# Air Density

$$\frac{P_{stn}\times{}100}{R_{specific}T}$$

\(P_{stn}\) = station pressure in millibars (mb)

\(T\) = temperature in Kelvin

\(R_{specific}\) = specific gas constant for dry air (287.058 J/(kg·K))

$$\frac{P_{stn}\times{}100}{R_{specific}T}$$

\(P_{stn}\) = station pressure in millibars (mb)

\(T\) = temperature in Kelvin

\(R_{specific}\) = specific gas constant for dry air (287.058 J/(kg·K))

Delta T, \(\Delta T\), is used in agriculture to indicate acceptable conditions for spraying pesticides and fertilizers. It is simply the difference between the air temperature (aka "dry bulb temperature") and the wet bulb temperature:

$$\Delta T = T - T_{wb}$$

Source: RSMAS

$$T_{d} = \frac{243.04 \bigg[\ln\big(\frac{RH}{100}\big) + \frac{17.625 \times{} T}{243.04 + T}\bigg]}{17.625 - \ln\big(\frac{RH}{100}\big) - \frac{17.625 \times{} T}{243.04 + T}}$$

\(T_{d}\) = dew point in degrees Celsius (°C)

\(T\) = temperature in degrees Celsius (°C)

\(RH\) = relative humidity (%)

The Feels Like temperature is equal to the Heat Index if the temperature is at or above 80°F and the relative humidity is at or above 40%. Alternatively, the Feels Like temperature is equal to Wind Chill if the temperature is at or below 50°F and wind speeds are above 3mph. If neither condition applies, the Feels Like temperature is equal to the air temperature.

Source: Weather.gov

Heat Index is calculated for temperatures at or above 80°F and a relative humidity at or above 40%.

$$T_{hi} = -42.379 + (2.04901523\times{}T) \\+ (10.1433127\times{}RH) - (0.22475541\times{}T\times{}RH) \\-(6.83783\times{}10^{-3}\times{}T^2) -(5.481717\times{}10^{-2}\times{}RH^2) \\+(1.22874\times{}10^{-3}\times{}T^2\times{}RH)+(8.5282\times{}10^{-4}\times{}T\times{}RH^2) \\-(1.99\times{}10^{-6}\times{}T^2\times{}RH^2)$$

\(T\) = temperature in degrees Fahrenheit (°F)

\(RH\) = relative humidity (%)

The Pressure Trend description is determined by the rate of change over the past 3 hours.

$$\Delta P = P_{0h} - P_{3h}$$

\(P_{0h}\) = the latest pressure reading in millibars (mb)

\(P_{3h}\) = pressure reading 3 hours ago in millibars (mb)

Description | Rate |
---|---|

Steady | \(-1 mb < \Delta P < 1 mb \) |

Falling | \(\Delta P \le -1 mb\) |

Rising | \(\Delta P \ge 1 mb \) |

The Rain Rate description is set according to the latest one minute accumulation, extrapolated to an hourly rate.

$$\Delta R = \frac{V_{r} \times{} 60min}{1h}$$

\(V_{r}\) = rain accumulation in millimeters over one minute (mm/min)

Description | Rate |
---|---|

None | \(\Delta R = 0 mm/h\) |

Very Light | \(0 mm/h < \Delta R < 0.25 mm/h\) |

Light | \(0.25 mm/h \le \Delta R < 1.0 mm/h\) |

Moderate | \(1.0 mm/h \le \Delta R < 4.0 mm/h\) |

Heavy | \(4.0mm/h \le \Delta R < 16.0 mm/h\) |

Very Heavy | \(16.0 mm/h \le \Delta R < 50.0 mm/h\) |

Extreme | \(\Delta R \ge 50.0 mm/h\) |

Source: AMS

$$P_{sl} = P_{sta}\Big[1 + \frac{P_{0}}{P_{sta}}^{\frac{R_{d}\gamma_{s}}{g}}\frac{\gamma_{s}(h_{el} + h_{ag})}{T_{0}}\Big]^{\frac{g}{R_{d}\gamma_{s}}}$$

\(P_{sta}\) = station pressure in millibars (mb)

\(P_{0}\) = standard sea level pressure (1013.25mb)

\(R_{d}\) = gas constant for dry air (\(287.05 \frac{J}{kg \cdot K}\))

\(\gamma_{s}\) = standard atmosphere lapse rate (\(0.0065 \frac{K}{m}\))

\(g\) = gravity (\(9.80665 \frac{m}{s^{2}}\))

\(h_{el}\) = ground elevation in meters (m)

\(h_{ag}\) = station height above ground in meters (m)

\(T_{0}\) = standard sea level temperature (\(288.15 K\))

Source: Weather.gov

Vapor pressure, \(P_{v}\) can be estimated in units of millibar (mb) as follows:

$$P_{v} = \frac{RH}{100} \times{} 6.112 \times{} e^{\Big(\frac{17.67 \times{} T}{T + 243.5}\Big)}$$

\(T\) = temperature in degrees Celsius (°C)

\(RH\) = relative humidity (%)

Source: Weather.gov

Wet Bulb Temperature (\(T_{wb}\)), is determined using the following formulas for actual vapor pressure (\(P_{v}\)) and the vapor pressure related to wet bulb temperature (\(P_{v,wb}\)) in millibar (mb):

$$P_{v} = P_{v,wb} - P_{stn} \times (T - T_{wb}) \times 0.00066 \times (1 + (0.00115 \times T_{wb}))$$

$$P_{v,wb} = 6.112\times{}e^{\Big(\frac{17.67\times{}T_{wb}}{T_{wb}+243.5}\Big)}$$

\(T\) = temperature in degrees Celsius (°C)

\(RH\) = relative humidity (%)

\(P_{stn}\) = station pressure in millibar (mb)

Note, the above equations can't be solved for \(T_{wb}\) directly, but several iterative methods may be used to determine \(T_{wb}\).

Source: Weather.gov

Wind Chill is calculated for temperatures at or below 50°F and wind speeds above 3mph.

$$T_{wc} = 35.74 + (0.6215\times{} T) \\- \Big(35.75\times{}V^{0.16}\Big) \\+ \Big(0.4275\times{}T\times{}V^{0.16}\Big)$$

\(T\) = temperature in degrees Fahrenheit (°F)

\(V\) = wind speed in mph