Nakamura (1996, JAS) propsed an effective diffusivity using tracer contour coordinate. How to compute this diffusivity using gridded tracer values without contour information? Is it necessary to incorporate the plot software such as Matlab to get contour information first? It seems that different interpolation schemes produce different contours.
I've not read the cited paper but it's something I'm interested in, so if you can upload a copy to RG then I could have a look at the paper and might have some advice. Also, have you tried just googling the original citation? I did that and found lots of papers that might be of interest to you.
PS. if you have gridded tracer information, there are really only two popular contouring algorithms and they tend to agree except at rare problematic points.
Oh, I now see Nakamura (1996, JAS) at https://www.researchgate.net/publication/249608497_Two-Dimensional_Mixing_Edge_Formation_and_Permeability_Diagnosed_in_an_Area_Coordinate and I see that the method is based on areas enclosed within contours. So that is more robust than contour shape.
You didn't mention your application but if it's including coastlines you will have to be clever about subtracting the land area.
For a quick answer you could just use an "if" statement to find the number of grid points with tracer value exceeding a certain amount. That's the A(q,t) referred to in equation 2.2a of the paper. If your grid is coarse, this will be only a rough estimate. But you could just do a bilinear interpolation to downscale to a finer grid. Or you could compute the contour, using a variety of software packages. In other words, you're going to have to do some computing. I recommend using the "contourLines" function within the (free and open-source) R language. Once you've got contours you'll need to write a bit of code to do the integration. Things will be a bit tricky if you have a large geographic extent because of the longitude convergence problem.
Article Two-Dimensional Mixing, Edge Formation, and Permeability Dia...
I haven't read Nakamura's paper, but looking at its title page, I have the feeling that his effective diffusivity is equivalent to Winters and D'Asaro's (1996, J. Fluid Mech.), which isn't difficult to compute from gridded data (I once did it). Griffies et al. (2000, Monthly Weather Review) shows more details of how to compute it.
sites that might be useful on the topic :
https://www.iap-kborn.de/1/research/department-theory-and-modelling/research-topics/transport-and-chemistry/effective-diffusivity-of-gravity-waves/
and, of course, Griffies' publications on mixing + ..see:
http://www.gfdl.noaa.gov/bibliography/results.php?author=1047
once you have a closed 'contour' (maybe via Matlab.. cs=contourc(x,y,map,[0 0]); the script polyarea(xedge, yedge) gives you the area, BUT be aware, for large surfaces on the sphere,as Dan points, .... the longitude convergence problem....
The tracer flux method by Griffies works great indeed and it will give you the magnitude of the effective (=physical+numerical) mixing but you will lose any information on where it occurs... You can check the work by Mehmet Ilıcak (http://folk.uib.no/mil021/), the work by Florian Lemarié (http://www-ljk.imag.fr/membres/Florian.Lemarie/) which developed on the work by Winters and D'Asaro and Griffies and allow to know the effective diffusivity (mixing) in a globally and local way. Best.
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