Bugfix in check_qsat

[Ian Culverwell]

There's a typo in subroutine check_qsat in ropp_fm/model_meto/ropp_fm_state2state_meto.f90 and ropp_fm/model_ecmwf/ropp_fm_state2state_ecmwf.f90. The SVP over water at 373.16 K is ten times too large.

    WHERE(temp >= 273.16)
      es = 1013246.0_wp * (10**Z)
    ELSEWHERE
      es = 610.71_wp * (10**X)
    ENDWHERE

should be replaced by

    WHERE(temp >= 273.16)
      es = 101324.6_wp * (10**Z)
    ELSEWHERE
      es = 610.71_wp * (10**X)
    ENDWHERE

(es is the saturated vapour pressure in Pa.)

This means that in the lower troposphere, where temp >= 273.16 K, the saturated humidity is too high, so the saturation check is not being applied as strongly or as often as it should be.

Note that the check on qsat was introduced in [2217], in response to #172. There's a simpler formula for SVP than the Goff & Gratch (1946) formula used in check_qsat, which agrees with it to within 0.25% (1): namely, the CIMO Guide formula (WMO 2008)

    theta = temp - t_freeze  ! temperature in deg C

    WHERE (theta >= 0.0_wp)  ! svp over liquid water

      svp = svp_freeze * EXP( c_wat(1) * theta / (c_wat(2) + theta) )

    ELSEWHERE  ! svp over ice

      svp = svp_freeze * EXP( c_ice(1) * theta / (c_ice(2) + theta) )

    END WHERE

This is used in ropp_apps/pblh/ropp_apps_pblh_rhum.f90, so now might be a good time to adopt it here.

(1) Fig 3 of ​http://cires1.colorado.edu/~voemel/vp.pro claims the two formulae are within ~1.5%, but I estimate the maximum difference to be 0.25% at T ~ 230 K ~ -45 deg C. Check this if I do decide to amend this part of check_qsat.

[Ian Culverwell]

The link in the footnote should be ​http://cires1.colorado.edu/~voemel/vp.html

[Ian Culverwell]

es_plot.gif

[Ian Culverwell]

The bug we're fixing is illustrated here:

[Ian Culverwell]

Forget the CIMO formula, but implement the fix described above at r4796.

No significant impact on results of passing bgr20090401_multi.nc through ropp_fm_bg2ro_1d, but it could have an effect below the freezing level.

[Ian Culverwell]

Everyone is happy, so closing ticket.

[Ian Culverwell]

Oops. Forgot to make the corresponding change to ropp_fm_state2state_meto.f90. This has been done at r4867. Reclosing ticket.