Fast Observation Operator for Global Navigation Satellite System Tropospheric Gradients

From the raw measurements at a single Global Navigation Satellite System (GNSS) ground-based station, the Zenith Total Delay (ZTD) and the tropospheric gradient can be estimated. In order to assimilate such data into Numerical Weather Prediction (NWP) models, the observation operator must be developed. Our previously developed tropospheric gradient operator is based on a linear combination of tropospheric delays and, therefore, is difficult to implement into NWP Data Assimilation (DA) systems. In this technical note, we develop a fast observation operator. This observation operator is based on an integral expression which contains the north-south and east-west horizontal gradients of refractivity. We run a numerical weather model (the horizontal resolution is 10 km) and show that for stations located in central Europe and in the warm season, the root-mean-square deviation between the tropospheric gradients calculated by the fast and original approach is about 0.15 mm. This deviation is regarded acceptable for assimilation since the typical root-mean-square deviation between observed and forward modelled tropospheric gradients is about 0.5 mm. We then implement the developed operator in our experimental DA system and test the proposed approach. In particular, we analyze the impact of the assimilation on the refractivity field. The developed tropospheric gradient operator, together with its tangent linear and adjoint version, is freely available (Fortran code) and ready to be implemented into NWP DA systems.