W-band radar observations for fog forecast improvement: an analysis of model and forward operator errors

The development of ground-based cloud radars offers a new capability to continuously monitor fog structure. Retrievals of fog microphysics are 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 (1D-Var) 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 obtain the optimal solution for the atmospheric state. In order to prepare for the use of ground-based cloud radar measurements for future applications based on variational approaches, the different sources of uncertainty due to instrumental, background, and forward operator errors 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 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 2018-2019 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 a domain and time window around the observation location and time. After selecting the background profiles with the best agreement with the observations, the standard deviation of innovations (observations-simulations) was found to decrease significantly. Moreover, innovation statistics were found to satisfy the conditions needed for future 1D-Var retrievals (unbiased and normally distributed).