Dealing with d13C budget in the new version

   Here is a schematic for how d13C can be inserted into the paper. It will
   take putting text into many of the existing sections.

   -In the introduction I think it is OK to eliminate the T/S plot figure
   from the paper. However, it is important that we define a `conservative'
   tracer here as any scaler that can only change its value by exchange at
   the boundaries and mixing in the interior. We can then point out that
   mixing will either be across or along isopycnals. This will seem trivial
   to the reader at this point, but will become very important in the
Methods
   section. I think this will get the reader used to the idea that
   d18O-calcite can be its own tracer, independent of temperature,
   d18O-water, or salinity. Getting people to accept the idea that they
don't
   have to divide d18O into its various parts has been one of the sticking
   points when I give this as a talk.

   -We can derive the oxygen and carbon isotope budgets in the Methods
   section as we do now, but we need to explicitly point out that these
   ignore along isopycnal mixing and refer folks to the Appendix. By the
way,
   we never evaluate equation (8) in the appendix to show that diapycnal
   fluxes dominate over along isopycnal fluxes, though we promise to do this
   in a separate section. This is important because we rely on it not to be
   true for the LGM d13C data coming up.

   -If we are not going to use the d13C data to constrain the LGM
   circulation, I don't think we need to spend a lot of time talking about
it
   in the modern.

   -The key data analysis part of d13C is the Monte Carlo analysis for Blake
   and Brazil where the max gradient in d13C does not come out at the same
   absolute value of d13C for the LGM at the two sites. This is the main
clue
   that something is different for carbon than it is for d18O and we should
   put this figure back in the paper. One reason we think the d18O budget is
   robust is that the max gradients both come out at ~4.4‰.

   -It seems like the right place to insert this analysis of the d13C data
is
   right after we do the same for d18O. We can put terms into the simplified
   d13C balance and show how far off the two sides of the equation are, and
   the sign of the imbalance.

   -There are only two ways that the d18O data can have results that are
   consistent with our simplified tracer balance but the d13C data do not.
   The first is the non-conservative (J) term, but as I remember this even
   has the wrong sign for balancing the above equation. The second way is
   along isopycnal fluxes. In this case we need to do the calculation for
   equation (8) in the appendix for both tracers. I suggest we do this
   directly in the text.

   -One reason I think the along isopycnal fluxes are greater for d13C than
   for d18O is that the LGM endmembers for North and South water are much
   larger for carbon than for oxygen, especially when compared with their
   modern counterparts. Other interesting things to investigate here are the
   lack of obvious vertical gradient in d13C for both Blake and Brazil at
the
   LGM, and some discussion of how d18O can have sharp vertical gradients
but
   not along isopycnal gradients.