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

中文翻译：

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主动辐射法和被动辐射法得出的平均辐射温度的精度

平均辐射温度（T _mrt）的概念允许研究人与环境之间的辐射交换。它假定对实际环境的人的辐射影响通常是异构的，而定义为同类的虚拟环境则是相同的。ISO 7726将所需的T _mrt精度指定为室外±5（K）的合理热指数的输入。Ť _MRT解释了皮肤/衣服从短波（SW）和长波（LW）光谱带吸收的辐射热。大多数辐射成分是各向同性的。但是，存在各向异性的SW组件。即直接辐照度，在晴朗或部分遮挡的天空下，漫射辐照度中有很大的绕太阳散射分数（f _cs）。两者都起源于太阳盘的近距离。这项研究强调了f _cs对T _mrt的影响。在人类生物气象学的范围内，站立的身体姿势是标准的。对于单向辐射，其辐射横截面随太阳高度而变化。主动辐射法推导T _mrt基于测得的辐照度。一种方法是Klima-Michel-Modell（KMM），它使用来自标准气象辐射观测的现成测量值。KMM引用了Fanger的区域投影因子，这些因子是根据对真实人类的精确测量得出的。因此，KMM可作为评估其他方法的参考。一种是六向仪器（T _{mrt，r ，6-Dir}）。稍微简化了站立的人，它以矩形实体表示一个对象。T _{mrt，r ，6-Dir}基于入射到垂直和水平面上的辐照度得出。在无源辐射测量中，求解了黑球温度计的能量平衡方程，从而得出T _{mrt，Tg ，BG}。f _cs显着影响T _mrt，高太阳高度值明显降低，低太阳高度值增加。因此，考虑f _cs对于T _mrt的准确性至关重要。对于KMM，提供了对现有算法的扩展，以便将f _cs包括在导致T _{mrt，r ，KMM}的T _mrt计算中。对于T _{mrt，r ，6-Dir}，固体的辐射截面在较小程度上取决于其相对于太阳方位角的方位角。结果，T _{mrt，r ，6-Dir}与T _{mrt，r，KMM}相比，略有分散。但是，它保持在±2（K）以内。Ť _{MRT，TG，BG}相比Ť _{MRT，R，KMM}只在夜间与±5 K的ISO 7726仓符合Ť _{MRT，TG，BG}显著高估Ť _{MRT，R，KMM}白天因为其更大的，与皮肤/衣服相比，SW吸收率较小，因为站立姿势由球表示，所以吸收率较小。特别是在阳光充足的条件下，T _{mrt，Tg ，BG会有}很大的差异。因此，白天在户外，T _{mrt，Tg ，BG} 不能用作计算基于有理量的热指数的适当输入。