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Estimates of marine phytoplankton primary productivity (PP) from satellite remote sensing observations are potentially used to assess global carbon budgets, biogeochemical response, pools and fluxes of carbon and its spatial and temporal variations due to ocean-atmospheric oscillations under climate change. According to the recent studies, satellite-based vertically integrated global PP products have significant uncertainties due to the limitations of the past models, challenges in deriving the appropriate parameters that account for the variation of PP with seasons and provinces, and specify the vertical structure of phytoplankton biomass from satellite observation data and scarcity of in-situ vertical profile data. To overcome these issues, we developed a depth-resolved and depth-integrated model to estimate PP for global oceanic waters. It comprises the depth-resolved primary productivity (DRPP) and satellitebased depth-integrated primary productivity (DIPP) parameterizations to accurately estimate the magnitude and variability of PP in the global ocean. These parameterization algorithms require knowledge of the relative chlorophyll-specific carbon fixation rate (P b rel ) and maximum chlorophyll-specific carbon fixation rate within the water-column P b opt in order to derive the spatial and temporal patterns of DRPP and DIPP. To estimate the chlorophyll-specific maximum rate of carbon fixation at a depth equal to z (P b z ), two different P b rel algorithms were developed based on the relative values of i) the subsurface photosynthetically available radiation (PAR rel ) and ii) the optical depth at depth z (ζ z ). Furthermore, a sensitivity analysis was conducted to understand the effect of sea-surface temperature (SST), sea-surface chlorophyll concentration (SCHL) and sea-surface photosynthetically available radiation (SPAR) on the photo-physiological parameter P b opt . These physical, biological and optical parameters were used to obtain accurate P b opt estimates. The model based on the SST-SCHL-SPAR (P b opt (SSTCP)) produced more accurate P b opt estimates than the global Vertically Generalised Productivity Model (P b opt (VGPM )). Comparison of the model results with in-situ measurement data demonstrated that the ζ z -based DRPP algorithm (DRPP(ζ z )) yields more accurate results than the PAR rel -based DRPP algorithm (DRPP(PAR rel )). This study also investigates the spatial and temporal patterns in MODIS-Aqua-derived P b opt and DIPP products and the impacts of climate-driven perturbations on the global ocean PP due to the La Niña and El Niño phenomenon during 2010 and 2015. INDEX TERMS Primary productivity (PP), maximum carbon fixation rate, depth-resolved PP, depthintegrated PP, ocean color remote sensing, global ocean.