Which of the following ecosystems will be more productive in terms of primary productivity? Justify your answer: $A$ young forest,a natural old forest,a shallow polluted lake,an alpine meadow.

(A) Primary productivity is defined as the rate at which radiant energy is captured by producers and converted into chemical energy in the form of biomass. It is typically measured in terms of weight $(g \cdot m^{-2} \cdot yr^{-1})$ or energy $(kcal \cdot m^{-2} \cdot yr^{-1})$.
Among the given options,a young forest is the most productive.
Justification:
$1$. $A$ young forest consists of rapidly growing trees that are in a phase of high metabolic activity and biomass accumulation.
$2$. $A$ natural old forest has reached a climax stage where the rate of photosynthesis is nearly balanced by the rate of respiration,leading to lower net primary productivity compared to a young,actively growing forest.
$3$. $A$ shallow polluted lake has limited primary producers due to toxicity and eutrophication,which inhibits healthy growth.
$4$. An alpine meadow has a short growing season and harsh environmental conditions,which limits its primary productivity.