Feels Like: Difference between revisions

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* There is much more divergence on what formula to use at higher temperature, reflecting that the highest temperature seen vary across the world, and because other factors like humidity also vary it is harder for Scientists to agree on what is the best way to measure effects.  
* There is much more divergence on what formula to use at higher temperature, reflecting that the highest temperature seen vary across the world, and because other factors like humidity also vary it is harder for Scientists to agree on what is the best way to measure effects.  
** In the USA, a dimensionless [[Heat index]] measure is used, for temperatures above 27 °C (80 °F). The measure combines air temperature and relative humidity, and thus gives an indication of evaporation rate.
** In the USA, a dimensionless [[Heat index]] measure is used, for temperatures above 27 °C (80 °F). The measure combines air temperature and relative humidity, and thus gives an indication of evaporation rate.
***From a very early build Cumulus used the formula exactly as defined in Wikipedia for heat index.<math>\mathrm{HI} = c_1 + c_2 T\text{°F} + c_3 R + c_4 T\text{°F} R + c_5 T^2 + c_6 * RH^2 + c_7 * T_\text{°F}^2 * RH + c_8 * T_\text{°F} * RH^2 + c_9 * T_\text{°F}^2 * RH^2</math>
***From a very early build Cumulus used the formula exactly as defined in Wikipedia for heat index. <tt>HI = c_1 + c_2 x  T°F + c_3 x RH + c_4 x T°F x R + c_5 x T<sup>2</sup> + c_6 * RH<sup>2</sup> + c_7 x T°F<sup>2</sup> x RH + c_8 x T°F x RH<sup>2</sup> + c_9 x T°F<sup>2</sup> x RH<sup>2</sup></tt>
***This was improved from version 1.9.0 (11 Sept 2010) in Cumulus 1 with a new formula covering a greater range of humidities accurately.  Steve Loft did not document this change, however his MX beta source (as handed over to the community) uses Rothfusz adjustments to reduce the index reported if the relative humidity is below 13%, and he stated he created MX beta from a machine-level translation of Cumulus 1.9.4.
***This was improved from version 1.9.0 (11 Sept 2010) in Cumulus 1 with a new formula covering a greater range of humidities accurately.  Steve Loft did not document this change, however his MX beta source (as handed over to the community) uses Rothfusz adjustments to reduce the index reported if the relative humidity is below 13%, and he stated he created MX beta from a machine-level translation of Cumulus 1.9.4.
***The current MX release has not changed that MX beta code, it uses a minimum of 80 <sup>o</sup>Fahrenheit air temperature cut-off in MX, and on the assumption that this measure is only of interest in USA, the calculation is entirely done in Fahrenheit. Mark did remove any temperature conversion of output.
***The current MX release has not changed that MX beta code, it uses a minimum of 80 <sup>o</sup>Fahrenheit air temperature cut-off in MX, and on the assumption that this measure is only of interest in USA, the calculation is entirely done in Fahrenheit. Mark did remove any temperature conversion of output.
*** In the UK, with its cooler climate, some people use a modified formula for Heat Index with the cut-off revised to 20 <sup>o</sup>Celsius (68 <sup>o</sup>Fahrenheit).  (All Cumulus releases, for temperatures below 80 <sup>o</sup>Fahrenheit, will show the air temperature wherever Heat Index would appear).
*** In the UK, with its cooler climate, some people use a modified formula for Heat Index with the cut-off revised to 20 <sup>o</sup>Celsius (68 <sup>o</sup>Fahrenheit).  (All Cumulus releases, for temperatures below 80 <sup>o</sup>Fahrenheit, will show the air temperature wherever Heat Index would appear).
** In Canada, [[Humidex|Humidity Index]] also combines the effects of heat and humidity.  The actual formula involves air temperature and dew point:  
** In Canada, [[Humidex|Humidity Index]] also combines the effects of heat and humidity.  The actual formula involves air temperature and dew point:  
<math>\text{Humidity Index} = Temperature_\mathrm{air_in_Celsius} + \frac{5}{9} \left[6.11\times 2.71828^{5417.7530 \left(\frac{1}{273.16} - \frac{1}{273.15+T_\text{dew_in_Celsius}}\right)} - 10\right]</math>
<tt>Humidity Index = Temperature<sup>air_in_Celsius</sup> + 5÷9 x 6.11 x 2.71828<sup>5417.7530</sup> x 1÷273.16 - 1÷273.15 + T<sup>{dew_in_Celsius</sup> - 10</tt>


:5417.7530 is a rounded constant based on the molecular weight of water, [[Enthalpy of vaporization|latent heat of evaporation]], and the [[universal gas constant]]. The humidity adjustment approximately amounts to one Fahrenheit degree for every millibar by which the [[Vapour pressure of water|partial pressure of water]] in the atmosphere exceeds {{convert|10|mb}}.
:5417.7530 is a rounded constant based on the molecular weight of water, Enthalpy of vaporization|latent heat of evaporation, and the universal gas constant. The humidity adjustment approximately amounts to one Fahrenheit degree for every millibar by which the Vapour pressure of water(partial pressure of water) in the atmosphere exceeds 10 mb.


** In Australia, [[Apparent temperature]] uses a mathematical model of the effects of temperature, humidity, wind speed, and (optionally) solar radiation.
** In Australia, [[Apparent temperature]] uses a mathematical model of the effects of temperature, humidity, wind speed, and (optionally) solar radiation.
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***All releases of MX use that same formula for any output labelled '''Apparent Temperature'''.
***All releases of MX use that same formula for any output labelled '''Apparent Temperature'''.
*** There are many alternative formulae for calculating the vapour pressure of water, so there is a certain lack of consistency in how any '''Feels Like Temperature''' based on ''Apparent Temperature'' is reported. Cumulus MX has tried various formulas for calculating vapour pressure.
*** There are many alternative formulae for calculating the vapour pressure of water, so there is a certain lack of consistency in how any '''Feels Like Temperature''' based on ''Apparent Temperature'' is reported. Cumulus MX has tried various formulas for calculating vapour pressure.
***For versions 3.5.4 (25 Apr 2020 build 3075) to version 3.6.7 (4 June 2020 build 3083) of MX used a different formula for water vapour to that used for version 3.6.8 build 3084. These differences affected the calculation these releases did for '''Feels Like Temperature''' at higher air temperatures. Because these have been superceded, I have deleted the formula that was quoted here.
***For versions 3.5.4 (25 Apr 2020 build 3075) to version 3.6.7 (4 June 2020 build 3083) of MX used a different formula for water vapour to that used for version 3.6.8 build 3084. These differences affected the calculation these releases did for '''Feels Like Temperature''' at higher air temperatures. Because these have been superseded, I have deleted the formula that was quoted here.


===How to express '''Feels Like''' when air temperature is above 20 <sup>o</sup>Celsius (68 <sup>o</sup>Fahrenheit)===
===How to express '''Feels Like''' when air temperature is above 20 <sup>o</sup>Celsius (68 <sup>o</sup>Fahrenheit)===
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** For versions 3.5.4 (25 Apr 2020 build 3075) to version 3.6.7 (4 June 2020 build 3083) of MX used a different formula for water vapour to that used for version 3.6.8 build 3084. These differences affected the calculation these releases did for '''Feels Like Temperature''' in this temperature range.
** For versions 3.5.4 (25 Apr 2020 build 3075) to version 3.6.7 (4 June 2020 build 3083) of MX used a different formula for water vapour to that used for version 3.6.8 build 3084. These differences affected the calculation these releases did for '''Feels Like Temperature''' in this temperature range.
** From Cumulus release version 3.6.10 build 3086, the apparent temperature element (before weighting) is based on the same formula as used to report 'Apparent Temperature'.
** From Cumulus release version 3.6.10 build 3086, the apparent temperature element (before weighting) is based on the same formula as used to report 'Apparent Temperature'.


=Support for these derivived parameters in daily extremes, monthly extremes, yearly extremes, all-time extremes, and monthly all-time extremes=
=Support for these derivived parameters in daily extremes, monthly extremes, yearly extremes, all-time extremes, and monthly all-time extremes=
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