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