Eta vertical coordinate in IFS

Hello everybody,

I have difficulties to understand the connection between the hybrid sigma vertical coordinate, eta, and the model levels used in the IFS model. More specifically, I would like to know how to determine the value of the eta-coordinate of a specific model level. As I understand from the documentation (e.g. here 4.4 OpenIFS: Vertical Resolution and Configurations ), the value of eta is 0 at the top of the atmosphere and 1 at the very bottom of the atmosphere. But how can I get the values in between, or even more interesting for me, the difference in eta between two model levels?

I ask this question because I would like to compute the vertical advection term etadot * gradient(delta X /delta eta), where X is a specific quantity and etadot is the eta-coordinate vertical velocity. Is that possible? Or should I better use the vertical velocity omega on pressure levels, thus omega * gradient(delta X /delta pressurelevels), where omega is given in Pa/s?

I hope I could make my problem clear. Thanks for your help in advance.

Best regards,


Hello Amelie,

You don't need to know eta in order to evaluate the vertical advection. The procedure is described in the IFS documentation:

eg CY41R2 for ERA5, Part III Dynamics and numerical procedures, Chapter 2 Basic equations and discretisation. Use equation 2.18 in 2.19 to obtain the vertical advection. Note, the IFS actually uses finite elements in the vertical discretisation, but these equations provide a good approximation to those.

Let us know if you have further questions.

Best wishes,


Dear Paul,

I'm resurrecting this topic from the past because I am having similar problem as Amelie. I have large dataset of ERA-5 reanalysis where there's also etadot, "eta-coordinate vertical velocities". I would need to convert this information to vertical wind w (dz/dt). I have the pressure at model levels, also the height (z) at model levels, but I have not been able to find a clear definition of how eta is defined in IFS (if I knew eta at model levels, problem would be solved). For example in WRF it is simply eta=(Ph - Pht)/(Phs - Pht) where Ph, Pht and Phs are pressure at some height, pressure at top and pressure at surface. Some IFS documentation refers to Simmons & Burridge (1981) which shows different definition (sigma, hybrid, continuous and discrete etc.), but it is unclear what is actually used in IFS.

Would be great to see clearly how eta is defined in IFS, more specifically in ERA-5 reanalysis hybrid levels (with 137 levels). Maybe you can point me to the source? Thank you in advance!