**4. Discussion**

#### *4.1. Summary of the Method*

The above results sugges<sup>t</sup> that the new EDVI-based LE algorithm can e ffectively estimate instantaneous LE during midday at three di fferent forests. Compared with the early EDVI method of Li et al. [29] based on in situ measurements as inputs, the developed method in this study was completely driven by all-sky satellite-retrieved radiation fluxes and reanalysis-based meteorological data. Therefore, this method has the potential capability to estimate LE in unfrequented places, such as area in the deep forests and high mountains.

Which is central to our method is using microwave EDVI to quantify the stomatal and canopy resistance under both clear sky and cloudy sky. Most of previous resistance-based LE methods are based on optic VIs [17–19] which cannot be e ffectively implemented under cloudy sky. Their validations are thus limited to under clear or partly cloudy sky. Barraza et al. [23,24] compared the estimated surface conductance based on the di fferent regression models of microwave and optical VIs in forest and savanna ecosystems. Although they concluded that the combined microwave-optical VIs method produced the best conductance and LE estimation at the 8-day mean scale, the performances under di fferent sky conditions were not investigated at finer temporal resolution. EDVI-based LE method is designed for the instantaneous all-sky LE. The validations under di fferent cloudy skies show that our method can produce stable forest LE from clear to cloudy sky with good accuracy, which could be important for the study of EF and LE under cloudy sky.

#### *4.2. Uncertainties in the Results*

In spite of these, some uncertainties in our EDVI-based LE method should be noted.

The retrieved EDVI (EDVI) over a landscape is the integration of EDVI from vegetation (EDVIveg) and bare soil (EDVIsoil). During growing seasons, EDVI is dominated by EDVIveg and can be used as a good indicator of vegetation states. Thus, the LE estimated from EDVI approximates the in-situ measured LE. However, for some vegetation regions such as deciduous forests, EDVI can be a ffected by soil signals to di fferent extent during transient periods.

Since the EDVI-based LE method is implemented over forests in this study, the evaporation of intercepted water and bare soil are simply omitted in the forest LE estimation. This simplification could result in some underestimation, particularly during the non-growing seasons of deciduous forests when soil evaporation may dominate the total LE. Further, as we discussed in Section 3.3, the algorithm could be a ffected by heavily rainy events occurring near the time when Aqua satellite overpasses. The wet canopy surface can reduce EDVI and thus result in the underestimation of LE in our method. In spite of these, results in this study (Table 3) indicate that our current method for instantaneous LE estimation at forests with the overall mean bias of 16% (DHS), 11.4% (QYZ) and −9.6% (CBS) (Table 3) is well within the typical error range of 30% for satellite VI-based LE method [8].

As the surrogates for in situ measurements, the quality of the satellite remotely sensed and reanalyzed data, which are the inputs of our algorithm, particularly net radiation, which is the direct driving force for evapotranspiration, would highly a ffect the accuracy of the LE estimate, and the e ffect of this would vary at di fferent sites (Figure 3). Yan et al. [60] compared CERES surface radiation fluxes with in situ measurements over Loess Plateau and found CERES surface downward radiation fluxes have higher accuracies in clear sky than those in cloudy sky. The standard deviations of the dSW di fferences rise from ~30 W m<sup>−</sup><sup>2</sup> to ~130 W m<sup>−</sup><sup>2</sup> when cloud coverage increases from 5% to 80%. The errors of CERES estimated net radiation will be directly transferred to the results of EDVI-based LEcal.

Due to the inhomogeneity of vegetation coverage on the ground and the inconsistency of spatial resolution among the input datasets (Table 2), the matching of these data over the selected area (0.15º × 0.15º) around each forest flux tower may introduce errors. In addition, spatial mismatch of the geolocation between satellite field of view to the forest sites also can result in some poor performances in validations. For example, the flux tower at DHS is on a steep 30◦ slope and is close to a city, and there is a river located in the southeast. However, in our algorithm, the input data averaged over the 0.15º × 0.15º area surrounding the flux tower are used to estimate the regional mean LE. This certainly introduced additional discrepancies between the satellite EDVI-based LEcal and the in situ measured LEobs.

In addition, it should be noted that the validation results are also a ffected by the accuracies of the in situ measurements. The EC method may produce potential errors or uncertainty of 10%–30% [5]. Also, the EC flux towers frequently su ffer energy closure errors. In this study, the three ChinaFLUX forest sites achieve approximately only 70% energy balance closure during daytime, with about 30% of variation unexplained [35].

Although a ffected by the above uncertainties, the accuracies of instantaneous LE estimations in this study are comparable with those in Li et al. [29] which utilized both local in-situ measurements and satellite retrieved EDVI as data input. The results of this study demonstrate that it is feasible to operate the EDVI-based LE algorithm under both clear and cloudy skies with all satellite observations as data input.

#### *4.3. Pros and Cons of this method*

In comparison to Li et al. [29], the biggest improvement of this method is that its inputs do not depend on any in-situ measurements. This feature makes it applicable to any places with available satellite observations. Further, with proper calibration and validation, it can be developed to be a global algorithm in the future.

Compared to other optical VIs-based methods, the most significant advantage of this method is its capability for estimating ET related LE under cloudy sky. As shown in Section 3.4, no matter in what cloud fraction condition, the retrieved LE keeps small bias and good consistency with the in situ measurements. The most serious disadvantage of this method could be its poor spatial resolution, i.e., ~20 km. It is certain that the vegetation states and the evapotranspiration rate can vary significantly over this scale since the heterogeneous surfaces. This shortcoming may o ffset its merit of being useful under all weather conditions. A study of downscaling this method to the finer spatial resolution of optical VI is undergoing in our lab.

It should be noted that some parameterization schemes in our EDVI-based ET method need to be further improved in the future, especially for those resistance estimations based on EDVI and dEDVI. Since the selected three forests are similar to the Harvard forest where the initial method was developed [29], EDVI-based resistance schemes (e.g., a and b in Equation (8)) are thus assumed to be the same in this study. In addition, this method is recommended in flat or moderate terrain due to the associated errors with large scale satellite imagery of steep slope and LE estimation.

The real LE in the forest can be significantly a ffected by heavy rainfall due to the enhanced evaporation from interception water on the leaves. However, such an e ffect cannot be captured by the current method because it only takes into account one evapotranspiration source from inner vegetation water. In contrast, the plant water deficit will induce leaf stomatal closure to prevent excessive water deficits. However, this response is not described in the current model. A further study to consider more ET sources and the phenology response of vegetation to drought should be conducted to improve the retrieving performance.

Besides EDVI, there are several other vegetation water content related indexes that have been developed. For example, the normalized di fference water index (NDWI) [67] and land surface water index (LSWI) [68]. Due to the di fferences in their physical connections to vegetation water and their distinct spatial and temporal resolution, they may be used to estimate ET and LE with particular advantages and disadvantages, respectively. A comprehensive comparison study among them will be valuable for improving the satellite based global estimation of evapotranspiration and latent heat flux.
