New concepts for dynamic plant uptake models

Arno Rein, Charlotte Nielsen Legind, Stefan Trapp

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Models for the prediction of chemical uptake into plants are widely applied tools for human and wildlife exposure assessment, pesticide design and for environmental biotechnology such as phytoremediation. Steady-state considerations are often applied, because they are simple and have a small data need. However, often the emission pattern is non-steady. Examples are pesticide spraying, or the application of manure and sewage sludge on agricultural fields. In these scenarios, steady-state solutions are not valid, and dynamic simulation is required. We compared different approaches for dynamic modelling of plant uptake in order to identify relevant processes and timescales of processes in the soil–plant–air system. Based on the outcome, a new model concept for plant uptake models was developed, approximating logistic growth and coupling transpiration to growing plant mass. The underlying system of differential equations was solved analytically for the inhomogenous case, i.e. for constant input. By superposition of the results of n periods, changes in emission and input data between periods are considered. This combination allows to mimic most input functions that are relevant in practice. The model was set up, parameterized and tested for uptake into growing crops. The outcome was compared with a numerical solution, to verify the mathematical structure.
Original languageEnglish
JournalS A R and Q S A R in Environmental Research
Issue number1-2
Pages (from-to)191-215
Publication statusPublished - 2011


  • Analytical solution
  • Dynamic
  • Steady-state
  • Plant growth
  • Plant uptake
  • Modelling

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