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Calculating Australian Aparant Temperature

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iisfaq:
double RelativeHumidity = 32;
double TemperatureInC = 7.170000;
double SolarRadiationInWSquareMeter = 174;
double WaterVapourPressure = RelativeHumidity / 100 * 6.105 * Math.Exp(17.27 * TemperatureInC / (237.7 + TemperatureInC));
double WindSpeedMetersPerSecond = 0;

double ApparentTemperature_NonRadiation = TemperatureInC + (0.33 * WaterVapourPressure) - (0.70 * WindSpeedMetersPerSecond) - 4;
double ApparentTemperature_Radiation = TemperatureInC + (0.348 * WaterVapourPressure) - (0.70 * WindSpeedMetersPerSecond) + (0.70 * (SolarRadiationInWSquareMeter / (WindSpeedMetersPerSecond + 10))) - 4.25;

I have taken the formula from http://www.bom.gov.au/info/thermal_stress/

In my case it is quite cold, 7.17C

The first method ApparentTemperature_NonRadiation returns 4.23C
The second method ApparentTemperature_Radiation returns 16.22C (so I have a problem here)

The only difference in the formulas are

 0.70×Q/(ws + 10) 

Q = Net radiation absorbed per unit area of body surface (w/m2) 

My Solar is 177 at the moment (not a very strong day) so does that mean Q = 177?

If there is no wind speed then that would be

0.70 * 174= 121.8

Now 121.8 / (ws + 10) = 12.18f ws = 0 (no wind)

Well we can not add 12.18C to the temperature

Can anyone spot my problem?


Here is the original formula

The formula for the AT used by the Bureau of Meteorology is an approximations of the value provided by a mathematical model of heat balance in the human body.

It can include the effects of temperature, humidity, wind-speed and radiation. Two forms are given, one including radiation and one without.

On this site we use the non-radiation version.

Version including the effects of temperature, humidity, and wind:
AT = Ta + 0.33×e − 0.70×ws − 4.00

Version including the effects of temperature, humidity, wind, and radiation:
AT = Ta + 0.348×e − 0.70×ws + 0.70×Q/(ws + 10) − 4.25

where:
Ta   = Dry bulb temperature (°C)
e   = Water vapour pressure (hPa) [humidity]
ws   = Wind speed (m/s) at an elevation of 10 meters
Q   = Net radiation absorbed per unit area of body surface (w/m2)

The vapour pressure can be calculated from the temperature and relative humidity using the equation:

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

where:
rh   = Relative Humidity [%]

Source: Norms of apparent temperature in Australia, Aust. Met. Mag., 1994, Vol 43, 1-16

mackbig:
I loaded up the calcs into excel and played a bit.  AT is very close to our Humidex here in Canada.

I came up with similar results to you.
4.24C and 16.23C

Q cannot be Solar radiation as we know it here.
1000 W/m2 gives an AT of 74C

I found this PDF.  Good read...  :shock: I just glanced at it, you might be able to decipher it, but its over my head.
http://reg.bom.gov.au/amm/docs/1994/steadman.pdf
There are hundreds of variables and formula's in there.

Maybe you could pop a note to Bureau of Meterology to see what they say about Q.  But they use the non-Q version on their site.

Andrew

WeatherBeacon:

You did your calculations correctly.

The article you cite says that AT is an approximation to the WBGT (wet Bulb Globe Temperature). Thus, both ATs (with and without radiation) are to be compared the the WBGT rather than to one another.

The article also has this comment:


--- Quote ---The AT used here does not include the effect of the sun, but this can be factored in. Under Australian conditions the effect of full sun produces a maximum increase in the AT of about 8°C when the sun is at its highest elevation in the sky.

--- End quote ---

Using the data you provided, we obtain


* WBGT = 9.3C
* AT without radiation = 4.2C (this is consistent with the chart they provide)
* AT with radiation = 16.2C
Thus, the AT with radiation is 7C higher than the WBGT (consistent with the article's comment).

The article also states:


--- Quote ---... the Bureau uses an approximation to the WBGT. This approximation uses standard meteorologically measured temperature and humidity to calculate an estimation of the WBGT under moderately sunny light wind conditions. Real variations of sunshine and wind are not taken into account. The formula is likely to overestimate the WBGT in cloudy or windy conditions, or when the sun is low or below the horizon. Under clear full sun and low humidity conditions the approximation underestimates the WBGT slightly.

. . .

Because the Bureau of Meteorology uses an approximation to the WBGT, the user should clearly understand the limitations of this approximation as compared to a real measured WBGT. The fact that the values we produce assume a constant 'moderately sunny' day with 'light winds' may be overlooked, and it might be assumed that we have measured the true WBGT. This can cause confusion. The Apparent Temperature (AT) (see below) does not have this ambiguity and consideration should be made as to whether this is a more appropriate guide for your activity.

--- End quote ---

Kevin...

mackbig:
Kevin,
If 8C is the maximum apparrent bump due to full sun, a measely 174w/m2 with a low start temp almost bumps to the max?
Why does using a good sunny 1000w/m2 seem to bump 70 degrees?

My calc on a 30C day with 40% rh, and 1000w/m2 is giving an AT(with Q) of 101C.  That's literally boiling.
The without Q AT looks normal and matches the chart.

Andrew

WeatherBeacon:

--- Quote from: mackbig on July 22, 2011, 10:36:13 AM ---Kevin,
If 8C is the maximum apparrent bump due to full sun, a measely 174w/m2 with a low start temp almost bumps to the max?
Why does using a good sunny 1000w/m2 seem to bump 70 degrees?

My calc on a 30C day with 40% rh, and 1000w/m2 is giving an AT(with Q) of 101C.  That's literally boiling.
The without Q AT looks normal and matches the chart.

Andrew

--- End quote ---

Yeah, I readily admit that I don't understand these formulas. When using formulas for any calculations, it is important to know the assumptions behind them, the exact meaning of each parameter involved, and the range of validity for each parameter. For example, in the U.S., the heat index formula is valid only for temps above 80oF, dew point temperatures exceeding 54°F, and relative humidities exceeding 40%.

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