Date: 201306
Local time of day: 0601-1200
Location: ZMA.ARTCC, FL
Flight conditions: IMC
Weather elements / visibility: Rain; Turbulence; 6
Light: Daylight
Aircraft: PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Personal
Flight phase: Cruise
Airspace: Class E ZMA
ATC / advisory: Center ZMA
Reporter organization: Personal
Reporter function: Pilot Flying; Single Pilot
Reporter qualification: Flight Crew Instrument; Flight Crew Private
Human factors: Human-Machine Interface; Training / Qualification
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Contributing factors: Human Factors; Weather
Primary problem: Ambiguous

Narrative: I took off in the morning; on an IFR flight plan MYAM; Marsh Harbor; Bahamas.  After contacting Miami Center and a slight deviation for buildups; I was instructed to fly direct ZFP; Freeport VOR; and then fly BR70V direct MYAM.  After passing ZFP and turning toward MYAM on BR70V; we were advised to switch to another Miami Center Frequency; and around the same time observed a wall of towering cumulus clouds between us and our destination; stretching without apparent end to the north and to the south.  ATC was advising at least 3 other aircraft (2 IFR and one VFR) heading for the same airport; reporting locations of moderate to heavy precipitation.  I talked to the Controller as I was approximately 15-20 miles east of ZFP on BR70V and he advised either deviating north or to the south of the heavy precipitation that was at my 12 o'clock.  (I should note that our plane is equipped with ADS-B Out but after the immediate coastal area out of FPR was not painting any weather at all on the ADS-B at or east of ZFP; so I had no help from that equipment and thus was relying on visual observation and ATC guidance).  I told the Controller I would take the southerly route and he suggested a heading of 140. I turned to that heading and actually flew about 145 degrees as I could see the fringe of a towering cumulus ahead that I wanted to avoid.  The new heading was not going to avoid the towering cumulus clouds altogether but per ATC would avoid the heaviest precip.  I could hear the transmissions of the VFR aircraft on ATC and it appeared she was at approximately 3;000 FT or below; ahead of me by about 30 miles or so; and reported a reasonably clear view ahead.  Consequently; as it was clear I was flying into rapidly building areas of precip and towering cumulus; I asked the Controller for lower; hoping to get down under the clouds; but he would not or could not give me a lower altitude.  As I approached the building clouds and began to enter them; we experienced some light turbulence and updrafts that began to lift the plane a few hundred feet.  As I had always been trained to do; I concentrated on holding wings level and did not make any aggressive attempt to hold altitude; though I knew I was climbing above my assigned altitude.  I called ATC and asked for another 500 FT which would get me to approximately 8;000 FT where I hoped to level off.  He did not immediately give me that clearance.  In a few more seconds; the Controller asked for my altitude; which I reported then as of 7;400 FT and I again asked for an additional 500 FT to get to 8;000 FT.  He admonished me for not telling him about the altitude change (which I had already asked for) but then shortly cleared me to climb to 9;000 FT.  I was out of the clouds and precip then and I immediately began the climb.  He also told me 'when able direct Marsh Harbour' but we were still trying to avoid the ever-growing towering cumulus and obvious areas of precipitation.  After flying a bit at 9;000 FT I again asked for lower; eventually getting cleared to 7;000 and then to 5;000 FT; at which point we were in solid IMC and some rain; and still approximately 25 miles or so from Marsh Harbour. Radio signals from MIA Center were becoming weaker but he cleared me down to 3;000 FT.  I had disengaged the autopilot at that time and while attempting to reprogram the GPS to direct MYAM had an unintended course deviation to the right of approximately 30 degrees.  I turned back on course as soon as I realized that and then descended; again through solid IMC and heavy rain.  I could hear the Controller calling asking me to call to report cancelling IFR on his frequency but at that point I could not do so.  At approximately 3;000 FT I broke out into VMC conditions and continued to descend to approximately 2;300 FT at which point I could see the airport at my 12 o'clock and approx 6 miles.  I called to cancel IFR but the Controller could not hear me.  A commercial aircraft relayed my cancellation; and then came back with ATC's direction approving the cancellation and to squawk VFR; which I did.  I then proceeded to land at MYAM without further incident.

Callback: The reporter states that on line checking of the weather in the Bahama's during preflight did not show any weather; nor did a post flight check.



Synopsis: PA28 pilot reports encountering thunderstorms during an IFR flight to MYAM and deviating with ATC assistance to avoid the heaviest weather.  On board ADS-B weather was not displaying any weather east of MYGF.