The Livestock Risk Index

The Livestock Risk Index (also known as the Comprehensive Climate Index), uses temperature, relative humidity, wind speed and solar radiation to produce an adjusted temperature value that represents risk to livestock 1. The index is output in °F, and the index stress levels for hot and cold conditions are provided in the table below:

Stress Level Hot Conditions Cold Conditions  
    Newborn Adult
No Stress <25 >5 >0
Mild 25 to 30 0 to 5 0 to -10
Moderate >30 to 35 <0 to -5 <-10 to -20
Severe >25 to 40 <-5 to -10 <-20 to -30
Extreme >40 to 45 <-10 to -15 <-30 to -40
Extreme Danger >45 <-15 <-40

This table is adapted from Mader et al. 2010

The Livestock Risk Index is calculated by correcting relative humidity, wind speed, and solar radiation values so they can be used to adjust temperature:

\(RH_{cor} = \exp{0.00182 \times RH_{avg} + 1.8 \times 10^{-5} \times T_{avg} \times RH_{avg}} \times (0.000054 \times T_{avg}^2 + 0.00192 \times T_{avg} - 0.0246) \times (RH_{avg} - 30)\)

\(WS_{cor} = \frac{-6.56}{\exp{\left[ \frac{1}{2.26 \times WS + 0.23}^{0.45} \times (2.9 + 1.14 \times 10^{-6} \times WS^{2.5}-\log_{0.3}{2.26 \times WS + 0.33}^{-2}) \right]}} - 0.00566 \times WS^2 + 3.33\)

\(RAD_{cor} = 0.0076 \times RAD_{avg} - 0.00002 \times RAD_{avg} \times T_{avg} + 0.00005 \times T_{avg}^2 \sqrt{RAD_{avg}} + 0.1 \times T_{avg} - 2\)

\[Livestock\ Risk\ Index = T_{avg} + RH_{cor} + WS_{cor} + RAD_{cor}\]

where $T_{avg}$ is average temperature (°F), $RH_{avg}$ is average relative humidity (%), $WS_{avg}$ is average wind speed (mph), and $RAD_{avg}$ is average solar radiation (W/m^2). Variables ending in “cor” are the corrected values for calculation the index.