The authors have sufficiently addressed my previous comments. However, on re-reading of the manuscript, there are still some points of potential confusion the authors may wish to address in terms of how they describe the application of the Garrett (1983) model to the present data. Specifically, there are a number of places in the manuscript where the authors refer to Garrett’s 2nd and 3rd phases of tracer dispersal (the streakiness and eddy diffusivity phases, which are the present manuscript’s 1st and 2nd phases) as “slow” and then “fast” respectively. One point of potential confusion with this is that one typically thinks of exponential growth as faster than linear growth, such that we might expect dispersion during the streaky phase to be faster than during the linear phase. When considering the two spreading phases in the context of diffusivity, however, the real quantity of interest is the time rate of change of the area. Comparing an exponential to linear growth rate in tracer area, linear growth will always be faster than exponential growth for small times. However, eventually, an exponential growth rate (which is also an exponentially growing diffusivity) will always overtake a linear growth rate (i.e., constant diffusivity). In terms of tracer patch areas, as I understand it, the theoretical time in Garrett’s analysis referred to in the appendix as the “lag time” is the cross-over point when an exponential growth in area (not diffusivity) will overtake a linear growth in area for the same initial condition. Considering the slopes of the linear and exponential area growth curves, i.e., the diffusivity, however, the slope of the linear growth curve is constant (i.e., constant diffusivity) for all time, while the slope of the exponential curve is itself exponential in time. Thus the slope of the exponential growth increases from a small value to large value with time. This then gets back to the point of potential confusion – the slope of the exponential growth phase, when interpreted as a diffusivity, starts out very small, then becomes large, at first being smaller than the linear growth rate (i.e., K_iso), then becoming larger, but both of these occur before the “lag time” is reached, i.e., both during the exponential growth phase of the tracer. Only if one samples early in the exponential growth phase would one expect to see a smaller slope, and hence infer a smaller diffusivity than K_iso. How early is early could be computed, but I believe it is different from Garrett’s 1/(4*\gamma). This should be clarified in any discussion of smaller inferred diffusivities during the exponential growth phase vs. the later linear growth phase.
The above points are confused even further when one considers that Garrett’s model addresses diffusivity defined in terms of growth of tracer area. Not clear is how the exponential vs. linear growth phases behave when considered in a large-scale natural tracer coordinate system as discussed in this paper, where both the anthropogenic tracer and the large-scale passive tracer are being advected and diffused. In that case, are there still slow and fast phases of the exponential growth, even though diffusion across isopycnal salinity contours is driven solely by small-scale diffusive processes, and not along-streak straining? This aspect likely gets into greater detail than is warranted in the present manuscript. However, it reinforces the point about being careful in how one describes the initial “slow” growth of tracer, despite this being during the exponential growth phase.
Lines 147-149, and Fig 5: Relative to Fig. 5 and associated analysis, if the ocean is also stratified vertically via salinity, then wouldn’t diapycnal mixing alone show a spread in both density and salinity in these pictures? By measuring the 2nd moment of spread in salinity only, and attributing this all to isopycnal mixing, doesn't this incorrectly include effects of diapyncal mixing? Put another way, for diapynal mixing in a salinity stratified ocean, wouldn’t the ellipses in Fig. 4 be tilted, with a covariance between density and salinity? If so, this effect would need to be accounted for in order to infer isopycnal mixing across lateral salinity gradients. It would seem that the possible importance of this could be easily estimated by considering the diapyncal mixing rate applied to the vertical salinity gradient compared to the isopycynal mixing rate applied to the lateral salinity gradient to see which dominates the change in salinity of the tracer.
Line 285: The statement that the actual area of tracer grows slowly in the "first phase" described here (Garrett's 2nd phase) is confusing for the reasons noted above - the streaky phase represents first a slow then a rapid growth rate (i.e., diffusivity), while the eddy stirring phase is a constant growth rate (i.e., diffusivity).
Line 296: Again, I would not call this a "slow growth" phase, as it is exponential growth of tracer area, first slow then fast, as opposed to linear growth (constant growth rate) that happens later in the eddy stirring regime.
Not with respect to any particular passage, but relative to the fitting of Garrett’s model to a large-scale multi-year tracer experiment, in addition to Ledwell et al (1993) and Ledwell et al (1998), it might also help for context to cite the analysis of Sundermeyer and Price (1998) as applied to the North Atlantic Tracer Release Experiment. In particular, note Figs. 2 and 10 in the latter showing observed and modeled tracer moments relative to Garrett’s exponential and eddy diffusion growth phases. |