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End_Report_Rick.Rmd
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---
title: "Improving on SOC storage models "
author: "**Rick Venema**"
date: "`r Sys.Date()`"
output:
pdf_document:
toc: False
number_sections: True
pandoc_args: [
"-V", "classoption=twocolumn"
]
header-includes:
- \usepackage{multicol}
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
\begin{abstract}
SOC storage models can give better insights in the amount of carbon in the soil. Existing models are not versatile. Existing models were changed to make them usable for further work with the models. Eventually a lot of the model could be simplified, there were however parts that could not be simplified. We used the model from Cardinael et al. 2018\cite{Cardinael18}. This model represents the SOC storage in the soil. The model was taken apart and the parts were examined to understand the code and what it does. The first idea was to add a nitrogen model to the code, this was however not possible due to the hard
\end{abstract}
***
# Introduction
Organic carbon in the soil is very important in good yield of products produced by the soil. A better understanding of organic carbon in the soil can give more insights in improving the yield of agricultural plots. Models for organic carbon storage exists, these models represent an existing agroforestry plot.
This paper extends the SOC (soil organic carbon) storage model by Cardinael et al. This model describes the flow of carbon in an agroforestry plot. The model of Cardinael et al 2018\cite{Cardinael18}. was however a hardcoded model. To be able to extend the model and use it for different locations, the model has to be improved on to be more versatile and more flexible. This can be done by rewriting big parts of the code and making tweaking parameters easier.
# Methods
## The model
The model is defined in the paper by Cardinael et al. (2018), this model follows a three pool model.
The fresh organic compound (FOC) difference can be found in formula \ref{eq:deltafoc}. This formula calculates the difference of FOC. This is calculated by using the input of carbon, given by $I_{t,z,d}$. This is calculated by adding all the imports from the different environmental inputs (Tree, Grass, and Crop).
\begin{equation} \label{eq:deltafoc}\
\begin{aligned}
\frac{\delta FOC_{t,z,d}}{\delta t} = I_{t,z,d} + \frac{\delta F_{AD}}{\delta z} + h * f_{2}* dec\_HSOC_{t,z,d} \\ + h *dec\_HSOC2_{tzd} - dec\_FOC_{t,z,d}
\end{aligned}
\end{equation}
The $\frac{\delta F_{AD}}{\delta z}$ parameter in formula \ref{eq:deltafoc} corresponds to the flux of carbon in the soil that is transported downwards. This flux is given by formula \ref{eq:FAD}.
\begin{equation} \label{eq:FAD}
F_{AD} = F_{A} + F_{D}
\end{equation}
In formula \ref{eq:FAD} the $F_{D}$ corresponds to Fick's law. This law is represented by formula \ref{eq:fick}.
\begin{equation} \label{eq:fick}
F_{D} = -D * \frac{\delta ^2 C}{\delta z^2}
\end{equation}
The $F_{A}$ parameter in \ref{eq:FAD} represents the advection. This represents the flow of C in the soil. This is given by formula \ref{eq:advec}
\begin{equation} \label{eq:advec}
F_{A} = A * C
\end{equation}
\begin{equation} \label{eq:deltahsoc1}
\frac{\delta HSOC1}{\delta t} = \frac{\delta F_{AD}}{\delta z} + h * f_{1} * dec\_FOC_{t,z,d} - dec\_HSOC1_{t,z,d}
\end{equation}
LORUM
\begin{equation} \label{eq:deltahsoc2}
\begin{aligned}
\frac{\delta HSOC2}{\delta t} = \frac{\delta F_{AD}}{\delta z} + h * (1-f_{1} * dec\_FOC_{t,z,d} \\ + h *(1-f_{2})*dec\_HSOC1_{t,z,d} - dec\_HSOC2_{t,z,d}
\end{aligned}
\end{equation}
## Understanding the model
The model was taken apart for better understanding of the code and its functions. The model was divided into several parts which each correspond to a parameter or group of parameters
wat gedaan met code
# Results
The code was after looking at the code divided into X parts.
## Bulk density
if statements
## Moyano et al. model
After looking at the model, the parameters were moved to a separate file, like the model by Moyano et al. 2012\cite{Moyano12}. This model was used to calculate the moist in the clay.
grafieken met onderschrift en uitleg over wat er te zien is
## SOC stocks
## Roots profile
# Discussion
The model by Cardinael et al. 2018 \cite{Cardinael18} was a hard model to rewrite. This was eventually not done due to time issues.
conclusie van het verhaal, hoe was het goed uit te voeren?, waarom niet helemaal belicht, verschil.
# Conclusion
WAT NU VERDER
\begin{thebibliography}{9}
\bibitem{Cardinael18}
Cardinael, R., Guenet, B., Chevallier, T., Dupraz, C., Cozzi, T., and Chenu, C.: \textit{High organic imputs explain shallow and deep SOC storage in a long-term agroforestry system - combining experimental and modeling approaches}, Biogeosciences, 15, 297-317, https://di.org/10.5194/bg-15-297-2018, 2018.
\bibitem{Soertaert10}
Soetaert, K., Petzoldt, T., and Woodrow Setzer, R.: \textit{Solving differential equations in R: package deSolve}, J. Stat. Softw., 33, 1-25, 2010.
\bibitem{Moyano12}
Moyano, F. E., Vasilyeva, N., Bouckaert, L., Cook, F., Craine, J., Curiel Yuste, J., Don, A., Epron, D., Formanek, P., Franzluebbers, A., Ilstedt, U., Kätterer, T., Orchard, V., Reichstein, M., Rey, A., Ruamps, L., Subke, J.-A., Thomsen, I. K., and Chenu, C.:\textit{ The moisture response of soil heterotrophic respiration: interaction with soil properties}, Biogeosciences, 9, 1173-1182, https://doi.org/10.5194/bg-9-1173-2012, 2012.
\end{thebibliography}