Can we find any relationship between the spatial variations in time mean ASC strength and cross slope heat transport? We could do this on very local scales, or group by regions (fresh, warm, dense). We could try using different measures of ASC strength (max speed, structure, position). We could also try different vertical integrations of cross-slope heat transport (e.g. depth integrated vs integrated over lower layers only or in certain density classes).

I just noticed that lon_bin_midpoints on the cross slope heat transport data only goes from -278.5 to 78.25, spaced 0.25deg apart within that interval. The actual grid goes from -280 to 80, so it looks like we're missing about 1.5deg at each end of the longitude grid. I'm guessing this is because when the binning was done, the grid wasn't wrapped around in the x-direction. Is that right @willaguiar? Can we fix that so we don't have any missing points?

As discussed in the hackathon today, different points on the isobath have different max depths, due to the discrete horizontal grid. Currently we are just doing straight depth averaging for the correlation plots. This means that some bottom points with depth 800m and being averaged with other points at 800m that are actually 400m above the bottom (where max depth = 1200m). It may be better to normalise depth and then average, so we always average bottom points together etc.

@ongqingyee is going to check what difference this makes for Figure 2.

When I presented this at CFP group meeting last week, we had some useful critical feedback on the choice of vertical coordinate. i.e. We're showing correlations in depth space on the 1000m isobath. The problems with this are:

1. The time mean heat transport in the depth range that we are saying is important is actually northward in both the dense and surface regimes (left panel here):

The scatterplots show that there are some temporal reversals of the heat transport in all regimes, when the CSHT switches direction to southward. But I'm not sure we can argue that those depths are what's important if the mean heat transport in those layers is actually northward.

2. For areas where the shelf break is relatively shallow, e.g. as shown below, I struggle to understand what cross-slope heat transport at 800-1000m depth actually means, because the isopycnals there intersect the slope just to the south of the 1000m isobath.

I'm not exactly sure what the solution to this issue is, but I'm sure a reviewer will also raise it, so I think we need to think about it. Possibly we could change to a density coordinate instead? Then look at the correlations in the CDW density range? Or would it be more meaningful to look at the correlations near the depth of the shelf break (but this varies along the isobath)?

Similar analysis to here, but instead of calculating total regime averages only averaged over the individual regions.

Hello everyone

I have done a previous short analysis with ACCESS-OM2-01 regarding the ASC speed and cross slope heat transport, and thought it would be useful to post here to start a discussion for our first hackathon.

Using Wilma code, I obtained the monthly velocities along the 1000m-isobath (along-slope speed) as a measurement of the ASC, and also calculated the heat transport across the 1000-m isobath (HT).

Spatial Variability

Temporal Variability
Because I used monthly output in the RYF simulation, all variability here is seasonal.

<<-old wrong fig, correct fig below check this comment for explanation on the correction.

Above we see the total average (depth and long/lat) ASC speed (positive = westward) vs the cross slope heat transport (negative = towards the South). Top is a circumpolar average, middle are averages for all points, except in the West Antarctic Peninsula, and bottom is the average only for the West Antarctic Peninsula (WAP).
It is quite surprising how well the circumpolar (top and middle) mean ASC speed time series matches the cross slope heat transport.

This analysis creates some points that could be useful to discuss in the next meeting:

[a] The definition used here for ASC is based on fixed points following the 1000m-isobath (@wghuneke , correct me if I'm wrong). It would be interesting to discuss alternative methods that can track the ASC, so we can distinguish if a decrease in speed is actually a decrease in ASC speed or a displacement of the front/ ASC centre. This is important to separate if the agreement we see in the second fig is valid or just an artifact of the ASC meridional displacement.

[b] The lower agreement between the ASC speed and HT when we remove the WAP from the calculations could be a method bias too. The points used to define the ASC speed are different than the ones for the HT. This could generate discrepancies when making regional correlations. So it might be a good idea to define a single isobath contour for both ASC and HT calculations.

[c] As we can see in the top b figure, we don't have HT calculated for the East Antarctic Peninsula. That has to do with the binning method used to remove the zonal heat convergence in the HT calculations (I can explain that better in the meeting). This could probably be fixed if we find a way to calculate the heat convergence along slope instead of zonal (perhaps a task for a hackathon ).

Feel free to create additional suggestions :)

Repeat much of the analysis (i.e. standard deviation on isobath, and correlations between ASC and heat transport for different regions) in this seasonal variability issue, but for annual averages in the IAF run. Also plot time series of the ASC and heat transport in different regions to see what the variability looks like and if there are trends.

Just occurred to me that picking the 1000m isobath to compute the heat transport across is another choice we've made in the analysis so far. Is the heat transport variability sensitive to using e.g. the 650m or 2000m isobath instead?

Test how different the results are when calculating the heat transport using different isobath definitions (known as "Adele's" and "Wilma's"...).

Currently, we calculate the heat transport using "Adele's" definition. I propose to compare how different the integrated heat transport is using "Wilma's" definition. If they're not too different, we can use the same isobath and calculate point-by-point correlations.

We are looking into potential alternative ways to reformat the $r^2$ vs $slope$ figure for easier visualization. This because the interpretation of the slope in this figure depends on which direction the ASC flows ( + or -), and if the CSHT is northward or southward. Until now we came up with a few possibilities.

1- Use transparency in the slope lines and r2 lines, whenever $r^2$ is too low, or the p value shows no significant correlation

2- Reformat each panel so negative slopes always means that as ASC strengthens the CSHT weakens, and positive slopes always means that as ASC strengthens the CSHT also strengthens .

3- Change the visualization to a scatter plot type, so the slope can be inferred visually, and add the depth information as a colorbar.

I opened this issue so we can plot our test visualizations, and discuss whatever we find best.

There are two obvious methods of computing the cross-slope heat transport:

1. Decompose the total heat transport at each point on the isobath into along-slope and across-slope components, i.e. following Wilma's ASC method/code here.
2. Use the zonal or meridional (depending on the local orientation of the contour) heat transport across each segment of a contour that borders the edges of the tracer-grid, following this notebook.

With method 2 we subsequently bin onto larger longitude bins and add the zonal convergence to remove the influence of the ASC crossing back and forth across the isobath. Possibly this extra step of adding the zonal convergence is not needed using method 1, because the ASC should already be decomposed into the along-slope rather than cross-slope component? I'm not sure.

It would be interesting to compute both methods and compare the spatial structure and magnitude of the cross slope heat transport.

Issue: The location (i.e. which isobath) of the ASC varies spatially and temporally.

How do we deal with this?

Also, which quantity do we expect to be best correlated with heat transport? i.e. dynamically what aspect of the ASC matters most? Max speed? Structure? Transport?

Possibilities:

• Use the along-slope transport integrated between 2 isobaths.
• Max speed between 2 isobaths.
• Some measure of the structure, i.e. how surface intensified or otherwise is the ASC?
• Unsupervised classification methods.
• ....

Maybe we just try a few of these and see which works best? Then try to understand why?

We are calculating the cross-slope heat transport following the method in Stewart et al. 2018, which adds the zonal convergence in a small longitude band on the shelf to the cross-isobath transport integrated in that same longitude band. This avoids the large cross-isobath heat transports that occur when the ASC crosses the isobath. However, this method does not work well around the peninsula (and in the western Ross Sea, anywhere else?), because a longitude band there covers a lot of length along the isobath, so we reduce our resolution in along-isobath space. We can fix this by using the meridional convergence in these regions instead of the zonal convergence.

Repeat much of the analysis (i.e. standard deviation on isobath, and correlations between ASC and heat transport for different regions) in #4, but using a daily timeseries with the daily climatology removed. i.e. to focus on frequencies higher than seasonal.

For particular regional locations (maybe we want different issues to look at different regions?), is there a relationship between temporal variability in ASC strength and cross-slope heat transport? We could look at different temporal scales (interannual, seasonal, high frequency), try different measures of ASC strength (max speed, structure, position), and different vertical integrations of cross-slope heat transport (e.g. depth integrated vs integrated over lower layers only or in certain density classes).

In the last meeting we redefine the CSHT($\sigma$) binned into $\sigma$ levels that reflects the water mass properties along the 1km isobath. CDW/DSW cutoff should be based in the maximum cumulative northward heat transport, while AASW/CDW should be based in a combination of maximum temperature + age from a TS diagram , taking into account a density range to classify the CDW.

This issue is for us to discuss these definitions. tasks are:

• Analyze mass transports integrated per regime
• Analyze TS diagrams averaged per regime
• Repeat the above analysis in large lon_bins along contour (i.e., $20^o$ lon bins)

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.

This is a place to record brief notes on past studies that have found a relationship (or not) between ASC strength and cross-slope heat transport. Some initial papers to get us started:

• Ellie's recent paper
• Silvano et al. 2019
• Nakayama et al. 2021
• Not sure if we want to go into the Amundsen papers looking at variations in the undercurrent on the slope and warm water intrusions - this might be a quite different mechanism to where there is a strong westward ASC. Maybe a very brief summary of a couple of these would be nice?

Let's add brief summaries of what these papers found below, and please add more suggestions of papers that have investigated the relationship between the ASC and cross-slope heat transport below.

I'm trying to calculate the statistics using 5deg longitude bins rather than averaged over the whole regime as we've been doing. I've included below a plot of the monthly along-slope current for both the original and binned into 5-deg longitude.

The problem occurs when trying to calculate the linear regression statistics. There are 2 loops (borrowed from the original GMM_ASC.ipynb), which were originally looping the scipy.stats.linregress function through (a) ASC regimes (n=3) and (b) depth levels (n=50).

For the binned CSHT/ASC, it means going through the whole binned contour (n=71). Using XXLargeMem, every stats.linregress takes ~14seconds to complete, which results in 14sec x 50 x 71 x 9 (doing it 9 times for _all, _annual, and _clima variables) = ~124 hours.

Tried to split these into 3 pbs scripts, and using hugemem, and it still ran out of walltime (max 48h).

I think one solution might be to vectorise the CHST/ASC inputs to the linregress, but when I tried I realised the CSHT has 75 vertical levels and ASC along-slope has only 50. Can anyone recall me why is that?

Hello everyone

We have submitted a while ago an abstract to IUGG ( next week), in which we will present some early results for this work. I produced a poster with some of our results (below). Please feel free to pitch in

Poster_IUGG_Will_AKM.pdf

To better reflect the range of depths of the 1000m isobath, we need to reduce the width of the longitude bins (which are currently 1/4-degree) that we use for the longitude binning of the CSHT and U_along array. We should test what impact this reduced bin width has on the layer-wise correlation between CSHT+ZC vs U_along. If not a huge difference, we can go ahead with the profile normalisation of these finer bins for use in the analysis, as discussed in #31.

We need to recreate the:

1. Depth-averaged ASC vs. CSHT correlation plots (Fig 1)
2. ASC vs CSHT in different time scales (Fig 2)
3. Do the ASC vs CSHT correlation with daily data to improve correlations and look at sub-seasonal time-scales
4. Mean vs Eddy decomposition correlations (Supp. Fig)

Using the time-mean regime definitions.

I have written a piece of example code that plots ocean properties binned by isobath, as shown below. I have remapped the isobath bins (which are the same as st_ocean) by the cumulative area held by each bin, normalised. This produces a 'normalised distance from Antarctica', creating a more realistic slope representation. We can also multiply the normalised cumulative area by latitude to create a "pseudo-Latitude". Anyway, I was wondering what we all think about this? We can mask the ocean properties by regime before binning, which would give us a clear representation of the average T, S and rho in each regime, without having to resort to using individual sections.
Let me know!

Many studies in the literature discuss the ASC as if it is a driver of heat transport, i.e. when the ASC weakens this drives (or allows) a strong cross-slope heat transport.

But the ASC is set by thermal wind balance. So you could also imagine a situation where the isopycnals at the slope move upwards (say due to wind), which allows intrusions onto the shelf along the now-connected isopycnal. The ASC strength also changes, because the density structure has changed, but this is a consequence not a driver of the onshore heat transport.

Also we should look into jet dynamics and topographic interactions.

Any ideas how we can distinguish if the ASC is a driver or a response? Maybe lag correlations? Though maybe they will change at similar times.

Motivated by key plots from OMO presentation.

Originally posted by @adele-morrison in #33 (comment)

Attaching my slides from the OMO meeting here. Morrison_ASC_heat_transport.pdf

Hi folks,

How do we feel about presenting this work at the Canberra July workshop? I don't have much other work to present at the moment, so would be happy to present if others are happy with that?

Here's a suggested title and abstract. I'm not quite sure about the title (because see the last sentence - this is not actually what we're investigating here. But it is a bit catchier than "The relationship between the Antarctic Slope Current and ocean heat transport towards Antarctica").

Any suggested changes?

Does the Antarctic Slope Current control ocean heat transport towards Antarctica?

Increased ocean heat transport towards Antarctica directly drives melting of ice shelves, leading to sea level rise and reduced dense water formation. A common dynamical assumption is that poleward heat transport across the Antarctic continental slope is controlled by the strength of the Antarctic Slope Current (ASC), which is thought to act as a barrier to heat transport. However, the relationship between poleward heat transport and the ASC has not been examined in detail. Here, using a global, eddy-rich ocean – sea ice simulation, we find that the strength of the relationship varies significantly around Antarctica, with local correlations between ASC speed and cross-slope heat transport ranging from r2 < 0.1 to r2 > 0.8. In the temporal domain, the relationship between the ASC and heat transport is strongest on seasonal and interannual timescales, with surprisingly low correlations at high frequency, eddy timescales. Our results suggest that the relationship between ASC strength and poleward heat transport may not be as simple as is often assumed. Even for regions and timescales with a strong relationship, it remains an open question whether a strong ASC is dynamically limiting the heat transport, or whether both quantities are responding concurrently to external forcing.

I've been working on a) replicating the analysis from Huneke et al., 2022 to identify ASC regimes using an unsupervised clustering algorithm (Gaussian Mixture Modelling) and b) seeing if we can track changes to the GMM-based clusters on seasonal and inter annual time scales.

I fed the time-mean top-300m velocity profile minus time-mean bottom-700m velocity profile along the 1000-m isobath into the GMM, plus the sign of the along-slope velocity (to identify the reverse-ASC regime) at the surface. This ends up being OK at objectively identifying the regimes, aligning well with the Huneke et al., 2022 work:

Now, I will work on seeing if this analysis is replicable over seasonal time scales, and what information this can give us.

I have been using xhistogram to bin the ASC speed along the 1 km isobath into density levels according to this notebook. However, I noticed that after rebbinning the maximums and minimums (along vertical) of the speed increase.:

Since we want the average for the rebining, I calculated the new ASC speed as xhist(weight=speed*Area)/xhist(Area), as suggested by Xhistogram . I tried using volume instead of Area for weighting, and the same intensification happens...... It seems weird to me, as I think we could have different means in the ASC speed between $\sigma$ and $z$ (for non-weighted averages), but the maximums should be the same... Unless I am missing something......

Any ideas @adele-morrison ?

Here's an issue we can discuss figure formatting etc for the paper. There is a list of the figures here.