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Dear Mikhail,
I agree with your assumption.
See also the paper
Buzzi, Matteo; Rotach, Mathias W.; Holtslag, Matthias; Holtslag, Albert A.M. (2011):
Evaluation of the COSMO -SC turbulence scheme in a shear-driven stable boundary layer
Meteorologische Zeitschrift Vol. 20 No. 3 (2011), p. 335 – 350, DOI : 10.1127/0941-2948/2011/0050
Which model version are you using? What are the values of tuning parameters tkhmin and tkmmin?
In older versions the minimum value for both parameters was 1., which was too high for nocturnal conditions (see the paper above).
In more recent versions of the model you can choose smaller values.
For more “expert” opinions, please contact Mathias Raschendorfer and/or Michael Baldauf from DWD .
Best regards
Hans-Juergen