Primary production and photoacclimation models are two important classes of physiological models that find applications in remote sensing of pools and fluxes of carbon associated with phytoplankton in the ocean. They are also key components of ecosystem models designed to study biogeochemical cycles in the ocean. So far, these two classes of models have evolved in parallel, somewhat independently of each other. Here we examine how they are coupled to each other through the intermediary of the photosynthesis-irradiance parameters. We extend the photoacclimation model to accommodate the spectral effects of light penetration in the ocean and the spectral sensitivity of the initial slope of the photosynthesis-irradiance curve, making the photoacclimation model fully compatible with spectrally resolved models of photosynthesis in the ocean. The photoacclimation model contains a parameter θm, which is the maximum chlorophyll-to-carbon ratio that phytoplankton can attain when available light tends to zero. We explore how size-class-dependent values of θm could be inferred from field data on chlorophyll and carbon content in phytoplankton, and show that the results are generally consistent with lower bounds estimated from satellite-based primary production calculations. This was accomplished using empirical models linking phytoplankton carbon and chlorophyll concentration, and the range of values obtained in culture measurements. We study the equivalence between different classes of primary production models at the functional level, and show that the availability of a chlorophyll-to-carbon ratio facilitates the translation between these classes. We discuss the importance of the better assignment of parameters in primary production models as an important avenue to reduce model uncertainties and to improve the usefulness of satellite-based primary production calculations in climate research.