The equations shown in (80) are clearly wrong as the author points out. But they are not done in any literature I have ever seen. The paper is full of red herrings like that, basically trying to prove that since some red herring is wrong, the whole approach is wrong. That isn’t the case, the earth blackbody calculation is valid although only approximate.
“The paper is full of red herrings like that”
Oh really? what are the other ones?