The total amount of energy that plants assimilate by photosynthesis is called

Gross primary production is the total amount of solar energy transformed into chemical energy by green plants (via photosynthesis). 

Producers employ a share of gross production for their numerous metabolic processes. Net primary production refers to the energy that remains after certain energy has been employed by the plants to cater to their own metabolic needs. 

Biomass is the weight of living plant material at a given point in time.

Eutrophication is the natural aging of a lake by nutrient enrichment of its water. 

Hence, the total amount of energy that plants assimilate by photosynthesis is called gross primary productivity.