This document discusses several models for predicting the transformation and uptake of micronutrients in soils, including iron, zinc, copper, boron, and molybdenum. It describes the Barber-Cushman mechanistic nutrient uptake model, which uses equations to describe nutrient influx and plant growth to model nutrient uptake. It also discusses applications of this model to predict zinc uptake in rice crops. Additionally, it examines the use of Michaelis-Menten kinetics to determine copper uptake parameters in durum wheat and mentions the constant capacitance model and 3MRA models for analyzing copper, boron, and molybdenum transformation and transport.

1. Models for Transformation and
Movement of Micronutrients in Soils

3. Iron

4. Zinc transformation

5. Zinc models
• Ronde – Venen measurements – Alterra
(2000)
• ROAD – RES model – Birgisdottir et al.( 2007)
• Landfill model - Obersteiner (2007)

6. Barber-Cushman mechanistic
nutrient uptake model
 This model consists of equations describing nutrient influx are
combined with equations describing plant growth in order to describe
nutrient uptake.
 This model allow to understand the nutrient uptake process by crops
in a complex system, which is governed by chemical, physical and
biological factors.
 The development of a mechanistic nutrient uptake model such as the
Barber-Cushman model (1984) with the computer program increases
the availability of the model and broadens the application potential.

7. Modelling zinc uptake by rice crop using a Barber-Cushman approach
Tapan Adhikari & Rattan, 2000
Barber-cushman model extensively to describe and predict nutrient uptake by
crop plants at different stages of crop in rice.
Uptake of the nutrient is, therefore, determined by the rate of nutrient supply to
the root surface by mass flow and diffusion.
mass flow and diffusion each supply zinc to the root, the process can be
described mathematically using the model of Barber-Cushman (1984).

8. Zinc uptake at different growth stages predicted by the model was compared to
measured zinc uptake by rice cultivars.
The 11 parameters of the model for the uptake by rice cultivars were measured
by established experimental techniques.
Imax = maximum influx rate (I) at high concentration.µ mol cm-2s-1
C min= ion concentration in solution below which influx ceases, µ mol cm-3
Km = ion concentration in solution – C min where In is one half Imax, µ mol cm-3
Lo = initial root length, cm,
K = rate of root growth, cm s-1
r o = mean root radius, cm
Vo = mean water influx,
r1 = half distance between root axes, cm
De = effective diffusion coefficient for the nutrient in the soil, cm-2s-1
b = buffer power of nutrient on the solid phase for nutrient in solution,
dimensionless
C li = initial concentration of the nutrient in the soil solution, µ mol cm-3
Cont-

9. T is total uptake at any determined time tm,
Jr (ro, Sr ) is the rate of influx at Sr
Integrated equation developed by Barber and Cushman (1981):

10. Tapan Adhikari & Rattan, 2000

11. Tapan Adhikari & Rattan, 2000

12. Tapan Adhikari & Rattan, 2000

13. The highest Imax value recorded was 9.2 x 10-7 µ mol cm-2s-1 at 5 mg Kg-1 Zn rate
for Pusa 933-87-1-11-88-1-2-1
Lowest for Pusa-44, being 4.6 x 10-7 µ mol cm-2s-1 at 5mg k-1 Zn rate.
According to Barber (1984), increasing Imax has a greater effect on uptake at higher
level of nutrient concentration in solution Cli .
Root length increased with the days of transplanting and was also higher with 5 mg
Zn kg-1 rate.
Root length density (Lv) (Table 2) showed the same trend as did the root length, at
the time of transplanting.
 Increase in root density was generally observed with increase in zinc rates
Conclusion:

14. Copper transformation

15. Copper Models
• 3 MRA – model
- Multimedia, Multi - pathway and Multi
receptor exposure and risk assessment

16. Kinetic parameters of Cu uptake by durum wheat were determined from
the Michaelis–Menten equation:
Fmax is the maximal flux of Cu in plant (ng Cu m−2 s−1)
KM the {Cu2+} at 1/2
Michaelis–Menten equation was fitted on plant Cu flux accounting for Cu in root
apoplasm (uptake flux) or not (absorption flux).
Parameters of Michaelis–Menten equation and its statistical significance were
calculated with Statistica (version 7, Statsoft) using the Marquardt–Levenberg algorithm.

17. Matthieu N. Bravin & Bastien Le Merrer & Laurence Denaix & André
Schneider & Philippe Hinsinger ,2009

19. Boron transformation

20. Molybdenum transformation

21. Boron & Molybedenum Models
• Constant capacitance model