Direct 4D-Var assimilation of space-borne cloud radar reflectivity and lidar backscatter. Part I: Observation operator and implementation

The direct assimilation of space-borne cloud radar and lidar observations into a global numerical weather prediction model has not previously been attempted for several reasons. Firstly, the modification of a data assimilation system to handle space-borne profiling observations is a technical challenge. Secondly, the relationship between model-scale control variables and the relatively narrow footprint of the radar and lidar instruments were thought to be unrepresentative and too nonlinear for a variational assimilation system that is based on assumptions of linearity. However, motivation was provided when previous experiments assimilating cloud radar and lidar profiles showed, using an intermediary step to generate pseudo-observations of temperature and humidity, that there was potential for the observations to improve both the analysis and the subsequent forecast. This article presents the developments made to facilitate the direct assimilation of cloud radar and lidar observations into the four-dimensional variational assimilation (4D-Var) system of the European Centre for Medium-Range Weather Forecasts (ECMWF). A review of the observation operators shows how they have been optimised for data assimilation with an emphasis on efficiency, consistency and differentiability. A key part of this work is the specification of a new fully flow-dependent characterisation of the observation error. By taking an error inventory approach, we account for different sources of error in a physical way. Also, to avoid degrading the analysis, careful screening, quality control and bias correction is necessary and is described herein. Finally, an initial assessment of the impact of the observations is achieved through single-analysis tests that show that the analysis fit to the new observations is improved. In-depth results demonstrating the impact of these observations are shown in the second part of this two-part series.