Citationjet (C525/C526) - CJ I / II / III / IV
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 50; Flight Crew Total 2200; Flight Crew Type 200
Communication Breakdown; Situational Awareness
ATC Issue All Types; Deviation - Altitude Undershoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Human Factors; Procedure
Called Denver Center on remote station from the SNY airport.  Requested IFR clearance.  The clearance given was 'Cleared as Filed; maintain 5;000; squawk XYZA'.  I wrote the clearance down; and read the clearance back to the Denver Center controller.  There was no response on whether the readback was correct.  An initial altitude of 5;000 feet seemed low since the airport altitude is around 4;300 feet.  I called the controller back and there was no answer.  I called again; and broadcast to Denver Center that I was number one for departure; and the response from the Center controller was 'I know.  I hope you're not waiting on me for something.'  I asked if he assigned a heading on the Departure; and he said he gave me the clearance already.  I was a bit confused as to what this meant. I took off on Runway 31 at the Sidney; northeast of airport and climbed to 5;000 feet.  I called the Denver controller and reported airborne at 5;000 ft.  There was no answer on 118.475.  I tried several times to reach Denver Center.  I looked down at the radar altimeter; and it read 800 feet AGL.  I tried several more times to reach the center controller; with no response.  I tried alternate radios thinking the radio had a problem.  No answer.  I looked up an alternate center frequency and tried that frequency.  No answer.  I switched back to the initial frequency of 118.475 and repeatedly tried to reach the controller.  The radar altimeter was slowly closing 600 feet AGL.  Outside conditions were IMC with precipitation and freezing temperatures.  I manually broke the squelch on the number 1 radio; and tried calling desperately several times.At this point the ground proximity activated at 5;000 feet; and I quit trying to raise the Center Controller.  I climbed to 6;500 feet MSL to resolve the terrain conflict.  I tried the controller again; and with squelch broken; the controller responded that 'I can hear you; what's the problem?'  I responded that I was climbing from 5;000 feet due to a terrain proximity activation.  The response from the controller was 'I suggest you increase your rate of climb then'.  I was still confused; he gave me an initial altitude of 5;000 feet; and did not revise his clearance higher after I told him I was deviating from 5;000 feet due to a ground proximity activation.   I knew I needed to climb to get away from the ground and out of the icing situation; so I continued to climb to about 10;000 feet to remove the terrain threat.  I then tried to raise the controller again; at which point he asked for an IDENT reply; which I obliged.  He then cleared me to 15;000 feet.There was no further discussion regarding the incident; and I was starting to calm down as I climbed away from the ground.Looking back on it; could it be that the initial clearance was to ONE FIVE thousand; not FIVE thousand?  But there was no readback confirmation from the controller; and no subsequent help from the controller to either verify or correct the altitude clearance; or give me a new clearance to a higher altitude.  But I knew 5;000 feet wasn't sufficient terrain clearance so I started climbing regardless of the altitude clearance.Even after I told the controller there was a ground proximity activation; he never gave me a new altitude; or even repeated the new altitude.The rest of the flight was uneventful.
CE-525 Captain reported receiving a confusing clearance from DEN Center departing SNY that led to a GPWS terrain warning.