What effect will a few degrees of climate change have on human heat balance? Implications for human activity

Abstract

While many factors affecting human health that will alter with climate change are being discussed, there has been no discussion about how a warmer future will affect man’s thermoregulation. Using historical climate data for an Australian city and projections for Australia’s climate in 2070, we address the issue using heat balance modelling for humans engaged in various levels of activity from rest to manual labour. We first validate two heat balance models against empirical data and then use the models to predict the number of days at present and in 2070 that (1) sweating will be required to attain heat balance, (2) heat balance will not be possible and hyperthermia will develop, and (3) body temperature will increase by 2.5°C in less than 2 h, which we term “dangerous days”. The modelling is applied to people in an unacclimatised and an acclimatised state. The modelling shows that, for unacclimatised people, outdoor activity will not be possible on 33–45 days per year, compared to 4–6 days per year at present. For acclimatised people the situation is less dire but leisure activity like golf will be not be possible on 5–14 days per year compared to 1 day in 5 years at present, and manual labour will be dangerous to perform on 15–26 days per year compared to 1 day per year at present. It is obvious that climate change will have important consequences for leisure, economic activity, and health in Australia.

Appendix 1—the algorithms used in heat balance calculations

The data from the Bureau of Meteorology were the average every 3 h from January 1990 to December 2001, for:

Ta	= dry bulb temperature	°C
RH	= relative humidity	%
Vkmh	= wind speed from historical records	km h−1
V	= wind speed converted to m s−1	m s−1
	= Vkmh / 3.6

Some of the terms are common to both the Kata model and MANMO. These terms are:

Mb	= body mass	kg
H	= height	cm
SAb	= body surface area	m2
	$= 0.007184 * \left( {{\hbox{M}}_{\rm{b}}^{0.425}} \right) * \left( {{{\hbox{H}}^{0.725}}} \right)$
MR	= metabolic rate per unit surface area	W m−2
MRb	= metabolic rate of a body	W
	= MR × SAb
MHP	= metabolic heat production	W m−2
	assumed to be 80% of the metabolic rate when work is performed (20% efficiency), and 100% of the metabolic rate when at rest (0% efficiency)
MHL	= metabolic heat load on the body	W
	= MHP × SAb
SRmax	= maximum sweat rate	g min−1 m−2
SRb	= maximum sweat rate from a body	g min−1
	= SRmax * SAb
ESR max	= maximum evaporation rate due to sweating from a body (supply side)	W
	$\left( {{\hbox{S}}{{\hbox{R}}_{\rm{b}}} * 2400\;{\hbox{j}}\;{{\hbox{g}}^{ - 1}}/60} \right) * {\hbox{Ef}}{{\hbox{f}}_{{\rm{evap}},}}$
	where Effevap is the efficiency of evaporation and was assumed to be 85% (see text)
RADinc	= total incident radiation load	W
	see text and Table 1, adjusted by a scaling factor if the individual’s SA is not 1.81 m2

Terms used in MANMO;

Tskin	= skin temperature ( assumed to be 36°C )	°C
Tclo	= surface temperature of clothing exposed to the sun	°C
	$= {{\hbox{T}}_{\rm{a}}} - 21.9 + {{\hbox{T}}_{\rm{skin}}}$
Albsk	= albedo of the skin ( assumed to be 0.3 )
Albclo	= albedo of the clothing ( assumed to be 0.3 )
Pclo	= proportion of the body clothed ( assumed to be 0.4 )
hc	= convective heat loss co-efficient	W m−2 °C−1
	$\begin{array}{*{20}{c}} {{\hbox{if}}\;{\hbox{V}} < 0.5; = \left[ {2.3 + 5.6 * {{\hbox{V}}^{0.67}}} \right] * 1.16} \hfill \\{{\hbox{if}}\;0.5 < {\hbox{V}} < 2; = 6.56 * {{\hbox{V}}^{0.618}} * 1.16} \hfill \\{{\hbox{if}}\;2 < {\hbox{V}} < 4; = 5.83 * {{\hbox{V}}^{0.805}} * 1.16} \hfill \\{{\hbox{if}}\,{\hbox{V}} > 4; = 5.38 * {{\hbox{V}}^{0.9}} * 1.16} \hfill \\\end{array}$
	where 1.16 is a scaling factor to convert kcal m−2 h−1 °C−1 to W m−2 °C−1
Fcl	= clothing factor that increases the resistance to heat loss across clothed surfaces
	$= 0.577 - 0.0886 * {\hbox{V}} + 0.00516 * {{\hbox{V}}^2}$
Fpcl	= factor that adjusts evaporation rate for the clothing permeation to water vapour
	$= 0.858 - 0.246 * {\hbox{V}} + 0.0372 * {{\hbox{V}}^2} - 0.0019 * {{\hbox{V}}^3}$
RADabs	= absorbed radiant heat load	W
	$= \left[ {{\hbox{RA}}{{\hbox{D}}_{\rm{inc}}} * \left( {1 - {\hbox{Al}}{{\hbox{b}}_{\rm{sk}}}} \right) * \left( {1 - {{\hbox{P}}_{\rm{clo}}}} \right)} \right] + \left[ {\left( {{\hbox{RA}}{{\hbox{D}}_{\rm{inc}}} * \left( {1 - {\hbox{Al}}{{\hbox{b}}_{\rm{clo}}}} \right) * {{\hbox{P}}_{\rm{clo}}} * 1.08} \right) - \left( {{{\hbox{h}}_{\rm{c}}} * \left( {{{\hbox{T}}_{\rm{clo}}} - {{\hbox{T}}_{\rm{a}}}} \right) * 1.08 * \left( {{{\hbox{P}}_{\rm{clo}}} * {\hbox{S}}{{\hbox{A}}_{\rm{b}}}} \right)} \right.} \right]$
	where 1.08 is a scaling factor that increases the surface area of clothed surfaces by 8% relative to the underlying skin. The final term subtracts the component of radiant heat load that is incident on the clothing and is lost directly by convection.
	Occasionally at high wind speed the solution of this term was negative, in which case the term was resolved to the radiant heat load on the skin only = $\left[ {{\hbox{RA}}{{\hbox{D}}_{\rm{inc}}} * \left( {1 - {\hbox{Al}}{{\hbox{b}}_{\rm{sk}}}} \right) * \left( {1 - {{\hbox{P}}_{\rm{clo}}}} \right)} \right]$
HLtot	= total heat load	W
	= MHL + RADabs
Cr	= respiratory convective heat exchange	W
	$= 0.001173 * \left( {37 - {{\hbox{T}}_{\rm{a}}}} \right) * {\hbox{M}}{{\hbox{R}}_{\rm{b}}}$
Cclo	= convective heat exchange across clothed surfaces	W
	$= {{\hbox{h}}_{\rm{c}}} * \left( {{{\hbox{T}}_{\rm{sk}}} - {{\hbox{T}}_{\rm{a}}}} \right) * {{\hbox{F}}_{\rm{cl}}} * \left( {{{\hbox{P}}_{\rm{clo}}} * {\hbox{S}}{{\hbox{A}}_{\rm{b}}}} \right) * 1.08$
Cunclo	= convective heat exchange across unclothed surfaces	W
	$= {{\hbox{h}}_{\rm{c}}} * \left( {{{\hbox{T}}_{\rm{sk}}} - {{\hbox{T}}_{\rm{a}}}} \right) * \left( {1 - {{\hbox{P}}_{\rm{clo}}}} \right) * {\hbox{S}}{{\hbox{A}}_{\rm{b}}}$
Ctot	= total convective heat exchange	W
	$= {{\hbox{C}}_{\rm{r}}} + {{\hbox{C}}_{\rm{clo}}} + {{\hbox{C}}_{\rm{unclo}}}$
IR	= infra-red radiant heat loss	W
	$= - 1 * \left\{ {\left[ {\sigma * {{\left( {{{\hbox{T}}_{\rm{a}}} + 273.16} \right)}^4}} \right] - \left[ {\sigma * {{\left( {{{\hbox{T}}_{\rm{clo}}} + 273.16} \right)}^4} * {{\hbox{P}}_{\rm{clo}}}} \right] - \left[ {\sigma * {{\left( {{{\hbox{T}}_{\rm{sk}}} + 273.16} \right)}^4} * \left( {1 - {{\hbox{P}}_{\rm{clo}}}} \right)} \right]} \right\} * \left( {{\hbox{S}}{{\hbox{A}}_{\rm{b}}} * 0.725} \right)$
	where σ is the Stefan Boltzmann constant, and 0.725 reduces the total body surface area to the area involved in radiant heat exchange
Er	= respiratory evaporative heat loss	W
	$= {\hbox{M}}{{\hbox{R}}_{\rm{b}}} * 0.0023 * \left[ {44 - \left( {{\hbox{RH/100}}} \right) * \left( {1.372 + 0.851 * {{\hbox{T}}_{\rm{a}}} - 0.0161 * {\hbox{T}}_{\rm{a}}^2 + 0.00071 * {\hbox{T}}_{\rm{a}}^3} \right)} \right]$
Eunclo	= evaporative heat loss from unclothed surfaces	W
	$= \left\{ {2.2 * {{\hbox{h}}_{\rm{c}}} * \left[ {\left( {1.91 * {{\hbox{T}}_{{\rm{sk}}}} - 25.33} \right) - \left( {{\hbox{RH/100}}} \right) * \left( {1.372 + 0.851 * {{\hbox{T}}_{\rm{a}}} - 0.0161 * {\hbox{T}}_{\rm{a}}^2 + 0.00071 * {\hbox{T}}_{\rm{a}}^3} \right)} \right]} \right\} * \left[ {{\hbox{S}}{{\hbox{A}}_{\rm{b}}} * \left( {1 - {{\hbox{P}}_{{\rm{clo}}}}} \right)} \right]$
	where 2.2 is a factor to convert the convective heat exchange coefficient to an evaporative heat exchange coefficient
Eclo	= evaporative heat loss from clothed surfaces	W
	$= \left\{ {2.2 * {{\hbox{h}}_{\rm{c}}} * \left[ {\left( {1.91 * {{\hbox{T}}_{{\rm{sk}}}} - 25.33} \right) - \left( {{\hbox{RH/100}}} \right) * \left( {1.372 + 0.851 * {{\hbox{T}}_{\rm{a}}} - 0.0161 * {\hbox{T}}_{\rm{a}}^2 + 0.00071 * {\hbox{T}}_{\rm{a}}^3} \right)} \right]} \right\} * \left[ {\left. {{\hbox{S}}{{\hbox{A}}_{\rm{b}}} * {{\hbox{P}}_{{\rm{clo}}}}} \right)} \right] * {{\hbox{F}}_{{\rm{pcl}}}}$
Esk max	= maximum evaporation from the skin surface	W
	$= {\hbox{the}}\;{\hbox{lesser}}\;{\hbox{of}}\;\left( {{{\hbox{E}}_{\rm{clo}}} + {{\hbox{E}}_{\rm{unclo}}}} \right){\hbox{OR}}\left( {{{\hbox{E}}_{{\rm{SR}}\,\max }}} \right)$
Etot	= total evaporative heat loss from the body	W
	= Esk max + Er
Hs	= heat storage	W
	$= {\hbox{H}}{{\hbox{L}}_{\rm{tot}}} - {{\hbox{C}}_{\rm{tot}}} - {\hbox{IR}} - {{\hbox{E}}_{\rm{tot}}}$
	if Hs is positive then hyperthermia will develop
	sweating is required for heat balance if ${\hbox{H}}{{\hbox{L}}_{\rm{tot}}} > {{\hbox{C}}_{\rm{tot}}} + {\hbox{IR}} + {{\hbox{E}}_{\rm{r}}}$
	A dangerous day is defined when Hs > 1.2153 × Mb

Terms used in the Kata model;

Tn	= natural wet-bulb temperature	°C
	$= 0.85 * {{\hbox{T}}_{\rm{a}}} + 0.17 * {\hbox{RH}} - 0.61\,{\hbox{x}}\,{{\hbox{V}}^{0.5}} + 0.0016 * {\hbox{S}} - 11.62$
	where S is direct solar radiation and was assumed to vary sinusoidally from 960 W m−2 at the summer solstice to 500 W m−2 at the winter solstice. Errors induced if S varies from the predicted value are minor.
DKCPa	= dry kata cooling / warming power per unit area;	W m−2
	$\begin{array}{*{20}{c}} {{\hbox{if}}\,{\hbox{V}} = 0; = 0.27 * {{\left( {36.5 - {{\hbox{T}}_{\rm{a}}}} \right)}^{1.06}} * 41.84} \hfill \\{{\hbox{if}}\,0 < {\hbox{V}} > 1; = 0.2 + 0.4 * {{\hbox{V}}^{0.5}} * \left( {36.5 - {{\hbox{T}}_{\rm{a}}}} \right) * 41.84} \hfill \\{{\hbox{if}}\,{\hbox{V}} > 1; = 0.13 + 0.47 * {{\hbox{V}}^{0.5}} * \left( {36.5 - {{\hbox{T}}_{\rm{a}}}} \right) * 41.84} \hfill \\\end{array}$
	where 41.84 is a scaling factor to convert mcal cm−2 sec−1 to W m−2
DKCPb	= dry kata cooling / warming power from a body, adjusted by a 30% clothing factor	W
	$= {\hbox{DKC}}{{\hbox{P}}_{\rm{a}}} * {\hbox{S}}{{\hbox{A}}_{\rm{b}}} * 0.7$
WKCPa	= wet kata cooling / warming power per unit area;	W m-2
	$= \left[ {0.648 * \left( {36.4 - {{\hbox{T}}_{\rm{n}}}} \right) + 0.833 * \left( {36.4 - {{\hbox{T}}_{\rm{n}}}} \right) * {{\hbox{V}}^{0.5}}} \right] * 41.84$
WKCPb	= wet kata cooling / warming power from a body, adjusted by a 30% clothing factor	W
	$= {\hbox{WKC}}{{\hbox{P}}_{\rm{a}}} * {\hbox{S}}{{\hbox{A}}_{\rm{b}}} * 0.7$
RADabs	= same as MANMO
HLtot	= same as MANMO	W
Cr	= same as MANMO	W
Er	= same as MANMO	W
HLCmax	= maximum heat loss capacity
	$= {\hbox{the}}\,{\hbox{lesser}}\,{\hbox{of}}\,\left( {{\hbox{DKC}}{{\hbox{P}}_{\rm{b}}} + {{\hbox{E}}_{{\rm{SR}}\,\max }} + {{\hbox{C}}_{\rm{r}}} + {{\hbox{E}}_{\rm{r}}}} \right){\hbox{OR}}\left( {{\hbox{WKC}}{{\hbox{P}}_{\rm{b}}} + {{\hbox{C}}_{\rm{r}}} + {{\hbox{E}}_{\rm{r}}}} \right)$
Hs	= heat storage
	= HLtot – HLCmax
	if Hs is positive then hyperthermia will develop
	sweating is required for heat balance if HLtot > DKCPb
	A dangerous day is defined when Hs > 1.2153 × Mb