the root-zone, surface evaporation, and the influence of immobile wetted pore space. The models were based on: (i) the water movement equation which included an exponential water-uptake function (-e) or the 40-30-20-10 water-uptake function (-4); (ii) the solute movement equation for a reactive salt of a linear reaction term (the Lrchem-e and Lrchem-4 models); or the employment of output (salinity of soil solution, EC vs concentration factor, CF) of the SAO comprehensive chemical model (the LrSAO-e and LrSAO-4 models); and (iii) the inclusion of an effective soil solution volume in the transport equations. The root-zone average relative effective soil solution volume νeff (L | L50, p) was of sigmoidal response to leaching fraction (L) with two adjustable parameters L50 and p; the root-zone average reduced retention coefficient decreased linearly with L; and salt concentration at soil surface was related to salt concentration of irrigation water (ECi) by the fraction of irrigation water that evaporated (∈). The resulted concentration profiles indicated the salt behaved as a conservative one down to a threshold depth (xs) below of which salt was retained and precipitated. The depth of the conservative-salt front, xs increased with L and the 40-30-20-10 water-uptake pattern overestimated the xs depth relative to the exponential pattern. Concentration profiles were integrated to compute the root-zone average salinity, which was converted to crop salt-tolerance threshold (AE). The four conceptual models were successfully calibrated using experimental AE/ECi vs. Lr data with the input parameter values: ς = 0.27, p = 1.44, L50 = 0.16, ω = 2, and ∈ = 0 or 0.1 for the exponential or the 40-30-20-10 pattern, respectively; where ς is relative root length parameter and ω is a weighing parameter. No significant difference existed between the four model correlations at the 0.05 level. The four models require ECi and AE of the crop as input for Lr prediction. Sensitivity analysis revealed predicted Lr was sensitive the least to error in ∈. For tolerant and moderately tolerant crops Lr was sensitive the most to ς, and for sensitive crops to L50 and p. Model verification and validation were discussed. In deriving the present Lr models, no osmotic adjustment was required and both the exponential and the 40-30-20-10 water uptake patterns were, equivalently, applicable. This revised version was published online in July 2006 with corrections to the Cover Date.     

Novel Methods of Measuring Hydraulic Conductivity of Tree Root Systems and Interpretation Using AMAIZED (A Maize-Root Dynamic Model for Water and Solute Transport)

Steady-state and dynamic methods were used to measure the conductivity to water flow in large woody root systems. The methods were destructive in that the root must be excised from the shoot but do not require removal of the root from the soil. The methods involve pushing water from the excised base of the root to the apex, causing flow in a direction opposite to that during normal transpiration. Sample data are given for two tropical (Cecropia obtusifolia and Lacistema aggregatum) and two temperate species (Acer saccharum and Juglans regia cv Lara). A hysteresis was observed in the relationship between applied pressure and resulting flow during dynamic measurements. A mathematical model (AMAIZED) was derived for the dynamics of solute and water flow in roots. The model was used to interpret results obtained from steady-state and dynamic measurements. AMAIZED is mathematically identical with the equations that describe Munch pressure flow of solute and water in the phloem of leaves. Results are discussed in terms of the predictions of AMAIZED, and suggestions for the improvement of methods are made.     

Modelling the contribution of arbuscular mycorrhizal fungi to plant phosphate uptake

In this paper, we investigate the role of arbuscular mycorrhizal fungi in plant phosphorus nutrition. We develop a mathematical model which quantitatively assesses the contribution of external fungal hyphae to plant phosphate uptake.We derive an equation for solute uptake by a growing fungal mycelium which we couple with a model for root uptake. We analyse the model using nondimensionalization and numerical simulations.Simulations predict that removal of phosphate from soil is dominated by hyphal uptake as opposed to root uptake. Model analysis shows that the depletion zones around hyphae overlap within 8 h and that the transfer between fungus and root is a critical step for the behaviour of phosphorus within the mycelial phase. We also show that the volume fraction of mycelium is negligibly small in comparison to other soil phases.This is the first model to quantify the contribution of mycorrhizal fungi to plant phosphate uptake. A full data set for model parametrization and validation is not currently available. Therefore, more complete sets of experimental measurements are necessary to make this model more applicable.     

Short-term responses of Brassica rapa plants to low root temperature: Effects on nitrate uptake and its translocation to the shoot

Brassica rapa L. plants were grown hydroponically for 5 or 6 weeks at 20°C and then half batches of plants were transferred to tanks in which the root temperature was lowered decrementally over 1 h to 7°C. Changes in nitrate uptake rate (NUR) and nitrate transfer from roots were studied in relation to transpiration and root pressure xylem exudation flow rates over a 48- or 72-h period. The response of plants following the root temperature decrease was biphasic. During phase 1, NUR and water and solute flow rates through the root decreased sharply. Coping mechanisms came into operation during phase 2, and tended to offset the effects of low temperature. The 3-h cold-treated roots exhibited a very low NUR but 48-h cold-treated roots partly recovered their ability to absorb nitrate. Transpiration rate decreased more slowly (during 24 h) than both root xylem exudation and parameters of root conductivity (during 6 h). Beyond these respective times, transpiration rate was balanced while root xylem exudation clearly increased, but without returning to the level of control plants. Nitrate transfer to the root xylem was strongly and rapidly affected by low root temperature, but the subsequent readjustment was such that no or little difference compared with the control was apparent after 48 h. Water and solute flows were strongly decreased when nitrate was replaced by chloride in the culture solution during exudation sampling. The major role of nitrate in root hydraulic conductivity and root xylem exudation is discussed.     

A split-pot experiment with sorghum to test a root water uptake partitioning model

Correct modeling of root water uptake partitioning over depth is an important issue in hydrological and crop growth models. Recently a physically based model to describe root water uptake was developed at single root scale and upscaled to the root system scale considering a homogeneous distribution of roots per soil layer. Root water uptake partitioning is calculated over soil layers or compartments as a function of respective soil hydraulic conditions, specifically the soil matric flux potential, root characteristics and a root system efficiency factor to compensate for within-layer root system heterogeneities. The performance of this model was tested in an experiment performed in two-compartment split-pot lysimeters with sorghum plants. The compartments were submitted to different irrigation cycles resulting in contrasting water contents over time. The root system efficiency factor was determined to be about 0.05. Release of water from roots to soil was predicted and observed on several occasions during the experiment; however, model predictions suggested root water release to occur more often and at a higher rate than observed. This may be due to not considering internal root system resistances, thus overestimating the ease with which roots can act as conductors of water. Excluding these erroneous predictions from the dataset, statistical indices show model performance to be of good quality.     

重金属对黄瓜籽苗发育影响的研究

选用黄瓜(Cucumis sativus)籽苗为材料,硫酸铜,醋酸铅、硫酸锌、氯化镉和氯化镍为化学处理试剂,研究它们对黄瓜籽苗的生长及其根尖细胞有丝分裂的影响。发现随着化学处理试剂浓度的增大,黄瓜籽苗根长度、苗高度、侧根数和最长侧根的长度均有所下降,其中下降最明显的是根长度。同样,根尖细胞有丝分裂的细胞数量明显减少,细胞分裂速率减慢。5种重金属盐中,硫酸铜的毒性最甚,氯化镉、醋酸铅次之。