Online Resource 1
This resource describes the implementation of heat stress indices in CLM4.
Interactions between Urbanization, Heat
Stress, and Climate Change
K.W. Oleson, A. Monaghan, O. Wilhelmi, M. Barlage, N. Brunsell, J. Feddema,
L. Hu, D.F. Steinhoff
K.W. Oleson – Corresponding Author
National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307
303-497-1332
FAX: 303-497-1348
oleson@ucar.edu
A. Monaghan, O. Wilhelmi, M. Barlage, D.F. Steinhoff
National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307
N. Brunsell, J. Feddema, L. Hu
University of Kansas, 1475 Jayhawk Blvd, Lawrence, KS 66045
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Five commonly used heat stress indices are implemented directly in the model
and are calculated at each time step. These are the National Weather Service
(NWS) Heat Index (HI; Rothfusz 1990), Apparent Temperature (AT; Steadman
1994), Simplified Wet Bulb Globe Temperature (SWBGT; Willett and Sherwood
2012), Humidex (Masterson and Richardson 1979), and Discomfort Index (DI;
Epstein and Moran 2006).
The HI (°F) is determined from multiple regression analysis by Rothfusz
(1990) on data from Steadman (1979)
HI  C1  C2Ta  C3 Rh  C4TaRh  C5Ta 2  C6 Rh 2  C7Ta 2 Rh
C8TaRh2  C9Ta 2 Rh2
(A.1)
where C1  42.379 , C2  2.04901523 , C3  10.14333127 , C4  0.22475541 ,
C5  6.83783  103 , C6  5.481717 102 , C7  1.22874 104 ,
C8  8.5282 104 , C9  1.99  106 , Ta is air temperature (°F), and Rh is
relative humidity (%).
The AT (°C) is taken from equation (22) of Steadman (1994)
AT  Ta  3.30e  0.70u10  4.0
(A.2)
where Ta is air temperature (°C), e is water vapor pressure (kPa) and u10 is 10-m
height wind speed (m s-1). Water vapor pressure is calculated following CLMU
(Oleson et al. 2010a) from saturated water vapor pressure determined by the
eighth-order polynomial fits of Flatau et al. (1992).
The SWBGT (°C) is taken from Table I of Willett and Sherwood (2012)
SWBGT  0.567Ta  0.393e  3.94
(A.3)
where Ta is air temperature (°C) and e is water vapor pressure (hPa).
The Humidex is
Humidex  Ta   5 9 e 10
(A.4)
where Ta is air temperature (°C) and e is water vapor pressure (hPa).
The DI is taken from equation (4) of Epstein and Moran (2006) and is a
unitless index
DI  0.5Tw  0.5Ta
(A.5)
where Tw is wet-bulb temperature (°C) and Ta is air temperature (°C). Wet-bulb
temperature is from equation (1) of Stull (2011)
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Tw  Ta  atan 0.151977  Rh  8.313659  


atan Ta  Rh   atan  Rh  1.676331
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(A.6)
0.00391838Rh3 2  atan  0.023101Rh   4.686035
where Ta is air temperature (°C) and Rh is relative humidity (%). This equation
is valid for standard sea level pressure of 101.325 kPa, relative humidity between
5% and 99% and for air temperatures between -20°C and 50°C, except for cases
having both low humidity and cold temperature (Stull 2011). In the simulations
here, the temperature limits are never exceeded and the humidity limits are rarely
exceeded. However, for completeness and since the model cannot process
discontinuous data these limits are applied as follows. If Ta is greater than 50°C,
it is reset to 50°C. Relative humidity greater than 99% is set to 99% and below
5% is set to 5%. To account for the combination of low humidity and cold
temperatures, a minimum relative humidity is calculated based on the equation of
the line describing these limits in Fig. 2 of Stull (2011). If humidity is below this
limit or if Ta is less than -20°C, the Tw is set to Ta .
Fig. S1 shows how the heat indices vary with temperature, humidity, and wind
speed. The indices are implemented for rural and urban surfaces in the model.
The rural calculations use the 2-m height model diagnostics for air temperature
and humidity and the diagnostic 10-m wind speed (Oleson et al. 2010b). The
urban calculations use CLMU’s air temperature and humidity in the UCL, and the
diagnostic 10-m wind speed (Oleson et al. 2010a).
REFERENCES
Flatau PJ, Walko RL, Cotton WR (1992) Polynomial fits to saturation vapor pressure. J Appl
Meteor 31:1507-1513
Epstein Y, Moran DS (2006) Thermal comfort and the heat stress indices. Ind. Health 44:388-398.
Masterson J, Richardson F (1979) Humidex, a method of quantifying human discomfort due to
excessive heat and humidity. CLI 1-79, Environment Canada, Atmospheric Environment
Service, Downsview, Ontario.
Oleson KW, Bonan GB, Feddema JJ, Vertenstein M, Kluzek E (2010a) Technical description of
an urban parameterization for the Community Land Model (CLMU). NCAR Tech Note
NCAR/TN-480+STR, 169 pp.
http://www.cesm.ucar.edu/models/cesm1.0/clm/CLMU_Tech_Note.pdf
Oleson KW, Lawrence DM, Bonan GB, et al. (2010b) Technical description of version 4.0 of the
Community Land Model (CLM). NCAR Technical Note NCAR/TN-478+STR, 257 pp.
http://www.cesm.ucar.edu/models/cesm1.0/clm/CLM_Tech_Note.pdf
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Rothfusz LP (1990) The Heat Index “Equation” (or, more than you ever wanted to know about
heat index. Scientific Services Division, NWS Southern Region Headquarters, Fort Worth,
TX
Steadman RG (1979) The assessment of sultriness. Part I: A temperature-humidity index based on
human physiology and clothing science. J Appl Meteor 18:861-973
Steadman RG (1994) Norms of apparent temperature in Australia. Aust Met Mag 43:1-16
Stull R (2011) Wet-bulb temperature from relative humidity and air temperature. J Appl Meterol
Climatol 50:2267-2269
Willett KM, Sherwood S (2012) Exceedance of heat index thresholds for 15 regions under a
warming climate using the wet-bulb globe temperature. Int J Climatol 32:161-177
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Fig. S1 Isopleths of heat indices as a function of temperature and relative humidity. All indices
have units of °C except the Discomfort Index which is a unitless index.
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