bathymetry induced extreme values about divand.jl

[jmbeckers]

Le 2018-10-11 à 9:28 PM, JianghuiDu a écrit :

I'm doing analysis on a 2d lat-depth section. The data is relatively sparse and when adding bottom bathymetry divand introduced some extreme values in some convex regions at the bottom of seafloor where there is actually no data. Smoothing the bathymetry helped but not completed remove these extremes. Removing bathymetry as use a flat bottom doesn't do this. Is there a way to control how much influence bathymetry has on the analysis? — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#20>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ASzFlozkHeblfc8ushYMCkDoapb6Hgqdks5uj5v6gaJpZM4XYN4s>.

Difficult to answer in general, it will depend on your vertical correlation length and the noise/signal ratio (I suspect the latter to be very low?)

…

--

[ctroupin]

@Alexander-Barth : might be similar to an issue mentioned (by mail) by Orjan.
Let's keep it in mind for the present issue.

[jmbeckers]

Was'nt that solved with the optional arguments
coeff_laplacian::Vector{Float64} = ones(ndims(mask)),
coeff_derivative2::Vector{Float64} = zeros(ndims(mask))
in divandrun ? Needs to be documented in function description and example ?

[jmbeckers]

Normally solved since version 2.3.1 with optional parameter coeff_derivative2 = [0., 0., 0.0000001]

[JianghuiDu]

Is there a guideline on what's the best value to use? The docs say 1e-8, but it makes the results too smooth. If it's too low then it doesn't work. The RMS always increases with this number so there's the conflict between fitting the data and removing this anomaly. What would be the "objective" choice?

[jmbeckers]

Can you provide some more details on the situation ? Normally the parameter should only have an effect in particular situations for isolated points in a topology like

1 1 1 1 1 1 1 1 1
0 0 0 1 0 0 0 0 0 <- the sea point 1 in land 0
0 0 0 0 0 0 0 0 0

[JianghuiDu]

See the extreme values in the circle. The interpolated values is very different from the surrounding data..
This is the original

This is with [1e-8,1e-8] for both lon and lat.

This is 1e-6, too smooth.

So this parameter does not only affect those points close to topography but also everywhere else, right?

[jmbeckers]

yes it acts everywhere but normally with low values its effect should be completely overshadowed by the normal regularity constraint away from boundaries controlled by the length scales. So what is the correlation length you selected and the grid spacing as well as the epsilon2 parameter ?

[JianghuiDu]

correlation length: 1e6 m
grid spacing: 4 deg by 4 deg
epsilon: 0.001, should probably be bigger.

I just wonder what criteria should be used to choose this parameter.

[jmbeckers]

epsilon: 0.001, should probably be bigger.

Yes I think that is the culprit. You are trying to pass almost exactly a curve across a noisy set of data some of which almost at the same location; that certainly will create you a lot of artefacts.

Also the grid spacing of 4x4 degrees only marginally resolves the correlation length of 1000km which can cause other problems.

I would not try to fix that with the parameter coeff_derivative2 which is only there to add a very weak additional regularity constraint on cases as depicted in #20 (comment)

[JianghuiDu]

OK. Thanks for the explanation.