fixes for 'lat=0' and 0 time series issues

[apatlpo]

No description provided.

[ocefpaf]

Don't compute np.trace twice and we can do the Duu division in place:

trace = np.trace(Duu)
if trace != 0. :
    Duu /= trace

[ocefpaf]

LGTM

[ocefpaf]

xref.: #60 and #61

[ocefpaf]

There is a trailing space after Duu.

[ocefpaf]

There is a whitespace before :.

[ocefpaf]

Any reason to not use the compact in place Duu /= trace?

[ocefpaf]

I'll leave this here so @efiring and @wesleybowman can take a second look before merging.

Thanks @apatlpo for the PR!

[efiring]

Two real problems have been identified, but based on a quick look, I'm not sure the solutions are good ones.

• For the zero-data situation, the solution might be OK; what is its net result? Does it leave zero-confidence limits, as it should? Are all outputs as expected in this pathological zero-data case?
• For the zero-latitude situation, the original low-lat code doesn't make sense to me, so I suspect a more fundamental fix may be in order. How can it be correct to pin low lats to +-5? Especially when a blow-up at lat==0 suggests sensitivity to low latitudes?

An oddity related to the latter point is that the code is using conditional statements involving only values in constants, which are of course constant, so no conditionals should be needed.

[efiring]

I think one of my potential objections is invalid, but the main one--the odd behavior within 5 degrees of the equator--still needs attention. I see that the behavior is inherited from t_tide, which includes some explanatory comments but still doesn't make sense to me. It implies a discontinuity at the equator.

[apatlpo]

Here are the explanatory comments:

  if nargin==4, % If we have a latitude, get nodal corrections.

    % Apparently the second-order terms in the tidal potential go to zero
    % at the equator, but the third-order terms do not. Hence when trying
    % to infer the third-order terms from the second-order terms, the 
    % nodal correction factors blow up. In order to prevent this, it is 
    % assumed that the equatorial forcing is due to second-order forcing 
    % OFF the equator, from about the 5 degree location. Latitudes are 
    % hence (somewhat arbitrarily) forced to be no closer than 5 deg to 
    % the equator, as per note in Foreman.

    if isfinite(lat) & (abs(lat)<5); lat=sign(lat).*5; end

    slat=sin(pi.*lat./180);
    % Satellite amplitude ratio adjustment for latitude. 

Maybe there is more in Foreman's code

It may be more simple to ask also experts.
I am attending a meeting next week and Richard Ray should be there, i'll ask him about this.

[apatlpo]

After a brief discussion and a lengthier email, Richard Ray's opinion is that ''bringing latitude dependence in the calculation of nodal modulations, as well as in the inference of minor tides is not a good idea''.

I asked him for a good reference in order to know what we are supposed to do instead, here is his reply:

Section 4.2.2 of the Pugh-Woodworth 2014 sea level book is ok.
(plus 4.2.3 on shallow water tides).

I've always liked Doodson & Warburg (1941) - Admiralty Manual of Tides,
which a few years ago was still in print.

[efiring]

@apatlpo Thank you, I hope he can provide a reference we can work with.

[efiring]

1. Is it clear that the problem of zero data occurs only in the non-white-noise case, so this is the ideal place to intercept it? Regardless, I think it might be best to just raise an exception when obviously useless data is provided. A sanity check could be done early on, as an alternative to checking the trace of Duu.
2. There must be a better way to handle the singularity at lat=0. We just have to find it. It's possible a horrible ad-hoc fix something like the one here will be necessary temporarily. Rather than having a jump at the equator, I suspect it would make more sense to have a linear transition in rr values from 5N to 5S. But I don't understand the math and physics behind rr right now, so I don't know how to handle it.

[efiring]

This is not the same as the original even in the normal case. The order of the two lines above would need to be swapped.

[efiring]

In a week or two I expect to be able to have a look at the Pugh-Woodworth book recommended by Richard Ray; I hope it will have a clear explanation of a replacement for the problematic calculation we have now. @DanCodigaMWRA, do you still work with tides? If so, do you have some ideas about this? Or know someone with the expertise and willingness to help out?

[apatlpo]

I don't have the time unfortunately to dive into this, sorry about this.

I would like to point out the pangeo-pytide library though.
A solution to the problem at hand may have been found there.

[DanCodiga]

In a week or two I expect to be able to have a look at the Pugh-Woodworth book recommended by Richard Ray; I hope it will have a clear explanation of a replacement for the problematic calculation we have now. @DanCodigaMWRA, do you still work with tides? If so, do you have some ideas about this? Or know someone with the expertise and willingness to help out?

@efiring thanks for asking. I do still work on tides a bit. Mostly just helping folks who are using the Matlab UTide functions.

As for the specific topic here, latitudes b/w -5 and +5, I don't have much insight and would have to dig around to try to come up to speed. The quoted documentation from t-tide shown above seems to attribute it to Foreman. He was helpful to me back when I was putting UTide together, would be worth getting his input if possible.

p.s. When working on tides I am @DanCodiga (not @DanCodigaMWRA).

p.s.s. I do aspire to revamp UTide as it has been almost 10 years now. I will probably start with a survey of all users to learn what would be the most helpful next step, i.e. update the Matlab version or the python version (or build an R version?); help you folks improve the python version here; add new features; add better tutorial/documentation; etc. (If it's python-focused I would see it as a chance for me to finally get up to speed with using github too...)