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update / solution:
For everyone having the same problem: my INT2LM setting is
irefatm = 2
From looking into the source code it seems to me that that:
reference_atmosphere_2
and thuspref3
is used because of my INT2LM settingirefatm = 2
I think the formula from the excel sheet and from the documentation are for the case
irefatm = 1
From the documentation I get the same as from the source code:
From the source code
vgrid_refatm_utils.f90
/reference_atmosphere_2
:which I interprete to be the equation
pref3
with(hhl[,,1:60]+hhl[,,2:61])/2
instead ofvcoord
When I did the analytical integration of the hydrostatic equation myself I got a different formula than pref3, but they give the same values :D so in short:
My opionion: If
irefatm = 2
thenp_reference(z) = p0sl * exp( -g*h_scal/ R/t00 * log( (exp(z/h_scal)*t00 + delta_t)/(t00 + delta_t)) )
with the values from my earlier posts