## 4 Results and Analysis
### Error Analysis
#### 4.4.2 Errors from H  
Based on Equations (1)-(4), it can be seen that the four energy balance components are related to LST. Because LE is calculated as a residual term in the energy balance equations, the sensitivity of \(R_{H}\), G and H to LST was analyzed first. However, except for LST, land surface variables, including canopy height, FVC, and LAI, and meteorological variables, including wind speed, air temperature, and relative humidity, are also the important factors for a sensitivity analysis of H. Figure 12 presents a sensitivity analysis for \(R_{\mathrm{n}}\), G and H. In this case, LST is 304 K, and it ranges from 297.5-311 K with a step size of 0.5 K; moreover, LAI ranges from 0.1-2.5 with a step size of 0.1. The canopy height is 0.69 m, and it ranges from 0.1-1.3 m. The wind speed ranges from 0.34-4.25 m\(\cdot\)s\({}^{-1}\), the air temperature \(T_{\mathrm{a}}\) = 297.11 K, FVC = 0.54, and the relative humidity RH = 35.43%. In addition, the land cover is maize. The air pressure is stable over short periods and has little effect on the LE results. Although H is sensitive to meteorological variables, such as wind speed (see Figure 12) and air temperature, the meteorological data used in the LE model are derived from ground observations; thus, the meteorological factors are relatively accurate. As shown in Figure 12, LAI, LST, and the canopy height are influential variables. H is sensitive to LAI when it is less than 1. The momentum roughness length increases as LAI increases, and the turbulent exchange is enhanced. However, when LAI is greater than 1, the plant canopy is regarded as a continuum that is not a sensitive variable. Because our study area is dominated by agriculture and the study period extended from June to September, the crops in the middle reaches of the HRB grew quickly; thus, LAI was usually greater than 1. Hence, LST and canopy height are the main sources of error. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Date**} & \multicolumn{2}{c}{**Downward Shortwave Radiation \(R_{s}\downarrow\) (W\(\cdot\)m\({}^{-2}\))**} & \multicolumn{2}{c}{**Downward Longwave Radiation \(R_{L}\downarrow\) (W\(\cdot\)m\({}^{-2}\))**} \\ \cline{2-7}  & \(R^{2}\) & **MBE** & **RMSE** & **\(R^{2}\)** & **MBE** & **RMSE** \\ \hline ECO1 & 0.97 & 25.23 & 27.73 & 0.85 & 4.16 & 17.21 \\ ECO2 & 0.84 & 28.29 & 33.57 & 0.88 & 0.11 & 14.23 \\ ECO3 & 0.97 & 17.56 & 19.25 & 0.91 & \(-\)18.65 & 20.88 \\ ECO4 & 0.98 & 6.07 & 9.34 & 0.88 & 3.36 & 16.38 \\ ECO5 & 0.98 & 10.60 & 12.29 & 0.88 & \(-\)0.79 & 15.02 \\ ECO6 & 0.93 & 27.68 & 30.71 & 0.84 & 2.55 & 15.43 \\ ECO7 & 0.89 & \(-\)17.69 & 27.59 & 0.75 & \(-\)5.90 & 19.72 \\ ECO8 & 0.83 & 15.63 & 25.50 & 0.80 & \(-\)1.35 & 17.49 \\ ECO9 & 0.96 & \(-\)2.27 & 9.96 & 0.86 & 10.44 & 17.99 \\ ECO10 & 0.94 & \(-\)3.50 & 11.97 & 0.87 & 7.98 & 16.05 \\ EC11 & 0.90 & 30.11 & 33.76 & 0.93 & \(-\)2.72 & 10.55 \\ EC12 & 0.96 & 24.35 & 26.43 & 0.87 & \(-\)0.84 & 14.80 \\ EC13 & 0.93 & 12.41 & 17.92 & 0.86 & \(-\)7.28 & 15.98 \\ EC14 & 0.98 & 32.40 & 33.49 & 0.82 & 4.07 & 16.42 \\ EC15 & 0.94 & 26.71 & 29.71 & 0.85 & 17.67 & 23.06 \\ EC17 & 0.94 & \(-\)20.25 & 24.54 & 0.90 & \(-\)1.11 & 12.87 \\ SD & 0.98 & 5.70 & 13.82 & 0.85 & \(-\)26.54 & 34.08 \\ SSW & 0.63 & 18.51 & 34.93 & 0.85 & 25.33 & 34.50 \\ GB & 0.89 & 25.34 & 30.63 & 0.88 & 9.50 & 27.82 \\ Overall & 0.81 & 13.80 & 25.35 & 0.73 & 0.28 & 21.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The station validation results of \(R_{s}\downarrow\) and \(R_{L}\downarrow\). (1) Errors in LST. As shown in Figure 12, \(R_{n}\) and G are not very sensitive to LST, but H is more sensitive to LST. A 1 K bias in LST would result in an error in H of 18.86%, whereas the corresponding errors in \(R_{n}\) and G are both only \(-0.96\%\). Therefore, in this paper, the LST is mainly affected by the impact of H on the role of LE. However, as we mentioned in Section 3.1, H depends on the temperature gradient between the surface and the atmosphere.