## 3 Results  
### Factor Analysis  
As a preliminary investigation of the relationships, Figure 2 shows the correlation matrices among all variables for all seasons at the hourly, daily, and weekly timescales. ET was moderately (\(\mid\) r \(\mid\) \(>\) 0.2) or highly correlated (\(\mid\) r \(\mid\) \(>\) 0.5) with R\({}_{n}\), VPD, sensible heat, and temperature at all timescales. Precipitation was weakly correlated with ET at all timescales, with positively increasing coefficients at higher timescales. Interestingly, windspeed showed a weak negative correlation at the hourly timescale, with an increasing negative correlation at the daily and weekly timescales. The strength of the correlation between R\({}_{n}\), H, and VPD was dependent on the temporal scale of the comparisons. Fur ther, temperature and VPD showed a strong correlation with increasing coefficients at larger timescales.  
Figure 2: Correlation matrices among all variables: sensible heat flux (H), evapotranspiration (ET), pressure (Pa), relative humidity (RH), temperature of air (Ta), Vapor Pressure Deficit (VPD), windspeed (WS), net radiation (R\({}_{\text{n}}\)), and precipitation (P) for all seasons at the (**a**) hourly, (**b**) daily, and (**c**) weekly timescales.  
As evidenced by the correlation plots above, many of these variables share similar variability patterns and are strongly influenced by each other. This necessitated a method to quantify the independent contributions of each variable to the variability in ET. As described in Section 2.6, a factor analysis was carried out across all seasons and variables shown above (excluding RH) to segregate them into groups showing similar variability patterns. The first factor loadings for these variables across different seasons are shown in Figure 3.  
Figure 3: Factor loadings for evapotranspiration (ET), net radiation (R\({}_{n}\)), sensible heat flux (H), temperature of air (Ta), Vapor Pressure Deficit (VPD), windspeed (WS), precipitation (P), and pressure (Pa) on the first pattern of factor analysis for spring, summer, autumn, and winter seasons.  
ET, R\({}_{n}\), sensible heat flux, temperature, and VPD all loaded highly positive on the first factor for all seasons except for the winter season, where ET and R\({}_{n}\) loaded comparatively lower than VPD and temperature. Also, sensible heat flux and pressure loaded highly negatively in winter. Windspeed and rain (precipitation) showed low factor loadings, as they become highly variable as the timescale increases and seasons change.  
The factor analysis yielded multiple factor loadings, with the first factor capturing approximately 60% of the variability in the dataset. The first and second factor loadings for all variables are shown in score plots in Figure 4 with groupings similar to that in Figure 3. Factor loading pairs were categorized by color for seasons and markers for timescales (hourly, daily, and weekly). Score plots revealed the spread of first and second factor loadings across seasons and timescales.  
Consistent with Figure 3, ET, Rn, temperature, and VPD loaded moderately or higher on the first factor for spring, summer, and autumn seasons. However, in winter, all three factors loaded moderately or higher in the second factor, while temperature loadings were low. For sensible heat flux and pressure, factor loadings were scattered, while windspeed and rain had loadings more clustered around the plot origin.