dew_point

Goal

Calculate and visualize dew point termperature (T_d) (1) and dew point margin across a wide range of relative humidity and temperature (RH & T) values with a consideration for preventing high humidity and condensation in small rooms, e.g. 3 m³.

Explanation & Equation Selection

If RH > 50 % then the dew point temperature (T_d) in °C can be caluclated fairly accurately using (2)

$$T_d = T - \left(\frac{100 - RH}{5}\right)$$

We want to use a more robust calculation to produce correct results across a broader range of RH & T.

RH  %   >  0  →  + 100
T  °C   - 45  →  +  60
T  °F   - 49  →  + 140

Consider a simplified form of the August-Roche-Magnus equation (5):
$$T_d = \frac{B \cdot \alpha(T, RH)}{A - \alpha(T, RH)}$$

where
$$\alpha = \frac{A \cdot T}{B + T} + \ln\left(\frac{RH}{100}\right) $$ and the coefficients A and B are

 17.27 < A <  17.625  =  17.625    dimensionless
237.04 < B < 243.12   =  243.04    °C

The python code to calculate this is

coef_a = 17.625  # dimensionless
coef_b = 243.04  # °C

alpha = (coef_a * TC) / (coef_b + TC) + log(RH / 100)  # natural log ln
Td = (coef_b * alpha) / (coef_a - alpha)

Sensirion, a company that specializes in sensors uses a similar approach and provides sample code (4)

there are additional details in

h = (log10(RH)-2.0) / 0.4343 + (17.62 * T) / (243.12 + T);
Td = 243.12*h/(17.62-h);

We can see that they are using similar coefficients as the previous example.
Note that the value 0.4343 is an approximation of 1 / ln(10) which is a conversion of base 10 log to natural log.

If we compare the output of the two from 0 < RH < 100 and -40 < TC < 60 we can determine that the differences between the two methods in °C are min 0.00, max 0.03 and avg 0.01

If we adjust the sensirion code to use the same coefficients and natural log then we see that the differences in output between the two approaches is zero out to at least 8 decimal places

https://journals.ametsoc.org/downloadpdf/view/journals/bams/86/2/bams-86-2-225.pdf

"For the range -45 °C to +60 °C, values given by this equation have an uncertainty of < ±0.6 % of value, at the 95% confidence level." https://www.npl.co.uk/resources/q-a/dew-point-and-relative-humidity

Adjusting the coefficients can reduce uncertainty for specific, narrower temperature ranges.

References

[1] https://en.wikipedia.org/wiki/Dew_point

[2] https://iridl.ldeo.columbia.edu/dochelp/QA/Basic/dewpoint.html

Bell, Michael

coefficients et al
Lawrence, Mark G., 2005
The relationship between relative humidity and the dewpoint temperature in moist air: A simple conversion and applications
Bulletin of the American Meteorlogical Society, Vol. 86, Issue 2, pages 225 - 234
http://dx.doi.org/10.1175/BAMS-86-2-225 https://journals.ametsoc.org/downloadpdf/view/journals/bams/86/2/bams-86-2-225.pdf

[3] https://en.wikipedia.org/wiki/Enthalpy_of_vaporization

[4] https://sensirion.com/media/documents/A419127A/6163F5FE/Sensirion_AppNotes_Humidity_Sensors_at_a_Glance.pdf

[5]

https://www.omnicalculator.com/physics/dew-point

####[6] https://irtfweb.ifa.hawaii.edu/~tcs3/tcs3/Misc/Dewpoint_Calculation_Humidity_Sensor_E.pdf plot of deviation of magnus from hardy min max for the entire plot of - 0.35 to 0.5 °C

ΔH_vap
  • enthalpy of vaporization
  • latent heat of vaporization of water
  • heat of evaporation: the amount of energy (enthalpy) that must be added to a liquid
  substance to transform a quantity of that substance into a gas. (3)

https://extensionpubs.unl.edu/publication/g1849/2008/pdf/view/g1849-2008.pdf

https://en.wikipedia.org/wiki/Vapour_pressure_of_water#Accuracy_of_different_formulations
could use the slightly more complex Buck equation for greater accuraccy

ttp://mc-computing.com/science_facts/Water_Vapor/Other_Formulas.html
comparison of many papers and the differences in them

dew point tables & Calculators

an effort to find known values to compare output of code. difficult to find anythign with references

terrible https://www.nwcg.gov/publications/pms437/weather/temp-rh-and-dew-point-tables?form=MG0AV3

https://xlbrands.com/wp-content/uploads/2021/09/TechnicalBulletin-SUBSTRATE_DewPointCalculationChartenglish-053118.pdf converted from F to C Bostik commercial floor covering 4 < TC < 33 30 < RH < 90

https://lamtec.com/technical-bulletins/dew-point-table/?form=MG0AV3
insulation vapor retarders and building facings
0 < TC < 43 10 < RH < 100

https://bmcnoldy.earth.miami.edu/Humidity.html

https://www.tis-gdv.de/tis_e/misc/klima-htm/
German Insurance Assoc. Transport Information Service -25 < TC < 50 10 < RH < 100

https://www.korff.ch/wp-content/uploads/2021/01/Taupunkt-Tabelle-EN.pdf
specialty aluminum foil vapour barrier
2 < TC < 50 45 < RH < 95

https://www.dur-a-flex.com/wp-content/uploads/2020/02/dew-point-calculation-chart.pdf
seamless flooring -70 < TC < 50 30 < RH < 90

https://www.prokol.com/wp-content/uploads/2021_Dew-point-table.pdf
protective coatings 2 < TC < 50 45 < RH < 95

mins and maxes from whole # tables include Min and max of data in all tables  
Temp (C) - 25  →  + 50  
RH (%)     10  →   100  

tables from Lamtec, KORFF, Prokol, and TIS have whole number input
tables from Dur_a_flex and XL brands have decimal input ∵ they were converted from F to C