Estimating heat stress from climate-based indicators: present-day ...

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Supplementary Materials for

“Estimating heat stress from climate-based indicators: present-day biases and

future spreads in the CMIP5 global climate model”

Zhao Y. (1), A. Ducharne (2), B. Sultan (1), P. Braconnot (3), R. Vautard (3)

1 LOCEAN/IPSL, UMR 7159, Sorbonne Universités, Unité mixte UPMC-CNRS-IRD-MNHN, 4 place

Jussieu, 75005, Paris, France

2 METIS/IPSL, UMR 7619, Sorbonne Universités, Unité mixte UPMC-CNRS-EPHE, 4 place Jussieu, 75005

Paris, France

3 LSCE/IPSL, UMR 1572, Unité mixte CEA-CNRS-UVSQ, Bât 712, 91191, Gif-sur-Yvette, France

Corresponding author: [email protected]

SM Table S1. Climate models included in the study.

Institute/group Model Version Atmospheric

Resolution

BCC, Beijing, China BCC-CSM1-1 128 x 64

CCCma, Victoria, Canada CanESM2 128 x 64

CNRM-CERFACS, Toulouse, France CNRM-CM5 256 x 128

CSIRO-BOM, Australia ACCESS1-0 192 x 145

CSIRO-QCCCE, Australia CSIRO-Mk3-6-0 192 x 96

INM, Moscow, Russia INM-CM4 180 x 120

IPSL, Paris, France ISPL-CM5A-LR 96 x 96

IPSL, Paris, France IPSL-CM5A-MR 144 x 143

IPSL, Paris, France IPSL-CM5B-LR 96 x 96

MIROC, JAMSTEC-AORI-NIES, Japan MIROC5 256 x 128

MIROC, JAMSTEC-AORI-NIES, Japan MIROC-ESM-CHEM 128 x 64

MIROC, JAMSTEC-AORI-NIES, Japan MIROC-ESM 128 x 64

MOHC, Exeter, UK HadGEM2-CC 192 x 145

MOHC, Exeter, UK HadGEM2-ES 192 x 145

MRI, Tsukuba, Japan MRI-CGCM3 320 x 160

NASA-GISS GISS-E2-R 144 x 90

NCAR, Boulder, USA CCSM4 288 x 192

NCC, Oslo, Norway NorESM1-M 144 x 96

NOAA-GFDL, Princeton, USA GFDL-CM3 144 x 90

NOAA-GFDL, Princeton, USA GFDL-ESM2M 144 x 90

NOAA-GFDL, Princeton, USA GFDL-ESM2G 144 x 90

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SM DM1: Background information on the selected heat stress indicators

Humidex (HD, Masterton and Richardson 1979) has been designed to describe how hot the weather is

perceived to be by the average person. It is increasingly used both in Europe and in North America due to its

easy calculation. HD was first designed as a comfort index in moderate environments where the main designer

goal was reaching thermal comfort conditions. It is validated in outdoor conditions, and has become a

generalized assessment of heat stress for both the indoors and outdoors. It is used in both moderate and severe

environments where workers’ health protection from hot stress is required.

Four HD thresholds (30, 40, 45 and 54°C) are suggested by ACGIH (1999) and an international standard ISO

7243 (1989) related to different discomfort levels. 35°C is the proposed threshold for reducing excessive hot

risks by the European Commission (Lavalle et al 2006). We thus take the four thresholds (35, 40, 45 and

54°C) to classify the four heat stress classes. That is, the ranges of 35-40°C, 40-45°C, 45-54°C and above

54°C define, respectively “Slight,” “Moderate,” “Strong” and “Extreme” heat stress classes.

Simplified Wet-bulb Global Temperature (W). The wet-bulb globe temperature (WBGT) is a well-established

heat index for workplace applications, with recommended rest/work cycles at different metabolic rates clearly

specified in ISO 7243 (1989). It is an index to measure hot extreme environments. WBGT is usually

calculated from measurements of the natural wet bulb temperature, the globe temperature, and the dry bulb air

temperature. The specialized measurements for WBGT are not available from routine weather stations, which

has motivated the development of some approximations. In this study, we use the simplified WBGT

developed by the Australian Bureau of Meteorology (ABOM, http://www.bom.gov.au/info/thermal_stress/),

which depends only on temperature and humidity and represents heat stress for average outdoor daytime

conditions. However, it is acknowledged that its accuracy of representing the original labor industry index

may be questionable. We chose it, however, due to its wide use (Kjellstrom et al 2009, Blazejczyk et al 2012,

Willett and Sherwood, 2012, Fischer and Knutti 2013, Oleson et al 2013, Buzan et al 2015).

Four W thresholds (28, 32, 35 and 38°C) are defined based on productivity loss levels for moderate labor

(Kjellstrom et al 2009). Thus, the ranges of 28-32°C, 32-35°C, 35-38°C and above 38°C define “Slight,”

“Moderate,” “Strong” and “Extreme” heat stress, respectively.

Apparent temperature (AT) was invented in the late 1970s (Steadman 1979a, 1979b) to measure thermal

sensations for hot and wet situations and was initially applied in Australia and the USA. It was extended in the

early 1980s to any combination of air temperature (T) and vapor pressure (VP) (Steadman 1984). Ignoring the

effects of wind and radiation, we use here the indoor version, which is meaningful for moderate environments.

However, there are no widely agreed thresholds with AT. Here, we define four empirically AT thresholds (28,

32, 35 and 40°C) following Gagge et al (1967) and Bradshaw (2012). In this case, 28°C is the value just above

the comfort range of temperatures in indoor situations (Bradshaw 2006) and 40°C is the body temperature

when heat stroke may occur (Gagge et al 1967). Thus, the ranges of 28-32°C, 32-35°C, 35-40°C and above

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40°C define “Slight,” “Moderate,” “Strong” and “Extreme” heat stress classes, respectively.

SM DM2: Error attribution analysis

Following Zhao et al (2012), the contribution of uncertainty T and VP on the overall uncertainty of the heat

indicators is measured by comparing the standard deviation between calculations based on modeled and

observed variables. Taking HD as an example, the total error is defined as follows:

√

(1)

where HDi is the mean heat indicator based on the ith model (we use the extreme mean in the present study),

HDOBS is the mean heat indicator based on observed data, N=21 models.

To quantify the contribution of T and VP biases to the total error, we carry out factorial calculations. For the

ith model, the errors attributed to T and VP is, respectively, defined as

√

(2)

√

(3)

where is computed based on the ith GCM modeled T and observed VP,

is computed based on the

ith GCM modeled VP and observed T.

The total error can then be decomposed into:

(4)

The third term, cov( ET, Evp), is proportional to the correlation between model errors on T and on VP because

the index is a linear function of the two variables, T and VP. A negative value indicates that the effects of

model biases in T and VP tend to counteract one another for heat indicators (referred as compensation effect),

whereas a positive covariance indicates that biases will further degrade the modeled heat indicators (referred

to as the additive effect). To keep this covariance term comparable with total error, it is converted to the root

square of absolute covariance while keeping the sign of covariance. The result is referred to as the offset term:

offset = ± sqrt ( abs(cov( ET, Evp)) )= ± sqrt ( abs(Etot

2 - ET

2 - Evp

2) )/2 (5)

Similarly, the error contributions from T, VP and offset to total errors in AT and W can be estimated by

applying the above procedure to AT and W instead of HD.

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SM DM3: Variance decomposition

To quantify the uncertainties of projected heat stress attributed to GCMs and heat indicators, we decompose

the variance of the ensemble of climate change responses of the indicators (i.e., the difference between the

2070-2099 and the 1979-2005 extreme means or mean annual heat stress frequencies) into contributions from

GCMs, indicators and the interactions among them. To do so, we use the analysis of variance (ANOVA) to

decompose the variance (see, e.g., von Storch and Zwiers (1999) for an introduction and Déqué et al (2007)

and Yip et al (2011) for an application in climate modeling). According to the ANOVA theory, the total sum

of the squares (SST) can be split into sums of squares due to the individual effects (SSA, SSB) and their

interactions (SSI). Because the classical application of the method tends to underestimate the variance in small

sample sizes (Déqué et al 2007, Bosshard et al 2013), we followed the method proposed by Bosshard et al

(2013) to subsample the 21 GCMs. In each subsampling iteration, we select three GCMs out of the 21, which

results in a total of 1330 possible GCMs combinations. For each of the 1330 subsampling iterations, we end

up with three GCMs (M=3) and three heat indicators (N=3), which define our model combination matrix

(MxN) for the variance decomposition.

Taking the ith (MxN) matrix as an example, Yi m,n

is the projected change in heat stress by the mth GCM based

on the nth indicator, and Yi o,o

, Yi m,o

and Yi o,n

, are the ith grand ensemble mean, mean across indicators and

mean across GCMS, respectively. The ANOVA model can be written as

∑ ∑ (

)

(6)

∑ (

)

(7)

∑ (

)

(8)

∑ ∑ (

)

(9)

(10)

where SSTi, SSAi, SSBi and SSIi are the total, GCM-attributed, indicator-attributed variances and the

interaction among them, respectively.

Then, for each effect, the variance fraction is derived as follows:

∑

(11)

∑

(12)

∑

(13)

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Values of 0 and 1 for the variance fraction correspond to a contribution of an effect to the total ensemble

variance of 0% and 100%, respectively.

The uncertainty of projected heat stress attributed to different factors can be further scaled to the grand

standard deviation (SD), that is

(14)

(15)

(16)

, and for the grand standard deviation attributed to GCM, indicator and the

interactions, respectively. In the present study, we take this form of expression, as shown in Figure 4e-f and

Figure 5.

SM DM4: Bias-correction approach

GCMs are far from being perfect (Randall et al 2007), thus, bias correction methods are widely applied to

GCM outputs for climate impact studies. This is designed to remove systematic statistical deviations from

observational data. However, the effects of bias correction on impact estimation are still in dispute (Ehret et al

2012) because they may alter relations among variables and violate conservation principles. In this study, we

adopted a solution that preserves the internal consistency of the indicators, and we corrected the thresholds of

each indicator rather than the input temperature and humidity for the estimation of heat stress classes. For a

certain threshold, taking HD at 35°C for instance, we kept the probability distribution of the modeled heat

indicator unchanged over the full reference period for each GCM at a specific pixel, and we determined the

value that ensures that the simulated number of days above

is exactly equal to the observed

number of days above 35°C over the same period. Thus, is the corrected threshold corresponding to

35°C for HD in observations. We can similarly determine corrected threshold values for other “reference”

thresholds and other heat stress indicators. The resulting sets of threshold values are different at each pixel for

each GCM. Based on these corrected sets of thresholds, the modeled heat stress frequencies “perfectly” match

the present-day observations. We then applied these corrected thresholds to project the heat stress frequency

in the future. A comprehensive evaluation of this bias-correction approach is beyond the scope of this study,

but we showed that the spread of modeled heat stress frequency among GCMs is significantly reduced (by

approximately 10-70%) compared to the spread derived directly from the raw outputs of GCMs simulations

(Figure 5b). The smallest improvement is found in central North America (E.UsCa(Dfab)), where GCMs

work reasonably well due to the compensation effect (Figure 2, Figure 5c; Willett and Sherwood 2012,

Fischer and Knutti 2013). Finally, “perfect” performance at present day does not guarantee an accurate

projection in the future, but this is a limitation to any bias-correction approach.

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SM References

ACGIH 1999 American Conference of Governmental Industrial Hygienists: Threshold Limit values for

Chemical Substances and Physical Agents and Biological Exposure Indices Cincinnati OH, USA.

Bradshaw V 2010 The Building Environment: Active and Passive Control Systems. (John Wiley & Sons New

York, USA)

Déqué M, Rowell DP, Lüthi D, Giorgi F, Christensen, JH, Rockel B, Jacob D, Kjellström E, de Castro, M and

van den Hurk B 2007 An intercomparison of regional climate simulations for Europe: assessing

uncertainties in model projections Clim. Change 81 53–70

Ehret U, Zehe E, Wulfmeyer V, Warrach-Sagi K and Liebert J 2012 HESS Opinions “Should we apply bias

correction to global and regional climate model data?.” Hydrol Earth Syst Sci 16 3391–3404.

doi:10.5194/hess-16-3391-2012

Gagge AP, Stolwijk J and Hardy JD 1967 Comfort and thermal sensations and associated physiological

responses at various ambient temperatures Environ. Res. 1 1–20

ISO 7243 1989 Hot environments - estimation of the heat stress on working man, based on the WBGT-index

(wet bulb globe temperature). Geneva: International Standards Organization

Lavalle C, Barredo JI, De Roo A, Feyen L, Niemeyer S, Camia A, Hiederer R and Barbosa P 2006 Pan

European assessment of weather driven natural risks. In European week of region and cities open day,

Brussels 2006, October 9-12, European Commission-Directorate General Joint Research Centre, Brussels,

Belgium

Randall D et al 2007 The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment

Report of the Intergovernmental Panel on Climate Change, Edited by Solomon S et al, Cambridge

University Press, Cambridge, United Kingdom and New York, NY, USA.

Steadman RG 1979a The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human

Physiology and Clothing Science J. Appl. Meteorol. 18 861-73

Steadman RG 1979b The Assessment of Sultriness. Part II: Effects of Wind, Extra Radiation and Barometric

Pressure on Apparent Temperature J. Appl. Meteorol. 18 874-85

Yip S, Ferro C, Stephenson DB and Hawkins E 2011 A Simple, Coherent Framework for Partitioning

Uncertainty in Climate Predictions J. Clim. 24 4634–43

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SM Figure S1: Synthesis of extreme mean temperature, indicators and vapor pressure. (a) Zonal mean of T5%,

AT5%, W5%, HD5% and the corresponding vapor pressure (VPAT5%, VPW5% and VPHD5%) based on the WFDEI

reanalysis data over 1979-2005; (b) Zonal mean of change in T5%, AT5%, W5% and HD5% between 2070-2099

and 1979-2005 under RCP8.5. For each variable, the ensemble mean of 21 simulations is plotted in thick, and

surrounded by ±1 standard deviation in color.

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SM Figure S2: Synthesis of annual mean frequency of the four heat stress classes defined in Table 1 for AT. Left column

(a-f): Reference annual mean frequency of the four heat stress classes calculated from the WFDEI reanalysis over 1979-

2005; Middle column (g-i): Ensemble-mean bias of the 21 GCMs compared to WFDEI over 1979-2005; Right column

(m-r): Change in ensemble mean annual frequency of the four heat stress classes between 2070-2099 and 1979-2005.

Rows from top to bottom are Frequency of (a,g,m) “Slight”; (b,h,n) “Moderate”; (c,i,o) “Strong”; (d,j,p) “Extreme”;

(e,k,q) Total frequency under heat-stress; (f,i,r) Frequency of no heat-stress. Units are in day/year. Areas with dots

indicate regions with robust biases/changes (at least 18 models agree on the sign of biases/change).

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SM Figure S3: Same as SM Figure S2, but for heat stress indicator W.

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SM Figure S4 : Percentile exceedance value for AT. From top to bottom row, it is the distribution map of the

values exceeding the 75th (a,d,g), 95th (b,e,h) and 99th (c,f,i) percentile, respectively. The left, middle and

righ columns are the distribution map based on WFDEI reanlaysis, ensemble mean exceedance values based

on historical simulations and the RCP85 simulations, respectively.

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SM Figure S5: Same as SM Figure S4, but for W.

SM Figure S6: Same as SM Figure S4, but for HD.

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SM Figure S7. The whisker plot of regional mean percentile exceedance values from 21 GCMs in six regions

for (a) AT and (b) W. The bar within the box represents the median, the bottom and top of the box show the

1st and 3

rd quartiles of the GCMs spread. The bottom and upper end of the dashed vertical lines represent the

minimum and maximum value, respectively. The exceedance values based on WFDEI reanalysis are

represented by superimposed crosses.

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