Figure discussion for paper about asc_and_heat_transport HOT 4 OPEN

Recording this here, because I will likely forget otherwise. I think there is a bug in the current Figure 2 script that correlates the heat transport with the depth-averaged ASC:
U_along_depthav = masked_u_along.mean('lon').mean('depth').regimes_mask
This averages u_along over depth with an even weighting of all z-levels, but we should use thickness-weighted averaging, so the lower thicker layers are weighted more than the upper thinner layers.

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I have a script for Figure 2 on my branch, below are two examples with the spaces for scatter/pdfs. Both figures below are the same except for row two - I have one with binned correlations and one with domain averages. We can change this after we finalise the binning problem. The thick line is for significant depths with p < 0.05.

Using domain averaged correlations - binned 5 deg in spatial picture. -- threshold of p < 0.05

Using binned layerwise correlations - 5 deg -- threshold of p = 0.05

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I've updated the weighting and the code with the pdfs. Currently the pdf shows a scatter of full depth averaged ualong (top rightmost) and depth averaged ualong for 433-1333m only (middle rightmost) so that's why the pdfs look the same (scatter of CSHT and Ualong in longitude bins and time). Could filter for only averaging over significant depths in pdf plot but won't pursue this more for now since we are moving to density but recording as the current state of Fig 2.

U_along_depthav = u_along_layerwise_binned.weighted(u_along_layerwise_binned.depth).mean('depth')

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I'm trying to get up to speed with where the project is at. I made a summary of my current understanding after going through the issues. I'd appreciate if you could confirm/correct me.

Research question: Does the ASC control ocean heat transport towards Antarctica?
Wide assumption used in a number of introductions to motivate the respective study and the importance of the ASC for the climate system. But nobody actually showed such general connection, that is, a weakening of the ASC drives/allows a larger cross-slope heat transport.

Literature: ... focuses on special cases

It is actually not a trivial thing to show such connection, we came across a number of challenges. Turns out, the devil is in the detail, e.g., how to define various variables. Challenges include
- large spatial variability
- large temporal variability
- ASC regimes: averaging over regimes does not give appropriate result because of large variability within regimes (Q1: Is this only an issue for the correlation of ASC and CSHT or also for ASC and CSHT separately?)

Definitions we've come up with:
- ASC: along-slope velocity along 1000 m isobath (following Huneke et al. 2022)
- ASC regimes: using an unsupervised clustering algorithm (Gaussian Mixture Modelling GMM) based on velocities (Taimoor's approach)
- CSHT: heat transport across the 1000 m isobath + taking into account zonal convergence (following Steward et al. 2018)
- Vertical coordinate: use density space to accurately capture CDW (properties differ around the continent)
- Time-scales of interest: interannual, seasonal, high frequency (~eddy time scale)

Figures:
Figure 1: Overview of ASC regime spatial distribution along 1000 m isobath, density along 1000 m isobath curtain, time-mean CSHT & slope current per regime (bar charts, function of density/water masses)
-> Poleward/offshore transport for AAIW, CDW, DSW in various regimes

Figure 2: Temporal correlation: (i) interannual, (ii) seasonal, (iii) high frequency
(Q2: Do this for the CDW density only or all water masses?)
-> large spatial variability in correlation, varies for different frequencies

Figure 3: Show exemplary a) time series of CSHT and slope current for appropriate locations for the different time scales and/or b) composite plots of cross-slope transects highlighting how the ASC and density/temperature is changing
-> helps the reader to visualise what's going on

Main findings:
- ASC is less correlated with poleward heat transport than assumed
- The correlation varies depending on the time scale and location

Suggested follow-up question:
Is the ASC a driver or a passive response to heat transport variability?

• I don't think it is possible to distinguish between the two. The adaptation of the ASC to, let's say, wind-driven lifting of the isopycnals will be instantaneously.
• Does it matter? I don't think it matters. We, the scientific community, might need to be more careful in the way we word things (no sloppy: the ASC controls onshore heat transport). But I see the value of this work in the finding that the ASC and CSHT are not generally highly correlated, nor is it true for a specific regime. It depends a lot on the location and timescale. For locations and time-scales where the correlation is high, we can use the ASC to estimate onshore heat transport variability but otherwise we cannot use the ASC as a guide to how the CSHT is behaving.

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