Dynamics and Structure of Forecast Error Covariance in the Core of a Developing Hurricane

Abstract

Abstract An ensemble of cloud-resolving forecasts from the Weather Research and Forecasting model (WRF) was used to study error covariance for Hurricane Katrina (2005) during a 64-h period in which the storm progressed from a tropical storm to a category-4 hurricane. Spatial error covariance between hypothetical measurements and model state variables was 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 tropical storm, error covariance structures in the 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 becomes markedly greater with increasing lead time, as diverging storm tracks cause large gradients of wind, temperature, and pressure to be concentrated farther from the mean vortex center. Ensemble variance for model state variables on storm-relative coordinates 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. Our results demonstrate the necessity of using flow-dependent error covariance for initializing a tropical cyclone with dynamically consistent inner-core structure, and provide motivation for future sensitivity experiments pertaining to model resolution and ensemble size.