## 3 Methodology
### Field Aerodynamic Roughness Calculation  
The profile data were pre-processed and quality controlled by removing singular and repeated values exceeding the range of physical possibility via date format unification and data arrangement into a standard Excel format for ease of use. The original wind profile data were collected at 10-min intervals, which resulted in 144 data records each day. The effects of the underlying surface were minimized by selecting the wind and atmospheric profiles above the landscape for the field AR calculations. The 10-min profile data were first used to calculate the instantaneous 10-min AR and then averaged into daily and eight-day average values for consistency with the remote sensing data. Meteorological profile time series data from the wind profile stations were processed to acquire the field AR based on Monin-Obukhov similarity theory (MOST). Following [PERSON] et al., the wind velocities and air temperatures measured at different heights can be expressed as follows [12; 22]:  
\[u=\frac{u_{*}}{k}\left[ln\frac{z-d}{z_{om}}-\psi_{m}\left(\frac{z-d}{L} \right)\right] \tag{5}\]  
\[\theta=\frac{\theta_{*}}{k}\left[ln\frac{z-d}{z_{oh}}-\psi_{h}\left(\frac{z- d}{L}\right)\right]+\theta_{0} \tag{6}\]  
where \(u\) is the wind velocity; \(u_{*}\) is the friction velocity, \(k\) is the von Karman constant (equal to 0.4); \(z\) is the height at which the wind velocity and air temperature are observed; \(\theta\) is the potential air temperature of each layer, which is defined with local surface pressure used as standard pressure; \(\theta_{*}\) is the friction temperature; \(z_{om}\) is the aerodynamic roughness; \(d\) is the zero-plane displacement; \(z_{oh}\) is the thermal roughness length; and \(\theta_{0}\) is the potential temperature near the surface. In addition, \(L\) is the Obukhov length, which is calculated as follows [12]:  
\[L=\frac{u_{*}^{2}\theta}{\theta_{*}kg} \tag{7}\]  
\[\theta=T\bigg{(}\frac{P_{0}}{P}\bigg{)}^{0.286} \tag{8}\]  
where \(g\) is the acceleration caused by gravity (equal to 9.8 m/s\({}^{2}\)), \(T\) is the mean air temperature, \(p\) is the ambient air pressure, and \(P_{0}\) is 101 kPa. The Richardson Number (\(R_{i}\)) is used to determine the atmospheric stability near the surface. When \(R_{i}\) ranges from \(-0.03\) to \(0.03\), it exhibits neutral stratification. When \(R_{i}\) is less than \(-0.03\), it exhibits unstable stratification. When \(R_{i}\) is greater than \(0.03\), it exhibits stable stratification. \[R_{i}=\frac{\frac{\delta}{\theta_{v}}\frac{\partial\overline{\theta_{v}}}{ \partial z}}{\left[\frac{\partial u}{\partial z}\right]^{2}} \tag{9}\]  
where \(\partial z\) is the height difference between the maximal observation height and the minimal height above the vegetation; \(\partial u\) is the wind velocity difference of the two heights; \(\theta_{v}\) is the virtual potential temperature at the observation height; and \(\psi_{m}\) and \(\psi_{h}\) are the stability correction functions for momentum and sensible heat transfer, respectively, which are determined based on atmospheric stratification. These functions for unstable conditions are expressed as follows [22]:  
\[\psi_{m}=2\ln\bigg{[}\frac{1+x}{2}\bigg{]}+\ln\bigg{[}\frac{1+x^{2}}{2}\bigg{]} -2\text{arctg(x)}+\frac{\pi}{2} \tag{10}\]  
\[\text{x}=(1-16\frac{z-d}{L})^{-0.25} \tag{11}\]  
\[\psi_{h}=\ln\Big{[}\Big{(}1+y^{2}\Big{)}/2\Big{]} \tag{12}\]  
\[\text{y}=(1-16\frac{z-d}{L})^{-0.5} \tag{13}\]  
These functions for stable conditions are expressed as follows [23]:  
\[\psi_{m}=-5\frac{z-d}{L} \tag{14}\]  
\[\theta=\frac{\theta_{*}}{k}\left[ln\frac{z-d}{z_{oh}}-\psi_{h}\left(\frac{z- d}{L}\right)\right]+\theta_{0} \tag{6}\]0  
The profile data at the six levels of 1 m, 2 m, 5 m, 10 m, 15 m, and 25 m were all used in the calculation. The aerodynamic roughness \(z_{om}\) and displacement height \(d\) are concurrently optimized and determined through iteration.