*4.2. Monthly ET*

ET observations from the flux towers followed a seasonal pattern that roughly tracked the length of daylight, with peak values occurring near the middle of calendar years and minimum values occurring near the end of calendar years (Figure 4). Outputs from the SWAT model followed a similar seasonal timing, although the shape of its annual waveforms was sometimes excessively narrowed and peaked, such as in year 2016 at the middle site (Figure 4, middle). The MODIS model produced annual waveforms in ET that were notably out of phase with observations and SWAT model predictions. ET-values from MODIS tended to be on a descending limb, or near their annual minima (within one month thereof), during summer when observed and SWAT-modeled ET were near their maxima. This out-of-phase characteristic of MODIS predictions was especially apparent

during years 2016–2018 at the lower and middle sites (Figure 4). In addition, the annual ET waveforms from MODIS appeared less distinct than those from observations and SWAT.

**Figure 3.** Average monthly ET versus elevation from flux towers, MODIS, and SWAT. Averages across all elevations are parenthesized in the legend. *m* = slope of linear-regression trendline, *R*<sup>2</sup> = coefficient of determination of linear-regression fit.

In terms of the NSE metric of model fitness, the SWAT model matched monthly ET observations better than the MODIS model. The NSE of SWAT across all flux tower sites was +0.36, ranging from +0.04 at the middle site to +0.68 at the upper site (Table 2). In comparison, the NSE of MODIS across all sites was −0.43, ranging from −0.73 at the middle site to −0.33 at the lower site. These negative NSE-values indicate a level of prediction efficiency lower than that provided by knowledge of long-term observed ET. Both SWAT and MODIS showed minimum prediction efficiency at the middle site (Table 2). In addition, both models showed slightly lower prediction efficiency (NSE lower by ~0.2) during wet years than dry years (Table 2).

**Figure 4.** Monthly ET from flux towers, MODIS, and SWAT at three sites in upper Kings River watershed.

In terms of model bias, both SWAT and MODIS underestimated long-term ET as shown by negative PBIAS-values in Table 2. However, the underestimates from MODIS were substantially greater in magnitude than those from SWAT. The SWAT model underestimated average monthly ET across all sites by 13% (PBIAS = −13%). These underestimates ranged from 23% at the middle site to 5% at the other two sites. In comparison, the MODIS model underestimated average monthly ET across all sites by 47% (PBIAS = −47%), with underestimates ranging from 50% at the middle site to 35% at the upper site.

#### *4.3. Seasonality in ET and Weather*

Seasonal distributions in ET, potential ET (PET), and weather variables are plotted in Figure 5. Observed ET at the flux towers reached peak values in June or July, following a seasonal distribution ("seasonal curve") that was well aligned with PET from MODIS (Figure 5, left column). Air temperature and vapor pressure deficit reached peak values in July or August (Figure 5, middle column), following seasonal curves that closely tracked one another. This close tracking indicated a strong cross-correlation of these weather variables on a monthly time scale (*R*<sup>2</sup> = 0.89–0.94 for three sites, not shown). Based on these results, air temperature and vapor pressure deficit reached maximum seasonal values within approximately one month of observed ET and MODIS PET. This timing seemed reasonable given that these weather variables are known to strongly influence atmospheric water demand.

**Table 2.** Error statistics of monthly ET from MODIS, SWAT, and air temperature corrected MODIS, relative to flux tower observations. "All site" statistics (bottom) are for monthly ET data concatenated across the three sites. "All years" are water years 2009–2018, "wet years" are water years 2009– 2011 and 2016–2017, and "dry years" are water years 2012–2015 and 2018. NSE = Nash-Sutcliffe efficiency [47], PBIAS = percent bias (positive = model overestimate) [48], N = number of months.


A seasonal asynchronicity was observed between MODIS ET and MODIS PET. MODIS ET reached a seasonal *minimum* only 1–2 months after the seasonal *maximum* in MODIS PET (Figure 5, left). MODIS PET reached a maximum value in July at all three sites. In comparison, MODIS ET reached a minimum value only one month later at the lower and middle sites, and two months later at the upper site (Figure 5, left). Such occurrences of minimum ET near the time of maximum atmospheric water demand are indicative of pronounced limitations on ET in the MODIS model.

Seasonal curves of SWAT ET tended to be skewed toward times earlier in the year relative to SWAT PET (Figure 5, right). These ET and PET curves closely tracked one another between December and mid-summer. Then, in mid-summer, the ET curves began following descending limbs 1–2 months before descending limbs of PET. This difference in timing of descending limbs produced summer and fall deficits of ET relative to PET (Figure 5, right). Such skewness of ET relative to PET is indicative of a seasonal shift in limitation on ET in the SWAT model.
