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\section{Radiative boundary condition}

\begin{equation}
-K{\partial T\over\partial z}=\sigmaSB T^4
\end{equation}
\begin{equation}
{\partial\ln T\over\partial z}=-{\sigmaSB T^3\over K}
\end{equation}

\section{Replace in terms $\rho$ and $s$}

\begin{equation}
{\partial s/\cp\over\partial z}
={1\over\gamma}{\partial\ln p\over\partial z}
-{\partial\ln\rho\over\partial z}
\end{equation}
\begin{equation}
{\partial s/\cp\over\partial z}
={1\over\gamma}{\partial\ln T\over\partial z}
-\left(1-{1\over\gamma}\right){\partial\ln\rho\over\partial z}
\end{equation}
\begin{equation}
{\partial s/\cv\over\partial z}
={\partial\ln T\over\partial z}
-\left(\gamma-1\right){\partial\ln\rho\over\partial z}
\end{equation}
\begin{equation}
{\partial s/\cv\over\partial z}
=-{\sigmaSB T^3\over K}
-\left(\gamma-1\right){\partial\ln\rho\over\partial z}
\end{equation}
\begin{equation}
{\partial s\over\partial z}
=-\cv{\sigmaSB T^3\over K}
-\cv\left(\gamma-1\right){\partial\ln\rho\over\partial z}
\end{equation}

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%\bibitem[Biskamp \& M\"uller(1999)]{BM99}
%Biskamp, D., \& M\"uller, W.-C.\yprl{1999}{83}{2195}

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