User:Wilderness

$$\theta = T \left (\frac{P_s}{P}\right )^{R/c_p}$$

$$Equivalent \ Potential \ Temperature = \theta_e = T_e \left (\frac{P_o}{P} \right) ^{R/c_p} $$,

where $$T_e = T \left (1 + \frac{Lw}{C_p T} \right) \, $$

$$\theta_e = \theta \left (1 + \frac{Lw}{C_p T} \right) \, $$

$$specific \ humidity = q = \frac{\epsilon e}{p - (1 - \epsilon) e} = \frac{\epsilon e}{p - e + \epsilon e} = \frac{mass \ water \ vapor}{mass \ of \ moist \ air} \, $$

where $$\epsilon = 0.622$$ the ratio of the molecular weight of water vapor to the molecular weight of dry air.

$$e$$ is the partial pressure of water vapor.

Relate these to the word description on http://meted.ucar.edu/awips/validate/thetae.htm

Specific hum in g/kg or kg/kg.

Absolute hum in g/m^3.

$$\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + w \frac{\partial u}{\partial z} = g \frac{\theta_d}{\theta_0}\sin \alpha + \cos \alpha \frac{g}{\theta_0}\frac{\partial(\theta_d h)}{\partial x} + fv - \frac{\partial \overline{u' w'}}{\partial z}$$

$$evaporation = \frac{\rho \omega * LatentHeatofVap * k^2 / Pressure * WindSpeed * (VapPre - VPsurf)*100*10*3600*24}{\log(\frac{H_{wind}}{Z_o}) \log(\frac{H_{RH}}{Z_{RH}}) * LatentHeatofVap * \rho_{ice}} $$

This is red text.

Simpler:

$$sublimation rate = \frac{\rho \ \omega \ k^2 * Wind Speed * (Vapor Pressure - VPsurface)*1000 mm/m *3600 s/hr *24 hr/day} {Pressure * \log(\frac{H_{wind}}{Z_o}) \log(\frac{H_{RH}}{Z_{RH}}) * \rho_{ice}}$$ in mm/day.

$$sublimation rate = \frac{\rho \ \omega \ k^2 * Wind Speed * (Vapor Pressure - VPsurface)*3600 s/hr *24 hr/day} {Pressure * \log(\frac{H_{wind}}{Z_o}) \log(\frac{H_{RH}}{Z_{RH}}) * \rho_{ice}}$$ in m/day.

$$sublimation rate = \frac{\rho \ \omega \ k^2 * Wind Speed * (Vapor Pressure - VPsurface)*3600 s/hr *24 hr/day *365 days/yr} {Pressure * \log(\frac{H_{wind}}{Z_o}) \log(\frac{H_{RH}}{Z_{RH}}) * \rho_{ice}}$$ in m/yr.

$$S.R. = \frac{\rho \ \omega \ k^2 * u_z * (e_z - e_s)*3.16e7} {P * \log(\frac{H_{wind}}{Z_o}) \log(\frac{H_{RH}}{Z_{RH}}) * \rho_{ice}}$$ in m/yr.

evap(n).AllInc = (rho*omega*LatentHeatOfVap*k^2./fD(n).DPress) ./ ...       (log(H.SpdTop(n)./fD(n).DZ_kno).*log(H.Temper(n)./fD(n).Z_humi))...        /LatentHeatOfVap/rho_ice*100*10*3600*24 ... .*fD(n).DSpdTo.* (fD(n).DVapPr - fD(n).VPsurf);

$$\lambda E = E_{available} - H\,$$

$$L^* = \sigma T_a^4 [E_a - E_s] $$

$$ \lambda E = \frac{sA + (\rho c_p G_a D_a)}{s + \gamma (1 + G_a/G_s)}$$

$$ G_s = c_L LAI + G_{s min}\, $$

$$ \lambda E = A - H = A - \left(\rho c_p \frac{(T_{sA} - T_a)}{R_a} \right)$$

$$ energy balance = $$

$$ LHF = \frac{ \rho \omega \lambda k^2 u_z (e_z - e_s)/P} {(\ln (z/z_o) + a_M z / \Lambda )(\ln (z/z_e) + a_E z / \Lambda)} $$

$$ \Lambda = \frac{\rho c_p u^{*3} T_K }{k g SHF} $$

$$ u^* = \frac{k u_z}{\ln(z/z_o) + a_x (z/\Lambda)}$$

$$ z_0 = e^{\frac{U_s*ln(H_2) - U_2*ln(H_s)}{U_s-U_2}} $$

$$ z_0 = k_s / 30 = 3 D_{84} / 30 = 0.1 * D_{84} $$