Spatially Variable Advection Correction of Radar Data. Part I: Theoretical Considerations

Abstract

Radar data-based analysis products, such as accumulated rainfall maps, dual-Doppler wind syntheses, and thermodynamic retrievals, are prone to substantial error if the temporal sampling interval is too coarse. Techniques to mitigate these errors typically make use of advection-correction procedures (space-to-time conversions) in which the analyzed radial velocity or reflectivity field is idealized as a pattern of unchanging form that translates horizontally at constant speed. The present study is concerned with an advectioncorrection procedure for the reflectivity field in which the pattern-advection components vary spatially. The analysis is phrased as a variational problem in which errors in the frozen-turbulence constraint are minimized subject to smoothness constraints. The Euler-Lagrange equations for this problem are derived and a solution is proposed in which the trajectories, pattern-advection fields, and reflectivity field are analyzed simultaneously using a combined analytical and numerical procedure. The potential for solution nonuniqueness is explored.

A Diabatic Lagrangian Technique for the Analysis of Convective Storms. Part II: Application to a Radar-Observed Storm

“…1). The application of a constant storm motion via the timemorphing scheme contrasts with the approach of Shapiro et al (2010), who instead adopt a variational approach to calculate a spatially variable reference frame motion vector. The advection-corrected gridpoint fields from each time-spaced analysis are then mapped back to the fixed radar analysis grid domain via bilinear spatial interpolation.…”

Mobile ground‐based SMART radar observations and wind retrievals during the landfall of Hurricane Harvey (2017)

“…Dual‐ and multiple‐Doppler analysis has long been utilized by the meteorological community to retrieve the three‐dimensional flow within storms. The errors associated with dual‐Doppler analysis are well known (Chong et al , ; Dowell and Shapiro, ; Shapiro et al , ; Potvin et al , ), often related to the temporal and spatial offset of radar observations, the underlying assumptions of mass continuity, and the under‐sampling of the boundary layer or storm top divergence.…”

“…As the current version of the wind retrieval programme only allows for advection of data using a single linear velocity (e.g. Shapiro et al , ), no advection correction was applied to the wind retrievals documented here. Given that our research focus was on meso‐beta (10‐100 km) features, the errors induced by the lack of advecting the data to a single point in time were deemed acceptable.…”

Comparison between Dual-Doppler and EnKF Storm-Scale Wind Analyses: Observing System Simulation Experiments with a Supercell Thunderstorm

“…The DDAs are obtained using the 3D-VAR technique described in Shapiro et al (2009) and Potvin et al (2012a). The technique weakly satisfies the radial wind observations, the anelastic mass conservation equation and a smoothness constraint, and exactly satisfies the impermeability condition at the ground (the vorticity equation constraint tested in the referenced studies was not used in our experiments).…”