Dew Point Temperature of Air (DPT) - marharyta/apparent-temperature GitHub Wiki

Dew Point Temperature of Air (DPT)

According to WeatherStreet.com (WeatherStreet.com 2013.) the dewpoint temperature is derived from temperature-humidity calculations. It is not a temperature per se, but rather a temperature indicator for when the air can no longer contain all the water vapor mixed into it. A certain percentage then has to condense into liquid water, and fog or clouds begin to form. The dew point is always lower than (or equal to) the air temperature. At the point where the dew point temperature equals the air temperature, the relative humidity is 100%.

"During the summer, the dewpoint temperature - not the relative humidity - is usually a better measure of how humid it feels outside." (WeatherStreet.com 2013.)

According to (Bright Hub Engineering 2018.), the dew point temperature of air depends on its moisture content levels, with the proportional relationship between the moisture content of the air and the dew point temperature. For the saturated air, the dry bulb temperature, the wet bulb temperature, and dew point temperature are same. The saturated air is the air that contains the maximum amount of water vapor that is possible at the given temperature and pressure, i.e., the air in which the relative humidity is 100%. (Bright Hub Engineering 2018.)

DPT, WBT, and DBT are equal if the relative humidity of the air is 100%. In other cases, the DPT has to be calculated since it is very often not a part of weather forecasts. The way to measure the DPT can be described by a series of formulas: they vary depending on the resource being used, but all take origin from the Magnus formula (Bright Hub Engineering 2018.) According to (Lawrence, M. G  2005), there is a way to calculate dew point temperature knowing dry bulb temperature and relative humidity only and more accurate calculations can be done in a combined equation. The way to derive the following combined equation comes from the following calculations: Relative humidity defined as the ratio of the actual water vapor pressure to the equilibrium vapor pressure over a plane of water: 


Figure 10. Lawrence, M. G  2005.         2. Magnus formula that calculates es is provided as:

Figure 11. Lawrence, M. G  2005      3. By moving the derivatives in both formulas we can derive the DPT formula through  vapor pressure and equilibrium vapor pressure: Figure 12. Lawrence, M. G  2005

Figure 13. Lawrence, M. G  2005 This way it is possible to get the full DPT by combining these 4 formulas:

Figure 14. Lawrence, M. G  2005

Where td -  dew point temperature C RH = relative humidity t = temperature in C

And coefficients: A1 = 7.625, B1 = 243.04 °C In the table provided the Eq.8 column represents the outcomes of the combined equations from the derived formula.

Figure 15. Table of Dewpoint temperature (Celcius)

After deriving a formula and assembling the module to calculate DPT and the formula, the first test suit was conducted with the exact table values of the ambient temperature being 15 degrees Celsius and the respective values of humidity in percentages.

This testing brought to unexpected outcomes: a more accurate formula did not output the same values that were provided in the comparison table and it appeared that with the coefficients provided from this paper (Lawrence, M. G  2005) had a typo.

As one example, the formula derived above with the table numbers of 15 C and relative humidity of 60% and coeffiecients equal to A1 = 7.625 and B1 = 243.04°C as per Lawrence, M. G. in The Relationship between Relative Humidity and the Dewpoint Temperature in Moist Air gives us  -2.14 C with the table values being 7.30 C. Another example: with the relative humidity of 90% and temperature 15 C the DPT was 11.27, which is 2.1 degrees different. After failing the first calculations suit, the recalculated formula was Figure 16. Recalculated Dewpoint formula

Dew point derived from that formula with same input of 15 C and relative humidity of 60% was -2.1351402605937295 c which could be rounded to -2.1 C

After conducting further research, it came to my attention that there is multiple ways to calculate the result of Magnus formula and different coefficients. (Alduchov, O. & Eskrodge, R. 1995)

From paper Improved Magnus Form Approximation of Saturation Vapor Pressure by Alduchov, O. & Eskrodge, R., according to AERK recommendation, the coefficients in the formula should be : const A1 = 17.625; const B1 = 243.04; As denoted in the table from Figure 16: Figure 17. Table of Saturation

By replacing these values and performing the calculations again, we get value closer to one mentioned in a table: 7.294445511297167. This value rounds to 7.3 C which corresponds to table values.

According to the same source, Improved Magnus Form Approximation of Saturation Vapor Pressure, Magnus formulation is the most accurate within -40 C to 50 C temperature range, which will be taken into account in testing and calculations.

Since in the previous table the values for the humidity levels below 50% were not represented, a table from Figure 17 will be used:

Figure 18. URL: https://www.mrfixitbali.com/air-conditioning/temperature-humidity-dew-point-251.html

Not all the tables on DPT present the same data and numbers. For example, https://www.koster.eu/files/6.0-Dew-point-table.pdf does represent the same DPT values as in the table presented above, whereas http://www.nationalcompressedair.com/dat/files/600.pdf Slightly deviates from those values, which could be due to unprecise rounding.

Another calculation that gave the values corresponding to the ones provided in the table was provided by the website AZoSensors in an article “Calculating the Dew Point From the Temperature and Relative Humidity”:

Figure 19. AZoSensors. 2019

Figure 20. AZoSensors. 2019

This formulas will not be taken into account in the core calculations, yet will be used in order to test calculation results. The first simplified version of formula worked, although the accurate formula that is supposedly giving better values provided in (Lawrence, M. G  2005) did not.

The simplified version of calculations is provided by the formula from (Lawrence, M. G  2005) will not be taken into account since this is an approximation.

Figure 21. Lawrence, M. G  2005

Where td - is dew point temperature Celcius RH = relative humidity T = temperature in C The formula above can be used to calculate the DPT when relative humidity is 50% and above and the output is accurate enough.

Conclusions: (Lawrence, M. G  2005) had a typo. Magnus formulation is the most accurate within -40 C to 50C temperature range, which will be taken into account in testing and calculations. Module for calculations is available at the URL: https://github.com/marharyta/apprent-temperature/blob/master/src/utils/dewPoint.js ; and the test are available at the URL: https://github.com/marharyta/apprent-temperature/blob/master/test/dewPoint.test.js