willaguiar
commented
8 months ago Possible solution: Closing the heat budget on the shelf by calculating the vertical heat divergence in each bin For example (check fig below), a case where our previous CSHT(z) calculation would be biased would be when ASC (or coastal current) enters a bin Z1 zonally, and then it moves downwards in the water column exiting in a deeper layer Z2. In the previous calculation, because no vertical heat fluxes are computed, the heat entering on Z1 would be assumed to contribute to the heat budget in that bin and depth, but that is not accurate because part of that heat would be leaving from below the cell at Z1 bottom. If we compute the differences of the vertical heat transport from the top and bottom of the cell (vertical divergence), we can add that difference back to the CSHT ( term 3) and then resolve this problem.
Below is a plot of heat transport along the contour including the vertical divergence, to see if/how much it changes the results. As far as I can see, and assuming there is no coding error, the vertical divergence makes the most differences where there is DSW formation (I guess these places would have strong vertical fluxes, so it makes sense?).
Here is a profile of CSHT on 2 small regions with and without the vertical divergence to see how it changes, and it seem to make a difference in the HT along the water column
PS: Vertical divergence integrated along the contour and depth is 0, so it doesn't change the total CSHT. code here That could be a way to correct the problem, so all vertical analysis is consistent. What do you all think? Suggestions welcome, flag if Im missing something!
taimoorsohail
wghuneke
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.