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### MDA

The Mesocyclone Detection Algorithm (MDA)
is the rotation algorithm from GR2Analyst. The MDA produces a Rotation (ROT) product which is invisible to the user and a Normalized Rotation (NROT) product which is visible to the user.  The algorithm is described below, and also in more detail in the powerpoint presentation GR2Analyst Algorithms in WFO Operations (Lincoln, 2012), which is the source of this page's images/tables.

The MDA algorithm is based upon:

Smith, T.M., and Elmore, K.L., 2004: The Use of Radial Velocity Derivative to Diagnose Rotation and Divergence. 11th Conf. on Aviation, Range, and Aerospace.  Hyannis, MA.  Amer. Meteor. Soc.

## Overview

Uses gradient in base velocity product and distance from the radar to create a normalized rotation product (NROT).
TVS/meso detections based on magnitude of rotation.

## Local Least Squares Derivative shear technique from Smith & Elmore (2004)

Smith & Elmore (2004) created a local, linear least squares derivative (LLSD) shear method in an attempt to improve estimates of shear magnitude and location of shear center.  The LLSD shear technique has been shown to improve upon simple peak-to-peak shear estimates because peak-to-peak estimates are not adjusted based on spatial resolution or radar scan elevation.

The LLSD is calculated by the equation:

*The equation and its usage is described further in Smith & Elmore (2004).

The LLSD shear technique was compared to the traditional peak-to-peak shear technique using two synthetic circulations of 0.01/s mangitude: one with a diameter of 5km and another with a diameter of 8km.  The 95% confidence interval for both circulations are shown below, wtih green indicating the LLSD shear technique and orange indicating the peak-to-peak shear technique.
For smaller circulations (such as the synthetic 5km circulation), the peak-to-peak shear method appears to do better at estimating shear magnitude at all ranges, but has a larger uncertainty range.  For the larger circulation (8km diameter), the LLSD technique does better on average across all ranges.

## The Mesocyclone Detection Algorithm in GR2Analyst

Base velocity data is dealiased based upon automated settings which are independent of those in the GR2Analyst "Dealias Settings" box.  The LLSD technique is applied over a 9x9 pixel area (5x5 pixel area for legacy resolution) to create the Rotation (ROT) product.  For the example below, the ROT value for the white cell is based on the velocity gradient across the darkened area.  ROT is then divided by a distance scaling factor (ROT Threshold) to create the Normalized Rotation (NROT) product.  The distance scaling factor is used to correct for radar distance issues like increased beam width vs. a fixed-size phenomena.

The center bin (white pixel) has a calculated ROT value of 0.0398/s, or 39.8/ks.  It is ~21km from the radar site.  From the default GR-MDA Settings, the ROT Threshold would be about 24.9/ks.  Dividing ROT by the ROT Threshold produces an NROT value of 1.6, which is dimensionless.

### MDA Trigger Criteria

Before NROT can turn into a TVS/meso detection, several criteria must be met:
1. Azimuthal pairs averaging 1.0 or more on each tilt
2. >=3 pairs becomes a run
3. Max pair becomes a node
4. Nodes correlated between tilts
5. ROT Count screens number of node correlations
6. Base elevation <10kft
7. VIL>5kg/m^2 within 10km
8. Weak rotation ignored if within 10km of stronger rotation
*An example set of radar data including a walk through of a MDA detection can be found in the associated powerpoint presentation.

### Mesocyclone/TVS Discrimination

If a detection is triggered, it becomes a TVS if the base elevation (lowest node) is below 5000ft, otherwise it is considered a mesocyclone.  Mesocyclone/TVS icons are colored based on the strength of NROT at the lowest node, where:
• NROT >1.0 (green from default color table)
• NROT >1.5 (yellow from default color table)
• NROT >2.0 (red from default color table).... rare detection, usually associated with significant tornadoes.**
• NROT >2.5 (purple from default color table)... very rare detection, almost always associated with strong to violent torandoes or obvious dealiasing failures.**
**This is my personal observation-based opinion, based upon review of easily 50-100 cases.  This has not yet been validated by a peer-reviewed publication.

Because the GR2Analyst MDA algorithm requires a base elevation of 10,000ft or less to trigger a detection and a base elevation of 5,000ft or less to trigger a TVS, there are some areas that are not close enough to a NEXRAD site for the MDA algorithm to indicate either.  Using the GR2Analyst equation for estimating beam centerline elevation above radar level, we can see the effective ranges for a TVS detection (green) and a mesocyclone detection (yellow).

## Sources of Uncertainty and Other Caveats

Mesocyclone/TVS strength is not dependent on a couplet or a certain gate-to-gate difference.  A MDA detection should be corroborated with other indicators like BV, BR, SW, and RHO/CC to make sure it makes sense and is based on good data.

Accurate calcuation of ROT, and thus, NROT, requires properly dealiased velocity data.  MDA detections near the radar or in heavy clutter should receive more scrutiny.  Check dealiasing algorithm by comparing data with/without algorithm.  Although dealiased through an independent algorithm than the one used for BV/SRV data, the presence of substantial failures of the BV/SRV dealiasing algorithm might suggest issues with the MDA algorithm and subsequent Meso/TVS detections.

Very low-topped cells may not trigger any MDA detection regardless of strength because of VILs near or below 5kg/m^2 or rotation height not reaching "ROT count" in GR-MDA Settings.  Nearby circulations might be dropped leaving only one MDA detection if too close together.