ECMWF Model Levels

The above link describes the coefficients used to define the ECMWF model levels in pressure in order to compute geopotential height. Is there a similar data for NCEP reanalysis model or is the data already on pressure levels in which case the above step is not required ? To be precise I am looking for the identical data for the T62 NCEP reanalysis data(2.5 x 2.5). The NCEP reanalysis model uses the sigma vertical coordinate. The same question can be rephrased in the following manner

1) What are the values of the sigma levels and where can they be downloaded? For e.g. if the sigma level is 0.995 and the surface pressure is 1000 hPa then the pressure at the sigma level 0.995 is 995 hPa.

2) Are the sigma levels of the NCEP reanalysis model comparable to the a and b coefficients of the ECMWF model ?


The hybrid vertical coordinate of UCAR Community Atmosphere Model(CAM 3.0) describes a similar equation to that of ECMWF and has explicit coefficients A and B as shown below

$p(\eta,p_s) = A(\eta)p_0 + B(\eta)p_s$

where p is pressure, $p_s$ is surface pressure, $p_0$ is a specified constant reference pressure and A and B are coefficients that specify the coordinate being used and are defined only at the discrete model levels.

GOAL - I have code that uses ECMWF data as input to run a few calculations. I am looking to run the same code using NCEP renanalysis model data.


  • Page 6 Section 2.2.1 Vertical Discretization

  • Simmons, A.J., Burridge, D.M., An Energy and Angular Momentum Conserving Vertical Coordinate Finite Difference Scheme and Hybrid Vertical Coordinate, Monthly Weather Review 758-766,1981

  • Collins, W. D., P. J. Rasch, and Others, Description of the NCAR Community Atmosphere Model (CAM 3.0), Technical Report NCAR/TN-464+STR, National Center for Atmospheric Research, Boulder, Colorado, 210 pp., 2004. CAM

  • $\begingroup$ To make sure: With T62 NOAA reanalysis data you mean the NCEP/NCAR Reanalysis 1 data? $\endgroup$ Jun 7 '16 at 10:10
  • $\begingroup$ @daniel.neumann - Yes the NCEP/NCAR reanalysis 1 data. Correct. $\endgroup$
    – gansub
    Jun 8 '16 at 4:53
  • $\begingroup$ Which data do you want to compare? $\endgroup$ Jun 8 '16 at 14:44
  • 1
    $\begingroup$ In the cdo releases 1.7.0 and 1.7.2 new vertical interpolation routines were introduced. Maybe they are useful for your work? $\endgroup$ Jul 7 '16 at 9:30
  • $\begingroup$ @daniel.neumann - this solution won't do for my problem. I verified with MPI. Now the problem still exists. I have data on isobaric levels from NCEP NOAA. Question is can I calculate the pressure field using the sigma values which are from another grid? $\endgroup$
    – gansub
    Sep 11 '17 at 10:09

Grid Resolution of the NCEP/NCAR reanalysis data

The data is available on different grids depending on the variables of interest:

  • The original grid is a T62 Gaussian grid, which grid cells do not have a constant lon-lat spacing over the whole globe (see e.g. Gaussian grid at Wikipedia), with 28 sigma levels. The sigma levels are listed on this page, where also the surface pressure is available for download. According to the FAQ, the sigma coordinate equals "pressure in current level"/"surface pressure". Thus, the pressure on each sigma level can be obtained via the available data.
  • Secondly, some variables, such as air temperature, are available interpolated onto an equally spaced lon-lat grid of 2.5° x 2.5° resolution with 17 pressure levels. These data are available here including data files with the geopotential height. The pressure levels are listed on the same page.

Comparability with A and B coefficients of ECMWF

The ECMWF uses the coefficients A and B as well as the reference pressure $p_0$ to describe the levels. NCEP uses just one coefficient ($\sigma$) for this purpose:

$$ \begin{align} & \text{ECMWF:} & p\left(\eta,p_s\right) &= A\left(\eta\right) \times p_0 + B\left(\eta\right) \times p_s \\ & \text{NCEP:} & p\left(\eta,p_s\right) &= \sigma\left(\eta\right) \times p_0 \\ \end{align} $$

When we had $p_0 = 0\ \text{bar}$, both representations were the same. In the given situation, there is no unambiguous mapping from a known $\sigma\left(\eta\right)$ to a set of $A\left(\eta\right)$ and $B\left(\eta\right)$. At least if there are no further limiting conditions.

Normally, I do not deal with vertical coordinate systems. Therefore, I am not sure how data on different vertical layers is compared with each other (except of the obvious: interpolating the one data set onto the vertical coordinates of the other data set).


1) Yes, here and here.

  • The variables Air Temperature, Geopotential Height, Relative Humidity, Specific Humidity, Omega (Vertical Velocity), U-Wind, and V-Wind are available on the second grid (2.5° x 2.5° horizontal resolution; 17 pressure levels).
  • The variables Divergence, Specific Humidity, Virtual Air Temperature, and Relative Vorticity are available on the first grid (T62 Gaussian grid; 28 sigma layers). In order to calculate the model pressure at each sigma level, the surface pressure is additionally provided (T62 Gaussian grid but no vertical resolution). Also the topographic data (Orography) is provided on the same resolution as the surface pressure.

2) The vertical layer representations by $\sigma$ coordinates, on the on side, and by a set of $A$, $B$ and $p_0$, on the other side, are similar to each other but not directly comparable to each other. However, for most practical applications the data on the second grid, which is easier to handle, might be sufficient.

I am not sure if these answers to the question are satisfactory.

  • 1
    $\begingroup$ can you clarify what you mean when you write " however this is not the case " ? $\endgroup$
    – gansub
    Jun 8 '16 at 13:23
  • $\begingroup$ Thank you for the remark. I modified that sentence and added some more. $\endgroup$ Jun 8 '16 at 14:43
  • $\begingroup$ @gansub, Maybe we should write in the chat and one of us edits the article later on? $\endgroup$ Jun 9 '16 at 8:46
  • $\begingroup$ if you make the changes I talked about I can go ahead and accept the answer. I am not sure on the bounty - you need to ask BHF about that $\endgroup$
    – gansub
    Jun 9 '16 at 9:28
  • 1
    $\begingroup$ looking at this old answer I can accept it if you can rewrite explaining what this means - "except of the obvious: interpolating the one data set onto the vertical coordinates of the other data set". What method of interpolation we are talking here ? You show us the method and some sort of typical example and I can accept your answer. I am basically asking how would you interpolate from vertical coordinate to another. $\endgroup$
    – gansub
    May 19 '18 at 16:06

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