Dear Ferreters
To fully expand this query is to compute e.g. thermal expansion coefficient (alpha)
alpha = -(1/rho) * d(rho)/d(theta)
d(rho)/d(theta) means a partial derivative of potential density wrt potential temperature.
Not knowing a better (and easy) way to do that, I would calculate "numerical derivatives".
To calculate how in-situ density changes if the local in-situ temperature changes under constant pressure (depth) and constant salinity,
∂ρ/∂T under constant p and S ≈ [rho_un(S, Tplus, p) - rho_un(S, Tminus, p) ]/ (2 * delT),
where Tplus = T + delT and Tminus = T - delT. If delT is too small, the result will be noisy. If delT is too large, the result will be inaccurate. So, you would test several values. You would plot graphs (curves) showing the calculated derivative versus various delT values at several sample points. As you decrease delT, the graph would become flat, which is where good delT values are.
If you want a derivative w.r.t. potential temperature, you would need one more step: Under constant p and S,
∂ρ/∂θ = (∂ρ/∂T) (∂T/∂θ)
(I think.) So, you calculate both ∂ρ/∂T and ∂T/∂θ numerically at each point in space-time (x,y,z,t) and multiply them together.
Another potential way would be to switch to "conservative temperature" and use the
gsw_alpha funcion from the TEOS-10 tool kit (
http://www.teos-10.org/index.htm ) from a language (like python) for which this tool kit is readily available.
(I don't know how hard or easy to plug TEOS-10 in to Ferret.)
Another potential way is to find an approximate polynomial _expression_ that relates ρ to (S, θ, p). If such an _expression_ is found, it would be straightforward to differentiate it.
Ryo
And I am not sure how to compute it.
The script suggested in the link
https://www.pmel.noaa.gov/maillists/tmap/ferret_users/fu_2017/msg00111.html is also attached to this email. However, it was an old script that computed the potential density using the state equation involving all the co-efficient. Now we can compute rho_un with the ferret functionality but how to compute partial derivative d(rho)/d(theta) is the part that I want to resolve.
Cheers, Saurabh
Dear Ferreters
G'day
I was wondering if does know how to compute the thermal expansion and haline contraction coefficient.
Any suggestion is appreciated.
Cheers, Saurabh