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 *σ*_{2} – 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: *γ*^{n} of Jackett and McDougall (1997); the Lorenz reference state density
*ρ*_{ref} of Saenz et al. (2015); and three potential density variables
*σ*_{0}, *σ*_{2} and *σ*_{4}. 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} m^{2} s^{−1}
in the deep ocean for all density variables, with
*γ*^{n} suffering the least from the isoneutral control of effective
diapycnal mixing and *σ*_{0} 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} m^{2} 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.