Before revision:  Due to re-projection, the OpInf is more costly than the POG-G, nevertheless, speed-up factors of order two are achieved for both ROMs. Numerical results demonstrate that the conserved quantities of the RTSWE are preserved for both ROMs over time and the long-term stability of the reduced solutions is achieved .
After revision:  Due to re-projection, the OpInf is more costly than the POG-G, nevertheless, speed-up factors of order two are achieved for both ROMs. Numerical results demonstrate that the conserved quantities of the RTSWE by both ROMs enables that the models fit better to data and stable solutions are obtained in long-term stability of the reduced solutions is achieved .