Dynamics and structure of three-dimensional error covariance of a mature tropical cyclone

Over the past decade, significant progress has been made in short-range track forecasts of tropical cyclones. However, our ability to predict rapid intensification, fluctuation, and decay remains quite limited. Despite improvements using advanced data assimilation methods, initializing a vortex with physically consistent dynamic and thermodynamic structure remains to be a limiting factor in our ability to accurately predict changes in tropic cyclone intensity. One deficiency comes from the use of isotropic, flow-independent background statistics in operational data assimilation systems, which are ill-suited for the highly flow-dependent background error covariances associated with tropical cyclones. Estimating non-static background statistics is a computationally expensive process, but may be required for the next generation of tropical cyclone prediction systems.

This study examines the flow-dependent correlation structure of an axisymmetric vortex through a progression of simple to complex models; beginning with a two-dimensional Rankine vortex, then advancing to the Rotunno-Emanuel (1987) axisymmetric hurricane model, and finishing with an ensemble of WRF forecasts for Hurricane Katrina near its peak intensity. For the Rankine vortex and axisymmetric experiments, random perturbations were added to initial conditions before numerical integration to create ensembles large enough for a reasonable estimation of forecast error. Correlations were calculated from azimuthally averaged WRF output for comparison. When the Rankine vortex and axisymmetric model were tuned to fit the WRF forecasts, i.e. in terms of maximum tangential wind speed and radius of maximum winds, they provided dynamically similar correlation structures. In fact, even with no changes made to the model dynamics, the axisymmetric hurricane model was able to resolve many of the same three-dimensional relationships observed with the WRF ensemble. Results from this study raise the question of whether or not a low-order axisymmetric vortex model can be used to estimate flow-dependant background error covariance for statistical data assimilation systems.