Accuracy of Mean Radiant Temperature Derived from Active and Passive Radiometry

Abstract

The concept of the mean radiant temperature (Tmrt) 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 Tmrt as input of rational thermal indices, outdoors ±5 (K). Tmrt 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 (fcs) in the diffuse irradiance. Both originate from the close proximity of the solar disk. This study highlights the effect of fcs on Tmrt. 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 Tmrt 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 (Tmrt,r,6−Dir). Slightly simplifying a standing human, it represents a subject as a rectangular solid. Tmrt,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 Tmrt,Tg,BG. fcs significantly impacts Tmrt with noticeably reduced values for high and increased for low solar altitudes. Hence, accounting for fcs is essential for the accuracy of Tmrt. For KMM an extension to an existing algorithm is provided in order to include fcs into the Tmrt calculation that results in Tmrt,r,KMM. For Tmrt,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 Tmrt,r,6−Dir slightly scatters compared to Tmrt,r,KMM. However, it remains within ±2 (K). Tmrt,Tg,BG compared to Tmrt,r,KMM complies only at night with the ISO 7726 bin of ±5 K. Tmrt,Tg,BG significantly overestimates Tmrt,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, Tmrt,Tg,BG is subject to considerable variance. Thus, outdoors during the daytime, Tmrt,Tg,BG is unable to serve as an appropriate input for the calculation of rational-based thermal indices.