Sub cloud layer thermo fit

[nilsnevertree]

In order to have better thermodynamic fits, it would be good to use only a linear fit of the relative humidity and temperature in the sub cloud layer between 500 and 1200 m

An example plot is shown here:

A solution to this would be:

• Use a simple linear regression model. But this gives the issue of intense supersaturation.
• Second option would be a splitted lienar regression, with slope inf above the height, at which relative humiditz reaches 100%.

The steps which need to be taken are:

1. Fit linear regression to sub cloud layer relative humidity. Get slope s and x_int.
2. Calculate saturation height x_split
3. set values for s, x_int and x_split.
4. Either fit linear regression above x_split or use slope value of inf to have sonstant supersaturation

[nilsnevertree]

BUT: CLEO needs specific humidity as input. Thus, a conversion from relative humidity to specific humidity is needed. Open question is, how to do so.

[nilsnevertree]

Linear fit beeing shitty when using the linear fit only is mainly due to

air_temperature = transfer.fit_thermodynamics(
    da_thermo=data.sel(alt = slice(200, 500)),
    thermo_fit=transfer.ThermodynamicLinear(),
    dim="alt",
    x_split=None,
    f0_boundaries=True, # True by default
)

Solve it by using f0_boundaries = False

air_temperature = transfer.fit_thermodynamics(
    da_thermo=data.sel(alt = slice(200, 500)),
    thermo_fit=transfer.ThermodynamicLinear(),
    dim="alt",
    x_split=None,
    f0_boundaries=False,
)

[nilsnevertree]

Also if reconstruction of potential temperature should be made, it is important to use this to reconstruct it:

ds_dropsondes["potential_temperature_recon"] = conversions.potential_temperature_from_tp(
    pressure=ds_dropsondes["pressure"],
    air_temperature=ds_dropsondes["air_temperature"],
    pressure_reference=100000
)

So the reference pressure in 1000hPa

With other values, there is a big discrepance