# Delta T

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:

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

# Dew Point Temperature

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 (%)

# Feels Like Temperature

If the temperature is at or above 80°F the Feels Like temperature equals the Heat Index. If temperature is below 50°F, Feels Like temperature equals the Wind Chill.

# Heat Index Temperature

Source: Weather.gov

Heat Index is calculated for temperatures at or above 80°F and a relative hummidity 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 (%)

# Pressure Trend

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 $$\Delta P \ge 1 mb$$

# Rain Rate

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 $$\Delta R \ge 50.0 mm/h$$

# Sea Level Pressure

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 ($$288.15 K$$)

# Vapor Pressure

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 (%)

# Wet Bulb Temperature

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 $$T_{wb}$$.

# Wind Chill Temperature

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