I am facing a problem in converting the depth axis from sigma coordinates to the "meter" axis. The formula that is provided in the model output is shown below.
double lev(lev) ;
lev:long_name = "ocean sigma coordinate" ;
lev:positive = "up" ;
lev:axis = "Z" ;
lev:bounds = "lev_bnds" ;
lev:formula = "z(n,k,j,i) = eta(n,j,i) + sigma(k)*(depth(j,i)+eta(n,j,i))" ; !!!!! formula !!!!!
As you can see, "z" depends on (n,k,j,i). It's not a coordinate variable.
What does that mean? A sigma level corresponds to a depth z, but that correspondence differs from place to place, that is, it depends on i and j (and n).
I'm sure you remember how you converted a quantity defined on the density coordinates to the depth coordinate using the ZAXREPLACE function. The situation you are now in is exactly the same as that. Replace "density" with "sigma". Then you'll realize that "z(n,k,j,i)" is the "iso-sigma depth".
Cheers,
Ryo