# Physics:Ellrod index

In meteorology the Ellrod index is a technique for forecasting clear-air turbulence. It is calculated based on the product of horizontal deformation and vertical wind shear derived from numerical model forecast winds aloft. The deformation predictors are calculated using following information.

• Shearing deformation:
$\displaystyle{ DSH=\frac{dv}{dx} + \frac{du}{dy} }$.
• Stretching deformation:
$\displaystyle{ DST = \frac{du}{dx} - \frac{dv}{dy} }$.

Where u and v are horizontal components of the wind.

• Total deformation equals to:
$\displaystyle{ DEF = \sqrt{DSH^2 + DST^2} }$.
• Convergence:
$\displaystyle{ CVG = -(\frac{du}{dx} + \frac{dv}{dy}) }$
• Vertical wind shear:
$\displaystyle{ VWS = \frac{\Delta V}{\Delta Z} }$

And the resulting index is given by:

$\displaystyle{ EI = VWS \times (DEF + CVG) }$

To correspond to clear-air turbulence pilot reports the following table can be used:

Reported EI value threshold
Light-Moderate 4
Moderate 8
Moderate-Severe 12

Reports of CAT are subjective in nature and, therefore, uncalibrated since they depend upon the pilot's perception of the degree of turbulence, which in turn depends upon the weight, speed, and aerodynamic characteristics of the aircraft being flown.

Gary P. Ellrod, M.S., CCM*

Gary has more than 35 years experience as a research meteorologist and weather forecaster, mostly with the National Oceanic and Atmospheric Administration’s (NOAA) National Weather Service (NWS) and National Environmental Satellite, Data, and Information Service (NESDIS). Since 2007, a consulting meteorologist with EwXC.