Cross-slope heat transport using different methods to extract an isobath

[wghuneke]

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.

[wghuneke]

The main difference between the two contour definitions is that "Adele's" definition is step-wise, while "Wilma's" definition allows for diagonal connections between grid cells (also used in the cross-contour transport COSIMA-recipe).

So far, we have the heat transport calculated on the step-wise contour. I now calculated the heat transport (1 year average) on the diagonal contour and get quite different results: (compare figures below with figures in e.g. issue #11 which has values more than one order of magnitude smaller)

unbinned:

binned:

→ The total heat transport towards Antarctica in the model is highly dependent on the contour used for calculating it (assuming no errors in the code).

@willaguiar is currently calculating the ASC velocity on the step-wise contour. Maybe that is the way to to forward so we can make cell-by-cell* correlations of heat transport and ASC time series.
*Acknowledging that the result is likely noisy and will require some smoothing.

[wghuneke]

I just realised that the values in the seasonal plot in issue #4 also has heat transport values (calculated on the step-wise contour) which are an order of magnitude larger = similar to what I show above. @willaguiar will look into this.

[willaguiar]

I just realised that the values in the seasonal plot in issue #4 also has heat transport values (calculated on the step-wise contour) which are an order of magnitude larger = similar to what I show above. @willaguiar will look into this.

ok, I went to the code and I realized that I forgot to factor out the binned transport. Basically, because we use a bin width (3 degrees long) larger than a bin spacing (0.25 degrees long) when we cumsum the binned heat transport along the contour we sum things twice due to overlapping bins. We correct that by scaling the final total binned heat transport back to the total value of the unbinned one (a factor of ~0.08 generally).
I checked the code of the issue 4 and noticed that I forgot to apply that factor on the binned transport. After applying the factor it seems that the values for the total heat transport go back to the O[100] TW. (Fig below, correcting it in the issue). Thanks for noticing Wilma!

[wghuneke]

Ok, (i) I found an error in my mistake, (ii) added the factor for the binned transport, and (iii) updated the code according to this issue. The new plot looks much more reasonable:

[wghuneke]

Update: We decided to not use this method to extract the isobath but instead go with the step-wise contour definition. The main argument is that the zonal convergence calculation might not be accurate. Also, we have already started to calculate heat transports using the step-wise contour.

[wghuneke]

Closing this issue now.