Biological nitrogen (N₂) fixation is a key process, contributing nearly one half of the bioavailable N input to the ocean. Limited spatiotemporal coverage of depth-integrated nitrogen fixation rates potentially induces uncertainty in estimations of N input. Previous studies have found depth-integrated N₂ fixation rates had significant relationships with surface measurements. However, the relationships were limited in specific regions. We proposed a globally applicable relationship between depth-integrated and surface measurements based on 635 profiles, (depth-integrated NFR) = 71 × (surface NFR)^0.83 (R² = 0.88), and provided operational guidelines, making in-situ work for integral values convenient. And we categorized the profiles into three cases (well-mixed, monotonous decrease and subsurface maximum) and computed a mean vertical profile for each after quality control. Most profiles predicted well except those where N₂ fixation rates increased with depth strongly and iron may play a role. Furthermore, we offered adjustment coefficients for ocean basins. The empirical formula appeared to overestimate some NFR observations sampled at depths shallower than euphotic zone depth (1% of surface light). It may suggest that we need to sample at least at euphotic zone depth to avoid neglecting N₂ fixation rates in deep layer. Based on this relationship, we used boosted random forest to estimate global oceanic N₂ fixation rates (64 - 127 Tg N yr ^-1; ranges based on one geometric standard error). Recently, a method for high frequency underway N₂ fixation measurements has been used in field. The relationship might be potential for underway measurements and we expect this will improve our understanding of biogeography of marine N₂ fixation rates.
 

marine nitrogen fixation, depth-integrated, global ocean