Comparison of weather service heat indices using a thermal model

ARTICLE IN PRESS

Journal of Thermal Biology 30 (2005) 65–72 www.elsevier.com/locate/jtherbio

Comparison of weather service heat indices using a thermal model William R. Santee, Robert F. Wallace Biophysics and Biomedical Modeling Division, US Army Research Institute of Environmental Medicine, Natick, MA 01760-5007, USA Received 28 January 2004; received in revised form 9 June 2004; accepted 1 July 2004

Abstract The US and Canadian weather service heat indices were evaluated to determine if one is a better predictor of the risk of heat injury. Heat index values were compared to the rectal temperature predicted by a heat-balanced-based thermal model to determine if there was a statistically significant relation between the heat index values and predicted rectal temperature. R2 values ranged between 0.96 and 0.99 for the conditions investigated. Equations that predicted rectal temperature from the heat indices are presented. Both indices are highly correlated with predicted rectal temperatures. Published by Elsevier Ltd. Keywords: Heat stress; Heat index; Modeling; Rectal temperature

1. Introduction Thermal indices that relate environmental conditions to the potential hazards of exposure to thermal stress are important to civilian, industrial, and military populations. Indices are easy to derive from basic weather inputs and provide the user with simple guidance for determining when a thermal hazard may exist. The US and Canadian weather services use heat indices to issue warnings when meteorological conditions present a significant hazard of heat injury. These indices are often available through radio and television media outlets. However, the heat indices used by the two countries differ. The Joint Action Group for Thermal Indices (JAG/ TI) of the Office of the Federal Coordinator for Meteorological Services and Supporting research (OFCM) was formed to review heat and cold indices Corresponding author. Fax: +1-508-233-5298.

E-mail address: [email protected] (W.R. Santee). 0306-4565/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.jtherbio.2004.07.003

used by the US and Canada (OFCM, 2003). The development and joint adoption of the new Wind Chill Temperature (WCT) index was a product of the JAG/ TI. The options for the heat index were to either adopt one of the two existing heat indices, or to await the development of a new Universal Thermal Climate Index (UTCI) by International Society of Biometeorology Commission 6. The UTCI will be based on more complex thermal modeling. This paper represents our attempt to provide guidance to the JAG/TI by conducting an analysis of the two indices. Both heat indices are temperature-humidity indices. The National Weather Service (NWS) heat index (HI) was derived from a database generated by a more complex mathematical model developed by Steadman (1979). Simplifying a complex, multi-input model into a single equation using two common meteorological values saved a considerable amount of computing time. HI values are calculated as 1F. Critical values for HI are possible fatigue from prolonged activity starting at HI=80 1F (27 1C); possible heat injury (‘‘sunstroke’’, heat cramps, and heat exhaustion) at 90–1051F

ARTICLE IN PRESS 66

W.R. Santee, R.F. Wallace / Journal of Thermal Biology 30 (2005) 65–72

(32–41 1C); the same injuries and possible heat stroke likely between 105 and 1301F (41–54 1C); and heat stroke highly likely when HIX130 1F (National Institute for Occupational Safety and Health (NIOSH), 1986). The Canadian index used by Meteorological Services Canada (MSC) is Humidex (HD). The present version of HD is described by Masterton and Richardson (1979). Based on guidance from Masterton and Richardson, HDp29 1C is considered comfortable. Discomfort starts at a HD of 30 1C, and most people should be uncomfortable when HD reaches 40 1C. When HDX46 1C, some activity restrictions may be implemented. The primary issue is a question of which existing North American thermal index is better. The approach of this study was to use an existing heat strain model to predict the incidence of injury and compare those predictions. Heat indices cover a wide range of environmental conditions. No single human study could cover the entire range of temperature-humidity conditions, and very few studies even match the combination of clothing and activity used as inputs into the indexes. Using data from human studies to compare HI and HD would involve assembling a series of short studies that approximate the requirements for temperature, humidity with no significant differences in wind speed, clothing, activity level, etc. from the standard conditions. Complex heat balance models distill the results of multiple human studies and the basic science of thermal physiology and heat exchange into a model that does cover the full range of temperature and humidity index inputs. It would be circular logic to use Steadman’s models to validate an equation derived from his model. However, other validated models that predict core temperature and maximum exposure time could be compared to the guidance provided by HI. The model used in this paper is a derivative of the Heat Strain Decision Aid (HSDA) model (Cadarette et al., 1999; Gonzalez et al., 1997; Pandolf et al., 1986; SAIC, 1993). The HSDA model targets relatively young, fit military populations. Our primary statistical analysis consisted of derived correlation coefficients (R2). A by-product of the analysis is a series of equations that predict the corresponding rectal temperatures (Tre) from either HI or HD. For thermal physiologists and health care providers, a measure of core temperature is the clearest indication of heat storage, heat strain or hypothermia. Indexes target the general population. A healthy, otherwise unimpaired individual may tolerate a higher core temperature than an individual exposed to other stress such as fatigue, dehydration or lack of acclimatization. Equations that convert an index value into Tre or another measure of core temperature are therefore of value, and for that reason has been included in the

results. In addition, by calculating the Tre that corresponds to the index safety guidance, it is possible to determine if those limits have any physiological merit. HI and HD are used primarily by the respective weather services to issue heat risk warnings based on weather forecasts. Other than temperature and humidity, all of the Index inputs are standardized. When conditions differ significantly from the standard conditions, such as a higher level of activity, different clothing, a higher or lower wind speed or solar load, the actual risk may also vary significantly from the level predicted using the standard inputs. Industry and the military more commonly use the Wet Bulb Globe Temperature (WBGT) index (Department of the Army and Air Force, TB MED 507, 2003; ACGIH, 2004; NIOSH 86-113, 1986). To accommodate differences in clothing, activity levels or weather, a variety of adjustments have been calculated for WBGT (ACGIH, 2004). To illustrate this aspect of indices, Tre values were recalculated HSDA using alternative input for wind and radiant load. The set of possible adjustments to the basic indices is almost infinite, but as HI and HD are primarily weather indices, manipulating weather inputs was deemed to be the most appropriate examples.

2. Methods The weather inputs for HI are TF (Ta in 1F) and percent RH. The inputs for HD are Ta and dew point temperature (Tdp); both in 1C. Index output values for HI and HD are in 1F and 1C respectively. The equation for HI (Rothfusz, 1990) is HI ¼  42:379 þ 2:04901523T F þ 10:14333127RH  0:22475541T F RH  6:83783E  3T 2F  5:481717E  2RH2 þ 1:22874E  3T 2F RH þ 8:5282E  4T F RH2  1:99E  6T 2F  RH2 ð FÞ: In addition, a correction factor is sometimes subtracted from HI when RHo13% and TF is between 80 and 112 1F (National Oceanic and Atmospheric Administration (NOAA), 2003). The adjustment factor was used in this study. The equations for HD are: HD ¼ T a þ hð CÞ; h ¼ 0:5555ðe  10Þ; e ¼ 6:11EXP½5417:753ð273:161  T 1 dp Þ ; T d ¼ T dp þ 273:16ðKÞ: HI was calculated for 71 combinations of Ta and RH that fall within the range of the tables and other restrictions for the adjusted HI. These restrictions included a minimum RH of 30% and a maximum HI

ARTICLE IN PRESS W.R. Santee, R.F. Wallace / Journal of Thermal Biology 30 (2005) 65–72

of 135 1F (57 1C). Ta input values ranged from 26.7 to 45 1C, and RH 30–100%. HD values were calculated for the same weather inputs, so there were corresponding values for HI and HD for all 71 conditions. The upper limit for HD within those HI-based restrictions is HDp56 1C. For input into HSDA, a set of constant inputs for height (170 cm), weight (67 kg), clothing (warm-weather BDU, clo=1.3) and metabolic rate (M=320 W), based on Steadman (Rothfusz, 1990; Steadman, 1979), were selected. The height and weight used by Steadman represent the ‘‘standard man’’ of the WWII era. The height and weight of the average male in military service (Hodgdon, 1992) has increased, and Steadman subsequently increased these inputs in a later version of his model (Steadman, 1999). However, the standard man values are now a reasonable compromise for a mixedgender population. The initial Tre was 37.0 1C. Wind speed for an individual was set at 2.5 m s1. The solar condition was SHADE-defined as Tmrt=Ta. An EXCEL version (Microsoftr Corporation, Bellevue, WA) of the USARIEM HSDA was run using each of these input sets. This is equivalent to the laptop version described by Cadarette et al. (1999). The important feature of this HSDA version is that the model over-predicts Tre, thereby creating a safety margin for a healthy military population. Acclimatization was set at 12 days of heat exposure, and the soldiers were normally dehydrated (1.24%). Calculation sets (n ¼ 71) using those inputs were considered the STANDARD condition. An alternate radiant load condition was defined as Tmrt=Ta+40 1C (Matthew et al., 2001). Calculation sets with the alternate value for Tmrt were labeled SUN. Calculations

were also made with alternate wind speeds of 1.5 and 5.0 m s1, but all other inputs matched the STANDARD input set. Those calculation sets were labeled WIND1.5 and WIND5. The Tre values calculated with the HSDA model at 30, 60, and 296 min for each weather input set were then copied into worksheets for each of the conditions (STANDARD, SUN, WIND1.5, WIND5). Linear regressions between HI and HD versus Tre were calculated for the STANDARD and SUN conditions. The results for HD suggested that a non-linear relationship existed between Tre and HD. Based on the pattern of the residual, simple second-order equations were then developed for the HD relationships. The R2 values were used as the basis for statistical evaluation. Additional linear regressions were also calculated for HI versus the WIND1.5 and WIND5 conditions for both STANDARD and SUN.

3. Results Fig. 1 for Tre plotted against HI for the STANDARD condition at 300 min. The relationship is clearly linear. Fig. 2 shows the relationship between Tre and HD. This relationship is curvilinear. R2 values for the linear regressions between the indices and Tre were X0.96 for HI and X0.90 for HD. Adding a squared term significantly improves the fit between the indices and the model. The R2 values for the second-order HD equations improve to X0.97. Table 1 lists the linear equations and R2 values for HI in the STANDARD and SUN conditions. Table 2 presents the second-order equations that predict Tre from HD. An important

PREDICTED RECTAL TEMPERATURE (°C)

39.2

39.0

38.8

38.6

38.4

38.2

R2 = 0.98

38.0 30˚C 37.8 75°F

85°F

35˚C 95°F

67

40˚C 105°F

45˚C 115°F

50˚ C 125°F

55˚C 135°F

HEAT INDEX (°C/°F)

Fig. 1. Relationship between Heat Index (HI) and HSDA predicted Tre for time=296 min, STANDARD conditions.

ARTICLE IN PRESS W.R. Santee, R.F. Wallace / Journal of Thermal Biology 30 (2005) 65–72

68

PREDICTED RECTAL TEMPERATURE (°C)

39.2

39.0

38.8

38.6

38.4

38.2 2

R = 0.98

38.0

37.8 25

30

35

40

45

50

55

60

HUMIDEX (°C)

Fig. 2. Curvilinear relationship between Humidex (HD) and HSDA predicted Tre for time=296 min, for STANDARD conditions.

Table 1 Linear predictive equations (Tre=b0+b1X, HIp135 1F) for Heat Index (HI) versus HSDA predicted Tre (1C) X

Time

Solar

Wind

b0

b1

R2

HI HI HI

30 60 296

SHADE SHADE SHADE

2.5 2.5 2.5

36.939 36.773 36.436

0.0061 0.0122 0.0189

0.99 0.98 0.98

HI HI HI

30 60 296

SUN SUN SUN

2.5 2.5 2.5

36.927 36.667 36.026

0.0075 0.0158 0.0272

0.97 0.97 0.96

Table 2 Curvilinear predictive equations (Tre=b0+b1X+b2X2, HDp56 1C) for Humidex (HD) versus HSDA predicted Tre (1C) X

Time

Solar

Wind

b0

b1

b2

R2

HD HD HD

30 60 296

SHADE SHADE SHADE

2.5 2.5 2.5

37.635 38.246 38.981

0.017 0.038 0.072

0.00035 0.00075 0.00130

0.99 0.99 0.98

HD HD HD

30 60 296

SUN SUN SUN

2.5 2.5 2.5

37.763 38.564 39.805

0.020 0.049 0.109

0.00042 0.00096 0.00194

0.98 0.97 0.97

limitation of this study is that the relationship between predicted Tre and HI or HD may under-predict actual Tre for HI values 4135 1F (57 1C). Fig. 3 compares the STANDARD shade condition to the SUN condition. Based on the results, the Tre for a radiant load (SUN) could be estimated from STAN-

DARD predicted values by adding between 0.13, 0.27, and 0.44 1C for t=30, 60, and 300 min, respectively, to the predicted Tre. For t ¼ 300 min; there is a large range of offset, from 0.24 to 0.70 1C (SD=0.13 1C), whereas for the lesser time intervals, the maximum range is 40.2 1C. For HD, the offsets were 0.13, 0.25, and

ARTICLE IN PRESS W.R. Santee, R.F. Wallace / Journal of Thermal Biology 30 (2005) 65–72

69

40.0

PREDICTED Tre (°C)

39.5

39.0

38.5

38.0

37.5 30°C 37.0 75°F

85°F

35°C

40°C

95°F

45°C

105°F

50°C

115°F

125°F

55°C 135°F

HEAT INDEX (°C/°F) T296

T30

T60

Fig. 3. Comparison of predicted Tre versus HI for STANDARD and SUN conditions at time=30, 60, and 296 min.

39.3

PREDICTED Tre (°C)

39.1 38.9 38.7 38.5 38.3 38.1 37.9 30°C 37.7 75°F

85°F

35°C

45°C

40°C

95°F

105°F

50°C

115°F

125°F

55°C 135°F

HEAT INDEX (°C/°F) 1.5 m/s

2.5 m/s

5 m/s

Fig. 4. Comparison of predicted Tre versus HI for wind speeds of 1.5, 2.5, and 5.0 m s1, time=296 min.

0.45 1C for t ¼30, 60, and 300 min. Fig. 4 compares the difference between STANDARD, WIND1.5 and WIND5 conditions at 60 min. Based on the results, Tre for the lower wind speed of 1.5 m s1 (WIND1.5) could be estimated from STANDARD predicted values by adding an average value of 0.04–0.12 1C to the predicted Tre. For the higher wind speed of 5.0 m s1 (WIND5), Tre could be estimated from the STANDARD values

by subtracting an average of 0.05–0.15 1C to the predicted Tre. The recommended limits for the indices were also considered. For HD, the threshold for concern was 46 1C. For HI values between 90 and 105 1F were identified as a zone with a high potential for heat injury. The equation from Table 1 (HI) and Table 2 (HD) were used to calculate the Tre for the SHADE

ARTICLE IN PRESS W.R. Santee, R.F. Wallace / Journal of Thermal Biology 30 (2005) 65–72

70

Table 3 Comparison of calculated Tre at critical thresholds for HI (105 1F) and HD (46 1C) 30 min

HI=105 1F HD=46 1C

60 min

300 min

Standard

Sun

Mean

Standard

Sun

Mean

Standard

Sun

Mean

37.6 37.6

37.7 37.8

37.6 37.7

38.1 38.1

38.3 38.3

38.2 38.2

38.4 38.4

38.9 38.9

38.7 38.7

and SUN conditions at 30, 60, and 300 min. The mean Tre (MEAN) for SUN and SHADE was also calculated. At each of the time intervals, the calculated Tre for HI=105 1F and 46 1C were essentially equal (Table 3).

4. Discussion Which heat index is better? The linear relationship between HI and the predicted rectal temperature is simple and easy to comprehend. An exponential or curvilinear relationship is slightly more complex mathematically. The R2 values for the predicted Tre for the STANDARD and SUN conditions for three time periods (30, 60, and 300 min) were averaged. The average R2 value for HD was 0.979 and for HI 0.975. For all intents, there is no difference. Our methods, based on the model input for HI, were skewed towards HI, but our bias favors HD as opposed to HI. One reason is that HD is a more direct derivation of the impact of Ta and humidity, and is therefore a more basic temperature–humidity index. The HI approach uses a more complex derivation from Steadman’s model to arrive at the same basic answer. The primary appeal of heat indices is simplicity. The acceptance of these thermal indices is due, in part, to the fact that the indices can be presented in the format of a simple look-up or survival table. Unfortunately, the simple outputs also limit the appropriateness of the value to a specific or special case. Both military (Department of the Army and Air Force, TB MED 507, 2003) and industrial (ACGIH, 2004; NIOSH 86113, 1986) manuals provide guidance for more specific cases. The best-known military adaptation is to add 8–10 1F to WBGT to compensate for Chemical Protective clothing. The ACGIH manuel (2004) devotes several pages to adaptations for different activities and clothing. In this report, examples of supplemental adjustments to the basic indices or STANDARD conditions include wind speed (WIND1.5, WIND5, SUN) and radiant load. The necessity of using numerous modifications to the basic indices to adjust for various conditions, to a large extent, negates the apparent advantage of indices—the inherent simplicity of the basic index.

HSDA v.2.1 (SAIC, 1993) is an example of a complex mathematical model that takes into account variability in height and weight, clothing, activity level, solar load, acclimatization and hydration—all factors which are either held constant or not considered in HI or HD. HSDA provides more guidance to the user, including maximum work time, recommended work-rest cycles for sustained activity, estimated water requirements, casualty rates, and equilibrium Tre values for a wide range of clothing and activities. In the electronic information age, complex mathematics is no longer a barrier. In the context of this paper, HSDA does not appear to present any advantage over the simpler heat indices. When HSDA is run with constant values for clothing, activity, etc., it functions as a heat index, with all the inherent limitations of a fixed index. Whereas the principle use of heat indices by weather services is to provide a simple, single average or worst-case characterization of environmental conditions that impact the general population, an advantage of HSDA or other complex models is the capability to account for variability in a population. One other clear advantage of HSDA over HI is that there are no reasonable environmental limits, whereas HI was only applicable to combinations of temperature and humidity that resulted in a maximum HI value of 130 1F. Table 3 suggests that, based on calculated Tre values, the HI warning zone of 90–105 1F is conservative relative to the guidance provided for the HD, where the threshold for limiting activities is 46 1C. Another facet of Table 3 is the time factor. If Treo38 1C is the threshold for prolonged heat exposure of a healthy adult (ACGIH, 2004; NIOSH, 1986), then a 30 min exposure remains under that limit. Beyond the industrial limit of 38 1C, guidance relating Tre to the potential for heat injury is a matter of debate. New military standards in TB MED 507 (Department of the Army and Air Force, 2003) distinguish between compensated heat stress (CHS) and uncompensated heat stress (UCHS). During CHS, the physiological processes for thermoregulation allow homeostasis at an elevated temperature. During UCHS, thermoregulatory processes are essentially overwhelmed when evaporative heat loss is insufficient to maintain a high but stable core temperature. As noted in TB MED 507, core temperature thresholds during work:rest cycles are 38.5 1C for

ARTICLE IN PRESS W.R. Santee, R.F. Wallace / Journal of Thermal Biology 30 (2005) 65–72

CHS, and 38 1C for UCHS, assuming adequate hydration and acclimatization. Sawka et al. (2001) looked at 747 laboratory heat exposure trials and found that 50% of heat-related trials occurred below 38.6 1C. Subjects tolerated higher rectal temperatures in field environments. For further data analysis, they set a threshold of 38.3 1C for heat-sensitive individuals. Based on those studies, they recommended a core temperature safety threshold of 38.5 1C for CHS. Given that this threshold is for an otherwise young and healthy population, for the general public, a ‘‘safe’’ limit of 38.3 1C is more reasonable to protect more vulnerable individuals. If the safe threshold for potential heat injury is 38.3–38.5 1C for a young, fit population under conditions of CHS, a HI of 105 1F (41 1C) or an HD of 46 1C at 60 min is at or near the lower threshold (Table 3). By NIOSH standards, a hazard (Tre438.0 1C) would exist. The hazard clearly becomes greater as the exposure time increases. At 300 min, calculated Tre values approach the limit, Tre values range between 38.4 and 38.9 1C, and heat-related effects could be expected to impact the performance. However, as the HSDA Tre values are conservative estimates for a young, fit population, they are most applicable to heat-sensitive individuals in the military and the general population. A limitation of both heat indices is time. The output for HSDA versus HI or HD was presented in this paper at 30, 60, and 300 min of continuous work. Under realistic conditions, an average individual is unlikely to sustain 320 W of activity for much longer than 60 min without a short break. Even a relatively short rest causes core temperature to drop, in effect lowering the restart temperature, but not to a value as low as the initial starting core temperature. A cycle of work-rest will result in a different, lower ‘‘equilibrium’’ temperature. One of the features of the HSDA model is to predict a work–rest cycle that allows a soldier to participate in an activity while remaining below a selected level of thermal strain. This study was initiated in the context of HI. It was determined that when HI values exceeded 135 1F, the predicted Tre values no longer fit a linear relationship. Consequently, at higher Ta values, when HI exceeds 135 1F, no values for higher humidities were entered. For 45 1C, the only RH represented is 30% RH, and for 40 1C, between 30% and 50%. The corresponding upper limit or HD is 56 1C. For combinations of Ta and RH that exceed an HI of 1351, Tre may rapidly increase to dangerous levels. An advantage of a physiological model such as HSDA is that these limits do not apply. This study describes a method to estimate Tre from the respective heat indices of the US (HI) and Canada (HD). The equations for the indices provide a meaningful measure of the thermal environment using only Ta and humidity. However, the results are still subject to the limitations of any thermal index. We prefer the HD over

71

HI, as it uses Tdp rather than RH and avoids certain assumptions of the Steadman model used to develop HI. HD is thus a more direct representation of the physical effects of temperature and humidity. The 46 1C threshold recommended for HD may also be more realistic than the limits recommended for HI, assuming a young, healthy adult population. The caveat is that a physiological model based on the heat balance equation, whether Steadman’s models or HSDA, is superior to either HI or HD. We strongly endorse physiologically based heat balance models, but heat indices may serve until thermal models can replace them. It is also important to emphasize that the results of this study are limited to conditions for HIp135 1F or HDp56 1C. This is a limit associated with the heat indices and is not a limitation of HSDA or other physiological models.

Acknowledgments The authors would like to thank the following individuals for their assistance in preparing this technical report: Pierre Tourigny and Joseph Shaykewich, Meteorological Services Canada (MSC), Environment Canada (EC); and Mark Tew and Lans Rothfusz, National Weather Service (NWS), National Oceanic and Atmospheric Administration (NOAA). Disclaimer Approved for public release; distribution is unlimited. The opinions of the author(s) are not to be construed as official or reflecting the views of the Army or the Department of Defense. Citations of commercial organizations and trade names in the report do not constitute an official Department of the Army endorsement or approval of the products or services of these organizations.

References ACGIH, 2004. 2004 TLVsr and BEIsr. Threshold Limit Values for Chemical Substances and Physical Agents and Biological Exposure Limits. American Conference of Government Industrial Hygiene, Cincinnati. Cadarette, B.S., Montain, S.J., Kolka, M.A., Stroschein, L.A., Matthew, W.T., Sawka, M.N., 1999. Cross validation of USARIEM heat strain prediction models. Aviat. Space Environ. Med. 70, 1–11. Department of the Army and Air Force, Headquarters, March, 2003. Heat Stress Control and Heat Casualty Management. TB MED 507/ UFPAM 48-152(I). Government Printing Office, Washington, D.C. Gonzalez, R.R., McLellan, T.M., Withey, W.R., Chang, S.K., Pandolf, K.B., 1997. Heat strain models applicable for protective clothing systems: comparison of core temperature response. J. Appl. Physiol. 83, 1017–1032.

ARTICLE IN PRESS 72

W.R. Santee, R.F. Wallace / Journal of Thermal Biology 30 (2005) 65–72

Hodgdon, J.A., 1992. Body composition in the military service: standards and methods. In: Marriott, B.M., GrumstrupScott, J. (Eds.), Body Composition and Physical Performance. National Academy Press, Washington D.C., pp. 57–70. Masterton, J.M., Richardson, F.A., 1979. HUMIDEX: A Method of Quantifying Human Discomfort Due to Excessive Heat and Humidity. CLI 1-79. Environment Canada, Downside, Ontario. Matthew, W.T., Santee, W.R., Berglund, L.G., 2001. Solar load inputs for USARIEM thermal strain models and the solar radiation-sensitive components of the WBGT Index. Technical Report T01/13. US Army Research Institute Environmental Medicine, Natick, MA. National Institute for Occupational Safety and Health, 1986. Criteria for Recommended Standard: Occupational Exposure to Hot Environments. NIOSH Publication 86-113. US Government Printing Office, Washington, DC. National Oceanic and Atmospheric Administration, retrieved November 24, 2003 from World Wide Web: http:// www.crh.noaa.gov/gjt/heat_index.htm. National Oceanic and Atmospheric Administration. Heat index. National Weather Service Forecast Office, Grand Junction, CO. Office of the Federal Coordinator for Meteorological Services and Supporting Research, January, 2003. Report on wind

chill temperature and extreme heat indices: evaluation and improvement projects. FCM-R19-2003. US Department of Commerce/National Oceanic and Atmospheric Administration, Washington, DC. Pandolf, K.B., Stroschein, L.A., Drolet, L.L., Gonzalez, R.R., Sawka, M.N., 1986. Prediction modeling of physiological responses and human performance in heat. Comput. Biol. Med. 16, 319–329. Rothfusz, L.P., 1990. The heat index ‘‘equation’’ (or more than you ever wanted to know about the heat index). NWS Technical Attachment SR90-23. NWS Southern Region Headquarters, Fort Worth, TX. SAIC, 1993. P2NBC2 Heat Strain Decision Aid User’s Guide Version 2.1. Scientific Applications International Corporation, Joppa, MD. Sawka, M.N., Latzka, W.A., Montain, S.J., Cadarette, B.S., Kolka, M.A., Kraning, K.K., Gonzalez, R.R., 2001. Physiologic tolerance to uncompensable heat: intermittent exercise, field vs. laboratory. Med. Sci. Sports Exerc. 33, 422–430. Steadman, R.G., 1979. The assessment of sultriness Part I: a temperature-humidity index based on human physiology and clothing science. J. Appl. Meteorol. 18, 861–873. Steadman, R.G., 1999. The free-convective anomaly. J. Appl. Physiol. 87, 54–73.