Diagnosing the relation between ocean circulation, mixing and water-mass transformation from an ocean hydrography and air-sea fluxes

The aim of this thesis is to understand the relationship between surface freshwater and heat fluxes, (interior) ocean mixing and the resulting changes in the ocean circulation and distribution of water-masses. The ocean circulation is analysed in Absolute Salinity (SA) and Conservative Temperature (SA) coordinates. It is separated into 1) an advective component related to geographical displacements in the direction normal to SA and ‚Äöv§v± iso-surfaces, and quantified by the advective thermohaline streamfunction ˜í¬Æadv/SA‚Äöv§v±, and 2) into a local component, related to local changes in SA and ‚Äöv§v± values, without a geographical displacement, and quantified by the local (temporal) thermohaline streamfunction ˜í¬Æloc/SA‚Äöv§v±. In this decomposition, the sum of the advective and local components of the circulation is given by the diathermohaline streamfunction ˜í¬Ædia/SA‚Äöv§v± and is directly related to the salt and heat fluxes of the surface forcing and ocean mixing. Interpretations of the streamfunctions is given and it is argued that the diathermohaline streamfunction provides a powerful tool for the analysis of and comparison amongst numerical ocean models and observational-based gridded climatologies. The relation between ˜í¬Ædia/SA‚Äöv§v± and fluxes of salt and heat is expressed as the Thermohaline Inverse Method (THIM). The THIM uses conservation statements for volume, salt and heat in (SA, ‚Äöv§v±) coordinates to express the unknown ˜í¬Ædia/SA‚Äöv§v± as surface freshwater and heat fluxes, and mixing parameterised by a down-gradient epineutral diffusion coefficient, and an isotropic down-gradient turbulent diffusion coeffcient of small scale mixing processes. The resulting system of equations that is solved in the THIM is tested against a numerical model and shown to provide accurate estimates of the unknowns ( ˜í¬Ædia/SA‚Äöv§v±, and the epineutral and small-scale diffusion coefficients). The THIM has been applied to observations to obtain constrained estimates of the epineutral and small-scale diffusion coefficients and ˜í¬Ædia/SA‚Äöv§v±. New insights in ˜í¬Ædia/SA‚Äöv§v± are revealed and the estimate of small-scale diffusion coefficient compares well with previous estimates. The estimates of the epineutral diffusion coefficient is about 50 times smaller than those typically used in coarse resolution climate models, suggesting that either the surfaces fluxes that are used under-estimate the production of epineutral anomalies of SA and ‚Äöv§v±) or the epineutral diffusion coefficients commonly used in climate models are too large. The geometry of interior ocean mixing is analysed and it is found that under the smallslope approximation there is a small gradient of tracer in a direction in which there is no actual epineutral gradient of tracer. The difference between the correct epineutral tracer gradient and the small-slope approximation to it, is quantified and it is shown that it points in the direction of the thermal wind. The fraction of the epineutral flux in this direction is very small and is negligible for all foreseeable applications. Smallscale mixing processes act to diffuse tracers isotropically (i.e. directionally uniformly in space), hence it is a misnomer to call this process 'dianeutral diffusion'. Both realisations affect the diffusion tensor, and a more concise diffusion tensor is derived for use in ocean models. The techniques, diagnostics and insights presented in this thesis lead to increased understanding of the relationship between ocean circulation and water-mass transformation due to ocean mixing and surface uxes, and result in enhanced ability to model the ocean and its role in the climate system.