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Improved methods for estimating mean radiant temperature in hot and sunny outdoor settings

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Abstract

Thermal comfort research has utilized various sensors and models to estimate the mean radiant temperature (MRT) experienced by a human, including the standard black globe thermometer (SGT), acrylic globe thermometers (AGT), and cylindrical radiation thermometers (CRT). Rather than directly measuring radiation, a temperature is measured in the center of these low-cost sensors that can be related to MRT after theoretically accounting for convection. However, these sensors have not been systematically tested under long-term hot and clear conditions. Further, under variable weather conditions, many issues can arise due to slow response times, shape, inaccuracies in material properties and assumptions, and color (albedo, emissivity) inconsistencies. Here, we assess the performance of MRT produced by various heat transfer models, with and without new average surface temperature (\( {\overline{T}}_{\mathrm{s}} \)) correction factors, using five instruments—the SGT (15 cm, black), tan and black CRTs, gray and black 38 mm AGTs—compared to 3D integral radiation measurements. Measurements were taken on an unobscured roof throughout summer-to-early-fall months in Tempe, Arizona, examining 58 full-sun days. Deviations without correcting for asymmetrical surface heating—found to be the main cause of errors—reached ± 15–20 °C MRT. By accounting for asymmetric heating through \( {\overline{T}}_{\mathrm{s}} \) calculations, new corrective algorithms were derived for the low-cost sensor models. Results show significant improvements in the estimated MRT error for each sensor (i.e., ∆MRTmodel − IRM) when applying the \( {\overline{T}}_{\mathrm{s}} \) corrections. The tan MRTCRT improved from 1.9 ± 6.2 to −0.1 ± 4.4 °C, while the gray AGT and SGT showed improvements from −1.6 ± 7.2 to −0.4 ± 6.3 °C and − 6.6 ± 6.4 to − 0.03 ± 5.7 °C, respectively. The new corrections also eliminated dependence on other meteorological factors (zenith, wind speed). From these results, we provide three simple equations for CRT, AGT, and SGT correction for future research use under warm-hot and clear conditions. This study is the most comprehensive empirical assessment of various low-cost instruments with broad applicability in urban climate and biometeorological research.

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Availability of data and material

Raw data and codes will be made available on the ASU Dataverse website (dataverse.asu.edu) prior to publication.

Abbreviations

D :

Diameter (of globe or cylinder)

d :

Index of agreement

\( \overline{h} \) :

Average heat transfer coefficient

\( {\overline{h}}_{\mathrm{forced}} \) :

Average heat transfer coefficient (forced convection) (Wm−2 K−1)

k air :

Thermal conductivity (0.0267 Wm−1 °C−1)

MRT :

Mean radiant temperature (°C)

MRT model :

Modeled MRT (°C)

MRT CRT :

MRT of CRT (°C)

MRT AGT :

MRT of acrylic globe thermometer (°C)

MRT IRM :

MRT from integral radiation measurements (°C)

MRT SGT :

MRT of standard black globe thermometer (°C)

∆MRT model − IRM :

Mean error between model and IRM (°C)

\( \overline{Nu} \) :

Nusselt number

Pr:

Prandtl number (0.7)

R 2 :

Coefficient of determination

R abs :

Total absorbed radiation

Re, Re D :

Reynolds number

RH :

Relative humidity (%)

SGT :

Standard globe thermometer

T a :

Air temperature (°C)

T CRT :

Center temperature of CRT (°C)

T g :

Center temperature of a globe thermometer (°C)

\( {\overline{T}}_{\mathrm{s}} \) :

Spatially averaged surface temperature of instrument (°C)

ν air :

Kinematic viscosity (1.64 × 10−5 m2 s−1)

V a :

Wind speed (m s−1)

W i :

Weighting factor

α air :

Thermal diffusivity of air (2.33 × 10−5 m2 s−1)

a k :

Short-wave absorption coefficient

a l :

Long-wave absorption coefficient

β :

Coefficient of thermal expansion (0.0033 °C−1)

ϵ l, ϵ IR :

Hemispherical emissivity of clothed person in the infrared (0.97)

σ:

Stefan-Boltzmann constant (5.67 × 10−8 Wm−2 K−4)

θ :

Solar zenith angle (°)

AGT:

Acrylic globe thermometer

ASHRAE:

American Society of Heating, Refrigerating & Air-Conditioning Engineers

C&B:

Churchill & Bernstein \( {\overline{h}}_{\mathrm{forced}} \)equation

CRT:

Cylindrical radiation thermometer

FTIR:

Fourier-transform infrared spectrometer

IRM:

3D integral radiation measurement (3D)

ISO:

International Organization for Standardization

MAE:

Mean absolute error (°C)

NR:

Net radiometer

RMSE:

Root mean square error (°C)

WBGT:

Wet bulb globe temperature (°C)

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Acknowledgements

We would like to express our gratitude to Scott Krayenhoff for aiding in the sensor setup, Paul Coseo for helping with roof access, and Liping Wang, Linshuang Long, and Rajagopalan Ramesh of ASU for help with the FTIR measurements.

Funding

Meteorological sensors were sponsored by University of Kaiserslautern, grant “Microclimate Data Collection, Analysis, and Visualization”.

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Authors and Affiliations

  1. School of Sustainability, Arizona State University, Tempe, AZ, USA

    Jennifer K. Vanos

  2. School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA

    Konrad Rykaczewski

  3. School of Arts, Media and Engineering, Herberger Institute for Design and the Arts, Arizona State University, Tempe, AZ, USA

    Ariane Middel

  4. Department of Geography, Texas A&M University, College Station, TX, USA

    Daniel J. Vecellio

  5. Department of Landscape Architecture and Urban Planning, Texas A&M University, College Station, TX, USA

    Robert D. Brown

  6. School of Environmental Sciences, University of Guelph, Guelph, Ontario, Canada

    Terry J. Gillespie

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  1. Jennifer K. Vanos
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Contributions

Conceptualization: JV, RB, AM, TG. Methodology: JV, KR, DV, AM, RB, TG. Data collection: AM, JV. Analysis: JV, KR, AM, DV. Writing–original draft: JV, AM, RB, TG. Writing–review and editing: JV, KR, DV, AM. Final review and editing: JV, KR, DV, AM, RB.

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Correspondence to Jennifer K. Vanos.

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Vanos, J.K., Rykaczewski, K., Middel, A. et al. Improved methods for estimating mean radiant temperature in hot and sunny outdoor settings. Int J Biometeorol 65, 967–983 (2021). https://doi.org/10.1007/s00484-021-02131-y

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