Weather World Calculations

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Weather World's Collection Of Weather Equations

The equations on this page have been collected from various sources, electronic, and print. Pay close attention to what units are required.

Note: The expression "x ** y" means raise
x to the ^y power.

Calculating Dewpoint, Relative Humidity, and Wetbulb
Calculating Heat Index and Wind Chill
- Calculating Heat Index
- Calculating Wind Chill Index
Unit Conversions

Calculating Dewpoint, Relative Humidity, and
Wetbulb

Given either dewpoint or relative humidity, the other can be calculated provided temperature is also given. If pressure is also given, then wetbulb can also be calculated. Given the wetbulb, dewpoint and relative humidity can be calculated provided temperature and pressure are also given.

Given Dewpoint: Calculate Relative Humidity and
Wetbulb

Input Variables

t = temperature (in Celsius)

p = pressure (in millibars)
(optional)

dp = dewpoint (in Celsius)

Output Variables

rh = relative humidity

wb = wetbulb (in Celsius)

es = vapor pressure when given temperature (in
millibars)

e = vapor pressure when given dewpoint (in
millibars)

Algorithm

es = VaporPressure(t)

e = VaporPressure(dp)

rh = RelativeHumidity(e, es)

if ( pressure variable was supplied )

wb = Wetbulb(t, p, dp)

[Contents]

Given Relative Humidity: Calculate Dewpoint and
Wetbulb

Input Variables

t = temperature (in Celsius)

p = pressure (in millibars)
(optional)

rh = relative humidity

Output Variables

dp = dewpoint (in Celsius)

wb = wetbulb (in Celsius)

es = vapor pressure when given temperature (in
millibars)

e = vapor pressure when given dewpoint (in
millibars)

Algorithm

es = VaporPressure(t)

e = es * (rh / 100)

dp =TemperatureFromVaporPressure(e)

if (rh < 100)

if ( pressure variable was supplied)

{

wb = Wetbulb(t, p, dp)

}

else

wb = dp

[Contents]

Given Wetbulb: Calculate Relative Humidity and
Dewpoint

Input Variables

t = temperature (in Celsius)

p = pressure (in millibars)

wb = wetbulb (in Celsius)

Output Variables

dp = dewpoint (in Celsius)

rh = relative humidity

es = vapor pressure when given temperature (in
millibars)

e = vapor pressure when given dewpoint (in
millibars)

wbvp = vapor pressure when given wetbulb (in
millibars)

Algorithm

es = VaporPressure(t)

wbvp = VaporPressure(wb)

e = wbvp-(0.00066 * (1+0.00155*wb)*p*(t-wb)

dp=TemperatureFromVaporPressure(e)

rh = RelativeHumidity(e, es)

[Contents]

Related Moisture Calculations

Approximate Wetbulb

Input Variables

t = temperature (in Celsius)

p = pressure (in millibars)

dp = dewpoint (in Celsius)

Output Variables

wb = wetbulb (in Celsius)

Temporary Variables

tmin = temperature or dewpoint, whichever
one is the lesser

tmax = temperature or dewpoint, whichever
one is greater

tcur

e

tcvp

peq

Algorithm

e = VaporPressure(dp)

while (true)

{

tcur=(tmax+tmin)/2

tcvp=VaporPressure(tcur)

peq=0.000660*(1+0.00155*tcur)*p*(t-tcur)

diff=peq-tcvp+e

if abs(diff) < 0.01

wb=tcur

return wb

if (diff < 0)

tmax=tcur

else

tmin=tcur

}

[Contents]

Calculate Relative Humidity

Input Variables

es = saturated vapor pressure (in millibars)

e = actual vapor pressure (in millibars)

Output Variables

rh = relative humidity

Algorithm

rh = e / es * 100

[Contents]

Calculate Vapor Pressure

Input Variables

t = temperature (in Celsius)

Output Variables

vp = vapor pressure (in millibars)

Algorithm

vp = 6.112 * (10 ** ((7.5*t)/(237.7+t)))

[Contents]

Calculate Temperature From Vapor Pressure

Input Variables

vps = supplied vapor pressure (in millibars)

Output Variables

t = temperature (in Celsius)

Temporary Variables

logs

Algorithm

logs=log₁₀(vps/6.112)

t = (237.7*logs)/(7.5-logs)

[Contents]

Calculate Specific Humidity

Input Variables

e = actual vapor pressure

p = pressure

Output Variables

spechum = specific humidity

Algorithm

spechum = (0.622*e)/(p-(0.378*e))

[Contents]

Calculate Mixing Ratio

Input Variables

e = actual vapor pressure

p = pressure

Output Variables

mixratio = mixing ratio

Algorithm

mixratio = ((0.622*e)/(p-e))*1000

[Contents]

Calculating Heat Index and Wind Chill

Calculating Heat Index

Input Variables

t = temperature (in Fahrenheit)

rh = relative humidity

Output Variables

heatindex = heat index (in Fahrenheit)

Temporary Variables

t2 = t * t

t3 = t2 * t

rh2 = rh * rh

rh3 = rh2 * rh

Algorithm

heatindex = 16.923 + 0.185212*t + 5.37941*rh - 0.100254*t*rh + (0.941695e-2)*t2 + (0.728898e-2)*rh2 + (0.345372e-3)*t2*rh - (0.814971e-3)*t*rh2 + (0.102102e-4)*t2*rh2 - (0.38646e-4)*t3 + (0.291583e-4)*rh3 + (0.142721e-5)*t3*rh + (0.197483e-6)*t*rh3 - (0.218429e-7)*t3*rh2 + (0.843296e-9)*t2*rh3 - (0.481975e-10)*t3*rh3

Note: A number like 0.38646e-4 is shorthand for 0.38646 *
10^-4 and 0.000038646 in many computer languages.

[Contents]

Calculating Wind Chill Index

Input Variables

t = temperature (in Fahrenheit)

speed = wind speed (in miles per hour)

Output Variables

chill = wind chill ((in Fahrenheit)

Algorithm

chill = 0.0817*(3.71*sqrt(speed)+5.81-0.25*speed)*(t-91.4)+91.4

if (chill > t ) then

chill = t

[Contents]

Unit Conversions

Temperature Conversions

Celsius to Fahrenheit

fahrenheit = (celsius * 9 / 5) + 32

Fahrenheit to Celsius

celsius = (fahrenheit-32) * 5 / 9

[Contents]

Wind Conversions

Convert wind units using the wind unit conversion table and the instructions below.

Find the unit you are converting in the Convert From column on
the left.
Then find the unit you are converting in the Convert To column
across the top.
The cell that intersects the selected unit on the left and the selected unit across the top
contain the number that you multiply by to convert your unit.

**Wind Unit Conversion Table**
Convert From	Convert To


Convert From		miles/hour	meters/sec	kilometers/hour	knots
	miles/hour	---	0.44704	1.60934	1.15193
	meters/sec	2.23693	---	3.6	1.96936
	kilometers/hour	0.62137	0.27778	---	0.54704
	knots	0.86811	0.50778	1.82800	---

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