pressure bounds derivations
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^{2\ln(p(1)) - \ln(p(2))} \\ p^{B}(i,1) & = & e^{\frac{\ln(p(i-1)) + \ln(p(i))}{2}}, 1 < i \leq N \\ p^{B}(i,2) & = & e^{\ln(p^{B}(i+1,1))}, 1 \leq i < N \\ p^{B}(N,2) & = & e^{2\ln(p(N)) - \ln(p(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 (\(p^{B}(1,1) = p(1)\), \(p^{B}(N,2) = p(N)\)).