Chapter 2 理论与公式
2.3 气象驱动
2.3.2 蒸散发
2.3.2.1 风廓线 (Wind profile)
Equation 2.3 in (Abtew and Melesse 2012)
\[\begin{equation} \boldsymbol{u}_{x}=\boldsymbol{u}_{m} \frac{\ln \frac{z_{x}-d}{z_{0}}}{\ln \frac{z_{m}-d}{z_{0}}} \end{equation}\]
- \(u_x\) - 目标高度的风速 [\(m s^{-1}\)]
- \(u_m\) - 测量高度的风速 [\(m s^{-1}\)]
- \(z_x\) - 目标高度 [\(m\)]
- \(z_m\) - 测量高度 [\(m\)]
- \(d\) - 零平面 [\(m\)]
- \(z0\) - 粗糙度(Roughness height) [\(m\)]
FAO56
植被覆盖的
开放水面和裸露土地的潜在蒸发(PET of bare soil and open water) \[\begin{equation} \lambda E_{a}=c_{2} \frac{e_{a}-e_{d}}{r_{a}} \end{equation}\]
\(E_a\) 是同温蒸发率(Isothermal evaporation rate)。
\[\begin{equation} \mathrm{E}_{\mathrm{o}}=\frac{\Delta\left(\mathrm{R}_{\mathrm{n}}-\mathrm{G}\right) / \lambda+\gamma \mathrm{E}_{\mathrm{a}}}{\Delta+\gamma} \end{equation}\]
2.4 地表过程 (Surface)
2.4.1 辐射
\(\vec{L}=L \uparrow-L_{a t m} \downarrow\)
\(T_{r a d}=\left(\frac{L \uparrow}{\sigma}\right)^{1 / 4}\)
\(L \uparrow=\left(1-\varepsilon_g\right) L_{a t m} \downarrow+\varepsilon_g \sigma\left(T_g^n\right)^4+4 \varepsilon_g \sigma\left(T_g^n\right)^3\left(T_g^{n+1}-T_g^n\right)\)
2.4.2 地表能量平衡
\(R_n + L_w = H_l + H_s + G\)
- \(R_n\): 短波辐射(input)
- \(L_w\): 长波辐射(input)
- \(H_l\): 潜热
- \(H_s\): 感热
- \(G\): 土壤热通量
\(H=-\rho_{a t m} C_p \frac{\left(\theta_{a t m}-\theta_s\right)}{r_{a h}}\)
\(e_{a t m}=\frac{q_{a t m} P_{\mathrm{atm }}}{0.622+0.378 q_{\mathrm{atm }}}\)
\(\rho_{\mathrm{atm }}=\frac{P_{a t m}-0.378 e_{a t m}}{R_{d a} T_{a t m}}\)