# Dry pressure, Pd # Dry surface pressure = Pds # Model top pressure = Pt # Dry mass in column (base + perturbation), Pcb + Pc = Pds - Pt # 1d column weighting term, B: BF is full levels, BH is half levels # Total dry pressure # Pd = BF ( Pds - Pt ) + ( eta - BF ) ( P0 - Pt ) + Pt # Note that when B (full levels, BF) is identically eta (full levels, ZNW), # the dry pressure, Pd = the terrain following coordinate. # Pd = eta ( Pds - Pt ) + Pt # Note that when B (full levels, BF) is zero, # the dry pressure, Pd = isobaric. # Pd = eta ( P0 - Pt ) + Pt # Hybrid coordinate: mu is still d(Pd)/d(eta) # new MUT = d Pd / d eta = d BF / d eta * ( Pcb + Pc ) + ( 1 - d BF / d eta ) * ( P0 - Pt ) # Define two columnar constants, function only of eta and other constants, specifically for the "mu" replacements. # C1 = d BF / d eta # C2 = ( 1 - d BF / d eta ) * ( P0 - Pt ) # Total field # new MUT(i,k,j) = C1(k) * ( Pcb(i,j) + Pc(i,j) ) + C2(k) # Base-state, background field # new MUB(i,k,j) = C1(k) * Pcb(i,j) + C2(k) # Perturbation field # new MU(i,k,j) = C1(k) * Pc(i,j) # Define two columnar constants, function only of eta and other constants, specifically for the "pressure" replacements. # C3 = BF # C4 = ( eta - BF ) * ( P0 - Pt ) # new dry pressure Pd(i,k,j) = C3(k) * ( Pds(i,j) - Pt ) + C4(k) + Pt #