# SimTraces a numerical simulator for predicting the accumulation of trace elements by crops

Christophe Nguyen, Claude Bruchou, Jean-Yves Cornu, Marie Launay, Marie-Aline Laporte, Zhongbing Lin, Ronan Maron, Olaia Liñero, Loic Pages, Dominique Ripoche, et al.

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Christophe Nguyen, Claude Bruchou, Jean-Yves Cornu, Marie Launay, Marie-Aline Laporte, et al. SimTraces a numerical simulator for predicting the accumulation of trace elements by crops. ICOBTE 2017 (International Conference on the Biogeochemistry of Trace Elements), Jul 2017, Zurich, Switzerland. 2017. [hal-02735722](https://hal.inrae.fr/hal-02735722)

HAL Id: hal-02735722

https://hal.inrae.fr/hal-02735722

Submitted on 2 Jun 2020

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Christophe Nguyenª, C. Bruchouᵇ, J.Y. Cornuª, M. Launayᶜ, M.A. Laporteª, Z. Linªᵉ, R. Maronᶜᵈ, O. Lineroª, L. Pagèsᵈ, D. Ripocheᶜ, A. Schneiderª, C. Sirgueyᵉ, T. Sterckemanᵉ

ª Interactions soil-plant-atmosphere INRA - Bordeaux Sciences Agro, ᵇ Biostatistics and Spatial Processes, INRA, ᶜ Agroclim, INRA, ᵈ Plant & Horticultural Systems, INRA,

ᵉ Laboratoire Sols et Environnement, Université de Lorraine - INRA, France.

**SimTraces** was built with the objective of integrating all the key steps governing trace element accumulation in plant parts, taking into account the environmental conditions (climate and agricultural practices).

<figure><img src="image_3.png" /></figure>

https://www6.inra.fr/simtraces
http://www6.paca.inra.fr/stics

**A phytoavailability model** predicts the movement of the trace metal in the rhizosphere while the root absorbs it. The model considers three chemical species: the metal free ion (M), a mean organic ligand (L) and the complex between the trace element and the ligand (ML). The model accounts for the transport by diffusion and advection, for the kinetics of sorption onto the solid phase and of complexation in solution, and for the uptake by roots.

$$ 
\begin{aligned}
\frac{\partial \tilde{C}_M}{\partial t} &= \frac{1}{r} \frac{\partial}{\partial r} \left( r f \theta D_M \frac{\partial \tilde{C}_M}{\partial r} + r_0 v_0 C_M \right) + \theta (k_d C_{ML} - k_a^{\text{cond}} C_M C_L) + (k_{\text{des}}^M S_M - \theta k_{\text{ads}}^M C_M) \\
\frac{\partial \tilde{C}_L}{\partial t} &= \frac{1}{r} \frac{\partial}{\partial r} \left( r f \theta D_L \frac{\partial \tilde{C}_L}{\partial r} + r_0 v_0 C_L \right) + \theta (k_d C_{ML} - k_a^{\text{cond}} C_M C_L) + (k_{\text{des}}^L S_L - \theta k_{\text{ads}}^L C_L) \\
\frac{\partial \tilde{C}_{ML}}{\partial t} &= \frac{1}{r} \frac{\partial}{\partial r} \left( r f \theta D_{ML} \frac{\partial \tilde{C}_{ML}}{\partial r} + r_0 v_0 C_{ML} \right) + \theta (k_a^{\text{cond}} C_M C_L - k_d C_{ML}) + (k_{\text{des}}^{\text{ML}} S_{ML} - \theta k_{\text{ads}}^{\text{ML}} C_{ML}) \\
\frac{dS_M}{dt} &= \theta k_{\text{ads}}^M C_M - k_{\text{des}}^M S_M \\
\frac{dS_L}{dt} &= \theta k_{\text{ads}}^L C_L - k_{\text{des}}^L S_L \\
\frac{dS_{ML}}{dt} &= \theta k_{\text{ads}}^{\text{ML}} C_{ML} - k_{\text{des}}^{\text{ML}} S_{ML}
\end{aligned}
$$

<figure><img src="image_4.png" /></figure>

Simulation of Cd species concentrations in soil solution from root surface uptake by 1 cm root segment for 30 days in an agricultural soil.

**A partitioning model** allows to allocate the amount of trace elements taken up at each daily time step between the different parts of the plant, the biomass of which is simulated by the Stics crop model. The partitioning is based on the transport by xylem and phloem, on exchanges between these two routes and on remobilization from senescing organs. Both the total amount of element extracted from the soil and the concentration in the plant organs are simulated along with time.

<figure><img src="image_5.png" /></figure>

Partitioning of Cd simulated by SimTraces for sunflower from germination to maturity.

<figure><img src="image_6.png" /></figure>

Concentrations of Cd in the different parts of sunflower as simulated by SimTraces based on the biomass dynamics simulated by the Stics crop model.

SimTraces relies on the **Stics crop model** that simulates the time course of crop growth and biomass partitioning. Three additional models have been developed and coupled with Stics.

<figure><img src="image_7.png" /></figure>

Growth of the different plant parts of sunflower as simulated by the Stics crop model for a given set of climatic and environmental conditions.

**An uptake model** was built by integrating an age- dependent uptake function into a model of 3D root system architecture (ArchiSimple), which is able to simulate a great variety of root systems from few input parameters. The uptake is dynamically and spatially simulated.

<figure><img src="image_8.png" /></figure>

Projections of simulated root systems for Noccaea caerulescens (Pages et al., 2013).

<figure><img src="image_9.png" /></figure>

Relationship between simulated and measured root growth of Noccaea caerulescens.

<figure><img src="image_10.png" /></figure>

Cumulative and daily total uptake (from left to right) of Cd by a growing root system of sunflower as simulated by SimTraces.

<figure><img src="image_11.png" /></figure>

SimTraces is an **open source** R package under construction. Besides being a **scientific tool**, it should help **agronomic expertise**, allowing agriculture and environment stakeholders to test scenarios of agricultural practices in order to optimize the quality of crop edible parts (nutrient and contaminant contents) as well as the phytoextraction of trace elements from polluted soils by dedicated crops.