Isoneutral control of effective diapycnal mixing in numerical ocean models with neutral rotated diffusion tensors

Abstract. It is well known that there is an infinite number of ways of constructing a globally defined density variable for the ocean, with each possible density variable having, a priori, its own distinct diapycnal diffusivity. Because no globally defined density variable can be exactly neutral, numerical ocean models tend to use rotated diffusion tensors mixing separately in the directions parallel and perpendicular to the local neutral vector at rates defined by the isoneutral and dianeutral mixing coefficients respectively. To constrain these mixing coefficients from observations, one widely used tool is inverse methods based on Walin-type water mass analyses. Such methods, however, can only constrain the diapycnal diffusivity of the globally defined density variable γ – such as σ2 – that underlies the inverse method. To use such a method to constrain the dianeutral mixing coefficient therefore requires understanding the relations between the different diapycnal diffusivities. However, this is complicated by the fact that the effective diapycnal diffusivity experienced by γ is necessarily partly controlled by isoneutral diffusion owing to the unavoidable misalignment between iso-γ surfaces and the neutral directions. Here, this effect is quantified by evaluating the effective diapycnal diffusion coefficient pertaining to five widely used density variables: γn of Jackett and McDougall (1997); the Lorenz reference state density ρref of Saenz et al. (2015); and three potential density variables σ0, σ2 and σ4. Computations are based on the World Ocean Circulation Experiment climatology, assuming either a uniform value for the isoneutral mixing coefficient or spatially varying values inferred from an inverse calculation. Isopycnal mixing contributions to the effective diapycnal mixing yield values consistently larger than 10−3 m2 s−1 in the deep ocean for all density variables, with γn suffering the least from the isoneutral control of effective diapycnal mixing and σ0 suffering the most. These high values are due to spatially localised large values of non-neutrality, mostly in the deep Southern Ocean. Removing only 5 % of these high values on each density surface reduces the effective diapycnal diffusivities to less than 10−4 m2 s−1. The main implication of this work is to highlight the conceptual and practical difficulties of relating the diapycnal mixing diffusivities inferred from global budgets or inverse methods relying on Walin-like water mass analyses to locally defined dianeutral diffusivities. Doing so requires the ability to separate the relative contribution of isoneutral mixing from the effective diapycnal mixing. Because it corresponds to a special case of Walin-type water mass analysis, the determination of spurious diapycnal mixing based on monitoring the evolution of the Lorenz reference state may also be affected by the above issues when using a realistic nonlinear equation of state. The present results thus suggest that part of previously published spurious diapycnal mixing estimates could be due to isoneutral mixing contamination.