# Calculating wind chill in Fortran

As temperatures fall and the wind howls, we begin hearing about the danger of “wind chill”. The “wind chill” factor W is reported by meteorologists during winter. W is an equivalent temperature that accounts for the increased chilling effects of wind on a human body. The wind chill factor combines the temperature and wind speed to tell you how cold the wind makes it “feel”. The coldest wind chill recorded in Canada was at Pelly Bay, Nunavut, on January 13, 1975, when 56 km/h winds (a wind chill factor of 3,357 watts/m²) made the temperature of -51°C feel more like -92°C.

The first wind chill formula and associated tables were based on research conducted by scientists Paul A. Siple and Charles F. Passel in Antarctica in the 1940s. The research found that the rate at which water freezes depends on three factors: how warm it was to begin with, the outside temperature and the wind speed. This Wind Chill Index was a 3-4 digit number with units of kilocalories per square metre per hour (kcal/m2/hr). For example 1400 was the threshold for frostbite. The original Siple-Passel equation for wind chill factor (°C) is:

C = (10.0√V - V + 10.5)(33-Ta)

where V is the wind velocity (m/s), and Ta was the air temperature (°C). One of the problems with this formula was that the units were not very user-friendly for the general public. In 2001 a new formula was derived , based on a model of how fast a human face loses heat and incorporates modern heat transfer theory, that is, the theory of how much heat is lost by the body to its surroundings during cold and windy days. (The face is the part of the body most often exposed to severe winter weather). It must be noted that although the wind chill factor is expressed on a temperature scale (the Celsius scale in Canada), it is not a temperature: it only expresses a human sensation. There are two formulas used by Environment Canada:

W = 13.12 + 0.6215Tair - 11.37V(10m)0.16 + 0.3965Tair V(10m)0.16
W = Tair + [(-1.59 + 0.1345Tair)/5]V(10m)

where W is the wind chill factor based on the Celsius temperature scale, Tair is the air temperature in degrees celsius, and V10m is the wind speed in km/h at 10 meters. The first equation is used when the temperature of the air is ≤ 0°C and the wind speed is ≥ 5km/h. Then second equation is used when the temperature of the air is ≤ 0°C and the wind speed is > 0km/h, but < 5km/h.

Here is the Fortran program to perform the calculation:

program wind_chill

real :: airTemp, windS, windCF

! Obtain the user input
write (*,*) 'Air temperature (Celsius): '
write (*,*) 'Wind speed (km/hr): '

if (airTemp <= 0.0) then
if (windS >= 5.0) then
windCF = 13.12 + 0.6215*airTemp - 11.37*windS**0.16 + &
0.3965*airTemp*windS**0.16;
else if ((windS > 0.0) .and. (windS < 5.0)) then
windCF = airTemp + ((-1.59+0.1345*airTemp)/5.0)*windS;
else
write (*,*) 'There is no wind!'
end if
write (*,100) windCF
100 format ('The temperature feels like ', F7.2, ' degrees Celsius')
else
write (*,*) 'Unable to calculate - the air temperature is too high'
end if

end program wind_chill

The program is inherently easy to write in Fortran. Here’s the program running:

Air temperature (Celsius):
-3
Wind speed (km/hr):
15
The temperature feels like   -8.12 degrees Celsius