# Modeling the Impact of Atmospheric Warming on Staple Crop Growth in China in the 1960s and 2000s
## 2 Methods
### The Modeling Approach  
We used the Agro-C model [31], which is a process-based model for simulating crop photosynthesis, respiration and other processes involved in crop growth and carbon/nitrogen dynamics in soils. The model runs on a daily time step, and the inputs of it are climatic, edaphic, atmospheric CO\({}_{2}\) concentration, crop calendar and field management data. The outputs of the model include crop biomass, leaf area index (LAI), gross primary productivity (GPP), crop respiration (RA) and net primary productivity (NPP). The model used in the present study has two functional modules to simulate crop photosynthesis and respiration. These modules incorporate impacts of the environmental variables of temperature, solar radiation, soil moisture and atmospheric CO\({}_{2}\) concentration on the crop growth, but the influence of pests and diseases cannot be captured at present. The effect of air temperature on photosynthesis is expressed by a piecewise function, and is determined by the lower and upper temperature limits, and optimum temperature subject to specific crop varieties. The optimum temperatures for the photosynthesis of rice, wheat and maize are 29, 18 and 30 \({}^{\circ}\)C, respectively [31]. The Agro-C model contains 29 basic formulas. For  
Figure 1: Locations of the sites with different rotation systems. Overlap of the symbols stands for crop rotations: maize/wheat rotation at Fengqiu, rice/wheat rotations in Changshu and rice/rice rotation at Taoyuan. The green colored background shows the distribution of cropland in China in 2015 ([[http://www.resdc.cn/lds.aspx](http://www.resdc.cn/lds.aspx)]([http://www.resdc.cn/lds.aspx](http://www.resdc.cn/lds.aspx))). more detailed information about the model, the reader is advised to refer to [PERSON] et al. (2009) [31]. The main processes are as follows:  
\[GPP_{i}=0.0432\times P_{i}\times DL_{i} \tag{1}\]  
where \(GPP\) (g C m\({}^{-2}\) d\({}^{-1}\)) is the gross primary production and \(P\) (\(\mu\)mol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)) is the photosynthetic rate. \(DL\) (h) is the day length:  
\[P_{i}=\frac{PM_{i}\times\overline{PAR_{i}}}{\beta+\overline{PAR_{i}}}\times f (T_{i})\times f(W_{i})\times f(CO_{2}) \tag{2}\]  
where \(PM\) (\(\mu\)mol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)) is the canopy photosynthetic rate at light saturation determined by the green leaf nitrogen content (\(NL\), g N m\({}^{-2}\) of ground); \(\beta\) is a coefficient that determines the shape of the photosynthetic active radiation (\(PAR\))-response curve of photosynthesis; \(\overline{PAR}\) (\(\mu\)mol m\({}^{-2}\) s\({}^{-1}\)) represents the mean value of \(PAR\) intercepted by the crop canopy; \(f(T)\), \(f(W)\) and \(f(CO_{2})\), are the impacts of air temperature, soil moisture and atmospheric CO\({}_{2}\) concentration on photosynthesis, respectively. \[PM_{i}=\alpha\times NL_{i-1} \tag{3}\]  
\[\overline{PAR_{i}}=\frac{(1-\rho)\times PAR_{Qi}}{k\times LAI_{i-1}}[1-exp(-k \times LAI_{i-1})] \tag{4}\]  
where \(\alpha\) is a coefficient representing the photosynthetic capacity per unit canopy leaf nitrogen. \(\rho\) is canopy reflectance, set at 6%, and \(k\) is an irradiance extinction coefficient that varies with crop development [31]. \(PAR_{0}\) represents the \(PAR\) above the crop canopy. \(LAI\) (m\({}^{2}\) m\({}^{-2}\)) is the green leaf area index determined by:  
\[LAI_{i}=\left\{ \begin{array}{l}\sum\limits_{i=1}^{\leq CDS}(PL_{i}\times( GPP_{i}-RA_{i})/0.45)\times SLA-DLAI_{i}(i\leq CDS)\\ \frac{LAI_{in}}{1+\sigma\times(DVI_{i}-1)^{2}}(i> CDS)\end{array} \right. \tag{5}\]  
\[DVI_{i}=\frac{\sum\limits_{i=1}^{\leq n}T_{ai}}{AT} \tag{6}\]  
where \(PL\) represents the fraction of photosynthesis partitioned to leaves. \(SLA\) is the specific leaf area (m\({}^{2}\) kg\({}^{-1}\)). \(DLAI\) represents the yellow leaves due to senescence. \(CDS\) represents a certain developmental stage of a crop, such as heading of rice. \(LAI_{max}\) represents the \(LAI\) at the \(CDS\) phase. \(DVI\)(developmental index) is the crop developmental index.