Evaluation of thermal indices for their applicability in obstacle-resolving meteorology models

A thermally comfortable design of outdoor spaces favors social interaction and outdoor activities and thus contributes to the overall well-being of urban dwellers. To assess such a design, obstacle-resolving models (ORM) combined with thermal indices may be used. This paper reviews existing thermal indices to identify those suitable for thermal comfort assessment with ORMs. For the identification, 11 criteria and six index features are derived from literature analysis focusing on the characteristics of human environmental heat exchange, of outdoor urban environments, and of ORMs. An air temperature weighted world population distribution is calculated to derive the minimal air temperature range; a thermal index should cover to be applicable to 95% of the world population. The criteria are applied to 165 thermal indices by reviewing their original publications. Results show that only four thermal indices are suitable to be applied globally in their current form to various outdoor urban environments and also fulfill the requirements of ORMs. The evaluation of the index features shows that they differ with respect to the comprehensiveness of the thermophysiological model, the assessed human response, the treatment of clothing and activity, and the computational costs. Furthermore, they differ in their total application frequency in past ORM studies and in their application frequency for different climatic zones, as a systematic literature analysis of thermal comfort studies employing ORMs showed. By depicting the differences of the thermal indices, this paper provides guidance to select an appropriate thermal index for thermal comfort studies with ORMs. Electronic supplementary material The online version of this article (10.1007/s00484-018-1591-6) contains supplementary material, which is available to authorized users.

: Indices excluded from further analysis with the first criterion (C) they do not meet. Indices are given 3 with their abbreviations (Abbr.) and reference in alphabetical order per failed criterion. Reasons for exclusion 4 and comments include equations for the calculation of the indices if they are short enough. Indices for which 5 differences are found in our literature review and the one by de Freitas and Grigorieva (2016) are marked with a 6 star (*). Details on the differences are given in the Appendix. The air temperature design range of indices ( ) 7 are taken from de Freitas and Grigorieva (2016). The following abbreviations of human body related parameter 8 are used: is clothing, is evaporative heat loss from skin surface, is heart rate, is heart beats, is 9 metabolic heat, is physical exertion, is thermal resistance of clothing, is sweat rate, is body temperature, is core temperature, is rectal temperature, is skin temperature, , is initial skin temperature, is thermal sensation, is water loss. Additional parameters: is a general function is water radiation, is air temperature, is diurnal temperature range, is dew-point temperature, is globe 16 temperature, is ground temperature, is mean temperature of surroundings, is wall temperature, is wet-bulb temperature, is turbulence intensity, is wind speed. Skin wettedness SkW Gonzalez et al. (1978) Requires / in original publication measurements were used. However, could be estimated from thermophysiological models (e.g. Gagge et al. (1986)) including all six variables. Nonetheless the index characterizes stress only for warm conditions and is thus rejected due to C7  Golovina and Rusanov (1993) No fitted equation / Table to read  weather classification from  ,  , ,  3 Comfort Index CI Terjung (1966); Terjung (1968) No fitted equation / Only available as nomogram 3 Corrected Effective Temperature CET Bedford (1964) No fitted equation / Only available as nomogram 3 Cylinder Brown and Gillespie (1986) No fitted equation  Jokl (1982) If ≠ , ℎ must be read from a diagram. Otherwise TRC is only a function of and the number of clothing layer (rejected due to C5) 3 Thermo-integrator Winslow et al. (1935) No fitted equation  (1971) Does not consider all 6 variables / Regression equation considering , , and fitted by Liopo and Cicenko (1971) to full heat balance equation by Budyko and Cicenko (1960)

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Atmosphere-related variable inputs are denoted "A" and body-related variable inputs are denoted "B". The following abbreviations are used: is clothing, is vapor pressure, 25 is saturation vapor pressure, , is saturated water vapor pressure at , is evaporative heat loss from skin surface, is heart rate, is clothing insulation, is 26 longwave radiation, is metabolic rate, is physical exertion, is relative humidity, is body tissue thermal resistance, is solar radiation, is air temperature, is core 27 temperature, is globe temperature, is ground temperature, is mean radiant temperature, is skin temperature, is mean temp of surroundings, is wet bulb temperature, is thermal sensation, is turbulence intensity, is wind speed.

Variable inputs considered according to de Freitas and Grigorieva (2016) (cited reference)
Variable inputs considered according to our review (reference)

Evidence, Comments
Apparent Temperature (AT) or Heat Index (HI) A: , , B: , (Steadman 1979;Steadman 1984) A: , , , B: No (Steadman 1979;Steadman 1984) Using the nomenclature of this paper the publication by Steadman (1984) reads: "The apparent temperature of a set of meteorological conditions , , , may be defined as equal to dry-bulb temperature at = = 0, and at a base vapor pressure of moderate humidity, which would require the same thermal resistance, in a walking adult, as this set of conditions". Clothing and activity are considered in AT but fixed and are therefore no variable inputs. From the full model regression equations were developed, which are used far more frequently. In the final development stage (Steadman 1979) the scope of the index "has been enlarged to cover the range of dry-bulb temperatures from -40 to +50 °C". This range is larger than +20 to +60 °C mentioned by de Freitas and Grigorieva (2016 A: , , B: (Bedford (1936) cited by Auliciems and Szokolay (2007)) A: , , , B: No (Bedford 1936) The definition is: = 9.979 − 0.1495 2 − 2.89 = 0.0556 + 0.0538 + 0.0372 − 0.00144 √ (100 − )

Exposed skin Temperature (EST)
A: , , B: (Brauner and Shacham 1995) A: , , B: No (Brauner and Shacham 1995) The equation reads: Wm -2 (comfortable steady state condition) is used for calculating : "The body tissue thermal resistance, , can be estimated from Eq. 7 by introducing known values of thermal comfort in a normal temperature room […]. Under such conditions […], the metabolic heat production while sitting at rest is approximately equal to 50 kcal h -1 m -2 (58 Wm -2 ), and […]. Thus, is approximately 0.08 kca1 -1 h °C m 2 […]." (Brauner and Shacham 1995) Heat Stress Index (HSI BH ) A: , , , B: , (Belding and Hatch  1955) A: , , , B: (Belding and Hatch 1955) "Clothing is the third variable fixed for the estimate, and it is unfortunate that limitations of available knowledge make it necessary to fix on a no-clothing basis." (Belding and Hatch 1955) Index of Clothing Required for Comfort (CLODEX) A: , , , , B: , (de Freitas 1986;de Freitas 1987) A: , , B: (de Freitas 1986;de Freitas 1987) The definition is  , (Young 1979) "The MRDE is determined by the level of exercise, the ambient temperature and humidity, the solar radiation and the clothing worn" (Young 1979) (Adamenko and Khairullin 1972) Not found in cited reference, however for cited in reference: A: , B: No (Adamenko and Khairullin 1972) In the publication cited by de Freitas and Grigorieva (2016) for the index MTTR no temperature termed Modified (Reduced) Temperature could be found. Instead an equivalent facial skin temperature ( ) derived only from and is presented in the publication.
Oxford Index (OxI)/ Wet-Dry Index (WD) A: , B: No (Lind and Hellon 1957) Not found in cited reference, however from secondary literature: A: , B: No (Lind et al. (1956) cited by Bedford (1957); Lind and Hellon (1957)) The cited publication is wrong: in the publication cited by de Freitas and Grigorieva (2016) for the Oxford Index no index termed Oxford Index or Wet-Dry Index could be found. However, from the book review by Bedford (1957) Table 1 could be retrieved and therefore the variable inputs could be confirmed.

Perceptual strain index (PeSI)
A: , B: , (Tikuisis et al. 2002) A: No B: No (Tikuisis et al. 2002) The definition is […] Next, the mean coincident with each calculated PeSI value was determined. These values subsequently replaced the PeSI values on the constructed figure therefore linking the perceptual variables of RPE and RTS with the physiological criterion of ." (Gallagher et al. 2012) Thus, PHI can be estimated either from and or from . Heart rate was measured and found to be well correlated with and but is not further integrated into the calculation of PHI ranges. Perceived Temperature (PT L ) A: , , B: No Linke (1926) cited by Eissing (1995) Not found (Linke 1926) In the publication cited by de Freitas and Grigorieva (2016) (1995)) Not found (Thilenius and Dorno 1925) In the publication cited by de Freitas and Grigorieva (2016) for the index physical saturation deficit (Thilenius and Dorno (1925) cited by Eissing (1995)) the following definition is given "Difference between the vapour pressure of the ambient air and the vapour pressure of exhaled air". However in the original publication (Thilenius and Dorno 1925) no such index is described. Instead the Frigorimeter (Table 1)  STOEC includes to estimate respiratory heat loss (using the nomenclature of this paper): = 1.73 ⋅ 10 −3 (44 − ) Clothing is taken into account for convective heat exchange but fixed ( = 4 clo). Thermal Insulation of Clothing (TIC A ) A: , , , , B: No (Aizenshtat 1964) Not found (Aizenshtat 1964) In the publication cited by de Freitas and Grigorieva (2016) for the index TIC A (Aizenshtat (1964)) no index TIC A could be found. Instead this paper describes how a globe thermometer can be used to evaluate the thermal balance of a person. Thermal Sensation Index (TSNI) "The activity was constant (school activity) and not considered to be an independent variable influencing the sensation of thermal comfort. In our studies, we do not treat the thermal insulation of clothes as an independent variable but as dependent on the external temperature" (de Paula Xavier and Lamberts 2000): = 0.219 + 0.012 − 0.547 − 5.83 Thus, clothing and metabolic heat are not variable inputs. Total Thermal Stress (TTS) A: , , , , B: No (Auliciems and Kalma 1981) A: , , , B: No (Auliciems and Kalma 1981) "The net gain of shortwave solar radiation must be incorporated […]. (Q+q) m is the sum of net direct (Q) and diffuse (q) radiation falling upon man" (Auliciems and Kalma 1981). Includes only direct and diffuse radiation and no longwave radiation , , (Rublack et al. (1981) cited by Graveling et al. (1988)) A: , , , B: , , (Rublack et al. 1981) The Q S -index cited by Graveling et al. (1988) should be named Δ -index since Q s according to the original publication (Rublack et al. 1981) describes only the longwave component in Δ : Δ = + + − ,max ( )

Appendix C Systematic literature review of thermal comfort studies with ORMs
A systematic literature review using the databases "Scopus" and "Web of Science" was conducted to identify which thermal indices have been used in the past with ORMs. Figure 1 shows the flow diagram corresponding to the method described in Sec. 2.4. Table 3 shows the 32 studies included in the analysis for F6 ordered by thermal index and climatic zone.