Two earlier posts provide some data that I haven't yet seen put together. The timining is interesting.
First, this from The Aviation Herald:
New information provided by sources within Air France suggests, that the ACARS messages of system failures started to arrive at 02:10Z indicating, that the autopilot had disengaged and the fly by wire system had changed to alternate law. Between 02:11Z and 02:13Z a flurry of messages regarding ADIRU and ISIS faults arrived, at 02:13Z PRIM 1 and SEC 1 faults were indicated, at 02:14Z the last message received was an advisory regarding cabin vertical speed. That sequence of messages could not be independently verified.
And then this from a weather analysis:
It appears AF447 crossed through three key thunderstorm clusters: a small one around 0151Z, a new rapidly growing one at about 0159Z, and finally a large multicell convective system (MCS) around 0205-0216Z. Temperature trends suggested that the entire system was at peak intensity, developing rapidly around 2300-0100Z and finally dissipating around dawn. From a turbulence perspective, these cold spots would be the areas of highest concern as they signal the location of an active updraft producing new cloud material in the upper troposphere.
If these are correct, it puts the ACARS messages occurring during the most severe convective system.