pressure bounds derivations

  1. pressure ranges from midpoints

    symbol

    description

    unit

    variable name

    \(p(i)\)

    pressure

    \(Pa\)

    pressure {:,vertical}

    \(p^{B}(i,l)\)

    pressure boundaries (\(l \in \{1,2\}\))

    \(Pa\)

    pressure_bounds {:,vertical,2}

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

    \begin{eqnarray} p^{B}(1,1) & = & e^{\frac{3\ln(p(1)) - \ln(p(2))}{2}} \\ p^{B}(i,1) & = & e^{\frac{\ln(p(i-1)) + \ln(p(i))}{2}}, 1 < i \leq N \\ p^{B}(i,2) & = & p^{B}(i+1,1), 1 \leq i < N \\ p^{B}(N,2) & = & e^{\frac{3\ln(p(N)) - \ln(p(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 (\(p^{B}(1,1) = p(1)\), \(p^{B}(N,2) = p(N)\)).