Hi jmbower,
I'd like to respectfully disagree with Wheatfield... DSLR's might not be as effective as film for 3-4 hour exposures, but that's not what we're discussing here...
I've done tons of 30s exposures with the K100, K10, and K20D.
Some with no "noise" to speak of.. I've also heard of people on the forum here doing 30 minute!!! exposures on Pentax DSLRs with nearly noise-free images...
To my eyes, the lines you are seeing are from an under-exposed image being automatically processed for contrast. The post-process (yes, even if it's in-camera JPEG) can expose this kind of noise.
Yes, long exposures can increase noise. But even short exposures (like 30s or 1/30s) will exhibit noise if their brightness is increased by post processing software.
I'm just guessing.... Are you using Picasa? I think Picasa is brilliant software, but it's automatic exposure adjustments will do this to a nearly black frame, or anything that's very under-exposed.
Are you shooting RAW or JPEG? If RAW, what did you do to process this shot?
-Chris