I am conducting an analysis of an CFD code for simulating waves in a wave tank.
I am comparing the analytical solution (dashed) of the free surface with the simulated surface elevation (blue) in order to quantify the error I get from different parameter settings.
Up to this point I used the NRMSE (Normalized root mean squared error) to calculate a mean error (one value) for each parameter configuration. In the following plot I have an exemplary plot of the free surface from one of those parameter configs and its analytical solution.
Now the problem is that I can observe a slight variance in the amplitudes of the single periods, so I want to decompose the total error into a variance and an error of the phase averaged signal (mean period). The averaged signal can be seen in the following plot.
The problem is that I have no idea how I can proceed with this. I already tried to do an MSE decomposition but I had no success with that. Does anybody have an idea how I can decompose my total error in a clever way into an error I calculate from the mean period and a variance (which is of course not considered in the mean period)?