Understanding measured radiation in the context of the explicit radiation balance

[Mandinec]

Dear WUFI team,

I am bewildered about the "Explicit radiation balance" option when using measured climate data for solar radiation (ISM) and long-wave radiation (ILM). I understand that WUFI does not change those variables anyhow. Therefore, based on the formula provided in https://www.wufi-wiki.com/mediawiki/ind ... veExchange (see below), I guessed that ISM goes directly to I_s while ILM goes to the I_l component.

rad_balance.PNG (29 KiB) Viewed 2349 times

However, I cannot reach understandable solutions using this reasoning. In a hypothetical case (results exemplified below), I modelled a wall using two sets of boundary conditions differing in the WAC file only the long-wave radiation option. Note that ISM is also there, but it is not changing between the two sets. In one, I used climate data for atmospheric counter radiation on a horizontal surface (ILAH). In the second, I changed the ILAH to ILM without changing any values.

Based on the explanation on the mentioned webpage, I thought the ILM option should result in higher temperatures inside the wall. ILAH, as I understand, should be first lowered by the following expression (where ILAH is I_{l, atm})

I_l.PNG (19.55 KiB) Viewed 2349 times

Presuming the ILAH and ILM have both values of 300 W/m2 in the WAC file. The ILAH option should then contribute to the "heating" with 104 W/m2 (see calculation below based on the procedure from the webpage), while ILM should contribute to the first equation directly with 300 W/m2.
#######################
g_atm = math.cos(45)**2 = 0.276
g_terr = 1 - g_atm = 0.724
I_refl = 0.1 * 300 = 30 W/m2
I_terr = 5.67e-8 * 0.9 * 20**4 = 0.008 W/m2
I_l = g_atm * 300 + g_terr * (I_refl + I_terr) = 104,51 W/m2
#######################

However, the results using ILM (on the left) are considerably lower compared to the ILAH (on the right)

combine results.png (57.06 KiB) Viewed 2349 times

Please, what am I missing? How do the measured climate variables fit into the Explicit radiation balance?

Thank you
Best regards
Jan Mandinec

p.s. I am using WUFI 3.4

[Thomas]

I guessed that ISM goes directly to I_s while ILM goes to the I_l component.

Dear Jan Mandinec,

yes, that is correct.

Presuming the ILAH and ILM have both values of 300 W/m2 in the WAC file. The ILAH option should then contribute to the "heating" with 104 W/m2 (see calculation below based on the procedure from the webpage), while ILM should contribute to the first equation directly with 300 W/m2.
#######################
g_atm = math.cos(45)**2 = 0.276
g_terr = 1 - g_atm = 0.724
I_refl = 0.1 * 300 = 30 W/m2
I_terr = 5.67e-8 * 0.9 * 20**4 = 0.008 W/m2
I_l = g_atm * 300 + g_terr * (I_refl + I_terr) = 104,51 W/m2
#######################

The atmospheric gases are relatively poor emitters of thermal radiation, they normally emit less radiation than the ground at the same temperature. So replacing a part of the atmospheric radiation with terrestrial radiation will in general increase the total incident radiation. The calculation is
#######################
g_atm = math.cos(45)**2 = 0.5 // assuming the calculation is for a vertical wall. Your math.cos apparently works in radians, not degrees
g_terr = 1 - g_atm = 0.5
I_refl = 0.1 * 300 = 30 W/m2
I_terr = 5.67e-8 * 0.9 * (273.15+20)**4 = 377 W/m2 // note use of absolute temperature
I_l = g_atm * 300 + g_terr * (I_refl + I_terr) = 354 W/m2
#######################

If the assumed 300 W/m2 are declared to be "ILAH", WUFI performs this calculation to convert the 300 W/m2 which it has read from the file into the total radiation which would be incident on a vertical wall (in this case), replacing some of it by an appropriate amount of reflected radiation and ground emission. You should see this resulting number and its components if you export the "counterradiation" and its components with the "ASCII export".

On the other hand, if the 300 W/m2 are declared to be "ILM", WUFI skips this step and assumes that the data already refer to this situation, either because they have been measured directly, or you have done the conversion with some more sophisticated method. The result is that WUFI takes the unmodified 300 W/m2 as the total long-wave input on the wall surface. This is less than the 354 W/m2 computed in the case above, so declaring the 300 W/m2 as ILM will result in lower wall temperatures.

Kind regards,
Th. Schmidt

[Mandinec]

Thank you for your explanation and for pointing out the need to use absolute temperature in the terrestrial counter-radiation equation. I have completely missed that. It makes perfect sense now.

Thank you
Best regards
Jan Mandinec