Suppose whole global atmosphere divided into cells of size 1 mile 1 mile 1 mile to a height of 10 miles (10 cells high) - about 5 108 cells.
Suppose each calculation requires 200 floating point operations. In one time step, 1011 floating point operations necessary.
To forecast the weather over 7 days using 1-minute intervals, a computer operating at 1Gflops (109 floating point operations/s) takes 106 seconds or over 10 days.
To perform calculation in 5 minutes requires computer operating at 3.4 Tflops (3.4 1012 floating point operations/sec)
Needs to be 34,000 faster.