Vorticity calculation (wrf.avo) - does it take into account curvature of sigma surfaces?

[Petar Golem]

Hello all,

    I was calculating the absolute vorticity using the wrf.avo function in the context of a downslope windstorm in fairly steep terrain. The inputs for the function are:

• u (staggered)
• v (staggered)
• map factor fields (at u, v and mass points)
• coriolis factor
• dx, dy (in m)

Source: https://wrf-python.readthedocs.io/en/latest/user_api/generated/wrf.avo.html

Am I wrong to conclude that this means that the algorithm approximates the sigma surfaces as basically flat? It seems that the derivatives (i.e., differences) are taken along the sigma surface, and not the real, physical space. Would the algorithm then be inaccurate in steep terrain, especially near to the ground?

Thank you,

Petar Golem