Parden me, are you saying that the electromagnetic waves go straight in the atmosphere, until they hit the dome? Let me put this into better perspective. You can detect how far away that a storm is with radar by measuring the times at which the light returns to the radar tower. If a storm is 20 miles away, then the radar will receive the light that bounced off the particles in the storm would take the amount of time for light to travel 40 miles. If they had bounced off the dome, then bounced off the storm farther away, then it would take much longer for the microwaves (that's the kind of light that is used) to return the tower, and the storms on the radar image would be grossly misplaced. Also, the beam becomes more diluted (the energy spreads out) over large distances, and by the time it reached the dome then got back, it would no longer be useful data.
Also, let me show how the radar beam would look on a flat plane:
I hope this helps.
HHunter, in your previous drawing you showed the radar cone bending downwards. Now, you are showing it bending upwards. This makes it a bit hard to answer your question. Could you please clarify?
The second image is showing a flat surface, and takes into account curvature of the earth and refraction. In most cases, the curvature of the earth bends more than refraction bends the light, so if viewed on a flat plane, it would appear to bend up. In the first drawing, curvature of the earth is included, and so is refraction. However, you can see that over distance is gets farther away from the ground. If you put it into a flat perspective, it would appear to bend upwards. However, different atmospheric conditions can make is so that the refraction bends light more than the curvature bends, which is when it hits the ground. The problem is, if curvature isn't taken into account, the light will bend into the ground due to refraction, as demonstrated in the second drawing of the image.
Basically, the new image (the nice looking one) is what it would look like from a flat perspective, when atmospheric conditions are normal. I apologize for the confusion, I hope this clears it up a bit.