## 3 Results and Discussion  
### Comparison of Observed H with SEBS and MDDI-Integrated SEBS  
To be able to analyze whether integrating MPDI into SEBS via kB\({}^{-1}\) improves the sensible heat (H) estimates in the study region, the H observations from EC (H\({}_{\text{EC}}\)) at the HJ-1 transit time were compared with H calculated by SEBS (H\({}_{\text{SEBS}}\)) and MPDI-integrated SEBS (H\({}_{\text{SEBS-MPDI}}\)). Figure 4a indicates an obvious underestimation of H by the original SEBS, with most scatter points below the 1:1 line, and the slope for the linear regressions was 0.73. A better agreement was obtained between the observed and modeled H in Figure 4b, with more scatter points around the 1:1 line, and the slope for the linear regressions was 0.96. When soil moisture information was incorporated in the calculation of H by SEBS, the coefficient of determination (\(R^{2}\)) was 0.85, indicating a strong correlation between the observed H and simulated H by the MPDI-integrated SEBS model. Figure 3: The scaling effect of MPDI to the kB\({}^{-1}\) parameter in SEBS. Figure 2: The flowchart of the modified perpendicular drought index (MPDI)-integrated surface energy balance system (SEBS) model. To further study the behavior of the two methods under low soil moisture and high soil moisture, the time series of soil moisture and the sensible heat fluxes of HEC, HSEBS, and HSEBS-MPDI in the Daman station and the Huazhaizi station were plotted in Figure 5. At Daman station, from late May to August, intensive rainfall or irrigation led the soil moisture to maintain a relatively high level (>0.30 m\({}^{3}\)/m\({}^{3}\)) sometimes. Although rain caused soil moisture to fluctuate during growing season, the values for soil moisture mostly stayed low (<0.20 m\({}^{3}\)/m\({}^{3}\)) at Huazhaizi station. Table 4 shows the error evaluation of HSEBS and HSEBS-MPDI based on EC observations under low soil moisture and high soil moisture conditions. When soil moisture was less than or equal to 0.30 m\({}^{3}\)/m\({}^{3}\), a large reduction in the root mean square error (_RMSE_) occurred and the mean absolute error (_MAE_) kept from 58.17 W m\({}^{-2}\) to 7.06 W m\({}^{-2}\), which indicated that the MPDI-integrated SEBS significantly improved the underestimation of H for the SEBS model. When soil moisture was greater than 0.30 m\({}^{3}\)/m\({}^{3}\), the RMSEs and MAEs between HSEBS and HSEBS-MPDI were close, which implied that the MPDI-integrated SEBS model slightly refined the SEBS model when adequate soil water was available. [PERSON] et al. revealed in 2010 that the process of evapotranspiration is controlled by the available energy rather than the soil moisture when the area is under saturated moisture conditions [54]. This is the reason why the MPDI-integrated SEBS cannot significantly improve the performance of the SEBS model under high soil moisture conditions. Figure 4: Comparison of HEC with HSEBS (**a**) and HSEBS-MPDI (**b**). Figure 5: _Cont._  
The specific comparison of instantaneous H estimated by SEBS with and without the integration of MPDI on an early dry summer day of 4 May, 2015 (day of year (DOY) 124) is plotted in Figure 6. At this time of year, maize was still in the seedling stage. The high MPDI (MPDI > 0.5) and bare to very sparse conditions (LAI < 2) observed in most of the study region confirmed water-limited conditions with sparse vegetation (e.g., purple circles in Figure 6). Accordingly, the instantaneous H estimated by the MPDI-integrated SEBS had the largest increase with about 42.5 W m\({}^{-2}\) in these areas.