latitude bounds derivations

1. latitude ranges from midpoints

   symbol	description	unit	variable name
   \(\phi(i)\)	latitude	\(degN\)	latitude {:,latitude}
   \(\phi^{B}(i,l)\)	latitude boundaries (\(l \in \{1,2\}\))	\(degN\)	latitude_bounds {:,latitude,2}

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

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

   Note that all latitude values will always be clamped to the range \([-90,90]\).