Gentlemen,
The FACTS we got from the ACARS messages clearly point to one possible cause: Unreliable Airspeed Indication/ADR check procedure. This is one of the most difficult failures you can have in an A330/A340 since you loose ALL air data. No speed or altitude info, not even on the stand-by system until you recover the 'right' ADR if any. The checklist asks to switch off the faulty ADR if known.
Anyway, the procedure is to fly pitch/power. Then troubleshooting can be done by using e.g. GPS speed against predicted wind (the wind on the ND is wrong), GPS altitude, etc... This is extremely difficult to accomplish, so I imagine barely impossible in the reported heavy turbulence at high altitudes with changing winds because of TS's.
Rests the question how such a failure can occur: given the flight conditions: either the pitots froze up because of severe icing, or the radome disintegrated due to hail impact (remember the pictures of that easyJet B737 in GVA that entered a CB? And that was just a 'European' CB, not a tropical one.)
How is it possible that this aircraft with experienced pilots fly through a dangerous CB? (This is pure speculation from my side!!)
First of all, not all CB's go with associated lightning, so if the radar is not on, they might be quite hard to spot on a dark night. (At the time of the events, the moon at present position was setting in the west while the aircraft was flying north east bound. No moonlight must be considered)
Why might the radar not be on? Ask ANY A330/A340 pilot and they will all agree that at some stage in their career they were caught out with the previous crew dimming the radar. For the non-Airbus guys: the ND 'control' knob is twofold. The inner knob is the dim for the ND display itself, while the outer ring is the dim function for the WX radar/Terrain information. If the outer knob is turned in the dim position, no WX/Terrain information will be visible on the ND. The WX radar with the tilt info (not the actual WX info) will be in bright since that is ND info, not WX info.
Looking at the SIGMET chart for that day, it seems that the route was basically clear of weather until they reached that wall of CB's around the ITCZ. So maybe they didn't have a chance to pick up that the radar was dimmed until it was too late.
Again, the last part is complete speculation and I would like to have input on my thoughts by experiences Airbus pilots.
MR8
Note: I do not believe the crew lost pressurization. Unreliable Airspeed Indication/ADR Check Procedure Checklist asks to switch off 2 ADR's if the affected ADR's can not be identified or if all ADR's are affected. If the ADR's that feed the active Cabin Pressure Controller are switched off, this will give a 'soft' warning (Amber Caution with no 'ding' - sorry, forgot the actual name of such a warning). Hence in my opinion it is just an ADVISORY on the ACARS and not a failure. Can someone please confirm the ACARS message regarding ATA21?