# Calculation of T2 and the energy budget

#### Lily_Zh

##### Member
Hi all,

Based on the relies on this link: WRF energy and moisture budget?, I know the energy balance calculation is: (1-ALBEDO)*SWDOWN+EMISS*(GLW-STBOLT*TSK**4)+GRDFLX-HFX-LH
I am not sure how WRF calculates T2, I am curious about which component's change in the energy budget explains my T2 change.

Lily

Hi Lily,
I do not believe WRF strictly calculates T2 from the surface energy budget, but utilizes similarity theory to do so. Essentially, WRF gets the skin temperature from the radiation as you have in your equation. Then, based on the strength of coupling between the land surface and the near-surface atmosphere, the skin temperature is modified by terms like the heat flux, surface winds, and stability of the atmosphere. Since I don't think I can type the full set of equations in this post, you can view the full set of equations in this Li & Bou-Zeid, 2014 paper (see methods section). Fortunately, the equations are not too complex.

Paper:
Dan Li & Elie Bou-Zeid, 2014: Quality and sensitivity of high-resolution numerical simulation of urban heat islands

~Eliott

Hi Lily,
I do not believe WRF strictly calculates T2 from the surface energy budget, but utilizes similarity theory to do so. Essentially, WRF gets the skin temperature from the radiation as you have in your equation. Then, based on the strength of coupling between the land surface and the near-surface atmosphere, the skin temperature is modified by terms like the heat flux, surface winds, and stability of the atmosphere. Since I don't think I can type the full set of equations in this post, you can view the full set of equations in this Li & Bou-Zeid, 2014 paper (see methods section). Fortunately, the equations are not too complex.

Paper:
Dan Li & Elie Bou-Zeid, 2014: Quality and sensitivity of high-resolution numerical simulation of urban heat islands

~Eliott
Hi Eliott,

Thank you very much for this useful information and the paper!

Thanks.

Lily