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