Dynamics and structure of forecast error covariance for a developing hurricane

An ensemble of cloud-resolving forecasts from the Weather Research and Forecasting (WRF) model was used to study error covariance for Hurricane Katrina (2005) during a 64-h period in which the storm progressed from a category 1 to category 5 hurricane. Spatial error covariance with respect hypothetical measurements of model state variables and TC-Vitals were found to be highly anisotropic, variable dependent, and ultimately determined by the underlying storm dynamics, which change dramatically over time. Early in the forecast, when Katrina passed over the southern tip of the Florida Peninsula as a highly asymmetric category-1 hurricane, error covariance structures in Eulerian coordinates were dominated primarily by position uncertainty, with a secondary dependence on land-air interaction, storm structure, and intensity. The ensemble error dependence on position uncertainty became markedly greater with increased lead-time, as diverging storm tracks caused large gradients of wind, temperature and pressure to be concentrated further from the mean vortex center.

With respect to storm-relative coordinates, ensemble variance associated with model state variables becomes increasingly symmetric about the vortex center at greater hurricane intensity. Likewise, spatial and cross-spatial correlations share a similar axisymmetric transition about the origin, while maintaining a large degree of local anisotropy with respect to the location chosen for the correlation point. During time steps at which Katrina maintained category 3 or greater intensity and a large degree of axisymmetry, error covariance was comparable to calculations from Rotunno and Emanuel's (1987) axisymmetric vortex model. Our results demonstrate the need for using flow-dependent error covariance for initializing a tropical cyclone with dynamically consistent inner-core structure, and provide incentives for future sensitivity experiments pertaining to model resolution and ensemble size.