Analyzing Radar Observed Mesocyclone using Vortex-flow-dependent Background Covariance

A variational method is developed in an incremental form with respect to a given background field for analyzing radar observed mesocyclone in a vortex-following coordinate system. This method has the following unique features: (i) The coordinate system tracks and follows the vortex center movement at each vertical level. (ii) The streamfunction and vertically-integrated velocity potential are used as the control variables for the incremental analysis, so the mass continuity equation can be satisfied exactly in a strong-constraint form and the background covariance functions can be conveniently formulated to include the desired vortex-flow-dependences. (iii) The square root of the background covariance matrix is derived, using the convolution theorem, and constructed directly from each covariance function and is then used to scale its associated control variable for optimal pre-conditioning of the cost-function. The two-dimensional version of the method has been incorporated into our real-time radar wind analysis system and successfully applied to tornadic mesocyclone observed by the operational KTLX and KFDR radars on 5/24/2011. The results will be represented at the conference. >