Interpolation to isentropic coordinates

Atmosphere
1

Greetings from the other side of the world!

I would like to use the ACCESS-CM2-Chem output contributed to the CCMI-2022 chemistry climate model intercomparison project for some stratospheric transport work. For this purpose I intend to first vertically regrid it to isentropic coordinates. The surface pressure data files (available via e.g. CEDA Archive Web Browser ) say “2-D field to calculate the 3-D pressure field from hybrid coordinates”, but it’s not wholly self-evident how to do that.

The most obvious possible approach is

  1. Using
    • the surface pressure
    • the temperature defined on 85 layers and
    • the definitions of the 86 layer edges,
    • integrate the hydrostatic equation to get the pressure on the 86 layer edges
  2. Using
    • the layer-edge pressures and heights and
    • the gravitational constant,
    • finite-difference the hydrostatic equation to get the layer-mean densities on 85 layers
  3. Use
    • the layer-mean densities and temperatures and
    • the gas law,
    • compute layer-mean pressures
  4. Combine the layer-mean pressures and temperatures to get layer-mean potential temperatures
  5. Interpolate to another set of potential temperatures as needed

but I am writing to inquire if there isn’t some “official” way to do it that would be more consistent with the model numerics. (If this information is available in any of the papers describing the model, I’m sorry I missed it.)

Thanks for any assistance you can provide.

Sincerely,

Todd Mooring

Research Associate, Linz Group, Department of Earth and Planetary Sciences, Harvard University

2 Likes
2

Hi Todd,

That’s a good question. I think what you said makes sense, assuming you don’t already know the pressure on the 85 levels (I guess this is the issue, that you don’t know that?). Is the surface pressure, the temperatures and the layer definitions all you have saved?

For step 1, I guess you could use the thickness equation P(z2) = P(z1)exp(- deltaz g / Rd Tav) for each layer. I think that amounts to the same thing as what you suggested. I wonder whether after step 1, you could just interpolate the layer edge pressures and calculate the layer means that way - it might give close to the same answer and be a bit computationally easier.

I guess this method might break down due to the hydrostatic assumption, but that’s probably OK if you’re up in the stratosphere away from deep convection.

I’m not really an expert, and I’ve never tried to to exactly what you’d doing, so these are just some thoughts.

Claire

3

Completely off-topic, but discourse does support LaTeX style math formatting:

P(z2) = P(z1)\exp(- \delta{z_{g}} / R_{d} T_{av})

which looks like this in the compose window:

$$
P(z2) = P(z1)\exp(- \delta{z_{g}} / R_{d} T_{av})
$$

NOTE: I have no idea if I have transcribed that correctly, which is kinda the point of support proper math markup!

1 Like
4

Hi Aidan,

Good point! I’d probably just put it as:

P(z_2) = P(z_1) exp(-\frac{ \Delta z g}{R_{d} T_{av}})
1 Like