An optimal estimation algorithm for the retrieval of fog and low cloud thermodynamic and micro-physical properties
Authors: Bell Alistair , Martinet Pauline , Caumont Olivier , Burnet Frédéric , Delanoë Julien , Jorquera Susana , Seity Yann , Unger Vinciane 
Published: September 2022

Abstract. A new generation of cloud radars, with the ability to make observations close to the surface, presents the possibility of observing fog properties with better insight than was previously possible. The use of these instruments as part of an operational observation network could improve the prediction of fog events, something which is still a problem for even high-resolution numerical weather prediction models. However, the retrieval of liquid water content (LWC) profiles from radar reflectivity alone is an under-determined problem, something which ground-based microwave radiometer observations can help to constrain. In fact, microwave radiometers are not only sensitive to temperature and humidity profiles but are also known to be instruments of reference for the liquid water path. By providing the thermodynamic state of the atmosphere, to which the formation and evolution of fog events are highly sensitive, in addition to accurate liquid water path, which can be used to constrain the LWC retrieval from the cloud radar alone, combining microwave radiometers with cloud radars seems a natural next step to better understand and forecast fog events. To that end, a newly developed one-dimensional variational (1D-Var) algorithm designed for the retrieval of temperature, specific humidity and liquid water content profiles with both cloud radar and microwave radiometer (MWR) observations is presented in this study. The algorithm was developed to evaluate the capability of cloud radar and MWR to provide accurate LWC profiles in addition to temperature and humidity in view of assimilating the retrieved profiles into a 3D- and 4D-Var operational assimilation system. The algorithm is firstly tested on a synthetic dataset, which allows the evaluation of the developed algorithm in idealised conditions. This dataset was constructed by perturbing a high-resolution forecast dataset of fog and low-cloud cases by its expected errors. The algorithm is then tested with real data from the recent field campaign SOFOG-3D, carried out with the use of LWC measurements made from a tethered balloon platform. As expected, results from the synthetic dataset study were found to contain lower errors than those found from the retrievals on the dataset of real observations. It was found that LWC can be retrieved in idealised conditions with an uncertainty of less than 0.04 g m−3. With real data, as expected, retrievals with a good correlation (0.7) to in situ measurements were found but with a higher uncertainty than the synthetic dataset of around 0.06 g m−3 (41 %). This was reduced to 0.05 g m−3 (35 %) when an accurate droplet number concentration could be prescribed to the algorithm. A sensitivity study was conducted to discuss the impact of different settings used in the 1D-Var algorithm and the forward operator. Additionally, retrievals of LWC from a real fog event observed during the SOFOG-3D field campaign were found to significantly improve the operational background profiles of the AROME (Application of Research to Operations at MEsoscale) model, showing encouraging results for future improvement of the AROME model initial state during fog conditions.