The development of ground based cloud radars offers a new capability to continuously monitor the fog structure. Retrievals of fog microphysics is key for future process studies, data assimilation or model evaluation, and can be performed using a variational method. Both the one-dimensional variational retrieval method or direct 3D/4D-Var data assimilation techniques rely on the combination of cloud radar measurements and a background profile weighted by their corresponding uncertainties to

more »

... n the optimal solution for the atmospheric 5 state. In order to prepare the exploitation of ground-based cloud radar measurements for future applications based on variational approaches, the different sources of uncertainty due to instrumental errors, background errors and the forward operator used to simulate the radar reflectivity need to be properly treated and accounted for. This paper aims at preparing 1D-Var retrievals by analysing the errors associated with a background profile and a forward operator during fog conditions. For this, the background was provided by a high-resolution numerical weather 10 prediction model and the forward operator by a radar simulator. Firstly, an instrumental dataset was taken from the SIRTA observatory near Paris, France for winter 2018-19 during which 31 fog events were observed. Statistics were calculated comparing cloud radar observations to those simulated. It was found that the accuracy of simulations could be drastically improved by correcting for significant spatio-temporal background errors. This was achieved by implementing a most resembling profile method in which an optimal model background profile is selected from 15 a domain and time window around the observation location and time. After selecting the best background profile a good agreement was found between observations and simulations. Moreover observation minus simulation errors were found to satisfy the conditions needed for future 1D-var retrievals (un-biased and normally distributed). considered in this study comes from a high-resolution NWP model-in this case the French convective-scale model 55 AROME (Seity et al., 2011) , valid at the time and location of the retrieval. The background profile must also be of the same variable type as the observation is made in. In the case of remote sensing instruments this requires either a 'backward' model, to transform the observation variables into those produced by the NWP model, or a 'forward' model to transform the variables given by an NWP model to those made by the instrument. Due to the ill-posed nature of transforming radar reflectivity measurements into 60 LWC estimates (Atlas, 1954; Bohren and Huffman, 2008; Maier et al., 2012) , the forward model approach has been chosen in this study. In order to make a 1D-Var retrieval, it is also necessary that the errors associated with the background and the observations are properly modelled (Rodgers, 2000) . For successful variational retrievals to be made, it is assumed that i) the distribution of errors should follow a normal distribution and ii) that there should be no systematic bias in 65