Final init

Define $\pi(\eta) = A(\eta) \pi_0 + B(\eta) \pi_s$

Suppose we are given $T(z), p(z)$, with $\pi_s = \int_0^\infty \frac{p}{R_d T} \intd{z}$. This needs only be calculated once.

In SA HOMME, we have $$

Then we can define $\pi'_s = \int_0^\infty \hat{r}^2 \frac{p}{R_d T} \intd{z}$, with $\pi'(\eta) = A(\eta) \pi_0 + B(\eta) \pi'_s$.

Then solve