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) & = & \frac{3z(1) - z(2)}{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) & = & \frac{3z(N) - z(N-1)}{2} \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 (\(z^{B}(1,1) = z(1)\), \(z^{B}(N,2) = z(N)\)).