Accuracy of Mean Radiant Temperature Derived from Active and Passive Radiometry

• Main Authors: Henning Staiger, Andreas Matzarakis
• Format: Article
• Language: English
• Published: MDPI AG 2020-07-01
• Series: Atmosphere
• Subjects: mean radiant temperature; black globe temperature; solar short- and terrestrial long-wave down- and upward radiant flux densities; direct and diffuse solar irradiance components; anisotropic circumsolar fraction in diffuse irradiance
• Online Access: https://www.mdpi.com/2073-4433/11/8/805

The concept of the mean radiant temperature (<i>T</i>_mrt) allows the study of radiative exchanges between a human and its environment. It presupposes that the radiant effects on the person of the actual environment, which is generally heterogeneous, and the virtual environment, which is defined as homogeneous, are identical. ISO 7726 specifies the required accuracy in <i>T</i>_mrt as input of rational thermal indices, outdoors ±5 (K). <i>T</i>_mrt accounts for the radiant heat absorbed by skin/clothing from the shortwave (SW) and longwave (LW) spectral bands. Most of the radiant components are isotropic. However, there are anisotropic SW components; namely the direct irradiance and under clear or partly obstructed skies a significant circumsolar fraction (<i>f</i>_cs) in the diffuse irradiance. Both originate from the close proximity of the solar disk. This study highlights the effect of <i>f</i>_cs on <i>T</i>_mrt. In the scope of human biometeorology a standing body posture is standard. For unidirectional irradiances its radiant cross-section varies dependent on the solar altitude. Active radiometry in deriving <i>T</i>_mrt is based on measured irradiances. One method is the Klima-Michel-Modell (KMM) that uses readily available measurements from standard meteorologically radiant observations. KMM references Fanger’s area projection factors that are derived from precise measurements of real humans. Thus, KMM serves as reference in evaluation of further methods. One is the six-directional instrument (<i>T</i>_mrt,r_,6−Dir). Slightly simplifying a standing human, it represents a subject as a rectangular solid. <i>T</i>_mrt,r_,6−Dir is derived based on measured irradiances incident on the vertical and horizontal planes. In passive radiometry the energy balance equation of a black globe thermometer is solved that leads to <i>T</i>_mrt,Tg_,BG.<i> f</i>_cs significantly impacts <i>T</i>_mrt with noticeably reduced values for high and increased for low solar altitudes. Hence, accounting for <i>f</i>_cs is essential for the accuracy of <i>T</i>_mrt. For KMM an extension to an existing algorithm is provided in order to include <i>f</i>_cs into the <i>T</i>_mrt calculation that results in <i>T</i>_mrt,r_,KMM. For <i>T</i>_mrt,r_,6−Dir the radiant cross-section of the solid depends to a minor extent on its azimuth relative to the solar azimuth. As a result <i>T</i>_mrt,r_,6−Dir slightly scatters compared to <i>T</i>_mrt,r,KMM. However, it remains within ±2 (K). <i>T</i>_mrt,Tg,BG compared to <i>T</i>_mrt,r,KMM complies only at night with the ISO 7726 bin of ±5 K. <i>T</i>_mrt,Tg,BG significantly overestimates <i>T</i>_mrt,r,KMM during the daytime, because of its greater SW absorptance compared to skin/clothing and to a smaller extent because the standing posture is represented by a sphere. Particularly in sunny conditions, <i>T</i>_mrt,Tg_,BG is subject to considerable variance. Thus, outdoors during the daytime, <i>T</i>_mrt,Tg_,BG is unable to serve as an appropriate input for the calculation of rational-based thermal indices.