Reply to the comment by T. J. McDougall, P. R. Gent and S. Drijfhout

Abstract

The comment by T.J. McDougall, P.R. Gent and S. Drijfhout (cited as MGD) contains two parts: the first and most relevant one [because of its physical implications to ocean global circulation models (OGCM)] and a second one of a more technical nature. We shall reply in that order. The main physical argument in the comment is that the diapycnal flux Σ that appears in the mean tracer equation can be dispensed with entirely (and thus there is no need to model it) provided one abandons the Eulerian averages in favor of the density averaging suggested by the Temporal Residual Mean (TRM) formalism. Specifically, the authors write that “the appropriate average tracer is the thickness-weighted rather than the Eulerian-mean assumed in DC6”. We reply to this criticism by showing that TRM does not get rid of Σ since we show that Σ reappears in the mean tracer equation via another term. Therefore TRM offers no advantages with respect to the Eulerian averaging since both contain the diapycnal flux Σ. As for the technical parts, we discuss each of them and show that MGD's criticism to our approximations in the treatment of the tracer equation is erroneous and that our approximation is fully justified.