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Crop Nutrient uptake models

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- 1. B.R.Iniyalakshimi Dept. of Soil Science and Agricultural Chemistry, TNAU
- 2. MODELS It is “an assembly of concepts in the form of a mathematical equation that portrays understanding of a natural phenomenon.”
- 3. Emprical models – statistical means and regression- black box models Mechanistic models- biophysical, biochemical and physiological mechanisms TYPES
- 4. NUTRIENT UPTAKE MODELS • Soil nutrient transformation models emphasize on soil properties. • Crop uptake models emphaize on plant characters especially on root characters and also soil characters. • Models are formed for (i) identifying the process which describe nutrient uptake and (ii) evaluating quantitatively the effect of different parameters of nutrient uptake.
- 5. • Extrapolation of a verified mechanistic model is more reliable than that of an empirical model(Claassen and Steingrobe, 1999). • The typical mechanistic nutrient uptake model describes the supply of nutrients from bulk soil to root surfaces, root growth and morphology, and root uptake kinetics (Barber, 1995).
- 6. MECHANISTIC MODELS Steady state models • Flow of nutrients through a soil- steady state • Soil – volume element conducting nutrient flow • Neither a sink nor a source of nutrients • based on diffusion theory Transient models • either a sink or source influencing / modifying its flux (time) • describes the dynamic process of nutrient uptake & the concomitant changes in the ion concentration & distribution in the rhizosphere.
- 7. SOIL NUTRIENT UPTAKE MODELING Mechanisms Mass flow Diffusion Root interception
- 8. Interception is used to describe the uptake of soil nutrients at the root interface when soil volume is displaced by root volume (Barber 1995). Although conditions in the rhizosphere are sometimes different from those in the bulk soil (Marschner 1995), the contribution of interception to nutrient uptake is negligible for most nutrients (Barber 1995). Therefore, only mass flow and diffusion are considered to be responsible for movement of nutrients to the root surface in mechanistic modeling. However, Tinker and Nye (2000) consider the concept of interception to be somewhat arbitrary and argued that it can be included in the diffusion component.
- 9. MASS FLOW Mass flow is the convective transport of nutrients through the soil to the root surface by water flow as a result of transpiration (Barber, 1995). The relative contribution of mass flow to nutrient uptake depends on the nutrient, plant species, plant age, and time of day (Marschner,1995). For example calcium and magnesium supplied to plants by mass flow is significant, but its contribution to potassium supply is negligible (Marschner, 1995). The influx by mass flow (FM) can be calculated by where v is the mean water flux in soil driven by transpiration, and CL is the nutrient concentration in the soil solution.
- 10. DIFFUSION Diffusion is the movement of nutrients from areas of high concentration to those of low concentration (Barber 1995). It is the main mechanism for at least phosphorus and potassium movement in the soil to plant roots (Marschner 1995). A depletion zone is produced when the concentration of nutrient is lowered near the root surface due to root absorption (Jungk and Claassen 1997). Diffusive flux FD can be described by Fick’s first law, where D is the diffusion coefficient of the nutrient in soil, C is the nutrient concentration in soil solution, and x is the distance.
- 11. SIMULTANEOUS MASS FLOW AND DIFFUSION Mass flow and diffusion occur simultaneously to supply nutrients to plant roots and cannot be treated as separate processes. Nye and Spiers (1964) presented a partial differential equation to describe simultaneous mass flow and diffusion, and this equation became the foundation of the most mechanistic nutrient uptake models.
- 12. The Barber-Cushman model is largely based on the work by Nye and Marriot (1969). Nye and Marriot (1969) revised the continuity equation proposed by Nye and Spiers (1964) to describe the flux of nutrient in the soil to the root surface with the nutrient concentration in soil solution (CL) Nye and Marriot (1969) defined boundary conditions and solved this equation numerically.
- 13. NYE AND MARRIOT (1969)
- 14. NYE AND TINKER MODEL Nye and Tinker, 1977 The uptake of nutrient per unit length (U) is given by, U= 2πrαC1 r = radius of the root α = root absorbing power C1= ion concentration at the root surface
- 15. Summarizing the work by Claassen and Barber (1976) and Cushman (1979), Barber and Cushman (1981) suggested new boundary conditions to include inter-root competition for nutrients. The new boundary conditions incorporated inter- root competition as well as Michaelis-Menten kinetics. When solved numerically, the enhanced mechanistic model evolved into Barber-Cushman model.
- 16. Crop uptake is assumed to follow Michaelis-menten relationship between concentration and flux. In 1983, Itoh and Barber developed a submodel to the Barber-Cushman model to include nutrient uptake by root hairs. In 1986 Claassen et al. published NST 1.0 model. In 1987 Oates and Barber published NUTRIENT UPTAKE model. Both were based on the Barber-Cushman model.
- 17. MICHAELIS- MENTEN KINETICS In=(Imax×Cla)/(Km+ Cla) Where, In = Rate of ion uptake Imax = maximum rate of ion uptake when concentration is not limiting Cla = concentration of nutrient ion in soil solution at the root surface Km = Michaelis – menten constant which represents a concentration of nutrient ion in soil solution when In=Imax/2.
- 18. COMPUTERIZED MODELS Based on Nye and Tinker model, Smethurst and Comerford (1993b) developed a computer model, COMP8 (Competition model version 8), which was able to calculate nutrient uptake between two competing and contrasting root systems. SSAND was a revision and expansion of COMP8 by Comerford et al. (2006). Its main improvements lie in the functions of predicting nutrient uptake as influenced by mycorrhizae and simulation of fertilization effects (Comerford et al. 2006).
- 19. Based on COMP8 and an earlier version of SSAND, another steady state model, PCATS was developed to simulate nutrient uptake by a single species by Smethurst et al. (2004). For transient models –NST 1.0, NST 3.0.
- 20. NYE AND TINKER, 2000 where b is the soil buffer power, hence c = bc is the total amount of solute bound to the soil particles; θ is the volumetric soil water content, thus is the overall amount of solute per unit volume of soil; D is the solute diffusivity in water; f is the soil impedance factor, Dfθ is the effective diffusion coefficient for the solute in the soil; and v is the water flux in the soil.
- 21. MODELLING CROP N UPTAKE Benbi, Prihar and Cheema (1991) – used mass flow approach & predicted N uptake for wheat matched with measured N uptake (wet treatments). In dry moisture regime other process of N uptake like diffusion & root interception should be used.
- 22. BASED ON CROP DEMAND Several models - driven by demand from the plant. They calculate N demand for growth rates & concentration of N required. Whitmore and Addiscott (1987) – computed demand using a simple variant of the logistic function to compute the pattern of N uptake (Y), with thermal time (x): Y=(A-1/X + e-kx )-n A - maximum of Y, n - shape factor, k - rate constant.
- 23. • Tillotson and Wagenet (1982) and Hutson and Wagenet (1992) – modelled N uptake – based on Nye and Tinker model. • Warncke and Barber (1973) – value of α to be estabilished for different soils, crops and species under a range of concentrations. • De Willigen, 1991 – more complex models give better simulations than simpler ones.
- 24. TRANSFORMATION INCLUDING UPTAKE ANIMO Benbi’s model CANDY DAISY EPIC SWATNIT
- 25. M&M MODEL Satisfactorily describes P uptake flux (Fp, mol cm-1 root h-1 ) as a function of P concentration in a well-stirred solution (Cpb mol l-1 ). Fp = Fp max * Cpa /(Km +Cpa ) Fp max and Km denote the maximum Fp and Cpa at which Fp = 0.5*Fmax . P uptake models Plant roots have a major influence on P dynamics in the soil.
- 26. A= (b/a) w/2πDp a,b = midway distance between root and root radius Dp = diffusion co-efficient B = Fpmax /W W = solution velocity towards the root Bar and Yosef (1999)
- 27. K concentration in plant K in soil solution & exchangea ble K flux to roots by mass flow & diffusion from soil Root parameters Plant dry biomass Fixed K Weather parameters Pottasium fertilizers Multi- Parametric model for K uptake
- 28. S UPTAKE Mc Caskill and Blair (1988) have developed a pseudo- mechanistic computer simulation model for predicting perennial pasture growth and S uptake. But not verified. Later Heng (1991) and Phimsarn(1991), developed simple models of pasture S uptake using relationship between actual daily ET(AET), average root density in the soil profile, soil solution S levels, sulphate buffering capacities.
- 29. MICRONUTRIENTS Mathematical models of micro-nutrient uptake by plants have been based on models designed for uptake of major nutrients. This poses a number of problems, as the behaviour of micro-nutrients in the rhizosphere is different, particularly with respect to interactions between solid and solution compartments. There is no standard procedure for the measurement of soil parameters that affect the supply of micro-nutrient from the soil.
- 30. DPUM Dynamic Plant Uptake Model DGT (Diffusive Gradient in Thin-flims) tecnique is used.

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