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

Improvements have been made over the past two decades in our ability to accurately forecast the short-term track of tropical cyclones. Despite such progress, our ability to predict storm development and rapid intensification remains quite limited. 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 covariance 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 structure of forecast error 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 a 92-member ensemble of Hurricane Katrina forecasts using the Weather Research and Forecasting (WRF) model. For the Rankine vortex and axisymmetric experiments, random perturbations were added to initial conditions before numerical integration to create ensembles large enough for an accurate estimation of forecast error. Synoptic scale correlation structures estimated from all three models were highly anisotropic and consistent with the underlying model dynamics. When the two lower order models were tuned to fit Katrina 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 Rotunno-Emanuel hurricane model was able to resolve many of the same three-dimensional relationships observed with the WRF ensemble. Results from our experiments raise the question of whether or not a low-order axisymmetric vortex model can be used to estimate flow-dependant background error covariance for future tropical cyclone prediction systems.