Prototype calculation of cabelling and mixing of density from POP data

[rabernat]

Let's start by operating on a single timestep of data. The fields you will have are SST and SSS.

Step 1: Calculate tendency of SST and and SSS from mixing

From this, we want to calculate M(T) and M(S): the tendency from mixing for temperature and salinity.

How will you calculate M(T)? Using @paigem's code. She has already coded up the POP biharmonic mixing operator. We can just take that code directly and use it here.

Step 2: Convert these to a density tendency

The density tendency from mixing of T and S is given by

dρ/dT M(T) + dρ/dS M(S)

You can get the thermodynamic coefficients from fastjmd95.

Step 3: Decompose into the following form

dρ/dT M(T) + dρ/dS M(S) = M(rho) + C

You can calculate C as

C = dρ/dT M(T) + dρ/dS M(S) - M(rho)

Acceptance criteria

How will we know when this task is complete:

• [ ] We will have a standalone python script file (mixing_tendency.py) in this repo which, when executed python mixing_tendency.py, produces four figures independent figures
  • [x] M(T)
  • [x] M(S)
  • [x] M(rho)
  • [x] C

No notebooks!

[rabernat]

Here is the notebook from Paige which shows how to compute the biharmonic tendency:

https://github.com/ocean-transport/cesm-air-sea/blob/master/biharmonic_tendency.ipynb