This data is used in the article 
OPTIMIZATION-BASED MODAL DECOMPOSITION FOR SYSTEMS WITH MULTIPLE TRANSPORTS 
by 
Julius Reiss 
in section 8, the practical example. It is based on the data assimialtion of a detonative combustion chamber described 
in  
Gray, J.; Lemke, M.; Reiss, J.; Paschereit, C.; Sesterhenn, J.; Moeck, J. 
A compact shock-focusing geometry for detonation initiation: Experiments and adjoint-based variational data assimilation, Combustion and Flame,
2017, 183, 144 - 156, https://doi.org/10.1016/j.combustflame.2017.03.014

The data and the shifts to compensate the transports is loaded in the Matlab script readData.m where the data structure is also explained. 
The additional file Qfull.mat contains the original data with the resolution used in the simulation. It is down-scaled by taking every third point in space and every hundredth point in time for the shifted POD.
It reduces the data size, but produces in the fronts and peaks non-smooth data.