Issue with the calculation of net thermal radiation in RTMt_sb.m (SCOPE 2.1)

[ThangCiat]

Dear SCOPE developers,

We have a question regarding the calculation of net thermal radiation per element using Stefan Boltzmann's law in SCOPE version 2.1.
In line 153 in RTMt_sb.m: The downward and upward fluxes are not multiplied by the element's absorptance (or its emissivity):
Rnuc = (Emin(1:end-1) + Eplu(2:end) - 2*(Hcsu))
Since the vegetation foliage and soil cannot be considered as black bodies, we suggest that the equation should be:
Rnuc = (Emin(1:end-1) + Eplu(2:end))epsc - 2(Hcsu)
The following other lines in the Matlab code mentioned below exhibit the same issue: 150, 156, 157, and 158.
https://github.com/Christiaanvandertol/SCOPE/blob/2.1/src/RTMs/RTMt_sb.m

We noticed that this issue is not present in the previous SCOPE version 1.73.

When testing and comparing the same simulation in SCOPE using different versions of RTMt_sb (from SCOPE 1.73 and 2.1), we found out that the upward and downward thermal radiation are similar but the net thermal radiation is significantly different due to the overestimated absorption. Therefore, the temperature of an element computed in SCOPE v. 1.73 and v. 2.1 is different. We wonder if there is a particular reason to assume in SCOPE 2.1 that the soil and the canopy have absorptance = 1 or if it can be just a typo/error in the code. The results of the comparison between SCOPE 1.73 and 2.1 are shown in the attached figures.

Best regards.
Thang and colleagues

[Christiaanvandertol]

Dear Thang and colleagues,
Thanks for your comments. The concern you raised is that in the calculation of the net radiation in RTMt_sb, the emissivity of the leaves and the soil is not considered. I investigated this and conclude that this is indeed an unfortunate error. At low emissivities it causes an unacceptable closure error in the radiation balance. After implementing your solution, the radiation balance of the canopy nearly closes. The error is now corrected in the master branch.
Christiaan

[ThangCiat]

Dear SCOPE team,

From the latest code, I think there is a minor problem in the lines 157 and 158
Rnus = epss*(Emin(nl+1) - Hssu);
Rnhs = epss*(Emin(nl+1) - Hssh);

And I think it should be
Rnus = epssEmin(nl+1) - Hssu;
Rnhs = epssEmin(nl+1) - Hssh;

Since in SCOPE 2.1 the soil emission (Hss) is already calculated taking into account its emissivity, we might not need to multiply it by the emissivity in lines 157 and 158.
Hssu = epssStefan_Boltzmann(Tsu,constants);% Radiance by sunlit soil
Hssh = epssStefan_Boltzmann(Tsh,constants);% Radiance by shaded soil

Thank you for checking this problem.

Kind regards,
Thang