A thermohaline inverse method for estimating diathermohaline circulation and mixing

The thermohaline inverse method (THIM) is presented that provides estimates of the diathermohaline streamfunction ΨdiaS_AΘ, the downgradient along-isopycnal diffusion coefficient K, and the isotropic downgradient turbulent diffusion coefficient D of small-scale mixing processes. This is accomplished by using the water mass transformation framework in two tracer dimensions: here in Absolute Salinity S_A and Conservative Temperature Θ coordinates. The authors show that a diathermal volume transport down a Conservative Temperature gradient is related to surface heating and cooling and mixing, and a diahaline volume transport down an Absolute Salinity gradient is related to surface freshwater fluxes and mixing. Both the diahaline and diathermal flows can be calculated using readily observed parameters that are used to produce climatologies, surface flux products, and mixing parameterizations for K and D. Conservation statements for volume, salt, and heat in (S_A, Θ) coordinates, using the diahaline and diathermal volume transport expressed as surface freshwater and heat fluxes and mixing, allow for the formulation of a system of equations that is solved by an inverse method that can estimate the unknown diathermohaline streamfunction ΨdiaS_AΘ and the diffusion coefficients K and D. The inverse solution provides an accurate estimate of ΨdiaS_AΘ, K, and D when tested against a numerical climate model for which all these parameters are known.