The Potential for Nitrification and Nitrate Uptake in the Rhizosphere of Wetland Plants: A Modelling Study

Abstract

• Background and Aims It has recently found that lowland rice grown hydroponically is exceptionally efficient in absorbing

\(\mathrm{NO}_{3}^{{-}}\)

⁠, raising the possibility that rice and other wetland plants growing in flooded soil may absorb significant amounts of

\(\mathrm{NO}_{3}^{{-}}\)

formed by nitrification of

\(\mathrm{NH}_{4}^{+}\)

in the rhizosphere. This is important because (a) this

\(\mathrm{NO}_{3}^{{-}}\)

is otherwise lost through denitrification in the soil bulk; and (b) plant growth and yield are generally improved when plants absorb their nitrogen as a mixture of

\(\mathrm{NO}_{3}^{{-}}\)

and

\(\mathrm{NH}_{4}^{+}\)

compared with growth on either N source on its own. A mathematical model is developed here with which to assess the extent of

\(\mathrm{NO}_{3}^{{-}}\)

absorption from the rhizosphere by wetland plants growing in flooded soil, considering the important plant and soil processes operating.

• Methods The model considers rates of O₂ transport away from an individual root and simultaneous O₂ consumption in microbial and non-microbial processes; transport of

\(\mathrm{NH}_{4}^{+}\)

towards the root and its consumption in nitrification and uptake at the root surface; and transport of

\(\mathrm{NO}_{3}^{{-}}\)

formed from

\(\mathrm{NH}_{4}^{+}\)

towards the root and its consumption in denitrification and uptake by the root. The sensitivity of the model's predictions to its input parameters is tested over the range of conditions in which wetland plants grow.

• Key Results The model calculations show that substantial quantities of

\(\mathrm{NO}_{3}^{{-}}\)

can be produced in the rhizosphere of wetland plants through nitrification and taken up by the roots under field conditions. The rates of

\(\mathrm{NO}_{3}^{{-}}\)

uptake can be comparable with those of

\(\mathrm{NH}_{4}^{+}\)

⁠. The model also shows that rates of denitrification and subsequent loss of N from the soil remain small even where

\(\mathrm{NO}_{3}^{{-}}\)

production and uptake are considerable.

• Conclusions Nitrate uptake by wetland plants may be far more important than thought hitherto. This has implications for managing wetland soils and water, as discussed in this paper.

Ammonium, flooded soil, modelling, nitrate, nitrification–denitrification, rice, rhizosphere, root aeration, soil aeration, wetland plants

INTRODUCTION

In flooded soils,

\(\mathrm{NO}_{3}^{{-}}\)

added to the soil or formed by nitrification of

\(\mathrm{NH}_{4}^{+}\)

in aerobic zones near roots or at the soil surface tends to be rapidly lost through denitrification in the anoxic soil bulk, and it is therefore generally assumed that wetland plants take up little

\(\mathrm{NO}_{3}^{{-}}\)

compared with

\(\mathrm{NH}_{4}^{+}\)

⁠. However, in experiments using the radiotracer ¹³N and hydroponically grown seedlings of rice, it was found that a widely grown variety of lowland rice was exceptionally efficient in absorbing and assimilating

\(\mathrm{NO}_{3}^{{-}}\)

compared with

\(\mathrm{NH}_{4}^{+}\)

⁠, and compared with other plant species (Kronzucker et al., 1999, 2000). This suggests a particular adaptation of rice to

\(\mathrm{NO}_{3}^{{-}}\)

and raises the possibility that

\(\mathrm{NO}_{3}^{{-}}\)

absorption by rice and perhaps other wetland plants is more important than generally thought. Since growth and yield of most plant species are superior under mixed

\(\mathrm{NO}_{3}^{{-}}{\mbox{--}}\mathrm{NH}_{4}^{+}\)

nutrition (Taiz and Zeiger, 2002), this possibility is intriguing and warrants further investigation.

Three lines of evidence from Kronzucker et al. suggest unusually efficient

\(\mathrm{NO}_{3}^{{-}}\)

absorption. First, in the Michaelis–Menten relationships fitted to N influx data over an ecologically and agronomically relevant range of N supply, and plants of identical N status, V_max for steady-state N influx was 40 % greater for

\(\mathrm{NO}_{3}^{{-}}\)

than for

\(\mathrm{NH}_{4}^{+}\)

⁠, and K_M was 50 % smaller. Secondly,

\(\mathrm{NO}_{3}^{{-}}\)

absorption was inducible and, in plants deprived of

\(\mathrm{NO}_{3}^{{-}}\)

for 24 h, the induction of

\(\mathrm{NO}_{3}^{{-}}\)

uptake was exceptionally rapid, peaking within 2 h; in comparison, in barley, which is considered a highly efficient

\(\mathrm{NO}_{3}^{{-}}\)

user, full induction requires up to 24 h, and in white spruce, which is considered poor at using

\(\mathrm{NO}_{3}^{{-}}\)

⁠, full induction takes several days (references in Kronzucker et al., 1995, 1997, 2000). Thirdly, from the subcellular distribution of N absorbed by plants fed either

\(\mathrm{NO}_{3}^{{-}}\)

or

\(\mathrm{NH}_{4}^{+}\)

⁠, estimated from the kinetics of ¹³N efflux from labelled roots, the proportion of

\(\mathrm{NO}_{3}^{{-}}\)

translocated to the shoot was 50 % larger, and that lost through efflux back out of the roots 50 % smaller. When

\(\mathrm{NO}_{3}^{{-}}\)

and

\(\mathrm{NH}_{4}^{+}\)

were provided together at the same total N concentration as in the single N species experiments, absorption and assimilation of

\(\mathrm{NO}_{3}^{{-}}\)

were repressed, but those of

\(\mathrm{NH}_{4}^{+}\)

were stimulated to the extent that net N influx was doubled compared with plants fed solely on

\(\mathrm{NH}_{4}^{+}\)

⁠. Because very little free

\(\mathrm{NH}_{4}^{+}\)

is translocated to the shoot in rice (Kronzucker et al., 1998), this indicates that

\(\mathrm{NO}_{3}^{{-}}\)

enhances

\(\mathrm{NH}_{4}^{+}\)

assimilation in some way, possibly through the

\(\mathrm{NO}_{3}^{{-}}\)

-specific induction of additional pathways for

\(\mathrm{NH}_{4}^{+}\)

assimilation (Kronzucker et al., 1999; Britto and Kronzucker, 2004).

The extent of

\(\mathrm{NO}_{3}^{{-}}\)

uptake by roots in flooded soil will depend on its rate of formation from

\(\mathrm{NH}_{4}^{+}\)

near root surfaces, its rate of transport to and absorption by the root, and its rate of transport away from the root and loss through denitrification. The rates of

\(\mathrm{NO}_{3}^{{-}}\)

formation and subsequent denitrification will depend on reducing conditions in the soil and sinks for O₂ other than nitrification. The sinks include microbial and non-microbial processes.

In this paper, a mathematical model of these processes is developed with which to calculate rates of formation, uptake and loss of

\(\mathrm{NO}_{3}^{{-}}\)

over the range of conditions in which wetland plants grow.

THEORY

Consider the movements of O₂,

\(\mathrm{NH}_{4}^{+}\)

and

\(\mathrm{NO}_{3}^{{-}}\)

in anoxic flooded soil near a cylindrical root that simultaneously releases O₂ and absorbs

\(\mathrm{NH}_{4}^{+}\)

and

\(\mathrm{NO}_{3}^{{-}}\)

⁠. The microbial sinks for O₂ include both autotrophic processes, such as oxidation of

\(\mathrm{NH}_{4}^{+}\)

⁠, S²⁻ and CH₄, and heterotrophic processes (Conrad and Frenzel, 2002; Kirk, 2004). The non-microbial sinks include oxidation of inorganic reductants in the soil, such as Fe(II), which may be both mobile and immobile (Howeler and Bouldin, 1971; Reddy et al., 1980; Kirk and Solivas, 1994).

In initially anoxic soil, populations of aerobic microbes will be small, and therefore non-microbial processes consuming O₂ will initially tend to dominate. As inorganic reductants close to the roots become exhausted, the rate of non-microbial O₂ consumption will decline. Concomitantly, the rate of microbial O₂ consumption will increase as aerobic populations develop. Hence the system will be complex and dynamic. We have some understanding of the kinetics of the non-microbial processes (Ahmad and Nye, 1990; Kirk et al., 1990; Kirk and Solivas, 1994), but only a weak understanding of the microbial processes and the complex interactions they involve (Bodelier et al., 2000, 2004; Brune et al., 2000; van Bodegum et al., 2001). Therefore, a very elaborate treatment of the O₂-consuming processes, dissecting out the various contributors, is unjustified at this stage of our understanding, and, in our model, we therefore combine microbial and non-microbial processes. Likewise, our understanding of growth rates and activities of

\(\mathrm{NH}_{4}^{+}\)

-oxidizing microbes in the rhizosphere of wetland plants and interactions with nutrients, toxins and competing substrates is insufficient for a very elaborate treatment, and hence we apply the simplest realistic treatment, with the maximum rate of nitrification as a proportion of the maximum rate of overall O₂ consumption.

The following sections give the equations we use to describe the system. The symbols used are defined in Table 1.

Table 1.

List of symbols

Symbol	Meaning	Dimensions*
a	Root radius	Length
b	Radius of zone of root influence	Length
bNH4	Buffer power for \(\mathrm{NH}_{4}^{+}\) ⁠, \(\mathrm{d}\left[\mathrm{NH}_{4}^{+}\right]/\mathrm{d}\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}\)	VolumeL volume−1
DL	Solute diffusion coefficient in water, subscripted A, N or O for \(\mathrm{NH}_{4}^{+}\) ⁠, \(\mathrm{NO}_{3}^{{-}}\) and O2	Area time−1
FmNH4	Maximum influx of \(\mathrm{NH}_{4}^{+}\) into roots	Mass area−1 time−1
FmNO3	Maximum influx of \(\mathrm{NO}_{3}^{{-}}\) into roots	Mass area−1 time−1
f	Soil diffusion impedance factor
IDenit	Inhibition function for denitrification
KMDenit	Michaelis constant for denitrification	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
KMNH4	Michaelis constant for \(\mathrm{NH}_{4}^{+}\) uptake	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
KMNit1	Michaelis constant for nitrification (re O2)	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
KMNit2	Michaelis constant for nitrification (re \(\mathrm{NH}_{4}^{+}\) ⁠)	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
KMNO3	Michaelis constant for \(\mathrm{NO}_{3}^{{-}}\) uptake	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
KMO	Michaelis constant for O2 consumption	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
LV	Root length density	Length volume−1
\(\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}\)	Concentration of \(\mathrm{NH}_{4}^{+}\) in soil solution	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
\(\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}\)	Concentration of \(\mathrm{NO}_{3}^{{-}}\) in soil solution	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
[O2]L	Moncentration of O2 in soil solution	\(\mathrm{Mass\ volume}_{\mathrm{L}}^{{-}1}\)
VmDenit	Maximum rate of denitrification	Mass volume−1 time−1
VmNit	Maximum rate of nitrification	Mass volume−1 time−1
VmO	Maximum rate of O2 consumption	Mass volume−1 time−1
v	Water flux into root	Length time−1
λ	Root wall permeability factor	Length time−1
θ	Soil water fraction by volume	VolumeL volume−1

*

Subscript L indicates soil solution; no subscript indicates whole soil.

Oxygen

The transport of O₂ away from the root and its simultaneous consumption in soil processes is described by the equation

\[\frac{{\partial}\left[\mathrm{O}_{2}\right]}{{\partial}t}\ =\ \frac{1}{r}\ \frac{{\partial}}{{\partial}r}\ \left[rD_{\mathrm{LO}}{\theta}f\frac{{\partial}\left[\mathrm{O}_{2}\right]_{\mathrm{L}}}{{\partial}r}\ +\ av\left[\mathrm{O}_{2}\right]_{\mathrm{L}}\right]\ {-}\ R_{\mathrm{O}}\]

where R_O is the rate of consumption in soil processes. The whole-soil concentration of O₂ is related to the concentration in solution by [O₂] = θ[O₂]_L. Following the reasoning above, we lump together microbial and non-microbial sinks for O₂ and describe net O₂ consumption using Michaelis–Menten kinetics:

\[R_{\mathrm{O}}\ =\ V_{\mathrm{mO}}\frac{\left[\mathrm{O}_{2}\right]_{\mathrm{L}}}{K_{\mathrm{MO}}\ +\ \left[\mathrm{O}_{2}\right]_{\mathrm{L}}}\]

The boundary conditions for eqn (1) are as follows. The flux of O₂ across the root surface, r = a, depends on the rate of delivery of O₂ through the root, the external sink for O₂ in the soil and the permeability of the root wall separating the soil solution from the root gas spaces. Following Armstrong and Beckett (1987), we define a root wall permeability factor, λ, relating the flux across the root wall to the difference in O₂ concentration across it. The flux across the root wall is equal to the flux into the soil at r = a. Hence

\[D_{\mathrm{LO}}{\theta}f\frac{{\partial}\left[\mathrm{O}_{2}\right]_{\mathrm{L}}}{{\partial}r}\ +\ v\left[\mathrm{O}_{2}\right]_{\mathrm{L}}\ =\ {\lambda}\left(\left[\mathrm{O}_{2}\right]_{\mathrm{Lc}}\ {-}\ \left[\mathrm{O}_{2}\right]_{\mathrm{La}}\right){\ }r\ =\ \mathrm{a},\ t\ {\geq}\ 0\]

where subscripts c and a indicate the root cortical tissue and the soil at the root surface, respectively. Armstrong and Beckett give values of λ derived from experiments with polarographic electrodes (see Parameter Values, below). At the other boundary where the zones of influence of adjacent roots overlap, there is no transfer of O₂. Thus

\[D_{\mathrm{LO}}{\theta}f\frac{{\partial}\left[\mathrm{O}_{2}\right]_{\mathrm{L}}}{{\partial}r}\ +\ \frac{av}{b}\left[\mathrm{O}_{2}\right]_{\mathrm{L}}\ =\ 0{\ }r\ =\ b,\ t\ {\geq}\ 0\]

Ammonium

The transport of

\(\mathrm{NH}_{4}^{+}\)

towards the root and its simultaneous consumption in nitrification is described by the equation

\[\frac{{\partial}\left[\mathrm{NH}_{4}^{+}\right]}{{\partial}t}\ =\ \frac{1}{r}\frac{{\partial}}{{\partial}r}\ \left[rD_{\mathrm{LA}}{\theta}f\frac{{\partial}\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}}{{\partial}r}\ +\ av\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}\right]\ {-}\ R_{\mathrm{Nit}}\]

The whole-soil concentration of

\(\mathrm{NH}_{4}^{+}\)

is related to the concentration in solution by the soil

\(\mathrm{NH}_{4}^{+}\)

buffer power:

\(\mathrm{b}_{\mathrm{NH}4}\ =\ \mathrm{d}\left[\mathrm{NH}_{4}^{+}\right]/\mathrm{d}\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}\)

⁠. The rate of nitrification will depend on the concentrations of O₂ and

\(\mathrm{NH}_{4}^{+}\)

⁠, and we describe this using dual-substrate Michaelis–Menten kinetics (see McConnaughey and Bouldin, 1985, for

\(\mathrm{NO}_{3}^{{-}}\)

reduction, or Arah and Stephen, 1998, for CH₄ oxidation):

\[R_{\mathrm{Nit}}\ =\ V_{\mathrm{mNit}}\frac{\left[\mathrm{O}_{2}\right]_{\mathrm{L}}}{K_{\mathrm{MNit1}}\ +\ \left[\mathrm{O}_{2}\right]_{\mathrm{L}}}\frac{\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}}{K_{\mathrm{MNit2}}\ +\ \left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}}\]

where V_mNit is the rate in the absence of substrate limitation and K_MNit1 and K_MNit2 are Michaelis constants. The boundary conditions for eqn (5) are as follows. The flux of

\(\mathrm{NH}_{4}^{+}\)

into the root will depend on the concentration of

\(\mathrm{NH}_{4}^{+}\)

in solution at the root surface and the root

\(\mathrm{NH}_{4}^{+}\)

absorption properties. In accordance with conventional practice (Kronzucker et al., 1997, 2000), we describe this with a Michaelis–Menten equation:

\begin{eqnarray*}&&D_{\mathrm{LA}}\ {\theta}f\frac{{\partial}\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}}{{\partial}r}\ +\ v\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}\ =\ F_{\mathrm{mNH4}}\frac{\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{La}}}{K_{\mathrm{MNH4}}\ +\ \left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{La}}}\\&&{\ }r\ =\ a,\ t\ {\geq}\ 0\end{eqnarray*}

The quantities F_mNH4 and K_MNH4 are not constant during plant growth but vary with the plant's N status and other factors. However, we treat them as constants and test the model's sensitivity to them. At the other boundary, we assume there is no transfer of

\(\mathrm{NH}_{4}^{+}\)

⁠. Thus

\[D_{\mathrm{LA}}{\theta}f\frac{{\partial}\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}}{{\partial}r}\ +\ \frac{av}{b}\left[\mathrm{NH}_{4}^{+}\right]_{\mathrm{L}}\ =\ 0{\ }r\ =\ b,\ t\ {\geq}\ 0\]

Nitrate

The transport of

\(\mathrm{NO}_{3}^{{-}}\)

towards the root and its simultaneous production in nitrification and consumption in denitrification is described by the equation

\begin{eqnarray*}&&\frac{{\partial}\left[\mathrm{NO}_{3}^{{-}}\right]}{{\partial}t}\ =\ \frac{1}{r}\frac{{\partial}}{{\partial}r}\ \left[rD_{\mathrm{LN}}{\theta}f\frac{{\partial}\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}}{{\partial}r}\ +\ av\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}\right]\\&&+\ R_{\mathrm{Nit}}\ {-}\ R_{\mathrm{Denit}}\end{eqnarray*}

Because

\(\mathrm{NO}_{3}^{{-}}\)

is not adsorbed on the soil solid, its concentration in the whole soil is simply related to the concentration in solution by

\(\left[\mathrm{NO}_{3}^{{-}}\right]\ =\ {\theta}\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}\)

⁠. The rate of denitrification will depend on

\(\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}\)

and also on the concentration of O₂, which is the preferred electron acceptor. Following McConnaughey and Bouldin (1985), we describe this with a modified Michaelis–Menten equation:

\[R_{\mathrm{Denit}}\ =\ I_{\mathrm{Denit}}V_{\ \mathrm{mDenit}}\frac{\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}}{K_{\mathrm{MDenit}}\ +\ \left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}}\]

where I_Denit is a function for inhibition by O₂. We take inhibition to be linear up to a threshold concentration equal to the Michaelis constant for O₂ consumption (Arah and Vinten, 1995):

\[\mathrm{for}\ \left[\mathrm{O}_{2}\right]_{\mathrm{L}}\ {\geq}\ K_{\mathrm{MO}},\ I_{\mathrm{Denit}}\ =\ 0,\]

\[\mathrm{for}\ \left[\mathrm{O}_{2}\right]_{\mathrm{L}}\ {<}\ K_{\mathrm{MO}},\ I_{\mathrm{Denit}}\ =\ 1\ {-}\ \frac{\left[\mathrm{O}_{2}\right]_{\mathrm{L}}}{K_{\mathrm{MO}}}\]

As for

\(\mathrm{NH}_{4}^{+}\)

⁠, we use a Michaelis–Menten equation for the relationship between the flux of

\(\mathrm{NO}_{3}^{{-}}\)

into the root and the concentration in solution at the root surface:

\begin{eqnarray*}&&D_{\mathrm{LN}}{\theta}f\frac{{\partial}\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}}{{\partial}r}\ +\ v\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}\\&&=\ F_{\mathrm{mNO3}}\frac{\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{La}}}{K_{\mathrm{MNO3}}\ +\ \left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{La}}}{\ }r\ =\ a,\ t\ {\geq}\ 0\end{eqnarray*}

At the other boundary, we assume there is no transfer of

\(\mathrm{NO}_{3}^{{-}}\)

⁠. Thus

\[D_{\mathrm{LN}}{\theta}f\frac{{\partial}\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}}{{\partial}r}\ +\ \frac{av}{b}\left[\mathrm{NO}_{3}^{{-}}\right]_{\mathrm{L}}\ =\ 0{\ }r\ =\ b,\ t\ {\geq}\ 0\]

Numerical solutions

We expressed eqns (1)–(14) in finite-difference form using Crank–Nicholson approximations and solved the resulting sets of equations by standard numerical methods (Smith, 1985). With time steps of 0·1 h and distance steps of 0·1 mm, mass balances for all solute were conserved to within 1 % for simulations up to 10 d. Copies of the computer program for the numerical solutions, written in Fortran, are available from the first author.

PARAMETER VALUES

The standard set of parameter values used in the calculations are given in Table 2. Our reasons for choosing these values are as follows.

Table 2.

Standard parameter values

Parameter	Value	Reference
a	0·1 mm	Matsuo and Hoshikawa (1993)
b	2 mm	Matsuo and Hoshikawa (1993)
bNH4	50 cm3 cm−3	Kirk (2004)
DLA,N,O	2 × 10−5 cm2 s−1	Kirk (2004)
FmNH4	5 pmol cm−2 s−1	Kronzucker et al. (1999)
FmNO3	25 pmol cm−2 s−1	Kronzucker et al. (1999)
f	0·4	Kirk et al. (2003)
KMDenit	1 µm	See text
KMNH4	50 µm	Kronzucker et al. (1999)
KMNit1	1 µm	See text
KMNit2	200 µm	See text
KMNO3	10 µm	Kronzucker et al. (1999)
KMO	1 µm	See text
\(\left[\mathrm{NH}_{4}^{+}\right]_{t=0}\)	5 µmol cm−3	Kirk (2004)
[O2]Lc	0·18 µm	See text
VmDenit	2 pmol cm−3 s−1	See text
VmNit/VmO	0·25	See text
VmO	500 pmol cm−3 s−1	See text
v	0 cm s−1	See text
λ	1 × 10−4 cm s−1	Armstrong and Beckett (1987)
θ	0·6 cm3 cm−3	Kirk (2004)

Rate of O₂ release

The O₂ budget of an individual root depends both on the rate of O₂ movement and consumption within the root—which varies with position along the root and between main roots and laterals—and on the rate of O₂ consumption in the surrounding soil. Measurements of rates of release, therefore, need to allow for differences across the root and its laterals and must be made under O₂ sink conditions that are realistic for roots in soil. In practice, it is difficult to satisfy these conditions, and consequently reported rates of release for whole root systems vary by more than two orders of magnitude (Bedford et al., 1991; Begg et al., 1994; Sorrel and Armstrong, 1994).

However, mathematical models of root aeration show that rates of release at the upper end of the measured range can be sustained by rice roots with typical characteristics (Armstrong and Beckett, 1987; Kirk, 2003). Kirk (2003) developed a model of the steady-state diffusion of O₂ through a primary rice root and its laterals and the simultaneous consumption of O₂ in root respiration and loss to the soil. A sensitivity analysis showed that the basic architecture of rice root systems, i.e. a system of coarse, aerenchymatous, primary roots with gas-impermeable walls conducting O₂ to short, fine, gas-permeable laterals, provides the greatest absorbing surface per unit aerated root mass. With this architecture and typical rates of root respiration, rates of O₂ loss to the soil from the laterals and primary root tip can be at the upper end measured experimentally, equivalent to a flux of up to 25 pmol cm⁻² (root surface) s⁻¹.

Based on this and trial runs with the present model, we use as standard a root wall permeability factor, λ = 10⁻⁴ cm s⁻¹ and we specify the O₂ concentration in the root cortex {[O₂]_Lc in eqn (3)} as equal to half that in air [8·75 mol cm⁻³ (gas space) at s.t.p.].

Rate of O₂ consumption

For ten soils with a wide range of organic matter and reducible Fe contents, Howeler and Bouldin (1971, Table 4) found steady-state rates of O₂ consumption by reduced soil cores exposed to O₂ equivalent to 100–1000 pmol cm⁻³ s⁻¹ (mean value 500 pmol cm⁻³ s⁻¹). Roughly 50 % of this was microbial. We therefore take V_mO = 500 pmol cm⁻³ s⁻¹ as our standard value. Heterotrophic aerobes will operate efficiently at sub micromolar O₂ concentrations (Conrad and Frenzel, 2002) and we take as standard K_MO = 1 µm.

Rate of nitrification

The maximum rate of nitrification is taken as a proportion of the maximum overall rate of microbial O₂ consumption. From the stoichiometry of nitrification, 2 mol of O₂ are consumed per mol of

\(\mathrm{NO}_{3}^{{-}}\)

formed:

\[\mathrm{NH}_{4}^{+}\ +\ 2\mathrm{O}_{2}\ {\rightarrow}\ \mathrm{NO}_{3}^{{-}}\ +\ 2\mathrm{H}^{+}\ +\ \mathrm{H}_{2}\mathrm{O}\]

Therefore, an upper limit on the rate of nitrification is half the net rate of microbial O₂ consumption, i.e. V_mNit/V_mO = 0·5. We take as standard V_mNit/V_mO = 0·25. Also we take as standard K_MNit1 = K_MO = 1 µm and K_MNit2 = 200 µm based on typical concentrations of

\(\mathrm{NH}_{4}^{+}\)

in solution in rice soils.

Rate of denitrification

Experiments in which

\(\mathrm{NO}_{3}^{{-}}\)

fertilizer is added to flooded soils under field conditions indicate maximum rates of N₂ + N₂O loss through denitrification of a few kg of N ha⁻¹ d⁻¹ (e.g. Lindau et al., 1990; Samson et al., 1990). Assuming denitrification to be distributed over a soil depth of 10 cm, this is equivalent to a rate of denitrification per unit soil volume of a few pmol cm⁻³ s⁻¹. We therefore take as standard V_mDenit = 2 pmol cm⁻³ s⁻¹. Measured concentrations of

\(\mathrm{NO}_{3}^{{-}}\)

in flooded soils rarely exceed a few micromolar, unless the soil is fertilized with

\(\mathrm{NO}_{3}^{{-}}\)

(Arth and Frenzel, 2000; Liesack et al., 2000), and therefore denitrifier populations must operate at concentrations less than this. We assign as standard K_MDenit = 1 µm.

The ratio of nitrous oxide to nitrogen gas formed in denitrification will depend on the relative abundance of

\(\mathrm{NO}_{3}^{{-}}\)

and organic substrates and on other factors influencing the rates of the sequential steps in denitrification (Kirk, 2004). Small concentrations of

\(\mathrm{NO}_{3}^{{-}}\)

relative to organic substrates, as expected near the roots of wetland plants, will favour complete reduction to N₂. Also, the slow escape of any N₂O formed in flooded soil will favour its further reduction to N₂. Hence, reported denitrification losses from rice fields as N₂O are at least two orders of magnitude smaller than losses as N₂ (Galbally and Chalk, 1987; Mosier et al., 1989; Buresh et al., 1991; Bronson et al., 1997).

Root

\(\mathrm{NH}_{4}^{+}\)

and

\(\mathrm{NO}_{3}^{{-}}\)

uptake properties

Up to a certain point, plants can regulate the inflow of N across their roots according to their need for N, and the inflow for a given external N concentration therefore depends on the plant's past supply of N. Hence, Wang et al. (1993) found for rice grown for 4 weeks in 2, 100 and 1000 µm

\(\mathrm{NH}_{4}^{+}\)

solutions, the respective values of V_max (µmol g⁻¹ h⁻¹) and K_M (µM) were: 12·8 and 32·2; 8·2 and 90·2; and 3·4 and 122·1, i.e. V_max was 6-fold smaller and K_M 4-fold larger for 2 µM compared with 1000 µm

\(\mathrm{NH}_{4}^{+}\)

⁠. For rice grown in 100 µm N solutions, Kronzucker et al. (1999) found that V_max values were 8·1 and 5·7 µmol g⁻¹ h⁻¹ for

\(\mathrm{NO}_{3}^{{-}}\)

- and

\(\mathrm{NH}_{4}^{+}\)

-fed plants, respectively, and K_M values were 26 and 51 µm. Given that external

\(\mathrm{NO}_{3}^{{-}}\)

concentrations at the root surface will be far smaller than

\(\mathrm{NH}_{4}^{+}\)

concentrations,

\(\mathrm{NO}_{3}^{{-}}\)

uptake will be ‘upregulated’ to a greater extent than

\(\mathrm{NH}_{4}^{+}\)

uptake, and we take as standard F_max = 5 pmol cm⁻² s⁻¹ (calculated from V_max in µmol g⁻¹ h⁻¹ using root density = 1 g cm⁻³ and a = 0·1 mm) and K_M = 50 µm for

\(\mathrm{NH}_{4}^{+}\)

uptake, and F_max = 25 pmol cm⁻² s⁻¹ and K_M = 10 µm for

\(\mathrm{NO}_{3}^{{-}}\)

uptake.

Root geometry

The root system of rice plants in flooded soils comprises coarse primary roots, 0·3–1 mm in diameter, supporting a dense system of fine laterals, 50–150 µm in diameter (Matsuo and Hoshikawa, 1993). Total root length densities averaged over the 15–20 cm deep puddled soil layer may be as high as 20–30 cm cm⁻³. Calculations with the above parameters for root

\(\mathrm{NH}_{4}^{+}\)

absorption properties and measured concentrations of

\(\mathrm{NH}_{4}^{+}\)

in soil solutions indicate that almost the whole of this root length is required to account for measured rates of N uptake by rice in flooded soils (Kirk and Solivas, 1997).

The corresponding mean inter-root distance is calculated as follows. With a regular parallel array of roots, if each root is assigned a cylinder of influence such that the whole soil volume is divided equally between roots, the radius, b, of the cylinder is given by

\[b\ =\ \frac{1}{\sqrt{{\pi}L_{\mathrm{V}}}}\]

where L_V is the root length density. The value b = 3 mm, which is realistic for half the distance between neighbouring primary roots, corresponds to L_V = 3·5 cm cm⁻³; b = 1 mm, which is realistic for half the distance between laterals, corresponds to L_V = 31·8 cm cm⁻³.

MODEL PREDICTIONS

Predicted concentration profiles, fluxes and rates of nitrification–denitrification

Figure 1 shows the concentration profiles of O₂,

\(\mathrm{NH}_{4}^{+}\)

and

\(\mathrm{NO}_{3}^{{-}}\)

in the soil calculated with the standard set of parameter values over 10 d of root–soil contact, and Fig. 2 gives the fluxes of O₂ and N species across the root over time. Figure 1 shows that only very small concentrations of

\(\mathrm{NO}_{3}^{{-}}\)

in the soil solution develop: approx. 1–2 µm within <0·5 mm of the root and 0 µm at >1 mm from the root, i.e. given the radial geometry, all but undetectable averaged over the inter-root distance. Nonetheless, the fluxes of

\(\mathrm{NO}_{3}^{{-}}\)

into the root shown in Fig. 2 are substantial. The accumulated uptake of nitrogen over 10 d is 1·61 µmol cm⁻³ of soil, or 33 % of the initial

\(\mathrm{NH}_{4}^{+}\)

content of the soil (= 5 µmol cm⁻³, equivalent to 105 kg of N ha⁻¹ over a 15 cm depth), and the concentration of

\(\mathrm{NH}_{4}^{+}\)

in solution in the soil bulk concomitantly falls from 100 to 64 µm. Nitrate uptake accounted for 34 % of total N uptake, and nitrification accounted for 14 % of the total O₂ consumption in 10 d. The ratio of N denitrified to total N uptake was 0·20 or 6·6 % of the

\(\mathrm{NH}_{4}^{+}\)

initially in the soil.

Fig. 1.

Calculated concentration–distance profiles of O₂,

\(\mathrm{NO}_{3}^{{-}}\)

and

\(\mathrm{NH}_{4}^{+}\)

in the soil near a root after 10 d of root–soil contact. Parameter values as in Table 2.

Fig. 2.

Fluxes of O₂,

\(\mathrm{NH}_{4}^{+}\)

⁠,

\(\mathrm{NO}_{3}^{{-}}\)

and total N across the root over time. Parameter values as in Table 2.

To gauge how realistic these results are, we compare the calculated rates of denitrification with published values. Measurements of denitrification in flooded rice fields made by following the emission of ¹⁵N₂ and ¹⁵N₂O following addition of N-fertilizer strongly labelled with ¹⁵N indicate losses in the range 1–5 % of applied ammoniacal-N over the range of soils and management conditions considered (Buresh and Austin, 1988; Mosier et al., 1989; Reddy et al., 1989; Buresh et al., 1991). Arth et al. (1998) directly measured N₂ and N₂O emitted by rice plants grown in chambers with an atmosphere of O₂ and helium. This gave denitrification losses of the order of 6 % of added urea-N in 10 d and mean N₂ + N₂O emission rates of approx. 30 nmol (N) cm⁻² (soil surface) h⁻¹. The mean emission rate calculated here with the standard parameters is 14 nmol (N) cm⁻² (soil surface) h⁻¹ assuming 10 cm soil depth. We conclude that our calculated losses are realistic.

We know of no published direct measurements of rates of

\(\mathrm{NO}_{3}^{{-}}\)

uptake by wetland plants in flooded soil under field conditions. Because the

\(\mathrm{NO}_{3}^{{-}}\)

is rapidly assimilated, direct measurements of uptake are difficult.

Sensitivity analysis

Figure 3 shows the sensitivity of the calculated total N and

\(\mathrm{NO}_{3}^{{-}}\)

uptakes and denitrification to model parameter values over what we consider to be realistic ranges for wetland plants. As discussed above, we have some understanding of total rates of O₂ consumption in flooded soils, but a much weaker understanding of the growth rates and activities of nitrifying microbes under different circumstances. We therefore show the sensitivity to different parameters in interaction with a varying nitrification potential as represented by V_max for nitrification as a proportion of V_max for total O₂ consumption (V_mNit/V_mO).

Fig. 3.

Sensitivity of total N uptake, uptake of

\(\mathrm{NO}_{3}^{{-}}\)

as a proportion of total N uptake and denitrification as a proportion of total N uptake to model parameter values. (A) The top three graphs indicate sensitivity to V_max for total O₂ consumption [V_mO in eqn (2); numbers on curves are values in nmol cm⁻³ s⁻¹]; (B) the upper middle three graphs indicate sensitivity to parameters for root

\(\mathrm{NO}_{3}^{{-}}\)

uptake [F_m, K_M in eqn (13); numbers on curves are values in nmol cm⁻³ s⁻¹, μm]; (C) the lower middle three graphs indicate sensitivity to root length density [L_V in eqn (15); numbers on curves are values in cm cm⁻³]; and (D) the bottom three graphs indicate sensitivity to the soil

\(\mathrm{NH}_{4}^{+}\)

buffer power (b_NH4; numbers on curves are values in cm³ cm⁻³). Ten d of root–soil contact. Other parameter values as in Table 2.

Effect of nitrification and denitrification rates

Figure 3A shows the sensitivity to the maximum total rate of O₂ consumption (V_mO). At a given V_mNit/V_mO, with increases in V_mO the proportion of N uptake as

\(\mathrm{NO}_{3}^{{-}}\)

increases and total N uptake increases correspondingly. Also, the ratio of N denitrified to total N uptake decreases. This is because with a greater O₂ sink, the spread of the oxygenated zone around the root is smaller and nitrification occurs closer to the root. Therefore, the concentration gradient of

\(\mathrm{NO}_{3}^{{-}}\)

towards the root is steeper and a greater proportion of the

\(\mathrm{NO}_{3}^{{-}}\)

is taken up. The effect of V_mO varies with V_mNit/V_mO: when V_mNit/V_mO is large, denitrification losses decrease more rapidly with increases in V_mO.

Effect of root

\(\mathrm{NO}_{3}^{{-}}\)

uptake properties

As F_mNO3 increases and K_MNO3 decreases, an increasing proportion of N is taken up as

\(\mathrm{NO}_{3}^{{-}}\)

and a decreasing proportion of the

\(\mathrm{NO}_{3}^{{-}}\)

formed is denitrified (Fig. 3B). Over the range of F_mNO3 and K_MNO3 values shown in Fig. 3B, and other parameter values as standard,

\(\mathrm{NO}_{3}^{{-}}\)

accounts for 15 to nearly 40 % of N uptake. Denitrification losses increase sharply as root

\(\mathrm{NO}_{3}^{{-}}\)

uptake decreases.

Effect of root geometry

Figure 3C shows interactions between root geometry and rates of

\(\mathrm{NO}_{3}^{{-}}\)

uptake and denitrification. As root length density (L_V) increases, the rates of total N uptake and depletion of soil N increase. Simultaneously, with increasing L_V, the inter-root distance decreases and therefore the proportion of the inter-root zone that is oxygenated increases, and so nitrification and

\(\mathrm{NO}_{3}^{{-}}\)

uptake increase. Superimposed on this is the effect of root radius. With large inter-root distances, increasing the root radius tends to increase the capture of

\(\mathrm{NO}_{3}^{{-}}\)

and decrease denitrification (data not shown). However, with small inter-root distances, denitrification rates are small and the capture of

\(\mathrm{NO}_{3}^{{-}}\)

increases as the root radius decreases.

Effect of soil

\(\mathrm{NH}_{4}^{+}\)

buffer power

Figure 3D shows that uptake increases sharply as b_NH4 decreases, but the proportion of uptake as

\(\mathrm{NO}_{3}^{{-}}\)

is little influenced. As b_NH4 decreases, for a given total concentration of

\(\mathrm{NH}_{4}^{+}\)

in the soil, the concentration of

\(\mathrm{NH}_{4}^{+}\)

in solution increases, and hence the uptake of

\(\mathrm{NH}_{4}^{+}\)

tends to increase. Simultaneously, nitrification tends to increase as

\(\mathrm{NH}_{4}^{+}\)

in solution increases, and hence the rate of

\(\mathrm{NO}_{3}^{{-}}\)

uptake increases. Thus, the sensitivity of N uptake to V_mNit/V_mO increases as b_NH4 decreases. There is a corresponding decrease in denitrification relative to N uptake, because the gradient of

\(\mathrm{NH}_{4}^{+}\)

near the root is shallower at smaller b_NH4, and hence a greater proportion of nitrification occurs close to the root.

Effect of mass flow of the soil solution

Mass flow of solution towards the root in the transpiration stream tends to compress the zones of oxygenation and nitrification and extend the zone of

\(\mathrm{NH}_{4}^{+}\)

depletion. The above calculations were made with v = 0. The model shows that a rapid flux of water across the root surface (v = 10⁻⁵ cm s⁻¹) slightly compresses the profile of

\(\mathrm{NH}_{4}^{+}\)

but has a negligible effect on the profiles of O₂ and

\(\mathrm{NO}_{3}^{{-}}\)

and rates of

\(\mathrm{NO}_{3}^{{-}}\)

uptake and denitrification (data not shown). Approximate solutions of eqn (5) indicate that the fractional increase in

\(\mathrm{NH}_{4}^{+}\)

influx resulting from mass flow is about av/(0·5D_LAθf) (Kirk and Solivas, 1997), or approx. 2 % for the standard parameter values and v = 10⁻⁵ cm s⁻¹. Hence, for practical purposes, the effect of mass flow can be ignored.

CONCLUDING REMARKS

Our calculations show that wetland plants growing in flooded soil can take up a large part of their nitrogen as

\(\mathrm{NO}_{3}^{{-}}\)

formed from

\(\mathrm{NH}_{4}^{+}\)

in the rhizosphere, without excessive losses of N through denitrification. The extent of this will vary greatly between soils and management regimes, being sensitive to reducing conditions in the soil and the sinks for O₂ other than nitrification. Water regimes will particularly influence this. It is expected that in future rice will have to be produced with far less water across Asia as water resources are increasingly diverted to non-agricultural uses (IRRI, 2003). Therefore, water-saving irrigation methods, such as maintaining a minimal depth of standing water in the field and intermittently draining water from the field, will be increasingly widespread. This will favour increased

\(\mathrm{NO}_{3}^{{-}}\)

formation, and it will be important to manage conditions to maximize the capture of

\(\mathrm{NO}_{3}^{{-}}\)

by the crop and minimize denitrification.

We have focused on lowland rice, but it is probable that other wetland plants are similarly efficient in capturing

\(\mathrm{NO}_{3}^{{-}}\)

formed in the rhizosphere. This would have implications for the selection of plants for waste-water treatment in artificial wetlands.

Author notes

1National Soil Resources Institute, Cranfield University, Silsoe, Beds MK45 4DT, UK and 2Department of Life Sciences, University of Toronto, 1265 Military Trail, Toronto, Ontario M1C 1A4, Canada