Is there some graduated scale applicable to existing 3D ground planes or circles?

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I'm sorry, which application is this in reference to?  In most modelling apps, you could simply scale the "ground" plane up to the point where it seems to touch the horizon from the perspective view, or your could use an environment dome, which contains the background image or sky image, and then scale the ground plane to intersect the environment dome, which would make it appear to extend to the horizon.  Some apps actually have an "infinite" plane, which would extend indefinitely in the render, even if it doesn't appear so in the viewport.  So, it would depend on the application as to how you could handle this.

Poser

Actually it may not matter which application as the ocean in reality doesn't have vertical boundaries except for such as cities and mountains.  The real world also creates a horizon somewhat below infinity to accommodate the curvature of the earth. 

If that's Poser, then why not just scale the sea plane on X and Z until it appears to meet the background?  Unlike the real world, you're working with a flat surface for your sea here, mate.  So scale it up, and then scale down the materials to compensate for the larger object size.  Otherwise, your materials will appear stretched out.

Scaling the sea plane extents the same resolution to a point where it doesn't to the naked eye outside.  I have been trying successive sea planes with increasing resolution but this process must be as if on a algorithmic scale which is beyond my digital competence. 

You can do the multiple plane thing, but I believe Poser 10 and above has subdivision features built in.  If you don't have a version that supports subdivision surfaces, then there's a Python script out there that can do this. So you would scale the sea object larger, then apply an increased amount of subdivisions to regain a balanced resolution, and then resize the textures or materials as well.

TBH you'de be better doing the sea in a 2d app. Poser is just adding shadow (mast,oars) which shouldn't be visible over waves.

Turning receive shadows off for the water, or doing shadows in a separate shadow pass, and then erasing them in a 2d app is also possible.  I think you're best bet for realism is to use a good water material shader for the sea, with some SSS and translucency. Don't forget raytrace reflections.  It will be a pig to render in Poser, but will look way more realistic.  I'm sure bagginsbill has a great ocean shader.

One of the things i have done with my ships at sea is to use a bump map to show bow waves. This requires a mix of the best lighting and texture techniques, and tricks 

. This is shown in my gallery.

My next test will be to put a water texture of a large area onto a sphere, render, and use the resulting image on a disc,  This may take some fiddling like something round but not a whole sphere.

One of the things i have done with my ships at sea is to use a bump map to show bow waves. This requires a mix of the best lighting and texture techniques, and tricks 

. This is shown in my gallery.

My next test will be to put a water texture of a large area onto a sphere, render, and use the resulting image on a disc,  This may take some fiddling like something round but not a whole sphere.

Why not try the free version of Terragen, that has the earths curvature built in and many other wonderful features.

Terragen and Vue produce spectacular images, and wish I could do it in Poser.  Poser is where the options available for ships with oars and oarsmen who move can be used is best.   Daz Studio may eventually force me to dump 80% of my work as nontransferable