PET and PET* (PET Reviewed)

The Physiologal Equivalent Temperature (PET) is a thermal comfort index that is based on a prognostic model of the human energy balance that computes the skin temperature, the body core temperature, the sweat rate and, as an auxiliary variable, the clothing temperature. It is generally based on the 2-node model proposed by Gagge et al. (1971) and was compiled and extended by Höppe (1984) to the Munich Energy Balance Model for Individuals (MEMI). The core model can be used both in an instationary and a stationary approach, but for PET only the stationary solution of the body parameters is used.

Despite its popularity, PET long time lacked a proper and comprehensive documentation. Basically, one needed to read the 2 papers Gagge et al. (1971) and Höppe (1984) -in german- plus the computer source code provided by VDI 3787.

In 2018, this gap has been closed by the paper “The P.E.T. comfort index: Questioning the model” by E. Walther and Q. Goestchel (Link to Paper who take the effort to summarize all the equations and assumptions.

In this paper as well as in ENVI-met paper it was noted that there are some non-logical assumptions and errors in the original set of equations plus coding errors in the code published in VDI 3787. In addition, there have been better parametrisations for the Mean Radiant Temperature (TMRT) which is is not directly a part of PET but widely influences the results.

In the ENVI-met implementation of BIO-met, many of these errors have been corrected. As a consequence, PET values calculated by ENVI-met may differ from values calculated by other programs, but we see no sense in copying wrong code or non-logical assumptions.

Main changes in ENVI-met BIO-met compared to original PET in short are:

• For the indoor setting, the turbulent exchange coefficients for heat and vapour are calculated using the indoor air velocity instead of keeping them at the outdoor value
• The sweat rate and the amount of sweat on the skin is set to zero when starting calculating the indoor environment. It will start again if the reference temperature of the body $T_B=0.2 \cdot T_{skin}+0.9 \cdot T_{core}$ is above the sweating set point, here 36.34 °C.

For other issues, see next section.

With the Winter 22/23 release, the whole PET module has undergone a review to fix a number of accumulated errors and inconsistencies. This includes some of the suggestions from Walther and Goestchel (2018) plus several other improvements and changes. These modifications result in a PET* (for PET Reviewed) indicator which will show of course (again) differences to both the original and the corrected PET values already included in ENVI-met prior to Winter 22/23..

The main changes are:

• For the indoor setting, the metabolic rate is set to the basal rate (approx. 80 W) plus the work load for walking with 0.1 m/s, regardsless of the outdoor activity set.
• The new metabolic rate impacts the breathing settings and engery fluxes which are not updated in the iterations
• The fraction of wet skin is resetted to zero before calculating the indoor environment (but might increase then again based on the sweat rate and the indoor humidity)
• The energy balance equation of the skin node was re-worked to take into account the changes above. In addition, the skin energy balance now only consists of Radiation and Convection from/to base skin parts plus conduction flux from/to clothing layer and no other components.
• Finally, the number of output variables has been extended now providing T Skin static (°C), T Core static (°C), T Cloths static (°C), Fraction Wet Skin, Sweat Rate (g/h), Radiative Budget Skin (W) and Convective Flux Skin (W).

The general idea behind PET (and other outdoor thermal comfort indices) is that we can express the thermal comfort of a human body using the skin and core temperature as reference indicators.

So, the basic idea behind PET for an outdoor setting is

1. Define all incoming and outgoing fluxes at the human body
2. Calculate a skin and a core temperature, that matches all the calculated fluxes
3. Transpone the person into an indoor environment
4. Reset all data that are not available in an indoor environment (direct solar radiation, forced wind movement)
5. Search for an indoor air temperature (as only parameter) that results in the same skin temperature and core temperature as the outdoor setting.
6. This theoretically calculated indoor temperature is called PET.

• Walther, E and Goestchel, Q. (2018): The P.E.T. comfort index: Questioning the model, Building and Environment, Volume 137, June 2018, Pages 1-10; Science Direct
• Gagge, A., Stolwijk, J., and Nishi, Y. (1971): An effective temperature scale based on a simple model of human physiological regulatory response. ASHRAE Trans., 77(1):247–262.
• Höppe, P. (1984). Die Energiebilanz des Menschen: In: Münchener Universitätsschriften- Fachbereich Physik, Wissenschaftliche Mitteilungen Nr. 49. Meteorologisches Institut, Universität München, München.
• Höppe, P. (1999): The physiological equivalent temperature – a universal index for the biometeorological assessment of the thermal environment. - International Journal of Biometeorology 43, 71-75.
• VDI (2008): VDI 3787. Environmental meteorology. Methods for the human biometeorological evaluation of climate and air quality for urban and regional planning at regional level. Part I: Climate, Blatt 2/ Part 2