The CO2 amount of the actual year is calculated linearly by: CO2(year) = Slope*(year-startyear)+startvalue
The actual \(CO_2\) is calculated by a linear function
\[ \begin{equation} CO_2(Year) = Slope \cdot (Year-StartYear) + StartValue \label{co2} \end{equation} \]The LUE is calculated in dependence of CO2 by the formula:
\[ \begin{eqnarray} \lambda & = & 100 g MJ^{-1} \\ LUE(CO_2) & = & \lambda \frac{CO_2}{CO_2 +b_1 e^{-b_2 CO_2}} \label{lue} \end{eqnarray} \]Reference: Stockle, C.O., Williams, J.R., Rosenberg, N.J., Jones, C.A., 1992. A method for estimating the direct and climatic effects of rising atmospheric carbon dioxide on growth and yield of crops, Agr. Sys. 38 (3), 225–238. See http://dx.doi.org/10.1016/0308-521X(92)90067-X
Finally the LUE-curve is stretched by a factor so that it meets the reference values
\[ \begin{eqnarray} f & = & \frac{LUE(ReferenceCO_2Value)}{ReferenceLueValue} \label{factor} \\ LUE & = & LUE(CO_2(Year)) \cdot f \label{finallue} \end{eqnarray} \]Content Type | Name | Description | Data Type | Unit | Min Value | Max Value | Default Value |
---|---|---|---|---|---|---|---|
constant | cReferenceCo2Value | Used to rescale the curve to meet the reference point \(\eqref{factor}\). | DOUBLE | ppm | 0.0 | 2000.0 | 350.0 |
constant | cReferenceLueValue | Used to rescale the curve to meet the reference point \(\eqref{factor}\). | DOUBLE | g/MJ | 0.0 | 10.0 | 3.0 |
constant | cSlope | Slope to calculate CO2 amount of given year by linear function in \(\eqref{co2}\). | DOUBLE | parts_per_million_per_year | -1000.0 | 1000.0 | 3.5 |
constant | cStartValue | Reference CO2 amount of the StartYear, starting point of the line \(\eqref{co2}\) | DOUBLE | ppm | 0.0 | 2000.0 | 350.0 |
constant | cStartYear | Reference year, starting point of the line \(\eqref{co2}\) | INT | a | 0 | 10000 | 1990 |
constant | c_b1 | Parameter \(b_1\) to dertemine the shape of curve \(\eqref{lue}\) | DOUBLE | 1 | 0.0 | 1000000.0 | 6928.0 |
constant | c_b2 | Parameter \(b_2\) to determine the shape of curve \(\eqref{lue}\) | DOUBLE | 1 | -10.0 | 10.0 | -0.0014 |
LUE | Light use efficiency dependend on \(CO_2\) \(\eqref{finallue}\) | DOUBLE | g/MJ | null |