## Appendix A Methods of ET Partitioning
### The Flux Variance Similarity (FVS) Method  
The FVS method is based on the flux variance similarity theory and water use efficiency to achieve the separation of evapotranspiration components, and its greatest advantage is that only a set of high-frequency water vapor and carbon dioxide flux concentrations measured by eddy correlation are needed as input data, which can achieve the fine simultaneous separation of evapotranspiration components at the ecosystem scale at flux sites with long-term localized observations, avoiding the parameter complexity based on the mechanistic process model and directly achieving ET components at long-term localized flux sites [18; 19; 43]. Based on the principle of similarity of flux variance between stomatal and nonstomatal processes, this method provides a solid physical basis for fine-grained partitioning of ecosystem evapotranspiration, and has been applied in agricultural, grassland, and forest ecosystems. [PERSON] et al. simplified the solution of the nonlinear system of equations [46], and the simplified system of equations is  
\[W\frac{<w^{\prime}q^{\prime}>}{<w^{\prime}c^{\prime}>}\left(\frac{<w^{\prime} c^{\prime}>}{<w^{\prime}c^{\prime}>}+1\right)=\left(\frac{<w^{\prime}q^{ \prime}_{e}>}{<w^{\prime}q^{\prime}_{t}>}+1\right)\] (A7)  
\[W\rho_{q,c}c_{\sigma}c_{q}\sigma_{c_{p}}^{-2}=1+\frac{<w^{\prime}c^{\prime}>}{<w ^{\prime}c^{\prime}{}_{p}>}+\frac{<w^{\prime}q^{\prime}_{e}>}{<w^{\prime}q^{ \prime}_{t}>}+\rho_{cp,cr}^{-2}<\frac{<w^{\prime}c^{\prime}>}{<w^{\prime}c^{ \prime}{}_{p}>}<\frac{<w^{\prime}q^{\prime}_{e}>}{<w^{\prime}q^{\prime}_{t}>}\] (A8)  
By conditionally constraining the solution, both the initial and the boundary constraints developed in recent years [18; 19; 42; 43; 47] are as follows:  
\[-1<\rho_{c_{p},c_{\sigma}}<0\] (A9)  
\[\sigma_{c_{p}}^{2}>0;W<0\] (A10)  
\[\rho_{cd}^{-1}\frac{\sigma_{c}}{\sigma_{q}}\leq\frac{<w^{\prime}c^{\prime}>}{< w^{\prime}q^{\prime}>}<\rho_{c,q}\frac{\sigma_{c}}{\sigma_{q}}\ \ for\rho_{c,q}<0\] (A11)  
\[\frac{<w^{\prime}c^{\prime}>}{<w^{\prime}q^{\prime}>}<\rho_{c,q}\frac{\sigma_ {c}}{\sigma_{q}}\ \ for\rho_{c,q}>0\] (A12)  
Although the numerical solution process can be achieved under the above condition constraints, two uncertainties remain. First, the approximation of the two correlation coefficients associated with the water-carbon flux components requires coefficient corrections using large eddy simulations, a correction process that is essential but difficult for most station observations [48]. Second, the accuracy of the effective estimation of the leaf-scale water use efficiency, the only input term used for the numerical solution other than the raw vorticity HF data, can seriously affect the speed of the numerical solution of the flux component and the proportion of successful separations [36]. The process is parameterized as follows:  
\[W=\frac{0.625\cdot VPD\cdot m-\sqrt{0.625\cdot VPD\cdot m(Ca+0.625\cdot VPD \cdot m)}}{0.625\cdot VPD}\] (A13)where \(Ca\) is the average atmospheric CO\({}_{2}\) concentration at the canopy position. The estimation of \(m\) was introduced into the calculation of water use efficiency [43].