| Summary: | Diagnosis of the ocean's overturning circulation is essential to closing global budgets of heat, salt and biogeochemical tracers. This diagnosis is sensitive to the choice of density variable used to distinguish water masses and identify transformations between them. The oceanographic community has adopted neutral density for this purpose because its isopycnal slopes are approximately aligned with neutral slopes, along which ocean flows tend to be confined. At high latitudes there are often no tenable alternatives because potential density varies non-monotonically with depth, regardless of the reference pressure. However, in many applications the use of isoneutral fluxes is impractical due to the high computational cost of calculating neutral density. Consequently neutral density-related diagnostics are typically not available as output from ocean models. In this article the authors derive a modified Temporal Residual Mean (TRM) approximation to the isoneutral mass fluxes, referred to as the Neutral Density Temporal Residual Mean (NDTRM). The NDTRM may be calculated using quantities that are routinely offered as diagnostic output from ocean models, making it several orders of magnitude faster than explicitly computing isoneutral mass fluxes. The NDTRM is assessed using a process model of the Antarctic continental shelf and slope. The onshore transport of warm Circumpolar Deep Water in the model ocean interior approximately doubles when diagnosed using neutral density, rather than potential density. The NDTRM closely approximates these explicitly-computed isoneutral mass fluxes. The NDTRM also exhibits a much smaller error than the traditional TRM in regions of large isoneutral temperature and salinity gradients, where nonlinearities in the equation of state diabatically modify the neutral density.
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