# An Improved CASA Model for Estimating Winter Wheat Yield from Remote Sensing Images
## 3 Study Methods
### Improved Estimation of Light Use Efficiency  
Ideally, plant vegetation has maximum light use efficiency but, in reality, the light use efficiency is affected by many external environmental factors: mainly temperature and precipitation. The light use efficiency thus was calculated by using the model established by Potter and Field (2007, 2009) combined with the regional actual evapotranspiration model proposed by [PERSON] and [PERSON] in 1995 ([PERSON] and [PERSON], 2016). Specifically, the \(\varepsilon\) is calculated as follows:  
\[\varepsilon(x,t)=T_{\varepsilon 1}(x,t)\times T_{\varepsilon 2}(x,t)\times W_{ \varepsilon}(x,t)\times\varepsilon^{*}, \tag{12}\]  
\[T_{\varepsilon 1}(x,t)=0.8+0.002T_{opt}(x,t)-0.0005T^{2}_{opt}(x,t), \tag{13}\]  
\[ \begin{array}{l}T_{\varepsilon 2}(x,t)\\ =\frac{1184}{\left[1+\exp\left[02\left(T_{opt}(x)-10-T(x,t)\right)\right] \right]\left[1+\exp\left[03\left(-T_{opt}(x,t)-10+T(x,t)\right)\right]\right]},\end{array}  \tag{14}\]  
\[W_{\varepsilon}(x,t)=\left(\frac{1}{2}\right)\frac{EET(x,t)}{PET(x,t)}+\frac{1 }{2}, \tag{15}\]  
where \(T_{\varepsilon 1}(x,t)\) and \(T_{\varepsilon 2}(x,t)\) are the temperature stress factors of the light use efficiency for pixel \(x\) at time \(t\), \(W_{\varepsilon}(x,t)\) is the water stress factor of the light use efficiency for pixel \(x\) at time \(t\), \(\varepsilon^{*}\) [g C MJ\({}^{-1}\)] is the maximum light use efficiency under ideal conditions, \(T(x,t)\) is the average temperature for pixel \(x\) at time \(t\), \(T_{\mathrm{opt}}(x,t)\) is the appropriate temperature for plant growth for pixel \(x\) at time \(t\); \(EET(x,t)\) [mm] is the actual evapotranspiration and based on using Equation (16), which in turn depends on the Penman Equation (17) ([PERSON], 1966). \(PET(x,t)\) [mm] is the potential evapotranspiration, which is calculated as follows:  
\[EET(x,t)=\frac{\left\{P(x,t)\times R_{n}(x,t)\times\left[P^{2}(x,t)+R^{2}{}_{n }(x,t)+P(x,t)\times R_{n}(x,t)\right]\right\}}{\left\{\left[P(x,t)+R_{n}(x,t) \right]\times\left[P^{2}(x,t)+R^{2}{}_{n}(x,t)\right]\right\}} \tag{16}\]\[R_{n}(x,t)=[E_{p0}(x,t)\times P(x,t)]^{\frac{1}{2}}\times\{0.369+0.598\times[ \frac{E_{p0}(x,t)}{P(x,t)}]^{\frac{1}{2}}\} \tag{17}\]  
\[PET(x,t)=\frac{E_{p0}(x,t)+EET(x,t)}{2} \tag{18}\]  
where, \(P(x,t)\) [mm] is the precipitation for pixel \(x\) at time \(t\), \(R_{n}(x,t)\) [MJ m\({}^{-2}\)] is the net radiation for pixel \(x\) at time \(t\), \(E_{p0}(x,t)\) is the local potential evapotranspiration, which is related to the temperature for pixel \(x\) at time \(t\), and Reference [58] is referenced to calculate \(E_{p0}(x,t)\) based on vegetation-climate method established by [PERSON]. An important parameter of the CASA model is \(\varepsilon^{*}\), the ideal-condition maximum light use efficiency, which can be assigned a fixed value when processing data corresponding to a small area [55; 59]. \(\varepsilon^{*}\) directly affects the value calculated for the light use efficiency. Without distinguishing vegetation types and geographical types, [PERSON] et al. [55] used 0.389 g C MJ\({}^{-1}\) as the global \(\varepsilon^{*}\) of vegetation. [PERSON] [60] assigned an upper limit of 3.5 g C MJ\({}^{-1}\) to the \(\varepsilon\), and [PERSON] et al. [56] estimated the \(\varepsilon^{*}\) for various typical types of vegetation in China based on NPP estimated by remote sensing models. [PERSON] et al. [61; 62] claimed that the \(\varepsilon^{*}\) ranges from 0.42 to 3.8 g C MJ\({}^{-1}\), whereas, other results suggested that the \(\varepsilon^{*}\) of wheat ranges from 1.46 to 2.93 g C MJ\({}^{-1}\)[63; 64]. Different types of vegetation have different ecological and physiological structures, so their \(\varepsilon^{*}\) should differ. Since the present study focuses on winter wheat, the environmental conditions of the study area along with the results of previous research are considered to fix the \(\varepsilon^{*}\) of winter wheat at ranges from 0.42 to 2.93 g C MJ\({}^{-1}\).