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Re: [ferret_users] integration of flux vector along the coastline to compute the transport
- To: Ryo Furue <furue@xxxxxxxxxx>
- Subject: Re: [ferret_users] integration of flux vector along the coastline to compute the transport
- From: William Kessler <william.s.kessler@xxxxxxxx>
- Date: Mon, 17 Dec 2018 05:50:36 -0800
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- Cc: "William S. Kessler" <william.s.kessler@xxxxxxxx>, saurabh rathore <rohitsrb2020@xxxxxxxxx>, Ferret <ferret_users@xxxxxxxx>
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> On Dec 16, 2018, at 11:25 PM, Ryo Furue <furue@xxxxxxxxxx> wrote:
>
> Hi Saurabh and Ferret users,
>
> On Mon, Dec 17, 2018 at 3:31 PM saurabh rathore <rohitsrb2020@xxxxxxxxx> wrote:
> Here is the thing that I am looking for. I want to plot the cumulative sum of the flux let's say starting from location of Melbourne covering all around Australia and ending at Melbourne.
>
> So it will give me line plot which show where (lat,lon) the flux is increasing or decreasing.
>
> If I understand correctly, that's exactly what I did in my paper:
>
> https://doi.org/10.1175/JPO-D-16-0170.1
>
> The basic principle is "easy": Let our "coast line" exactly follow the outline of the gridboxes that form Australia. In this case, the "cross-shore direction" is either zonal or meridional exactly. Therefore, the cumulative sum you want is the running sum of u Δx or v Δy, depending on the orientation of the local "coastline".
>
> Unfortunately, implementing this is complicated in my experience.
Yes, complicated, especially where the coast has indentations. And you must pay careful attention to the grid structure of u,v and T (or whatever quantity is being advected). Is it a B or C grid? The method will be different, and the answer could be very systematically different in a long integral.
Why do you need a line plot and specific locations of the flux? If you only want the total integrated cross-shore transport then the divergence theorem is a better solution and not subject to these complications. (Though it will also require decisions about how to take the divergence derivatives at the edges ... then the difficulty will be at peninsulas, not indentations). The two methods would be a useful check on each other; the result will not be identical, and the difference would be a measure of uncertainty.
Billy
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