1. Estimates of Gradients in Radar Moments Using a Linear Least Squares Derivative Technique
- Author
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Brandon R. Smith, Travis M. Smith, Kimberly L. Elmore, Darrel M. Kingfield, Matthew C. Mahalik, and Kiel L. Ortega
- Subjects
Atmospheric Science ,Data processing ,010504 meteorology & atmospheric sciences ,Plane (geometry) ,Mathematical analysis ,0207 environmental engineering ,Convergence divergence ,02 engineering and technology ,Derivative ,01 natural sciences ,Least squares ,law.invention ,law ,Range (statistics) ,Radar ,020701 environmental engineering ,Physics::Atmospheric and Oceanic Physics ,Linear least squares ,0105 earth and related environmental sciences ,Mathematics - Abstract
The local, linear, least squares derivative (LLSD) approach to radar analysis is a method of quantifying gradients in radar data by fitting a least squares plane to a neighborhood of range bins and finding its slope. When applied to radial velocity fields, for example, LLSD yields part of the azimuthal (rotational) and radial (divergent) components of horizontal shear, which, under certain geometric assumptions, estimate one-half of the two-dimensional vertical vorticity and horizontal divergence equations, respectively. Recent advances in computational capacity as well as increased usage of LLSD products by the meteorological community have motivated an overhaul of the LLSD methodology’s application to radar data. This paper documents the mathematical foundation of the updated LLSD approach, including a complete derivation of its equation set, discussion of its limitations, and considerations for other types of implementation. In addition, updated azimuthal shear calculations are validated against theoretical vorticity using simulated circulations. Applications to nontraditional radar data and new applications to nonvelocity radar data including reflectivity at horizontal polarization, spectrum width, and polarimetric moments are also explored. These LLSD gradient calculations may be leveraged to identify and interrogate a wide variety of severe weather phenomena, either directly by operational forecasters or indirectly as part of future automated algorithms.
- Published
- 2019