information design - How to visualise two-dimensional scientific data-points in a chart... in grayscale?

I am not sure whether this is the correct site for this question. The model comes from Physics, the data comes from computational physics, the plot is made with LaTeX but my question is about the presentation and layout of it all.

You can click on all images to get a vector PDF.

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I have data points that depend on two parameters, so I have made a 3D plot with them:

http://chaos.stw-bonn.de/users/mu/uploads/2014-06-25/mesh.png

I think that this gives a good impression that the data falls off for small “a” and that there is a bump for moderate size “sigma”. However, you cannot really read any numbers off this. I need that, though.

So I put all the data into a two dimensional plot, encoding the “sigma” with a color. Since the data points overlap, I find it helpful to connect them with lines like so:

http://chaos.stw-bonn.de/users/mu/uploads/2014-06-25/a-E0-solid-dotted.pdf.png

To me, the above version is the most readable version of them all. The connecting lines between the points are not really justifiable from a scientific perspective, since I cannot assume that they describe the Physics there well. The only things that can have some meanings are the interpolated lines that I have dotted in the above version.

It would be more scientific to have it like this, without connecting line segments:

http://chaos.stw-bonn.de/users/mu/uploads/2014-06-25/a-E0-none-solid.pdf.png

Even with the color, it is harder to follow the points of each color. The first version shows me right away that the points drop down for small “a”. With the second one, it can be seen, but only if you look at it closely.

Maybe I can use dotted line to help the eye of the reader, but not implying anything, like so:

http://chaos.stw-bonn.de/users/mu/uploads/2014-06-25/a-E0-dotted-solid.png

Also, I would like to avoid using color. This will be printed a couple of times and color pages are tenfold in price compared to grayscale pages. I have tried to split up the data in the middle, such that they do not intersect any more. This is the second half of the data, the small “sigma” ones. I added the unscientific line segments and have the legend ordered from top to bottom:

http://chaos.stw-bonn.de/users/mu/uploads/2014-06-25/Abbildung-minus1-fein.pdf.png

I think this is readable, except for the connecting line segments. Splitting up the data in multiple plots makes each plot easier to read, but it is harder to compare the data.

Without the line segments, I need different markers for each data set to keep them apart. This yields cluttered plots right away, so I made the less important data sets a little lighter.

http://chaos.stw-bonn.de/users/mu/uploads/2014-06-25/Abbildung-minus1-grob.pdf.png

This has no line segments and does not use color, but I do not think that it is easy to see what is going on.

What could I do to get the data shown in a readable way?