Author Topic: Calculating Australian Aparant Temperature  (Read 11413 times)

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Offline iisfaq

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Calculating Australian Aparant Temperature
« on: July 21, 2011, 11:13:09 PM »
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

Offline mackbig

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Re: Calculating Australian Aparant Temperature
« Reply #1 on: July 22, 2011, 07:47:49 AM »
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

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Offline WeatherBeacon

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Re: Calculating Australian Aparant Temperature
« Reply #2 on: July 22, 2011, 09:35:57 AM »

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.

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.

Kevin...
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Offline mackbig

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Re: Calculating Australian Aparant Temperature
« Reply #3 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

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Offline WeatherBeacon

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Re: Calculating Australian Aparant Temperature
« Reply #4 on: July 22, 2011, 11:00:17 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

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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Offline mackbig

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Re: Calculating Australian Aparant Temperature
« Reply #5 on: July 22, 2011, 11:17:48 AM »
Well if you can figure it out, it must be broken.  :lol:

I thought it was strange that they define all the other variables pretty good, then just throw out that radiation variable like everyone has a w/m2 number handy.

Andrew

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Offline WeatherBeacon

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Re: Calculating Australian Aparant Temperature
« Reply #6 on: July 22, 2011, 11:44:56 AM »
Well if you can figure it out, it must be broken.  :lol:

Me? Wrong? (Too many times today already. :-))


I thought it was strange that they define all the other variables pretty good, then just throw out that radiation variable like everyone has a w/m2 number handy.

Andrew

Yeah, that part seemed vague to me, too. The article says:

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

What is meant by "absorbed"?

Of course, I don't have access to the article: Norms of apparent temperature in Australia, Aust. Met. Mag., 1994, Vol 43, 1-16.

Regards,

Kevin...

EDIT:  Well, I found the Steadman article online. Sigh.
« Last Edit: July 22, 2011, 11:47:06 AM by WeatherBeacon »
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Offline WeatherBeacon

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Re: Calculating Australian Aparant Temperature
« Reply #7 on: July 22, 2011, 12:01:35 PM »

Yeah, that part seemed vague to me, too. The article says:

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

Kevin...

EDIT:  Well, I found the Steadman article online. Sigh.

Well, upon a quick perusal of Steadman's article, it is clear that Q does not represent solar radiation. What Q does represent exactly isn't yet clear to me.

Kevin...
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Offline WeatherBeacon

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Re: Calculating Australian Aparant Temperature
« Reply #8 on: July 22, 2011, 01:01:11 PM »

Well... as stated in the article, Q represents net radiation absorbed by the human body.

Steadman's own article states that in Australia, this usually varies from -40 to 130 W/m2. To put it simply, it accounts for the fact that the human body also radiates heat, and sometimes it radiates more than it takes in. In the article, he accounts for variations in Q due to time of day, time of year, cloud type, diffuse radiation, etc. Pretty complicated and although interesting, it is not something I particularly want to study further. Sorry, but hope this helps.

Regards,

Kevin...
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Offline mackbig

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Re: Calculating Australian Aparant Temperature
« Reply #9 on: July 22, 2011, 01:09:55 PM »
Kevin,
When I saw you viewing this thread after I posted this morning, I somehow guess this might be hard for you to get off your mind...

Now get outside and enjoy the weather.

Andrew

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Offline WeatherBeacon

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Re: Calculating Australian Aparant Temperature
« Reply #10 on: July 22, 2011, 01:38:33 PM »
Kevin,
When I saw you viewing this thread after I posted this morning, I somehow guess this might be hard for you to get off your mind...

Now get outside and enjoy the weather.

Andrew

Exactly! You know me well, Andrew, and thanks for the good tip! :grin: Right now it's only 81oF (27oC), so quite tolerable considering it reached 98oF (37oC) yesterday.

Regards,

Kevin...
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Offline WeatherBeacon

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Re: Calculating Australian Aparant Temperature
« Reply #11 on: July 22, 2011, 01:58:38 PM »

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

No. Not if by that you mean solar radiation. See the posts above.

Regards,

Kevin...

p.s.  You have a nice looking web site!
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Offline iisfaq

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Re: Calculating Australian Aparant Temperature
« Reply #12 on: July 22, 2011, 03:14:36 PM »
I did some searches yesterday for the wording "Net radiation absorbed per unit area of body surface" and most just referred to the formula we have seen.

I did come across a Power Point http://www.google.co.nz/url?sa=t&source=web&cd=1&ved=0CBYQFjAA&url=http%3A%2F%2Fgeog-www.sbs.ohio-state.edu%2Fcourses%2FG230%2Fhobgood%2FASP230Lecture10.ppt&rct=j&q=%22Surface%20energy%20fluxes%20and%20Temperature%22&ei=usgpTqeTOdHegQeg8an8Cg&usg=AFQjCNFcQEvrJislXuG7Gaj9AAqKonDQPQ that mentioned this:

The net radiation is the difference between the radiant energy absorbed and the radiant energy emitted.

Net radiation = solar radiation absorbed
   + terrestrial radiation absorbed
   - terrestrial radiation emitted

If the solar radiation absorbed by the Earth’s surface is 600 W/m2, the terrestrial radiation absorbed is 80 W/m2, and the terrestrial radiation emitted by the Earth’s surface is 300 W/m2, then what is the net radiation at the surface?

Net Radiation = 600 W/m2 +   80 W/m2 -  300 W/m2

Net Radiation =  380 W/m2

I can determine the Solar Radiation (but is this absorbed) from my Solar Sensor
Terrestrial radiation absorbed = ?
Terrestrial radiation emitted = ?

Are those terrestrial real static values or values which change?

So in my case

double SolarRadiationInWSquareMeter = 174  + 80 - 300;

ApparentTemperature_Radiation = 0.82C

Using Kevins example

30C with 40% RH and 1000w

we get

ApparentTemperature_Radiation = 86.23C

So those terrestrial values change - and are not static.

I will have a look at the steadman PDF and see if I can make anything out of it.

Chris

Offline mackbig

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Re: Calculating Australian Aparant Temperature
« Reply #13 on: July 22, 2011, 03:19:01 PM »
Personally I would just go with the non-Radiation version.  It seems its good enough for the Bureau of Meteorology, then its probably good enough for the masses.  But trying to figure it out provided us with some fun today...

Andrew

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Offline JimLill

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Re: Calculating Australian Aparant Temperature
« Reply #14 on: November 27, 2011, 01:43:30 PM »
try this php snippet

 $wvp = pow((($hum / 100) * 6.105 * 2.718281828),((17.27 * $celsius) /
 (237.7 + $celsius)));
 $at = round($celsius + (0.33 * $wvp) - (0.70 * $mwind) - 4.00);

mwind is meters/sec

 

anything