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Zonal convergence bias in vertical profiles of CSHT #21
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Possible solution: Closing the heat budget on the shelf by calculating the vertical heat divergence in each bin PS: Vertical divergence integrated along the contour and depth is 0, so it doesn't change the total CSHT. code here |
@taimoorsohail I was talking to Adele on the matter of the vertical/zonal convergence. It is possible that we don't need them after all ( if we are trying to merely correlate ASC and CSHT). Would it be possible to repeat the r2/slope analysis without the zonal convergence ( binned_CSHT)*0.08, to see how much It differs? |
Sure! Here are the same plots without the zonal convergence part (this is for layer-wise U_along vs. layer-wise CSHT). For reference, below is the plot WITH zonal convergence also in #20 (comment): |
We can see that the Zonal convergence have little impact on the vertical profiles of correlations and slope - and therefore it shouldn't matter much. Therefore closing this issue (Let's keep that in mind for the manuscript tho) |
Noting that we decided to include the depth-averaged zonal convergence in our analysis. |
I'm reopening this issue, but with a different objective now. It might be useful to have the profiles of correlations calculated for CSHT, CSHT+ZC, and CSHT+VC in the supplementary, just to show that VC don't change much the results. I'll do these plot for a supp. mat |
The calculation of the CSHT has to account for zonal heat convergence on the shelf bin, but this comes with an issue when we analyze the cross-slope heat transport vertically.
Consider that we are calculating the CSHT in a bin between 110E and 160E in the fig below:
Initially we compute the term (I) (Just the total sum of all transports crossing the 1km isobath).
However, this first term does not account for heat being transported laterally along the shelf (lets say it, by ASC). To fix this problem ( and other problems) and close the heat budget we account for the zonal convergence ( term 2), which is the integrated zonal heat transport coming into the bin in 160E minus the same integration for the heat going out of the bin in 110E.
This fixes the problem when we are analyzing the CSHT in each bin, fully integrated with depth. However, when we slice the CSHT in different depth ranges, or calculate it as a function of depth this becomes a problem.
For example, if we calculate the same budget for each depth, we are assuming the heat that is coming into the bin in Cinit at a certain depth z, would be leaving at the same depth ( Which is not necessarily true, particularly in regions of DSW formation).
We can either have that in mind when analyzing the results ( and mention it in the paper), or we can think of ways of fixing this problem.
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