Learn Turkish: Karbon salınımı arttığından beri bunun etkisini görüyoruz. - Since carbon emission increased, we are seeing its effect.

This uses the structure you are currently learning for "since [action] happened". We start with the root art- (to increase). We add the participle -tık (which softens to -tığ), then the 3rd person possessive -ı to get arttığı (literally "its increasing"). Finally, we add the ablative case -ndan ("from") and the word beri ("since").

Why is there an -ı at the end of salınımı?

It is there to form a noun compound. To combine karbon (carbon) and salınım (emission) into the set phrase "carbon emission", Turkish requires the 3rd person possessive suffix on the second noun, creating karbon salınımı.

Why does etkisini have both -si and -ni at the end?

The root is etki (effect). The -si is the possessive suffix making it "its effect". The -ni is the accusative case suffix (with an -n- buffer) because "its effect" is the specific direct object that we are seeing (görüyoruz).

Do we really need bunun here if etkisini already means "its effect"?