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Published on September 29th, 2013 | by Simi

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# Weather wrangling

The Australian Bureau of Meteorology uses the following formula for the calculation of apparent temperature as a function of actual (dry bulb) temperature, wind speed and water vapour pressure. Note that for approximating wind chill it is assumed that appropriate dry clothing is worn while for extreme heat, cloud cover is not taken into account.

AT = Ta + 0.33×e − 0.70×ws − 4.00

where:
AT = Apparent temperature (°C)
Ta = Dry bulb temperature (°C)
e = Water vapour pressure (hPa) [humidity]
ws = Wind speed (m/s) at an elevation of 10 meters

The water vapour pressure can be calculated from the dry bulb temperature and relative humidity using this equation:

e = rh / 100 × 6.105 × exp ( 17.27 × Ta / ( 237.7 + Ta ) )

where:
rh = Relative Humidity [%]

(Reference: http://www.bom.gov.au/info/thermal_stress/#atapproximation)
For the first two questions state answers rounded up to the nearest tenth of a degree celsius.

1. Suppose the dry bulb temperature is 10°C and the relative humidity is 70%. This makes e = 8.58. Find the apparent temperature when the wind speed (at an elevation of 10m) is
a) 0
b) 5 m/s (18 km/h)
c) 10 m/s (36 km/h)

2. Suppose the dry bulb temperature is 35°C and there is no wind. Find the apparent temperature when the relative humidity is
a) 20%
b) 40%
c) 60%

3. Plot apparent temperature versus wind speed from 0 to 20m/s (at an elevation of 10m) for a dry bulb temperature of 5, 10, 15, 20°C and 70% humidity. Hence or otherwise, find at 10°C what wind speed achieves an apparent temperature of 0°C.

4. Plot apparent temperature versus humidity for a dry bulb temperature of 25, 30, 35, 40°C and 0km/h wind speed. Hence or otherwise, find at 35°C what relative humidity is required for an apparent temperature of 45°C.

Question created by Chaitanya Rao, Daniel Mathews, Norman Do and Michael Evans

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