altitude bounds derivations
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 tonan
or toextrapolate
. If the option is set toedge
then the first and last boundary value are set to the midpoints (\(z^{B}(1,1) = z(1)\), \(z^{B}(N,2) = z(N)\)).