# Calculate effective emissivity of urban and rural area

#### KeerZ

##### Member
Hi, I ran a CLM5 simulation using I2000Clm50SpGs compset with 25km resolution. I am wondering if we can calculate the effective emissivity of urban and rural area from model radiation and temperature output?

For example, I tried to calculate emissivity by Stefan-Boltzmann equation using emitted longwave radiation and ground temperature:
Emissivity_U=FIRE_U/(S-BConstant*TG_U**4.0)
Emissivity_R=FIRE_R/(S-BConstant*TG_R**4.0). However, the calculated urban and rural emissivity seems too large (mostly >0.95). Then I realized that maybe I need use radiative surface temperature instead of ground temperature. But radiometric surface temperature is not an output of CLM5.

Any suggestions on calculating urban and rural effective emissivity? I noticed that urban and rural emissivity were assumed to be ~0.88 and ~0.96 in previous studies but I am still not clear how to get these values. Thanks!!

#### oleson

##### CSEG and Liaisons
Staff member
Ground emissivity is somewhere between 0.96 and
0.97 (0.96 for soil, 0.97 for glacier, 0.96 for wetland, 0.97 for
snow). Vegetation or leaf emissivity is around 0.98. So in the model
the rural emissivity should be around 0.96-0.98.
One possible way to calculate the urban emissivity would be to weight
the emissivities of the individual surfaces by surface area and view
factor.

E.g.,

em_urban = em_roof*wtlunit_roof + em_canyon*(1-wtlunit_roof)

where em_roof is roof emissivity, wtlunit_roof is the roof fraction,
and em_canyon is the canyon emissivity, i.e.,

where em_wall is wall emissivity (the two walls have the same
i.e.,

The view factors are (they can be found in the CLMU technical note):

vf_sky_road = sqrt(canyon_hwr^2 + 1) - canyon_hwr

vf_sky_wall = 0.5 * (canyon_hwr + 1 - sqrt(canyon_hwr^2+1))/canyon_hwr

where canyon_hwr is the height to width ratio of the canyon. You
would need to use the surface dataset to get the individual urban
components.
I think the value of 0.88 might have been some kind of global average value based on the input dataset.

#### KeerZ

##### Member
Ground emissivity is somewhere between 0.96 and
0.97 (0.96 for soil, 0.97 for glacier, 0.96 for wetland, 0.97 for
snow). Vegetation or leaf emissivity is around 0.98. So in the model
the rural emissivity should be around 0.96-0.98.
One possible way to calculate the urban emissivity would be to weight
the emissivities of the individual surfaces by surface area and view
factor.

E.g.,

em_urban = em_roof*wtlunit_roof + em_canyon*(1-wtlunit_roof)

where em_roof is roof emissivity, wtlunit_roof is the roof fraction,
and em_canyon is the canyon emissivity, i.e.,

where em_wall is wall emissivity (the two walls have the same
i.e.,

The view factors are (they can be found in the CLMU technical note):

vf_sky_road = sqrt(canyon_hwr^2 + 1) - canyon_hwr

vf_sky_wall = 0.5 * (canyon_hwr + 1 - sqrt(canyon_hwr^2+1))/canyon_hwr

where canyon_hwr is the height to width ratio of the canyon. You
would need to use the surface dataset to get the individual urban
components.
I think the value of 0.88 might have been some kind of global average value based on the input dataset.

Hello Keith, thank you very much for your help! I successfully calculated effective urban emissivity using these formulas. And I assume rural emissivity to be 0.97. In my study, I need urban&rural emissivity (to calculate urban minus rural emissivity) and urban&rural surface temperature, so by inverting the Stefan-Boltzmann equation I got urban and rural surface temperature:

Ts_U=(FIRE_U/Emissivity_U/(SB_Constant))**0.25
Ts_R=(FIRE_R/Emissivity_R/(SB_Constant))**0.25 (SB_Constant is the Stefan Boltzmann constant)

The Ts_R results seem ok but some Ts_U can be as high as 370K, which are abnormally high. Then, by reading the document and CLM5 scripts, I found that FIRE is actually outgoing longwave radiation which includes both reflected and emitted longwave radiation (although it is called ‘emitted longwave radiation’).

Did I understand FIRE correctly? If yes,I guess it is better to calculate urban and rural surface temperature (Ts_U and Ts_R) by solving these functions?

FIRE_U =(1- Emissivity_U)*FLDS+Emissivity_U* SBConstant*Ts_U**4
FIRE_R =(1- Emissivity_R)*FLDS+ Emissivity_R * SBConstant*Ts_R **4

#### oleson

##### CSEG and Liaisons
Staff member
Yes, that is a good point, FIRE is total outgoing longwave (reflected + emitted from surfaces). Your second set of equations seems correct for rural and for urban roof. However, since there are multiple longwave reflections and absorptions in the urban canyon, I'm not sure offhand what the actual reflected longwave to the sky from the urban canyon itself would be. Seems like it could be derived from the model longwave equations or more likely approximated since the longwave solution is iterative. Or maybe it can be accounted for by the view factor weighting being used for emissivity. How does the computed urban canyon emissivity compare to the emissivities of the individual surfaces?

#### KeerZ

##### Member
Yes, that is a good point, FIRE is total outgoing longwave (reflected + emitted from surfaces). Your second set of equations seems correct for rural and for urban roof. However, since there are multiple longwave reflections and absorptions in the urban canyon, I'm not sure offhand what the actual reflected longwave to the sky from the urban canyon itself would be. Seems like it could be derived from the model longwave equations or more likely approximated since the longwave solution is iterative. Or maybe it can be accounted for by the view factor weighting being used for emissivity. How does the computed urban canyon emissivity compare to the emissivities of the individual surfaces?
I see. Considering that there are multiple longwave reflections and absorptions in the urban canyon. Can I use FLDS - FIRA_U as the 'outgoing longwave radiation' (it seems that multiple longwave reflections and absorptions are considered in this way?) and then still calculate urban surface temperature using effective urban emissivity?

The em_canyon can be a little larger (when it is MD) or much smaller (when it is TBD) than the emissivities of the individual surfaces (em_wall, em_road or em_roof) depending on the value of view factors.

#### oleson

##### CSEG and Liaisons
Staff member
The longwave balances as FLDS + FIRA_U = FIRE_U.
I think you could start by using the equations you propose and see if what you get seems reasonable.
Could maybe double-check this result by going into the code and creating a variable to sum the reflected longwave from each surface to the sky for all of the iterations and output that and see how it compares to (1-Emissivity_U)*FLDS.

#### KeerZ

##### Member
The longwave balances as FLDS + FIRA_U = FIRE_U.
I think you could start by using the equations you propose and see if what you get seems reasonable.
Could maybe double-check this result by going into the code and creating a variable to sum the reflected longwave from each surface to the sky for all of the iterations and output that and see how it compares to (1-Emissivity_U)*FLDS.
OK. Thanks a lot!