An Observation Operator for the Variational Assimilation of Vortex Position and Intensity Jeffrey D. Kepert Centre for Australian Weather and Climate Research, Bureau of Meteorology, 700 Collins St, Melbourne Vic 3000. Email: J.Kepert@bom.gov.au Fifth WMO Symposium on the Assimilation of Observations for Meteorology, Oceanography and Hydrology, Melbourne, 5 - 9 October 2009. 1. Introduction Tropical cyclone forecasters produce manual estimates of vortex position and intensity ev- ery few hours, based mainly on satellite imagery interpretation with assistance from radar, scat- terometer and aircraft reconnaissance when available. The volume of such estimates is small (a few thousand per year), but the high impact of tropical cyclones and the difficulties with util- ising many forms of conventional and satellite data within the cyclone core implies that these estimates are of high importance. In particular, track is one of the most critical parameters in tropical cyclone forecasting, and good forecasts of track clearly require that the initial position be accurate. Cyclone position estimates are currently either ignored by assimilation systems or used for the generation of synthetic observations, due to the limitations of current assimila- tion systems. Neither approach is completely satisfactory. Problems with the use of synthetic observations include that they will usually have correlated errors, that they may not represent the structure of a particular storm (including any asymmetries), and that is an essentially ad hoc procedure that can require careful tuning for good performance. The disadvantages of the alternative, ignoring the data, are obvious. To directly assimilate position estimates, an observation operator is required to estimate the vortex position and intensity from the background field. If the assimilation system is variational, this operator must be differentiable, since its tangent linear and adjoint are also required. Thus algorithms which search directly for the lowest pressure or maximum vorticity are unsuitable for variational assimilation. They have, however, been demonstrated in EnKF-based assimilation (Chen and Snyder 2007), who showed that assimilation of cyclone position could also improve the depiction of cyclone structure in the analysis. The cyclone centre has been defined in terms of wind, pressure or vorticity. Several objec- tive techniques have been developed to define the centre from observations. Willoughby and Chelmow (1982) presented a variational technique that minimised the distance from a set of lines drawn perpendicular to aircraft observations of wind direction. Marks et al. (1992) de- fined the centre as that which maximised the circulation around the centre of the storm. By the circulation theorem, this is equivalent to a vorticity-based definition. In contrast to these wind-based definitions, Kepert (2005) used pressure observations from reconnaissance aircraft 106.1