You could run an analysis on the remaining residue to determine the amount of inerts that are present. Then analyze a similar piece of unburned wood for the amount of inerts present.
 
Based on these two pieces of information, one could determine the amount wood that was present before it got burned.
 
This formula could be applied to wood that has been treated for outdoor exposure, since that would tend to preserve the wood.

Otherwise, exposing the wood to elements would probably result in loss that would be hard to predict.