**5. Discussion**

#### *5.1. Need to Assess Remotely Sensed ET before Use in Watershed Model Calibration*

Our results illustrate a case where spatiotemporal information about ET would be represented more accurately by a watershed model calibrated to streamflow than a watershed model calibrated to ETrs. This assertion follows from our finding that the ETrs (MODIS) data were less accurate than ET predictions from watershed model calibrated to streamflow. ET from the MODIS model had a PBIAS of −47% and NSE of −0.43 across all sites, compared to a PBIAS of −13% and NSE of +0.36 for ET from the stream-calibrated watershed model (Table 2). Moreover, the negative relationship between long-term ET and elevation (Figure 3) was underestimated by 81% in the MODIS model compared to only 8% in the stream-calibrated watershed model. In general, there would clearly be cases where a watershed model's representation of ET would likely be improved via calibration to ETrs, one example being a watershed not instrumented with any streamgages. More study is needed, however, to understand the conditions (e.g., climate, modeling frameworks, density of observations) for which the use of ETrs for watershed model calibration would produce superior ET accuracy over use of observed stream discharge.

#### *5.2. Representation of Water Iimitation in Remote Sensing Products*

Plants respond to water stress by regulating their stomata, which in turn modifies transpiration rate [8]. This regulation process is known to be a complex function of atmospheric conditions and plant water potential (including cell turgor pressure) [55,72]. The MODIS ET model accounts for this by numerically correcting the canopy conductance of water vapor using functions of minimum air temperature and vapor pressure deficit (VPD) [11,12,54]. The air temperature component of this conductance correction is meant to account for temperature limitation on plant growth while the VPD component is meant to account for water limitation. For weather at the lower site, the MODIS algorithm would predict an increase in canopy conductance with air temperature to approximately 15 ◦C, then a decrease in canopy conductance with further warming (Supplement Figure S7b). Below the transition temperature of 15 ◦C, the temperature-correction component dominates the overall correction to ET giving "temperature-limited" transpiration. Above the transition temperature, the VPD-correction component dominates giving "water-limited" transpiration. The transition temperature of 15 ◦C approximately coincides with the observed air temperature at which MODIS ET reaches a peak value at the lower site, 16 ◦C (Figure 6i). Based on this finding, the negative trend shown in Figure 6i between MODIS ET and air temperature for air temperatures > 16 ◦C, and absence of significant relationship between ET and temperature overall, can be explained by unrealistically high VPD-limitation on ET in the MODIS model.

This argumen<sup>t</sup> also seems to apply to the middle site. As a reminder, the air temperatures used in an ET-weather relationship were obtained from the watershed subbasin containing the selected site of interest (Section 3.2, Figure 1). Air temperatures at the middle site were 8 ◦C cooler on average than at the lower site (Figure 5e versus Figure 5h). This temperature difference exactly coincides with the −8 ◦C offset of maximum MODIS ET at the middle site relative to the lower site (Figure 6f versus Figure 6i). This can be explained as follows. The 8 ◦C difference in air temperature between the lower and middle sites occurred across a relatively short distance of approximately 7 km (Figure 1). A difference in weather across this short of distance would not be registered in the MODIS ET product because of its use of weather data at 1◦ × 1.25◦ resolution [11,12]. A mismatch in resolution of weather forcings between the SWAT model (0.042◦ × 0.042◦) and MODIS model (1◦ × 1.25◦) would thus introduce an apparent ET offset of −8 ◦C at the middle site relative to the lower site. This argumen<sup>t</sup> does not seem to apply at the upper site because at that location, a clear transition from temperature-limited ET to water-limited ET with increasing air temperature did not occur (Figure 6c).

Based on this interpretation, the relatively large underestimates in warm-season ET from MODIS (Figures 4 and 5) stemmed from excessive VPD-limitation on canopy conduc-

tance in the MODIS model. In addition to atmospheric conditions, canopy conductance is known to be a function of plant water potential, which in turn depends on subsurface water availability and the ability of plants to access that water through their roots [72]. Weather, water availability, and plant roots are independent factors (at least to some degree), which is likely a reason for differing ET-VPD relationships across different geographic regions [73,74]. In the snow-influenced Mediterranean climate of the study area, snowmelt is known to be an important source of water to forest during the dry season. In such environments, VPD and actual water availability in the subsurface may be more loosely coupled than in the environments to which the MODIS model has been trained [75].

#### *5.3. Regression-Based Correction to Remotely Sensed ET*

ET from observations and the MODIS model showed markedly different relationships to weather variables (Section 4.4). Correlations between ET and air temperature were significantly positive at the flux towers (Figure 6, left) and either negative or not significant from MODIS (Figure 6, right). These contrasting ET-temperature relationships provided a possible basis for correcting MODIS ET to weather using linear regression. MODIS ET error expressed as a fraction of PET, defined as *yregr* = (MODIS ET − flux tower ET)/(MODIS PET), was found to be well correlated to air temperature. Best fits from linear regression had slopes ranging from −0.010 to −0.024 ◦C−<sup>1</sup> and *R*2-values of 0.25–0.66 (Figure 7a−c). The best of all fits was found at the upper site, where the *R*<sup>2</sup> was 0.66 (Figure 7c). We used this regression model to predict corrected values of MODIS ET, set equal to MODIS ET − [(MODIS PET) × *yregr*]. The resulting predictions of corrected MODIS ET matched the flux tower observations better than both the original MODIS ET and the SWAT model (Figure 7d–f). The corrected MODIS ET had an NSE-value of +0.67 and a PBIAS of −0.9% across all sites, statistics considerably better than those of both the uncorrected MODIS model and the SWAT model (Table 2, bottom). In addition, most of the error in elevational trend in long-term MODIS ET was removed by the regression-based correction to weather (Figure 3 versus Figure 7f). The PBIAS of the corrected MODIS ET was noted to be 12% higher during dry years than wet years (Table 2, bottom), suggesting that regression models trained separately to dry and wet periods may provide further improvement to the correction method.

**Figure 7.** Weather correction to MODIS monthly ET using linear regression with air temperature as predictor variable. (**<sup>a</sup>**–**<sup>c</sup>**) Results of linear regression between MODIS ET error, as fraction of MODIS potential ET, and monthly air temperature for each site. MODIS ET error is defined as MODIS ET—flux tower ET. (**d**) Original (uncorrected) MODIS ET versus flux tower ET shown with 1:1 line. (**e**) Weather-corrected MODIS ET versus flux tower ET. (**f**) Average monthly ET from weather-corrected MODIS, flux tower, and SWAT versus elevation for comparison to Figure 3. Dashed lines are trendlines from linear regression, labeled with value of slope.
