An argument for using a variable Schmidt number exponent based on direct measurements of air–sea gas exchange

Abstract. Air–sea gas exchange is typically parametrized as a function of wind speed using the gas transfer velocity k. Since k ∝ Sc^-n and k ∝ ε^1/4, we can derive n based on eddy covariance measurements of k and turbulent kinetic energy dissipation rate (ε) measurements. We obtain a linear parameterisation of n as a function of wind speed. Allowing n to vary instead of using the commonly assumed value n=1/2 can have a significant impact on global k. To quantify this effect, n(U₁₀) was combined with the ERA5 reanalysis product and k was normalized to Sc=660. Global k₆₆₀ is estimated to decrease by about 12% when k₆₆₀ is determined using the dual tracer method, but to increase by 5% or less for EC-derived estimates.  To assess the resulting effect on air-sea CO₂ fluxes, n(U₁₀) was subsequently applied to an average of global fCO₂-based flux data products for 2023. Based on an EC-derived k₆₆₀ parameterisation, we find substantial relative increases in flux in large areas of the tropical and subtropical oceans, while global net uptake increases by only about 1%. Due to the direct dependence of k on n, using n(U₁₀) in the dual tracer method results in a significant relative decrease in flux across large parts of the global ocean, while global net uptake decreases by about 5%. We suggest applying a variable n under low-wind conditions, particularly for the EC method at low water temperatures or the dual tracer method at high water temperatures.