A robust empirical model for deriving depth-integrated N₂ fixation rates from surface measurements in the global open ocean

Abstract. Marine dinitrogen (N₂) fixation (NF) is a critical nitrogen source supporting ocean productivity, yet its global quantification remains challenging because vertically resolved measurements are logistically demanding. To address this, we developed an empirical model to predict depth-integrated NF (INF, μmol N m⁻² d⁻¹) within the euphotic zone directly from surface NF (SNF, μmol N m⁻³ d⁻¹) measurements. Using 690 measured NF profiles from the global open ocean, we established a robust relationship: log₁₀INF = 1.85 + 0.84 × log₁₀SNF (R² = 0.82, RMSE = 0.31). The model performed well globally, particularly for typical profiles in which NF decreased monotonically with depth. It tended to underestimate log₁₀INF for profiles with substantial subsurface NF maxima, especially in the subtropical South Pacific (bias = −0.20), where such maxima were likely sustained by deeper iron supply, and in the northwestern Pacific (bias = −0.33), where the maxima were likely driven by photoinhibition of surface unicellular diazotrophs. Overestimation of log₁₀INF occurred in the eastern Atlantic (bias = +0.24), likely reflecting steep depth declines in NF driven by rapid decreases in light and iron availability. A small subset of profiles had uniformly low NF rates throughout the euphotic zone, associated with low iron and/or phosphorus concentrations. When applied to historical surface measurements lacking corresponding INF observations, model-derived INF estimates were statistically consistent with available INF measurements, supporting its preliminary application. Our model enables more efficient global surveys of N₂ fixation, thereby improving our ability to map this critical process and refine understanding of ocean nutrient cycles.