**3. Results**

Since our objective of this study is to improve the EDVI-based LE method driven by satellite and reanalysis data under all sky conditions, the inputs of the method are crucial and were first investigated in this section. Section 3.1 shows the consistency between LEobs and two vegetation indices. Section 3.2 provides the validation of accuracy of satellite and reanalysis data. The estimated instantaneous LE (LEcal) under all skies are validate in Section 3.3. Then the accuracy of LEcal under different cloudy sky conditions are further investigated in Section 3.4.

#### *3.1. Time Series of EDVI, NDVI and In-Situ Measured LE*

The time series of midday in situ measured LEobs, satellite-based EDVI and NDVI at the three forest sites in this study are shown in Figure 2. The EDVI and NDVI show the consistent seasonal cycles with the LEobs at all forests (maximum in summer and minimum in winter). EDVI vary from -0.015 to 0.02 during growing seasons when NDVI vary from 0.3 to 0.9. The LEobs of forest ecosystems can have significant variations during the short-term period due to environmental and weather e ffects (e.g., precipitation and solar radiation). Daily EDVI can indicate such fast changes of vegetation status and show the similar day-to-day variations to the LEobs at all sites (Figure 2), which suggests that EDVI can be potentially used to retrieve LE over the three forests. As an indicator of vegetation foliage, 16-day NDVI are found to have the small and relatively slow changes within each 16-day interval, suggesting that the use of interpolated daily NDVI from 16-day NDVI for the calculation of VFC may introduce small errors.

#### *3.2. Validation of Satellite Radiation Flux and Air Temperature Inputs*

Studies have been conducted to validate the CERES surface fluxes over di fferent surface types (i.e., island, coastal, polar, continental, and desert) and have found good accuracies of the data [38,60]. In this study, since there is no in-situ measurements of net radiation (Rn) available, we therefore conduct the validation of downward shortwave radiation fluxes (dSW) between satellite observations and in-situ measurements instead.

Figure 3 shows the comparison of all-sky CERES dSW and in situ measured downward solar radiation flux at midday from 2003 to 2005. Over all forest sites, CERES dSW agrees well with the in-situ measured solar radiation, with high positive correlation coe fficients (R) of 0.81, 0.95, and 0.90 at DHS, QYZ, and CBS, respectively. The relative biases of all sites are less than 9%. Because dSW is the dominant term of Rn, we therefore conclude that CERES SSF estimated Rn is suitable for estimating the real net radiation for calculating ET.

**Figure 3.** Time series and scatter plots of in-situ measured solar radiation (averaged over 2 h around the satellite overpass) and matched surface downward shortwave radiative fluxes (dSW) from CERES SSF under all-sky conditions.

Photosynthetically active radiation (PAR) is required in the estimation of EDVI-based canopy resistance. Studies have reported that PAR is linearly related to incident solar radiation [61–63]. In our study, all-sky CERES dSW is used to estimate PAR by multiplying it by a constant of 1.70 μmol/W. The results in Figure 4 indicate these estimations agree well with in-situ observations across three sites. Correlation coefficients strongly vary from 0.81 to 0.95 with a small bias of no more than 11%.

**Figure 4.** Comparisons between in-situ measured PAR and estimated PAR (dSW\*1.70). dSW is surface downward shortwave radiative fluxes from CERES SSF in all sky conditions.

Air temperature is an important parameter for estimating forest ET. We compare the 2-m air temperature (t2m) from ERA-20C (t2m-ECMWF) and from NCEP FNL (t2m-NCEP) with in-situ measurements. As shown in Figure 5, both t2m-ECMWF and t2m-NCEP have a high correlation with in-situ measured temperature. However, t2m-NCEP estimations are systematically lower by 3–5 K than in-situ measurements. In contrast, t2m-ECMWF are in better agreemen<sup>t</sup> with in situ measurements with a smaller bias (0.1–2.7 K). The overall biases of t2m-ECMWF for all sites are within 3K. Therefore, we determine to use ERA-20C rather than NCEP FNL to provide complementary parameters to the satellite observations.

**Figure 5.** Time series and scatter plots of in-situ measured air temperature (Ta), 2-meter temperature from ECMWF reanalysis (t2m-ECMWF) and 2-meter temperature from NCEP reanalysis (t2m-NCEP). In-situ measurements at DHS, QYZ, and CBS are at 20 m, 23 m, and 26 m, respectively. In scatterplots, t2m-ECMWF and t2m-NCEP are marked by black and blue color, respectively. R1 represents the correlation coefficient (R) of in-situ Ta and t2m-ECMWF. R2 represents the R of in-situ Ta and t2m-NCEP. BIAS1 represents the difference between mean t2m-ECMWF and in-situ Ta. BIAS2 represents the difference between mean t2m-NCEP and in-situ Ta.

#### *3.3. The EDVI-Based LE Estimation*

The time series of EDVI-based LEcal, in situ LEobs, and their differences at the three forest sites are shown in Figure 6. Statistic results are shown in Table 3. Generally, LEcal has the capability to capture the seasonality of forest LEobs from 2003 to 2005 correctly. Both of them reach maximums in the mature stage of growing seasons in mid-summer due to the ample water and solar radiation for evapotranspiration (Figure 6). There is a strong correlation between LEcal and LEobs with the overall R being 0.56–0.88. In terms of magnitude, LEcal, ranging from 0 to 500 Wm−<sup>2</sup> at DHS and QYZ in southern China, and from 0 to 400 Wm−<sup>2</sup> at CBS in northeastern China, matches LEobs well. Large discrepancies occur at QYZ in 2005 due to the serious imbalance of energy, which leads to a significant underestimation of in situ LEobs [64,65] and should be responsible for the large bias in this year (Table 3). Because of this, we exclude the result of 2005 in QYZ in the following discussion.

**Figure 6.** Time series of in-situ LE (LEobs), estimated LE (LEcal), and their differences at three forest sites from 2003 to 2005. LEobs was averaged over 2 h around the satellite overpass. The dashed lines are ±150 Wm−2.


**Table 3.** Summary of comprehensive metrics for the results of three forest sites. LEcal is the mean value of all estimations. LEobs is the mean value of all in-situ measurements. BIAS = LEcal − LEobs.

The samples with the differences between LEcal and LEobs less than 150 Wm−<sup>2</sup> account for 94%, 93%, and 92% of total samples at DHS, QYZ, and CBS, respectively (Figure 6). Our algorithm tends to underestimate the LE during transient periods with about 30–100 Wm−<sup>2</sup> (particularly in non-snowy wintertime and early spring). In spite of this, results in Table 3 show that the method can produce the small bias varying from −30.7 to 32.8 Wm−<sup>2</sup> with the RMSE from 56.0 to 90.9 Wm−2, respectively. The relative bias at three forests was kept within 23% for most of the years and range from −18.6% to 22.8%. The regression lines between LEcal and LEobs are well close to a 1:1 line at all sites with slopes of 0.70–1.29 (Figure 7, Table 3).

**Figure 7.** Comparisons between daily LEobs and LEcal at three sites from 2003 to 2005. The two dashed lines are the 1:1 line±RMSE. Solid circles are samples severely contaminated by precipitation.

The algorithm performs better at QYZ and CBS in terms of R (0.80–0.88) and RMSE (56–83.5 Wm−2). CBS has the smallest mean RMSE (67.9 Wm−2), highest R (0.83) and lowest relative bias (−9.6%) for all study years (Table 3). The best LE estimations at DHS, QYZ, and CBS occur in 2005 (R = 0.73, bias = 17.4 Wm−2, RMSE = 73.1 Wm−2), 2003 (R = 0.82, bias = 3.0 Wm−2, RMSE = 74.2 Wm−2), and 2004 (R = 0.88, bias = −22.7 Wm−2, RMSE = 56.0 Wm−2), respectively. However, the estimation performed relatively poorly at DHS in 2003 (R = 0.58, bias = 32.8 Wm−2, RMSE = 90.9 Wm−2) (Figure 7, Table 3).

Our algorithm could be a ffected by heavily rainy events occurring before or after when Aqua satellite overpasses. For these rainy days, our retrieval algorithm is expected to underestimate the LE because of the reduced microwave EDVI over wet surfaces and the omission of interception evaporation. Some rainy samples severely contaminated by such precipitation are marked by solid circles in Figure 7. If we excluded these samples, the performances would be generally improved at all sites, particularly for R and RMSE. This comparison results are shown in Figure 8. The R would be improved to 0.66–0.91 for all years and the RMSE would be reduced to 48.2–84.5 Wm−2.

**Figure 8.** Comparison results of all LE estimations (white bars) and the LE estimations after removing the heavily rain-contaminated days (black bars).

Additionally, a few samples with much larger LEcal than LEobs occurred during growing seasons, such as 2003 at DHS (mainly in summer with less precipitation). A possible explanation is that under high temperature and less precipitation conditions, the plant water deficit will induce leaf stomatal closure to prevent excessive water deficits in the plants during summer time [66]. As a result, the real plant physiological activities, such as leaf transpiration, carbon gain, and growth, are remarkably suppressed [66].

The comparison results between LEcal and LEobs at monthly scale show the better performance (Figure 9). R can reach 0.84, 0.88, and 0.95 for DHS, QYZ, and CBS with the bias of 14.3%, 0.3%, and −12.9%, respectively. The standard deviations of monthly mean LEcal and LEobs are comparable. As discussed, the results can be improved after removing the heavily rain-contaminated days (Figure 9).

**Figure 9.** Comparisons between monthly mean LEobs and LEcal at DHS, QYZ, and CBS. Horizontal and vertical error bars stand for the standard deviations of LEobs and LEcal. Numbers in the brackets are the statistic results after removing the heavily rain-contaminated samples.

#### *3.4. Validation of EDVI-based LE under Di*ff*erent Cloudy Sky*

Since EDVI is able to indicate vegetation hydrological states under both clear and cloudy sky [26,27], EDVI-based LE method combined with all-sky satellite-retrieved radiation also has the capability of estimating LE under di fferent cloud covers (Frc). Figure 10 shows the comparison of LEcal and LEobs under a partly cloudy sky (Frc < 40%), cloudy sky (Frc >= 40%) and all cloudy sky (0% <= Frc <= 100%). Their corresponding statistical metrics are shown in Figure 11. In general, our method has good performance at three sites. The slopes of fit lines are all close to 1.0 with the range of 0.88 to 1.16 (Figures 10 and 11), suggesting that the method can produce small systematic bias in the estimation of instantaneous forest LE under di fferent cloud covers. The capability is also illustrated in the results of bias and relative bias in Figure 11. For all three sites, the method produces bias less than 35 <sup>W</sup>/m<sup>2</sup> (26%) at instantaneous scale when compared with in-situ measurements. These biases vary from −34.2 <sup>W</sup>/m<sup>2</sup> to 25.1 <sup>W</sup>/m<sup>2</sup> with the relative values from −25.9% to 16.7% (Figure 11), respectively. The mean bias (relative bias) under Frc < 40%, Frc ≥ 40% and all cloudy sky are well kept within 11 <sup>W</sup>/m<sup>2</sup> with the values of 10.6 <sup>W</sup>/m<sup>2</sup> (6.3%), 0.32 <sup>W</sup>/m<sup>2</sup> (0.8%) and 7.7 <sup>W</sup>/m<sup>2</sup> (5%), respectively. In addition, a good correlation between LEcal and LEobs under di fferent cloudy skies are also found at three sites with the R of 0.62–0.80, which suggests that the seasonal dynamics of forest LE under cloud cover can be well recaptured by the EDVI-based method. Because of the relatively coarse spatial resolution (see the related discussion in Section 4), the method could produce relatively large RMSE (59 to 90 <sup>W</sup>/m2) illustrated by the scattering of samples in Figure 10.

Most importantly, it can be found that the EDVI-based method is able to produce stable statistic metrics under di fferent cloud cover conditions for three typical forests. These results indicate that the developed EDVI-based method in this study, completely driven by satellite and reanalysis datasets, can be used to estimate forest LE e ffectively from clear sky to cloudy sky.

**Figure 10.** Validation of EDVI-based LEcal under different cloud cover (Frc). Partly cloudy sky (Frc < 40%), Cloudy sky (Frc >= 40%) and all cloudy sky (0% <= Frc <= 100%).

**Figure 11.** Statistical metrics at three sites under different cloud cover. Slope is the slope of fit line between LEcal and LEobs.
