${\displaystyle \theta =T\left({\frac {P_{s}}{P}}\right)^{R/c_{p}}}$

${\displaystyle Equivalent\ Potential\ Temperature=\theta _{e}=T_{e}\left({\frac {P_{o}}{P}}\right)^{R/c_{p}}}$,

where ${\displaystyle T_{e}=T\left(1+{\frac {Lw}{C_{p}T}}\right)\,}$

${\displaystyle \theta _{e}=\theta \left(1+{\frac {Lw}{C_{p}T}}\right)\,}$

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

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

${\displaystyle e}$ 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.

${\displaystyle {\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial x}}+w{\frac {\partial u}{\partial z}}=g{\frac {\theta _{d}}{\theta _{0}}}\sin \alpha +\cos \alpha {\frac {g}{\theta _{0}}}{\frac {\partial (\theta _{d}h)}{\partial x}}+fv-{\frac {\partial {\overline {u'w'}}}{\partial z}}}$

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

This is red text.

Simpler:

${\displaystyle sublimationrate={\frac {\rho \ \omega \ k^{2}*WindSpeed*(VaporPressure-VPsurface)*1000mm/m*3600s/hr*24hr/day}{Pressure*\log({\frac {H_{wind}}{Z_{o}}})\log({\frac {H_{RH}}{Z_{RH}}})*\rho _{ice}}}}$ in mm/day.

${\displaystyle sublimationrate={\frac {\rho \ \omega \ k^{2}*WindSpeed*(VaporPressure-VPsurface)*3600s/hr*24hr/day}{Pressure*\log({\frac {H_{wind}}{Z_{o}}})\log({\frac {H_{RH}}{Z_{RH}}})*\rho _{ice}}}}$ in m/day.

${\displaystyle sublimationrate={\frac {\rho \ \omega \ k^{2}*WindSpeed*(VaporPressure-VPsurface)*3600s/hr*24hr/day*365days/yr}{Pressure*\log({\frac {H_{wind}}{Z_{o}}})\log({\frac {H_{RH}}{Z_{RH}}})*\rho _{ice}}}}$ in m/yr.

${\displaystyle S.R.={\frac {\rho \ \omega \ k^{2}*u_{z}*(e_{z}-e_{s})*3.16e7}{P*\log({\frac {H_{wind}}{Z_{o}}})\log({\frac {H_{RH}}{Z_{RH}}})*\rho _{ice}}}}$ 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);

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

${\displaystyle L^{*}=\sigma T_{a}^{4}[E_{a}-E_{s}]}$

${\displaystyle \lambda E={\frac {sA+(\rho c_{p}G_{a}D_{a})}{s+\gamma (1+G_{a}/G_{s})}}}$

${\displaystyle G_{s}=c_{L}LAI+G_{smin}\,}$

${\displaystyle \lambda E=A-H=A-\left(\rho c_{p}{\frac {(T_{sA}-T_{a})}{R_{a}}}\right)}$

${\displaystyle energybalance=}$

${\displaystyle LHF={\frac {\rho \omega \lambda k^{2}u_{z}(e_{z}-e_{s})/P}{(\ln(z/z_{o})+a_{M}z/\Lambda )(\ln(z/z_{e})+a_{E}z/\Lambda )}}}$

${\displaystyle \Lambda ={\frac {\rho c_{p}u^{*3}T_{K}}{kgSHF}}}$

${\displaystyle u^{*}={\frac {ku_{z}}{\ln(z/z_{o})+a_{x}(z/\Lambda )}}}$

${\displaystyle z_{0}=e^{\frac {U_{s}*ln(H_{2})-U_{2}*ln(H_{s})}{U_{s}-U_{2}}}}$

${\displaystyle z_{0}=k_{s}/30=3D_{84}/30=0.1*D_{84}}$