Modeling compensated root water and nutrient uptake

Abstract

Plant root water and nutrient uptake is one of the most important processes in subsurface unsaturated flow and transport modeling, as root uptake controls actual plant evapotranspiration, water recharge and nutrient leaching to the groundwater, and exerts a major influence on predictions of global climate models. In general, unsaturated models describe root uptake relatively simple. For example, root water uptake is mostly uncompensated and nutrient uptake is simulated assuming that all uptake is passive, through the water uptake pathway only. We present a new compensated root water and nutrient uptake model, implemented in HYDRUS. The so-called root adaptability factor represents a threshold value above which reduced root water or nutrient uptake in water- or nutrient-stressed parts of the root zone is fully compensated for by increased uptake in other soil regions that are less stressed. Using a critical value of the water stress index, water uptake compensation is proportional to the water stress response function. Total root nutrient uptake is determined from the total of active and passive nutrient uptake. The partitioning between passive and active uptake is controlled by the a priori defined concentration value c_max. Passive nutrient uptake is simulated by multiplying root water uptake with the dissolved nutrient concentration, for soil solution concentration values below c_max. Passive nutrient uptake is thus zero when c_max is equal to zero. As the active nutrient uptake is obtained from the difference between plant nutrient demand and passive nutrient uptake (using Michaelis–Menten kinetics), the presented model thus implies that reduced passive nutrient uptake is compensated for by active nutrient uptake. In addition, the proposed root uptake model includes compensation for active nutrient uptake, in a similar way as used for root water uptake. The proposed root water and nutrient uptake model is demonstrated by several hypothetical examples, for plants supplied by water due to capillary rise from groundwater and surface drip irrigation.

Introduction

Root surfaces represent one of the most important phase boundaries in nature since most mineral nutrients essential for life enter the biosphere and the food chains of the animal world through the roots of higher plants (Nissen, 1991). Similarly, root water and nutrient uptake is one of the most important processes considered in numerical models simulating water content and fluxes in the subsurface, thus controlling water flow (recharge) and nutrient transport (leaching) to the groundwater, and exerting a major influence on predictions of climate change impacts (Feddes and Raats, 2004) on terrestrial ecological systems, driving new research at understanding roots and their functioning (Skaggs and Shouse, 2008).

There are two major approaches generally used for the simulation of root water uptake in vadose zone hydrological models, to be applied at the plot or field scale (Hopmans and Bristow, 2002). Early detailed quantitative studies of water extraction by plant roots were based on a microscopic or mesoscopic (Feddes and Raats, 2004) approach that considered a single root to be an infinitely long cylinder of uniform radius and water-absorbing properties (Gardner, 1960). Water flow to a root was described using the Richards equation formulated in radial coordinates, with flow into the root driven by water potential gradients between the root and surrounding soil and proportional to the hydraulic conductivity of the soil surrounding the root (Mmolawa and Or, 2000) or the root radial water conductivity parameter (Roose and Fowler, 2004). Recent numerical modeling studies are increasingly applying the integrated plant root–soil domain approach, whereby total plant transpiration is computed from solution of water potential in the combined soil and root domain, solving for both root and soil water potential (e.g., Doussan et al., 2006, Javaux et al., 2008). Several models have been suggested that simulate individual roots and overall plant root architecture (e.g., Clausnitzer and Hopmans, 1994, Kastner-Maresch and Mooney, 1994, Brown et al., 1997, Grant, 1998, Somma et al., 1998, Biondini, 2001). These models often consider specific processes such as biomass allocation to individual roots (e.g., Kastner-Maresch and Mooney, 1994, Grant, 1998, Somma et al., 1998, Biondini, 2001), root growth redirection to areas with high soil nutrient concentrations (e.g., Somma et al., 1998, Biondini, 2001), linking of functioning of microbial ecosystems (Brown et al., 1997) and mycorryzal growth (Grant, 1998) to spatial structure of roots, or competition of different plant species for nutrients (e.g., Biondini, 2001, Raynaud and Leadlley, 2005). In addition to being more realistic in simulating soil-root interactions at the individual rootlet scale, the main advantage of this approach is that it automatically allows for compensation of soil water stress, as root water uptake is controlled by computed local water potential gradients and root conductivity for the whole root system. However, because of the lack of relevant soil and root data and the huge computational requirements for simulation purposes at this microscopic scale, soil water flow models that consider flow to each individual rootlet or plant root architecture have been limited to applications at a relatively small scale of a single plant.

Most vadose zone models that are used at the plot or field scale (e.g., Jarvis, 1994, Flerchinger et al., 1996, van Dam et al., 1997, Fayer, 2000, van den Berg et al., 2002, Šimůnek et al., 2008) utilize the macroscopic approach, whereby the potential transpiration is distributed over the root zone proportionally to root density, and is locally reduced depending on soil saturation and salinity status (Molz, 1981). This much more widely used approach (e.g., Feddes et al., 1974, Bouten, 1995) neglects effects of the root geometry and flow pathways around roots, and formulates root water uptake using a macroscopic sink term that lumps root water uptake processes into a single term of the governing mass balance equation. A wide variety of root water uptake reduction functions have been suggested, ranging from a simple two-parameter threshold and slope function (Maas, 1990) or an S-shaped function (van Genuchten, 1987), to more complex functions that can include up to 5 fitting parameters such as suggested by Feddes et al. (1978). We refer readers to the review paper by Feddes and Raats (2004) for more details.

Usually, a compensation mechanism to balance reduced water uptake from one part of the rhizosphere by increased uptake in another less-stressed region of the rooting zone, while simulated in microscopic models, is neglected in vadose zone models. There is, however, growing experimental evidence that plants, especially non-cultural plants, can compensate for water stress in one part of the root zone by taking up water from parts of the root zone where water is available (e.g., Taylor and Klepper, 1978, Hasegawa and Yoshida, 1982, English and Raja, 1996, Stikic et al., 2003, Leib et al., 2006). The MACRO model (Jarvis, 1994) is an exception among the more widely used models as it uses a critical value of the water stress index, or root adaptability factor, to allow for compensated root water uptake. This factor represents a threshold value above which root water uptake that is reduced in stressed parts of the root zone is fully compensated for by increased uptake from other parts. Among the research models, in their ENVIRO-GRO model, Pang and Letey (1998) used a similar threshold value to compute partial root water uptake compensation. Similarly, Li et al. (2001) and Bouten (1995) distributed the potential transpiration across the root zone according to a weighted stress index, which was a function of both root distribution and soil water availability or water saturation fraction, respectively. A different approach was used by Adiku et al. (2000), who assumed that plants seek to minimize the total rate of energy expenditure during root water uptake. They formulated the root water uptake problem as a minimization problem and solved it using a dynamic program framework. Their optimized model simulated patterns of water extraction from uniformly wet soil profiles, with highest water extraction rates in the section where the root length density was also highest. For conditions with a dry soil surface, a reduction of root water uptake from the drier near soil surface zone was compensated for by an increased root activity at greater soil depths, irrespective of root distribution. A review of compensatory modeling approaches was recently presented by Skaggs et al. (2006).

Plant nutrient availability and uptake is controlled by both soil transport and plant uptake mechanisms. A detailed description of nutrient uptake is often included in agronomic models that simulate differentiation of plant nutrient demand during various physiological growth stages (e.g., Parton et al., 1987, Jones and Ritchie, 1990). These models, however, typically greatly simplify soil water flow and nutrient transport towards the root–soil interface. In contrast, vadose zone models greatly simplify root nutrient uptake, often considering only its passive component and neglecting plant growth dynamics (e.g., Jarvis, 1994, Flerchinger et al., 1996, van Dam et al., 1997, Fayer, 2000, van den Berg et al., 2002, Šimůnek et al., 2008).

Solute transport in soils occurs by both mass flow and molecular diffusion. In the case of non-adsorbing nutrients, nutrient uptake is controlled mainly by mass flow, as is the case of nitrate-N (e.g., Barber, 1995). In some cases, mass flow of specific nutrients (e.g., Ca²⁺ and Mg²⁺) may exceed the plant requirements, resulting in accumulation of particular ions or even precipitation of corresponding solids (e.g., CaSO₄) at the root surface (Neumann and Römheld, 2002). Alternatively, nutrients that exhibit low solubility in soil solutions, such as P, K, NH₄⁺, and most micronutrients, are rapidly depleted by root uptake in the soil solution (Neumann and Römheld, 2002), since roots absorb nutrients only in the dissolved state. A resulting concentration gradient causes nutrient diffusion from the bulk soil toward the root surface. A decrease in the solution concentration also disturbs the equilibrium between the nutrients in solution and those bound to the solid soil phase, resulting in their release from the solid phase and replenishing of the solution concentration (Jungk, 2002). Plants may utilize various additional strategies to mobilize nutrients, i.e., to release them from their association with the solid phase, such as modification of the chemical composition or association of roots with micro-organisms (Neumann and Römheld, 2002).

There are many physical, biological, and physiological mechanisms that are involved in the nutrient uptake by plant roots (e.g., Jungk, 2002, Hopmans and Bristow, 2002, Darrah et al., 2006). These can be broadly divided into passive and active components. While the passive component represents the mass flow of nutrient into roots with water, the active component represents a very diverse range of various biological energy-driven processes (e.g., Luxmoore et al., 1978, Jungk, 2002, Neumann and Römheld, 2002, Silberbush, 2002, Hopmans and Bristow, 2002) that affect the movement of specific nutrients from the root's free space (cell walls) into the plant. The term passive nutrient uptake is thus defined here as the movement of nutrients into the roots by convective mass flow of water, directly coupled with root water uptake. The term active nutrient uptake then represents the movement of nutrients into the roots induced by other mechanisms than mass flow. These other mechanisms include, for example, specific ion uptake by electro-chemical gradients, ion pumping and uptake through ion channels.

Different fractions of different nutrients are supplied by active and passive mechanisms (Jungk, 2002, Neumann and Römheld, 2002). Shaner and Boyer (1976) demonstrated that the nitrate xylem concentration varied inversely with transpiration rate, and that nitrate uptake is mostly a function of metabolic rate rather than transpiration rate. Active nitrate uptake is considered to occur via NO₃⁻/H⁺ cotransport, or NO₃⁻/H⁺ counter transport via carriers (Haynes, 1986), with the electrochemical gradient generated by proton pumping. Although not strictly proven, it is generally proposed that active uptake dominates in the low supply concentration range and under stress conditions, whereas passive uptake becomes more important at higher soil solution concentrations, via mass flow driven by root water uptake and transpiration (see also Porporato et al. (2003)). Rather than a priori defining the nutrient uptake mechanism, Somma et al. (1998) assumed that passive and active uptake can be considered as additive processes, and allowed for a flexible partitioning between active and passive uptake, with the relative contribution of each to be determined by the model user, and total nutrient uptake controlled by plant nutrient demand (Hopmans, 2006). A similar approach was adopted by Porporato et al. (2003) in their modeling study to evaluate the influence of soil moisture control on soil carbon and nitrogen cycling.

In addition to soil transport mechanisms, nutrient uptake is controlled by the spatial distribution of roots, as influenced by its architecture, morphology and presence of active sites of nutrient uptake, including root hairs (e.g., Somma et al., 1998, Biondini, 2001, Javaux et al., 2008). For nutrients that are immobile (e.g. P) or slowly mobile (ammonium), a root system must develop so that it has access to the nutrients, by increasing their exploration volume. Alternatively, the roots may increase its exploitation power for the specific nutrient by local adaptation of the rooting system, allowing for increased uptake efficiency of the nutrient. When considering the rhizosphere dynamics of water and nutrient uptake, many more mechanisms may have to be considered, including rhizosphere acidification (Pierre and Banwart, 1973) and nitrogen mineralization (Bar-Yosef, 1999).

The root water and nutrient uptake model presented in this manuscript links soil physical principles with plant physiological concepts, thereby providing for an improved integration of scientific principles as needed for an interdisciplinary ecological approach, as compared to most other approaches. We understand that such integration may polarize different view points between scientific fields, and create misunderstandings of notation and concepts that are unique within each discipline. However, the mathematical model introduced here is an honest attempt to cross disciplinary boundaries as required for advancing the science for the broad and complex study field of ecology. The presented subsurface modeling approach will greatly improve scenario testing for soil–plant systems, by including plant uptake mechanisms such as compensated root water and active root nutrient uptake. As we demonstrate in the example simulations, soil nutrient concentrations are controlled by the magnitude of partitioning between passive and active plant nutrient uptake. This is especially important for natural ecosystems, where soil nutrient concentrations are generally much lower for most plant nutrients than in agricultural systems. In addition, natural ecosystems often suffer from environmental stresses (water, nutrient, temperature), and the plant responses to such limiting factors are highly relevant for understanding their functioning and survival strategies. We note that comparison of model results as shown here at the single-plant scale is much more difficult for larger ecosystem models, because of inherent soil heterogeneities, thereby complicating model input requirements and model calibration (Wegehenkel and Mirschel, 2006). Alternatively, less data-intensive and simpler water- and nutrient uptake models may be warranted for ecosystem-scale analysis of soil environmental constraints (De Barros et al., 2004, van den Berg et al., 2002).

The objective of the presented study is to reformulate the mathematical and numerical model of root water and nutrient uptake, as commonly implemented in vadose zone flow and transport models (e.g., Jarvis, 1994, Bouten, 1995, Flerchinger et al., 1996, van Dam et al., 1997, Fayer, 2000, van den Berg et al., 2002, Šimůnek et al., 2008), by including compensation of local water and nutrient stresses, and partitioning between passive and active nutrient uptake. The model should be as general as possible so that it can be applied to an arbitrary nutrient (either adsorbing or non-adsorbing) without any further modifications by simply selecting the relevant model parameters, while at the same time simple enough so that it can be readily implemented in vadose zone flow and transport models. Therefore, we do not strive to simulate individual roots or plant root architecture (e.g., Biondini, 2001 and similar references given above), biomass allocation to roots (e.g., Grant, 1993, Kastner-Maresch and Mooney, 1994), or dynamics of the soil microbial system and the carbon, nitrogen and phosphorus cycles in the soil (e.g., Parton et al., 1987, Wegehenkel and Mirschel, 2006). The new root uptake model is implemented into the HYDRUS software packages (Šimůnek et al., 2006, Šimůnek et al., 2008) and several examples are given demonstrating the effects of the water and nutrient uptake compensation and active nutrient uptake on root zone soil moisture and nutrient distribution.