Answers to the Referee 2 about the paper amt-2021-361: “Towards the use of conservative thermodynamic variables in data assimilation: preliminary results a case study using ground-based microwave radiometer

This study aims at introducing two conservative thermodynamic variables (moist-air entropy potential temperature and total water content) into a one-dimensional variational data assimilation system (1D-Var) to demonstrate the benefit for future operational assimilation schemes. This sys5 tem is assessed using microwave brightness temperatures from a ground-based radiometer installed during the field campaign SOFGO3D ::::::::: SOFOG3D : dedicated to fog forecast improvement. An underlying objective is to ease the specification of 10 background error covariance matrices that are currently ::: that :: are : highly dependent on weather conditions :::: when ::::: using ::::::: classical :::::::: variables, : making difficult the optimal retrievals of cloud and thermodynamic properties during fog conditions. Background error covariance matrices for these new conser15 vative variables have thus been computed by an ensemble approach based on the French convective scale model AROME, for both all-weather and fog conditions. A first result shows that the use of these matrices for the new variables reduces some dependencies to the meteorological conditions (diurnal 20 cycle, presence or not of clouds) compared to usual variables (temperature, specific humidity). Then, two 1D-Var experiments (classical vs. conservative variables) are evaluated over a full diurnal cycle characterized by a stratus-evolving radiative fog situation, using 25 hourly brightness temperatures. Results show, as expected, that analysed brightness temperatures by the 1D-Var are much closer to the observed ones than background values for both variable choices. This is especially the case for channels sensitive to water vapour and 30 liquid water. On the other hand, analysis increments in model space (water vapour, liquid water) show significant differences between the two sets of variables.