If Superman existed, would he be detectable by radar? If the answer is yes, would he be quickly accompanied by air force jets, or would he be dismissed as an unusually large bird? Lets assume Superman is physically the same as the average human.
Sounds like a question for Sheldon, Leonard, Raj, and Howard.
The average human can’t fly, so this is probably a bad assumption. Anyway, assuming Superman can move quickly enough but has no anti-radar powers, he might occasionally be picked up by radar, but it’s unlikely that he’d show up as anything more than a blip.
There’s nothing about Superman that makes him inherently stealthy, so he’d show up just as well as a (very) large bird or a man-sized flock of smaller birds. If he can get up to aircraft speeds, the ground operator would notice that he was moving much faster than a bird and tag him as some sort of aircraft in the track list. With a low radar cross section and a high velocity, a military radar operator might assume that he’s a stealth aircraft of military origin and that could have repercussions… but he’s Superman. Even if they send up interceptors, what are the pilots going to do, shoot a missile at him?
NORAD tracks Santa pretty successfully. Superman is quite a few sizes smaller than the carriage, but still… they can track missiles with directional radars, can’t they?
I wonder if Superman can adjust the frequency of his eye-beams to act as a radar countermeasure.
Non-metallic objects don’t reflect radar well. I doubt that he’d be picked up by your typical search radar except at very close range.
Veritas by ShayneT is an excellent fanfic novel that attempts to answer the OP’s question and many more about how the Real World™ would deal with the appearance of the fictional Superman in our midst.
ShayneT postulates that at least military radar would notice him, and the jets would be scrambled shortly thereafter. 
*** Ponder
On the other hand, Superman reflects bullets, so any comparison to normal meat puppets is suspect.
Define typical search radar? Most airport radars do not get skin paints, they just look for transponders. But in a general sense, radar is certainly able to detect things other than metal; radar altimeters reflect from ground features/water, weather radars look very closely at clouds.
A radar on an E-3 Sentry will detect birds (stealth aircraft supposedly have a radar signature about the same as a large bird). A person-sized meatbag could certainly be picked up and noticed. The Aegis system also has an incredibly powerful radar that would be more than capable of picking up a human sized radar return.
The radar on a luxury yacht I was on could pick up swimmers in the water around it.
Wouldn’t the USAF only be alarmed the first few times? Let’s face it, man sized object traveling at Mach 8 towards trouble could only be The Man of Steel. Speaking of which, steel has a large radar cross section. As does Iron Man. I recall that in the recent Iron Man movie that he was picked up on radar. But Iron Man is Marvel and Supes is DC.
I imagine that in any world where Superman exists, a certain segment of the military would be continually alarmed by the mere fact of Superman’s existence. Yeah, sure, he’s been pretty good, so far. But if he goes bad, what are we going to do about it then? We have contingency plans against the possibility of the UK nuking us or Canada invading; I have to imagine that someone (other than just Batman) would be making contingency plans against Supes, too.
Mr. President, we must not allow a kryptonite gap! …
Ya’ll need to read Watchmen to really learn how a superpowered being gets (over)integrated into military planning.
He’s the Man of Steel, isn’t he? Sure he’d show up, and with a pretty large RCS too.
I do not think this is correct.
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I do believe that civilian control towers generally track transponders, as what they’re looking at wants to be seen. They have the capability to track off of skin paints, but that massively clutters up the screens, what with birds, balloons, superheros, and light aircraft cluttering up the picture.
That’s part of the reason air traffic control had such a hard time tracking planes on 9/11. After they switched off their transponders, they had to go to skin paints (with ensuing clutter) to track them and couldn’t isolate them till after the fact.
I took him to mean they don’t have the capability. If I’m mistaken about that, well then, retracted.
Our airborne search radar picks up trees, ice boxes, and other bits and pieces in calm water. I believe though that the paint primarily comes from the curved water/object boundary on the opposite side of the object. Our radar will not pick up flocks of flying birds, but then it is designed to find boats not birds.
FAA radar allows for several levels of filtering. Often they are only looking at transponder returns, and as others have mentioned, primary returns (AKA skin paints) are not displayed. Even when primary returns are selected, anything moving less than 100 mph is typically filtered out, so as to avoid ground returns, birds, etc.
In some cases, transponders set to code 1200 (VFR) will be filtered out. These are aircraft not under air traffic’s control.
However, when I am flying my sailplane in/near one of ABQ’s traffic corridors, I will often monitor the tower frequency, and it is fairly common for them to “call traffic” for transport pilots based on primary returns. The fact that ABQ shares runways and ATC with Kirtland AFB may be a factor in this…not sure how military aircraft are equipped with regards to transponders.
I’m told that F-117 pilots can tell the rough from the fairways if they have a golfcourse on thier radar.