## 2 Materials And Methods
### Description of the INLAND Surface Model
#### 2.1.3 Distribution of Surface Energy  
Net radiation and turbulent fluxes of sensible heat and water vapor determine changes in temperature and surface moisture levels. Solar and infrared radiation balances between the land surface, atmosphere, and vegetation canopy are simulated using the two-stream approach [41; 42]. The approximation separately considers direct and diffuse radiation emitted within two wavelengths bands, visible (0.4-0.7 \(\upmu\)m), and infrared (0.7-4.0 \(\upmu\)m), which involve reflectance (_rhovegN1R_,_rhovegVIS_) and transmittance parameters (\(tauvegNIR\), \(tauvegVIS\)) of the upper and lower layers of the canopy. Infrared radiation is simulated such that each vegetation layer is considered a semi-transparent plane [29]. Canopy emissivity is calculated as a function of the Leaf Area Index (LAI) and average diffuse optical depth coefficient (\(avmuir\)) through an exponential relation. \[emu=1-\exp\left(-\frac{LAI}{avmuir}\right) \tag{23}\]  
Additionally, in calculating the radiative surface balance, fractions of direct and diffuse radiation that are directly scattered into the atmosphere are taken into account. For this, the model considers the canopy geometry through the orientation parameters of leaves of the upper (\(chifuz\)) and lower (\(chifz\)) canopy. Vegetation is dynamically represented by LAI estimates and by the amount of carbon assimilated by leaves for each PFT. Thus, plant growth or mortality is simulated in association with climatic conditions and is modeled by LAI and biomass variations for each PFT. The \(plai\) parameter indicates the potential LAI that contributes to plant carbon exchange, estimated by the product between \(cbiol\) and \(specla\) (specific leaf area (m\({}^{2}\) Kg\({}^{-1}\)). \[LAI_{tot}=\sum_{i=1}^{12}cbiol(i)\times specla(i) \tag{24}\]  
After estimating the surface net radiation (\(Rn\)), the INLAND model partitions available energy into latent (\(LE\)), sensible (\(H\)), and soil (\(G\)) heat fluxes, using the relation:  
\[R_{n}=LE+H+G \tag{25}\]  
\(H\) is calculated using the temperature difference of the air and upper canopy (\(T_{a}-T_{u}\)) and inversely proportional to aerodynamic resistance (\(r_{a}\))  
\[H=\rho c_{p}\left(\frac{T_{a}-T_{u}}{r_{a}}\right) \tag{26}\]  
where \(\rho\) and \(c_{p}\) are the air density and specific heat of air at constant pressure, respectively. Index \(u\) corresponds to the properties of the upper canopy. \(r_{a}\) is dependent on properties of the land surface and on the logarithmic profile of wind  
\[r_{a}=\frac{\left[\frac{1}{k}\log(\frac{z_{a}-d}{z_{0}})\right]^{2}}{ws_{a}} \tag{27}\]  
where \(z_{a}\) is reference height, \(d\) is displacement of zero plane, \(z_{0}\) is roughness length, \(ws_{a}\) is wind speed in reference height, and \(k\) is von Karman constant. Similarly, \(LE\) is calculated as the sum of three water vapor fluxes  
\[LE=E_{canop}+T_{canop}+E_{soil} \tag{28}\]  
where \(E_{canop}\) is evaporation of water intercepted by canopies (leaves and stems), \(T_{canop}\) is canopy transpiration of canopy, and \(E_{soil}\) is evaporation from soil surface. \[E_{canop}=(f_{lu}^{wet}\times(q_{a}-q_{u})\times LAI)+(f_{s}^{wet}\times(q_{a }-q_{u})\times SAI) \tag{29}\]  
\[T_{canop}=\rho(q_{a}-q_{uJ})\times\frac{1}{r_{b}}\times LAI \tag{30}\]\[E_{soil}=\rho(q_{0}-q_{u})\times\frac{1}{r_{a}} \tag{31}\]  
where \(f_{lw}^{uct}\) (\(f_{s}^{wet}\)) is fraction of leaves (stems) wetted by intercepted water, (\(q_{a}-q_{u}\)) is the air moisture deficit (\(q_{u}\) (\(q_{a}\)) is specific humidity of air at upper layer (reference height above upper layer), \(SAI\) is stem area index, and \(r_{b}\) is stomatal resistance, calculated from  
\[r_{b}=\frac{C_{b}}{(ws_{u})^{2}} \tag{32}\]  
where \(C_{b}\) bulk canopy resistance coefficient and \(ws_{l}\) is wind speed at upper layer. Stomatal resistance denotes resistance imposed by vegetation on the evapotranspiration process.