N uptake
The N uptake of the crop from soil is modelled following an idea of Kersebaum (1989). The crop’s daily N requirement is calculated using:
\(N_{pot}\) Daily N uptake potential \([kg \, N \, ha^{-1}]\)
\(N_{target}\) Maximum N concentration in above-ground plant parts \([kg \, N \,kg \, TM^{-1}]\)
\(W\) Above-ground dry matter biomass \([kg \, N \, ha^{-1}]\)
\(N_{max \, root}\) Maximum N concentration in the root \([kg \, N \,kg \, TM^{-1}]\)
\(W_{root}\) Root dry matter biomass \([kg \, N \, ha^{-1}]\)
\(W_b\) Below-ground dry matter biomass (not root) \([kg \, N \, ha^{-1}]\)
\(p_N\) N distribution coefficient
\(N_{crop}^{*}\) Total crop N content in the past time step \([kg \, N \, ha^{-1}]\)
\(\Delta t\) Time step \([d]\)
Its maximum amount is \(6 \, kg \, N \, ha^{-1} \, d^{-1}\). The daily N uptake is determined by the root length and a threshold which decreases linearly with the plant’s ontogenesis and thus considers the decreasing fraction of active root surface as compared to transport roots.
\(\Delta N_{lim}\) Limit of the daily N uptake \([kg \, N \, m^{-2}]\)
\(L_{root}\) Total root length \([m \, m^{-2}]\)
\(N_{up \, max}\) Plant-specific maximum N uptake \([kg \, N \, m \, Wurzel^{-1}]\)
\(DD_{act}\) Actual temperature sum \([^{\circ}C \, d]\)
\(DD_{crop}\) Plant-specific total temperature sum \([^{\circ}C \, d]\)
It is assumed that N is taken up solely in the form of nitrate. In this form it is convectively transported in the upward stream of transpiration water.
\(N_{konv \, max}\) Maximum convective N uptake \([kg \, N \, m^{-2}]\)
\(R_z\) Rooting depth \([m]\)
\(q\) Ratio absolute to simulated rooting depth
\(T_z\) Transpiration \([mm]\)
\(c_z\) N concentration in the soil solution \([kg \, N \, m^{-3}]\)
\(\Delta z\) Layer depth \([m]\)
\(\Delta t\) Time step \([d]\)
In case the convective supply exceeds the crop’s uptake potential, N uptake will be calculated in the single layers as:
\(N_{konv_z}\) Daily convective N uptake from the soil layer \(z\) \([kg \, N \, m^{-2}]\)
\(T_z\) Transpiration from layer \(z\) \([mm]\)
\(c_z\) N concentration in the soil solution \([kg \, N \, m^{-3}]\)
\(N_{pot}\) Daily N uptake potential \([kg \, N \, ha^{-1}]\)
\(N_{mas}\) Limit of the daily N uptake \([kg \, N \, m^{-2}]\)
\(\Delta z\) Layer depth \([m]\)
\(\Delta t\) Time step \([d]\)
In case the convective N supply does not satisfy the uptake potential, an additional supply via diffusion will be considered (Baldwin et al., 1973) whose maximum contribution is calculated as follows:
\(N_{diff \, max}\) Maximum diffusive N uptake \([kg \, N \, m^{-2}]\)
\(R_z\) Rooting depth \([m]\)
\(q\) Ratio absolute to simulated rooting depth
\(N_{diff \, max_z}\) Maximum diffusive N uptake from soil layer \(z\) \([kg \, N \, m^{-2}]\)
\(r_w\) Root radius \([m]\)
\(\Lambda_z\) Root length density in layer \(z\) \([m \, m^{-3}]\)
\(D\) Effective dispersion coefficient \([m^2 \, d^{-1}]\)
\(c_z\) N concentration in the soil solution \([kg \, N \, m^{-3}]\)
\(c_{min}\) Minimum N concentration at the root surface (1.4·10–6) \([kg \, N \, m^{-3}]\)
\(r_z\) Half distance between roots \([m]\)
\(\Delta z\) Layer depth \([m]\)
\(\Delta t\) Time step \([d]\)
using half the distance between neighbouring roots, for which an equal distribution is assumed:
\(r_z\) Half distance between roots \([m]\)
\(\Lambda_z\) Root length density in layer \(z\) \([m \, m^{-3}]\)
and the effective dispersion coefficient:
\(D\) Effective dispersion coefficient \([m^2 \, d^{-1}]\)
\(\tau\) Tortuosity
\(D_0\) Diffusion coefficient in solution (2.14·10–5) \([m^2 \, d^{-1}]\)
\(d_v\) Dispersion factor (0.05) \([m]\)
\(q\) Water flux density \([m^2 \, d^{-1}]\)
\(\theta\) Volumetric water content \([m^3 \, m^{-3}]\)
where
\(\tau\) Tortuosity
\(\theta\) Volumetric water content \([m^3 \, m^{-3}]\)
\(a, b\) Factors
In case the additional diffusive supply exceeds the crop’s uptake potential, it will be distributed over the soil layers, only limited by the uptake potential.
\(N_{diff_z}\) Daily diffusive N uptake from the soil layer \(z\) \([kg \, N \, m^{-2}]\)
\(N_{pot}\) Daily N uptake potential \([kg \, N \, m^{-2}]\)
\(N_{konv \, max}\) Maximum convective N uptake \([kg \, N \, m^{-2}]\)
\(N_{diff \, max_z}\) Maximum diffusive N uptake from soil layer \(z\) \([kg \, N \, m^{-2}]\)
\(N_{diff \, max}\) Maximum diffusive N uptake \([kg \, N \, m^{-2}]\)
The daily N uptake is finally calculated from:
\(N_{up_z}\) Daily N uptake from soil layer \(z\) \([kg \, N \, m^{-2}]\)
\(N_{konv_z}\) Daily convective N uptake from soil layer \(z\) \([kg \, N \, m^{-2}]\)
\(N_{diff_z}\) Daily diffusive N uptake from soil layer \(z\) \([kg \, N \, m^{-2}]\)
\(N_z\) N content of the soil layer \(z\) \([kg \, N \, m^{-2}]\)
\(N_{min\,av}\) Minimum N content in the soil layer \(z\) \([kg \, N \, m^{-2}]\)
and
\(N_{up}\) Daily N uptake \([kg \, N \, m^{-2}]\)
\(R_z\) Rooting depth \([m]\)
\(q\) Ratio of absolute to simulated rooting depth
\(N_{up_z}\) Daily N uptake from soil layer \(z\) \([kg \, N \, m^{-2}]\)
References
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Baldwin, J.P. et al. (1973): Uptake of solutes by multiple root systems from soil. III. A model for calculating the solute uptake by a randomly dispersed root system developing in a finite volume of soil. Plant Soil 38, 621 – 635.
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Groot, J.J.R. (1987): Simulation of nitrogen balance in a system of winter wheat and soil. Simulation Report CABO-TT 13. Centre for agrobiological research and Department of Theoretical Production Ecology, Landwirtschaftliche Universität Wageningen, Niederlande.
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Kersebaum, K.C. (1989): Die Simulation der Stickstoff-Dynamik von Ackerböden. Dissertation, Universität Hannover, p. 143.