altitude bounds derivations

1. altitude ranges from midpoints

   symbol	description	unit	variable name
   \(z(i)\)	altitude	\(m\)	altitude {:,vertical}
   \(z^{B}(i,l)\)	altitude boundaries (\(l \in \{1,2\}\))	\(m\)	altitude_bounds {:,vertical,2}

   The pattern : for the dimensions can represent {time}, or no dimension at all.

   \begin{eqnarray} z^{B}(1,1) & = & 2z(1) - z(2) \\ z^{B}(i,1) & = & \frac{z(i-1) + z(i)}{2}, 1 < i \leq N \\ z^{B}(i,2) & = & z^{B}(i+1,1), 1 \leq i < N \\ z^{B}(N,2) & = & 2z(N) - z(N-1) \end{eqnarray}

   This formula applies if the harp option regrid_out_of_bounds is set to nan or to extrapolate. If the option is set to edge then the first and last boundary value are set to the midpoints (\(z^{B}(1,1) = z(1)\), \(z^{B}(N,2) = z(N)\)).