Estimates of Gradients in Radar Moments Using a Linear Least Squares Derivative Technique

Mahalik, Matthew C.; Smith, Brandon R.; Elmore, Kimberly L.; Kingfield, Darrel M.; Ortega, Kiel L.; Smith, Travis M.

doi:10.1175/WAF-D-18-0095.1

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Estimates of Gradients in Radar Moments Using a Linear Least Squares Derivative Technique

2019
By Mahalik, Matthew C. ; Smith, Brandon R. ; Elmore, Kimberly L. ; ...
Source: Wea. Forecasting (2019) 34 (2): 415–434

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Journal Title:

Weather And Forecasting
Personal Author:

Mahalik, Matthew C. ; Smith, Brandon R. ; Elmore, Kimberly L. ; Kingfield, Darrel M. ; Ortega, Kiel L. ; ... More +

Mahalik, Matthew C. ; Smith, Brandon R. ; Elmore, Kimberly L. ; Kingfield, Darrel M. ; Ortega, Kiel L. ; Smith, Travis M. Less -
NOAA Program & Office:

CIRES (Cooperative Institute for Research in Environmental Sciences) ; CIMMS (Cooperative Institute for Mesoscale Meteorological Studies) ; OAR (Oceanic and Atmospheric Research) ; NSSL (National Severe Storms Laboratory)

CIRES (Cooperative Institute for Research in Environmental Sciences) ; CIMMS (Cooperative Institute for Mesoscale Meteorological Studies) ; OAR (Oceanic and Atmospheric Research) ; NSSL (National Severe Storms Laboratory) Less -
Description:

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.
Keywords:

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Radar
Source:

Wea. Forecasting (2019) 34 (2): 415–434
DOI:

https://doi.org/10.1175/WAF-D-18-0095.1
Document Type:

Journal Article
Funding:

Grant no. NA11OAR4320072
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Submitted
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urn:sha256:361ce0ca9a66a5da86de1c010f5b973662a57b23119eea43433695728c9e9862
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/view/noaa/25111/noaa_25111_DS1.pdf
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Estimates of Gradients in Radar Moments Using a Linear Least Squares Derivative Technique

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