Add loading efficiency to xsection plot

[MattBrst]

I would like to add the loading efficiency to the cross section plots.

Example from the benchmark with the following line of code:

ml_leff[0].plots.xsection(params=True, names=False, labels=False, sep="\n")

So basically non-zero loading efficiencies for aquifers are plotted.

[dbrakenhoff]

Good addition, but could you modify it to use the symbol $\beta$, similar to Mark's paper? Looks a bit cleaner than load eff written out, though it is a bit more obscure as to what that means.

We could consider a small list of symbols somewhere to help users understand what's what. Or at least have the loading_efficiency notebook mention $\beta$.

[mbakker7]

And to be one step ahead in the process, the loading efficiency of the leaky layer is on its way. So can we include that right away as well?

[mbakker7]

In the mathematical formulation, we use \beta for the loading efficiency. In the code it is called leffaq and leffll. I don't think that betaaq and betall is better (definitely less readable). But I think the $\beta$ symbol in the xsection plots is better, since the other parameters are also symbols, like $k_h$ and $S_s$.
Once #74 has been merged, we can also add $\beta$ to the leaky layers in this PR.

[MattBrst]

@dbrakenhoff:

• I modified the PR to use the β symbol for both aquifers and leaky layers. This should work even when leffll is not yet defined in the model.
• I had to add the labeling code twice (once in plots.py for the normal models and once in inhom1d.py for the 1D models).

@mbakker7:

• I had to make some changes in aquifer_parameters.py for leffaq, and would guess you will have to do the same for the leffll.

Currently my plot from the benchmark River1D becomes:

And for an 'normal' model with the code below:

import timflow.transient as tft

ml = tft.ModelMaq(
    kaq=50,
    z=[7, 5, 2, 1, 0],
    c=100,
    leffaq=[0.3, 0.1],
    leffll=0.7,
    topboundary="semi",
    tmin=0.1,
    tmax=100,
)

ml.plots.xsection(params=True)

[mbakker7]

Pictures look nice! But I think it should work w/o any changes to aquifer_parameters, I would think. Let's first merge #74, which is almost done (working on some benchmark notebooks) and then see what needs to be done.

[mbakker7]

When Sll=0, Timflow substitutes Sll=1e-20 (as it cannot deal with exactly zero). Maybe this can be done more elegant in the code. But that is what it is for now. In the xsection plot, can you check if Sll=1e-20 and print 0 instead?

[mbakker7]

#74 has been merged. This PR can now be compared to dev. And the suggestion about printing Sll=0 (see above) can be implemented. Also, the changes in aquifer_parameters.py should be reconsidered. I wouldn't be surprised if they are not needed anymore.

[dbrakenhoff]

Ok I took the liberty of updating your PR @MattBrst. Sll now shown as 0.0 if timflow uses default 1E-20.

Maybe one final thought is necessary on the leffaq/leffll parsing in param_maq for the confined branch? I guess we should just force leffaq and leffll to zeros with the correct dimensions for this case? That way plotting continues to work (the correct layer is selected), but never plotted because values are 0.0.

[MattBrst]

@dbrakenhoff: Thanks for updating the work!

Are you sure that we do not need loading efficiency for confined aquifers? In the paper of Mark I see also for the confined case differences between beta=0 and beta=1.

[dbrakenhoff]

Isn't it that the river section is always semi-confined and has loading efficiency but the section next to it can have different top boundaries?

[MattBrst]

In the paper, loading efficiencies are only shown below the river section and those are semi-confined. So I guess you are right.

[mbakker7]

Just to confirm, the loading efficiency only has an effect with a semi-confined top (otherwise the load on the aquifer system cannot increase - well, if a trains rides by, but we don't have a train element yet). To be honest, I am not sure what happens when a value is specified for the case that the top is not semi-confined. It shouldn't do anything, but has anybody tried that? I think it would be best not to show the loading efficiency when the topboundary is not semi-confined.

[mbakker7]

I just checked and the loading efficiency is not shown in xsection plots when the topboundary is not semi. Nice.
I also updated the doc strings in the xsection models to make clear that loading efficiency is only used when the topboundary is semi and hstar varies with time.

[mbakker7]

Ready to go. Nice job.