## 2 Materials and Methods
### Model Structure and Statistical Assessment  
The multiplication equation has been widely used to determine the relationship between canopy conductance and multifactor responses [37; 46]. Due to the difficulty in measuring canopy conductance, T is often used for derivation [47; 48]; therefore, we assume that the relationship between the daily transpiration of a stand in response to multiple environmental factors is similar to that of the canopy conductance, which can be expressed as a multiplicative function (refer to the infrastructure of the Jarvis-Stewart model) [28; 49]. There are many environmental factors that affect Tt or T, and each factor affects each other, so it is difficult to distinguish the influence of a single factor. In order to eliminate the interference from other factors, upper boundary line [50] analysis was conducted, which is useful for determining the effect of one single factor under optimal levels of other factors, to clarify how the T responded to every single factor. The upper boundary line was obtained by the following steps. Scattergrams were plotted between the T as a dependent variable and each of the independent variables (individual influential factors, i.e., Rn, VPD, and REW). For the calculation of boundary points, the data set of one scattergram needed to be split up. The response of a single factor (Rn, VPD, and REW) to T was divided into six equally spaced segments based on the range of observed data. Then, the data that were at least one standard deviation greater than the arithmetic mean of T within each variation interval were screened out. All data points of each segment were represented by only one boundary point. Finally, the boundary points along the x axis (arithmetic center of each segment) were used to describe the upper boundary line [45]. It was assumed that the effects of each single factor on transpiration are independent of each other, so the coupled model of transpiration affected by each factor was the multiplication relationship between transpiration and the response function of each single environmental factor [51]. The numerous factors influencing daily T can be simplified and divided into the three driving factors of Rn, VPD, and REW. Thus, the response of T to Rn, VPD, and REW was assumed to follow a multiplicative-type function coupling the response of T to Rn, VPD, and REW:  
\[\mathrm{T=f(R_{n})\times f(VPD)\times f(REW)} \tag{8}\]  
where \(\mathrm{f(R_{n})}\), \(\mathrm{f(VPD)}\), and \(\mathrm{f(REW)}\) are functions describing the T responses to Rn, VPD, and REW, respectively. The coefficient of determination (R\({}^{2}\)) and the Nash-Sutcliffe efficiency coefficient (NSE) were used for quantitative analysis of the T model performance, using Equation (9):  
\[\mathrm{NSE=1-\sum\frac{\left(\mathrm{T-T^{\prime}}\right)^{2}}{\left(\mathrm{ T-\overline{T}}\right)^{2}}} \tag{9}\]  
where T and T\({}^{\prime}\) are the measured and predicted values, respectively; \(\overline{\mathrm{T}}\) is the observed mean. When R\({}^{2}\) is close to 1 and NSE exceeds 0.6, the model performs well [52]. To provide some evaluation of the T models, several statistical tests were used in addition to NSE. Individually, the explained variance (R\({}^{2}\)) is not suitable as a measure of model performance, as it fails to account for model bias [53]. To provide a more robust statistical validation for the performance of models used in this study, the mean absolute error (MAE) and root mean square error (RMSE) were used to provide additional measures of the variation in the error. The RMSE and MAE are effective measures of the deviation of model predictions from the observed data, calculated as Equations (10) and (11) [54; 55]\[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}\left(\text{T}_{i}-\text{T}^{\prime}_{i} \right)^{2}}{n}} \tag{10}\]  
\[\text{MAE}=\frac{\sum\left|\text{T}-\text{T}^{\prime}\right|}{n} \tag{11}\]  
where T and T\({}^{\prime}\) are the observed and predicted values; \(n\) is number of data points.