Noise level x amount of meters away from an outdoor singer: sphere or semi-sphere?

When computing the noise level x amount of meters away from a singer who is singing outdoors, should one rely on the standard formula

$I=\frac{P}{4πr^2}$

(and then convert 'I' into decibels)

or rather on the formula $I=\frac{P}{2πr^2}$, given that the sound waves cannot spread downwards, and are thus forming a "half-sphere" only?

My confusion stems from the fact that I remember calculating the radio waves emitted by an antenna using the formula $I=\frac{P}{2πr^2}$, based on the fact that the antenna was located on the ground, meaning that the waves formed a semi-sphere only. This was confirmed by my textbook.

However, that same textbook uses $I=\frac{P}{4πr^2}$ for the scenario given above, which does not seem to make sense.

Can anybody help out?

Thank you!