The mechanisms of spring phytoplankton blooms are investigated from a Lagrangian framework by using a Lagrangian NPZD model that can track the movement and transfers of nutrient parcels in a turbulent environment. The model reveals that the onset of spring blooms depends on the cumulative euphotic age, which is the total time that inorganic nutrient is exposed to light before the photosynthetic conversion to phytoplankton biomass. A spring bloom, defined as a tenfold increase of near-surface phytoplankton, occurs when this cumulative euphotic age is approximately µ-1eff, where µeff is the effective growth rate in the euphotic layer, regardless of the underlying mechanism. If the turbulent layer depth is shallower than the critical depth and turbulence is strong, nutrient parcels accumulate enough light exposure through multiple entries to the sun-lit zone near the surface. If turbulence is weak, as that considered in the critical turbulence theory, the accumulation of the light exposure depends on the residence time of the nutrients parcels near the surface. The spectral shape of the cumulative euphotic age can clearly distinguish these two modes of spring blooms. The spectrum shows a peak at the theoretical growth timescale when multiple entries become important, while it shows a maximum near age zero that decays with age when the near-surface residence time becomes important. Mortality increases the cumulative euphotic age necessary for a bloom but does not affect the spectral shape, suggesting that it does not alter the primary mechanism behind the accumulation of cumulative euphotic age.
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