The topic of this question is the collection of radiation from the sun. (renewable energy course) The total radiation flux is $$I_\text{total} = I_\text{direct}+I_\text{diffracted}+I_\text{reflected} .$$
According to the Threlked & Jordan model $$I_\text{diffracted}=d\cdot I_\text{direct}$$ and $$I_\text{reflected}=f(d,r,I_\text{direct})$$ where $d,r$ are constants.
But how is this possible? How can we get a total flux > direct radiation flux?
Your first equation seems to be assuming that the sun is shining on something unobstructed, but that there's also e.g. a window reflecting to it as well, plus the diffracted term. As you can imagine, in that case you could have more total flux hitting that object than just the direct flux, because the reflected light adds to the direct light. If you're talking about solar panels, assuming that $I_\text{direct}$ is from unobstructed sunlight would make sense, since you're (hopefully!) putting them where they have an unobstructed view of the sun.
That equation wouldn't work for sunlight shining on something on the other side of the window, since it doesn't take into account that the direct radiation is reduced some by the window. You would instead use something like
$$I_\text{direct} = T ⋅ I_\text{radiated},$$
along with
$$I_\text{diffracted} = d ⋅ I_\text{radiated}$$
and
$$I_\text{reflected} = f(d,r,I_\text{radiated})$$
where $T$ is the transmission coefficient of the window. $T$ will be less than 1.
