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Meteorological calculations translate raw atmospheric measurements—including air pressure, relative humidity, solar declination, and wind velocity—into actionable environmental metrics like Heat Index, Wind Chill, and Astronomical Day Length.

1. The Heat Index (Apparent Temperature) Formula

The National Weather Service (NWS) calculates the Heat Index ($HI$) using the multivariate Rothfusz regression equation when ambient temperature $T \ge 80^\circ\text{F}$ ($26.7^\circ\text{C}$) and relative humidity $RH \ge 40\%$:

Where coefficients model human sweat evaporation resistance under warm, humid conditions.

2. Magnus-Tetens Dew Point Approximation

The Dew Point ($T_d$) is the temperature to which air must be cooled at constant pressure for water vapor to condense into liquid water (dew or fog):

Using standard Magnus coefficients $a = 17.27$ and $b = 237.7^\circ\text{C}$.

3. Astronomical Sunrise & Sunset Equations

Sunrise and sunset times are calculated using the Solar Hour Angle ($\omega_0$):

Where $\phi$ is the observer's latitude, $\delta$ is the solar declination angle, and $-0.833^\circ$ accounts for atmospheric refraction and the sun's angular semidiameter.