We develop and analyse a simple, two–compartment (chlorophyll and nitrate) model of the surface mixed layer of the ocean. The mixed–layer depth is modulated intermittently to simulate the effects of storms. The optical properties of the water column are linked to changes in the chlorophyll biomass. The model can be treated analytically. Mathematical bounds are found for the autotrophic biomass and the residual nitrate in terms of the intensity and frequency of storms and the bio–optical properties of the phytoplankton. The results are discussed in the context of the high–nutrient, low–chlorophyll regimes, where unconsumed nitrate is a persistent occurrence.