Resilience Metrics[LINK]

With increasing frequency and severity of extreme weather events (e.g., heat waves), it is crucial to ensure urban buildings and infrastructure are resilient to provide critical services to preserve human life and properties during natural disasters. Building resilience has the opportunity to become an additional value proposition for technologies and systems if it can be reliably quantified, valued, and trusted by stakeholders. Metrics or an assessment of potential vulnerability, likelihood, and consequence for each risk would help to prioritize further consideration of these risk factors of building resilience [1]. Measuring the resilience of buildings help owners make better decisions and protect their assets, better assess the built environment resilience of larger geographic units such as communities and cities, and complement existing assessments of building sustainability.

The following metrics are added in EnergyPlus as optional report variables and summary tables in three aspect: thermal, visual, and $C{O}_2$ resilience. Each metric can be calculated and reported when users declare it as an input. The selected resilience metrics (e.g., thermal metrics: Heat Index, Humidex, and SET) are well defined, calculable, and have been adopted by government agency and industry.

Thermal Resilience[LINK]

Heat Index[LINK]

The heat index (HI) is an index that combines air temperature and relative humidity (Steadman 1979), in shaded areas, to posit a human-perceived equivalent temperature, as how hot it would feel if the humidity were some other value in the shade. The HI measures the temperature feels like to the human body when relative humidity is combined with the air temperature. HI is widely used in the United States. The Occupational Safety and Health Administration (OSHA) uses HI as an indicator to assess heat stress [2]. This has important considerations for the human body’s comfort. When the body gets too hot, it begins to perspire or sweat to cool itself off. If the perspiration is not able to evaporate, the body cannot regulate its temperature. When the atmospheric moisture content (i.e. relative humidity) is high, the rate of evaporation from the body decreases. In other words, the human body feels warmer in humid conditions. The opposite is true when the relative humidity decreases because the rate of perspiration increases.

Table 1 developed by U.S. National Oceanic and Atmospheric Administration (NOAA) is used to look up the heat index by temperature (°C) and relative humidity (%) [3]. The HI effects on human health are categorized at five levels: Safe, Caution, Extreme caution, Danger and Extreme danger, defined in Table 1 and color coded in Figure 1.

The computation of the heat index is a refinement of a result obtained by multiple regression analysis carried out by Lans P. Rothfusz and described in a 1990 National Weather Service (NWS) Technical Attachment (SR 90-23) [4-5]. The calculation is based on degree Fahrenheit.

The regression equation of Rothfusz is $$HI=c_1+c_{2}T+c_{3}R+c_{4}TR+c_5{T}^2+c_6{R}^2+c_7{T}^{2}R+c_{8}T{R}^2+c_9{T}^2{R}^2$$

where

HI = heat index (expressed as an apparent temperature in degrees Fahrenheit),

T = ambient dry-bulb temperature (in degrees Fahrenheit),

R = relative humidity (percentage value between 0 and 100),

$c_1$ = -42.379,

$c_2$ = 2.04901523,

$c_3$ = 10.14333127,

$c_4$ = -0.22475541,

$c_5$ = -0.00683783,

$c_6$ = -0.05481717,

$c_7$ = 0.00122874,

$c_8$ = 0.00085282,

$c_9$ = -0.00000199.

If the RH is less than 13% and the temperature is between 80 and , then the following adjustment is subtracted from HI:

$$HI=(13-R)/4\ast \left(\right(17-|T-95|)/17{)}^{0.5}$$

Otherwise, if the RH is greater than 85% and the temperature is between 80 and , then the following adjustment is added to HI:

$$HI=(R-85)/10\ast (87-T)/5$$

The Rothfusz regression is not appropriate when conditions of temperature and humidity warrant a heat index value below about . In those cases, a simpler formula is applied to calculate values consistent with Steadman’s results:

$$HI=0.5\ast (T+61.0+(T-68.0)\ast 1.2+(R\ast 0.094\left)\right)$$

In practice, the simple formula is computed first based on the temperature and humidity. If this heat index value is or higher, the full regression equation along with any adjustment as described above is applied. The Rothfusz regression is not valid for extreme temperature and relative humidity conditions beyond the range of data considered by Steadman.

The Heat Index Hours (accumulated hours for a space) and Heat Index OccupantHours (accumulated hours for the sum of all occupants in a space) of each level for each zone and the whole building are reported under the Annual Thermal Resilience Report.

Humidex[LINK]

The humidex (short for humidity index) is an index number used by Canadian meteorologists to describe how hot the weather feels to the average person, by combining the effect of heat and humidity. The term humidex was first coined in 1965 [6]. The humidex is a nominally dimensionless quantity (though generally recognized by the public as equivalent to the degree Celsius) based on the dew-point temperature [7].

The Humidex effects on human health are categorized at five levels: Little to no discomfort, Some discomfort, Great discomfort; avoid exertion, Dangerous and Heat stroke imminent, defined in Table 2 and color coded in Figure 2.

The humidex (H) formula is:

$$H=T_{air}+\frac{5}{9}(6.11\ast ex{p}^{5417.7530\ast (\frac{1}{273.16}-\frac{1}{273.15+T_{dew}})}-10)$$

Where,

$H$ = the Humidex,

$T_{air}$ = the air temperature in °C,

$T_{dew}$ = the dew-point temperature in °C,

$exp$ = 2.71828.

The Humidex Hours (accumulated hours for a space) and Humidex OccupantHours (accumulated hours for the sum of all occupants in a space) of each level for each zone and the whole building are reported under the Annual Thermal Resilience Report.

Standard Effective Temperature Hours[LINK]

Standard Effective Temperature (SET) is a model of human response to the thermal environment. Developed by A.P. Gagge and accepted by ASHRAE in 1986, SET is also referred to as the Pierce Two-Node model [8]. Its calculation is similar to PMV because it is a comprehensive comfort index based on heat-balance equations that incorporate personal factors of clothing and metabolic rate. Its fundamental difference is it takes a two-node method to represent human physiology in measuring skin temperature and skin wettedness. ASHRAE 55-2010 defines SET as “the temperature of an imaginary environment at 50% relative humidity, $<$ 0.1 m/s [0.33 ft/s] average air speed, and mean radiant temperature equal to average air temperature, in which total heat loss from the skin of an imaginary occupant with an activity level of 1.0 met and a clothing level of 0.6 clo is the same as that from a person in the actual environment, with actual clothing and activity level” [9].

LEED Pilot Credit IPpc100 - Passive Survivability and Back-up Power During Disruptions - defines “Livable conditions” as SET between and . The credit requires buildings to maintain safe thermal conditions in the event of an extended power outage or loss of heating fuel, or provide backup power to satisfy critical loads. Accumulated SET-degree-days and SET-hours are metrics to measure thermal safety and temperatures. The SET-degree-days and SET-degree-hours are in Celsius/Fahrenheit degrees days/hours based on the indoor SET.

LEED Passive Survivability defines the Thermal Safety Temperatures for Path 2 using the SET:

• Cooling: Not to exceed $\cdot$day SET-degree-days ($\cdot$hr SET-degree-hours) above for residential buildings. (SI Metric: Not to exceed 5 °C$\cdot$day SET-degree-days (120 °C$\cdot$hr SET-degree-hours) above 30 °C SET for residential buildings.)

• Cooling: Not to exceed $\cdot$day SET-degree-days ($\cdot$hr SET-degree-hours) above SET for non-residential buildings. (SI Metric: Not to exceed 10 °C$\cdot$day SET-degree-days (240 °C$\cdot$hr SET-degree-hours) above 30 °C SET for non-residential buildings.)

• Heating: Not to exceed $\cdot$day SET-degree-days ($\cdot$hr SET-degree-hours for all buildings. (SI Metric: Not to exceed 5 °C$\cdot$day SET-degree-days (120 °C$\cdot$hr SET-degree-hours) below 12 °C SET-degree-hours for all buildings.)

EnergyPlus calculates and reports SET as a time-step report variable when Pierce method is chosen as the People’s thermal comfort model. The aggregated SET-Degree-Hours Occupant-Weighted Degree-Hours, and Occupied Degree-Hour (at zone level) for both cooling and heating are reported under the Annual Thermal Resilience Summary. The tables also include the longest continuous unmet time duration in hours and the start time of their occurrences during the occupied period (first occurrence if multiple time slots have the same duration).

Hours of Safety[LINK]

Hours of Safety is a framework developed by EPA and RMI to help understand how long a home can maintain thresholds of comfort and safety before reaching unsafe indoor temperature levels [10]. The concept attempts to define the duration of time that homes can be expected to provide safe temperatures when the power goes out based on building characteristics and energy efficiency levels (e.g., insulation, infiltration). This metric can be used to quantify the amount of time people are exposed to extremely hot or cold temperatures indoors. The information can be used to guide weatherization efforts and emergency response measures in considering the health and safety of vulnerable populations as extreme weather events increase in frequency.

Hours of Safety for cold or hot weather events should be defined by the longest duration (number of hours), starting from the beginning time of the risk period (e.g., the start time of a power outage), to not exceed temperature thresholds defined for a specific type of population (e.g., cold stress safety temperature for the healthy population as , or 16 °C). To define the thresholds, we will use EnergyPlus’s existing thermal comfort model controlled primarily by the People input object, and add two fields in the People object, namely “Cold Stress Temperature Threshold” and “Heat Stress Temperature Threshold”. The risk period is specified in the Output:Table:ReportPeriod object (details available in the InputOutputReference document.

The default “Cold Stress Temperature Thresholds”: (16 °C) for the healthy population [10]. Other values can be used: (18 °C) for the elderly [10], and (22 °C) for nursing home residents [11]. The default “Hot Stress Temperature Threshold” is selected as (30 °C) [11]. Users can modify these default thresholds with the “Cold Stress Temperature Threshold” and “Heat Stress Temperature Threshold” input fields in the People object.

Setpoint Unmet Degree-Hours[LINK]

The concept of UDH is analogous to that of temperature-weighted exceedance hours, a metric defined in Section L.3.2.2(b) of ASHRAE Standard 55–2020 [12]. The UDH metric is based on indoor cooling or heating setpoint and weights each hour that the temperature of a conditioned zone exceeds a certain threshold by the number of degrees Celsius by which it surpasses that threshold. Compared with average temperature or unmet hours, UDH provides a more complete picture of the overall history of temperature exceedance.

The UDH is calculated as follows:

$$\text{UDH}={\int }_{t_1}^{t_2}\left[T\right(t)-T_{\text{threshold}}{]}_{+}dt$$

where $T$ is the indoor air temperature [°C]; $t$ is time [h]; and $x_{+}=x$ if $x>0$, or 0 otherwise. $T_{\text{threshold}}$ is the indoor cooling or heating setpoint [°C] in both the grid-on and grid-off scenarios. A similar metric, the Exceedance Degree-Hour, is recently developed by Salimi et al [13]. Instead of thresholding, this metric weights each hour by the distance from the current SET to the comfort zone [13].

Discomfort-weighted Exceedance[LINK]

Discomfort-weighted exceedance hours is the sum of the positive values of predicted mean vote (PMV) exceedance during occupied hours, where PMV exceedance = (PMV – threshold) for warm or very-hot conditions, and PMV exceedance = (threshold - PMV) for cool or very-cold conditions [14]. Warm, cool, very-hot, and very-cold exceedance hours are the number of hours in which occupants are uncomfortably warm (PMV>0.7), cool (PMV<−0.7), very hot (PMV>3), and very cold (PMV<−3). For example, discomfort-weighted warm exceedance hour is the sum of the positive values of (PMV - 0.7) during occupied hours, while discomfort-weighted cool exceedance hour is the sum of the positive values of (-0.7 - PMV) during occupied hours. Discomfort-weighted very-hot and very-cold exceedance hours are calculated analogously, using thresholds of 3 and -3, respectively. CBE developed an online tool to compute thermal comfort metrics including PMV, PPD, thermal sensation, SET, etc [15].

Indoor Air Quality - CO2 Resilience[LINK]

For indoor air quality, we chose to use $C{O}_2$ concentration at the zone level as an indicator. $C{O}_2$ at very high concentrations (e.g., greater than 5,000 ppm) can pose a health risk, referring to Appendix D Summary of Selected Air Quality Guidelines in ASHRAE Standard 62.1-2016, “Ventilation for Acceptable Indoor Air Quality”. At concentrations above 15,000 ppm, some loss of mental acuity has been noted. The Occupational Safety and Health Administration (OSHA) of the US Department of Labor defined the Permissible Exposure Limits (PEL) and Short-Term Exposure Limit (STEL) of $C{O}_2$ level to be 5,000 ppm and 30,000 ppm accordingly [16].

$C{O}_2$ increases in buildings with higher occupant densities, and is diluted and removed from buildings with outdoor air ventilation. High $C{O}_2$ levels may indicate a problem with overcrowding or inadequate outdoor air ventilation. Thus, maintaining a steady-state $C{O}_2$ concentration in a space no greater than about 700 ppm above outdoor air levels will indicate that a substantial majority of visitors entering a space will be satisfied with respect to human bio-effluents (body odor). With outdoor $C{O}_2$ concentration varies from 350 to 500 ppm, we assume 1000 ppm is the safe threshold of indoor $C{O}_2$ concentration.

EnergyPlus calculates and reports the Zone Air $C{O}_2$ Concentration [ppm] as a report variable, and the thresholds of different levels defined in Table 3. The Annual CO2 Resilience summary reports the Hours and OccupantHours of each level for each zone and the whole building.

To activate the $C{O}_2$ concentration calculation in EnergyPlus, the ZoneAirContaminantBalance object needs to be specified and with the field “Carbon Dioxide Concentration” set to Yes. Users can define a schedule of outdoor air $C{O}_2$ concentration in the field “Outdoor Carbon Dioxide Schedule Name”. $C{O}_2$ generation rate at the zone level can be specified using the ZoneContaminantSourceAndSink:CarbonDioxide object.

Visual Resilience[LINK]

Adequate indoor lighting level is crucial for occupant safety, health and productivity. The ${10}^{th}$ edition of The Lighting Handbook published by IESNA recommends illuminance levels for various types of spaces in a building. The US General Services Administration provides lighting levels for US Government buildings (Table 4), which can be used as a guide for other types of buildings. The required light levels are indicated in a range because different tasks, even in the same space, require different amounts of light. In general, low contrast and detailed tasks require more light while high contrast and less detailed tasks require less light.

For resilience reporting purpose, we chose three thresholds: a bit dark - less than 100 lux, dim – 100 to 300 lux, adequate – 300 to 500 lux, bright – more than 500 lux.

• 100 lux – This level of light is sufficient for lifts, corridors and stairs. Areas that are transitory for occupants and don’t require any detailed work. Warehouse areas and bulk stores will also require this minimal light level.

• 300 lux – Assembly areas, like village halls require at least 300 lux.

• 500 lux – Retail spaces should have this as a minimum light level, as should general office spaces. This level should be suitable for prolonged work on computers, machinery and reading.

• More than 500 lux – If you have an area where intricate work is being carried out, then very high lux values may be needed. Where fine detailed work is being carried out, anything up to 2,000 lux can be used – this is usually only necessary in fairly unusual circumstances.

To activate the indoor illuminance calculation in EnergyPlus, users need to define the Daylighting:Controls and the Daylighting:ReferencePoint objects, even if no daylighting controls are actually implemented in the building simulation model.

The Annual Visual Resilience summary reports the Hours and OccupantHours of each illuminance level for each zone and the whole building.

Timespan of Report[LINK]

Resilience metrics are more often evaluated during a certain period when a building is at risk (e.g., during the power outage event or heatwave event), and the period is not necessarily the same as the whole simulation period. This can be achieved through the Output:Table:ReportPeriod input object.

References[LINK]

[1] K. Sun, M. Specian, T. Hong, Nexus of thermal resilience and energy efficiency in buildings: A case study of a nursing home, Build. Environ. 177 (2020) 106842. doi:10.1016/j.buildenv.2020.106842.

[2] M.E. Kiersma, Occupational Safety and Health Administration, Encycl. Toxicol. Third Ed. (2014) 642. doi:10.1016/B978-0-12-386454-3.00344-4.

[3] G. Brooke Anderson, M.L. Bell, R.D. Peng, Methods to calculate the heat index as an exposure metric in environmental health research, Environ. Health Perspect. 121 (2013) 1111–1119. doi:10.1289/ehp.1206273.

[4] R.G. Steadman, The assessment of sultriness. Part I. A temperature-humidity index based on human physiology and clothing science., J. Appl. Meteorol. 18 (1979) 861–873. doi:10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2.

[5] L.P. Rothfusz, N.S.R. Headquarters, The heat index equation (or, more than you ever wanted to know about heat index), Fort Worth, Texas Natl. Ocean. Atmos. Adm. Natl. Weather Serv. Off. Meteorol. (1990) 23–90. papers://c6bd9143-3623-4d4f-963f-62942ed32f11/Paper/p395.

[6] F.R. JM Masterton, Humidex: a method of quantifying human discomfort due to excessive heat and humidity, Print book, Environment Canada, Atmospheric Environment, 1979.

[7] R. Rana, B. Kusy, R. Jurdak, J. Wall, W. Hu, Feasibility analysis of using humidex as an indoor thermal comfort predictor, Energy Build. 64 (2013) 17–25. doi:10.1016/j.enbuild.2013.04.019.

[8] L.G. Gagge, A. P., Fobelets, A. P. and Berglund, A standard predictive Index of human response to thermal environment, Am. Soc. Heating, Refrig. Air-Conditioning Eng. (1986) 709–731.

[9] ASHRAE, ASHRAE STANDARD 55-2010: Thermal Environmental Conditions for Human Occupancy, 2013.

[10] S. Ayyagari, M. Gartman, and J. Corvidae, “A Framework for Considering Resilience in Building Envelope Design and Construction,“ Feb. 2020.

[11] USGBC, “Passive Survivability and Back-up Power During Disruptions | U.S. Green Building Council,” Oct. 2018. https://www.usgbc.org/credits/passivesurvivability (accessed Oct. 26, 2021).

[12] ASHRAE, “Thermal Environmental Conditions for Human Occupancy,” p. 9, Apr. 2021.

[13] S. Salimi, E. Estrella Guillén, and H. Samuelson, “Exceedance Degree-Hours: A new method for assessing long-term thermal conditions,” Indoor Air, vol. 31, no. 6, pp. 2296–2311, 2021, doi: 10.1111/ina.12855.

[14] R. Levinson et al., “Key performance indicators for cool envelope materials, windows and shading, natural ventilation, and personal comfort systems,” Nov. 10, 2020.

[15] F. Tartarini, S. Schiavon, T. Cheung, and T. Hoyt, “CBE Thermal Comfort Tool: Online tool for thermal comfort calculations and visualizations,” SoftwareX, vol. 12, p. 100563, Jul. 2020, doi: 10.1016/j.softx.2020.100563.

[16] ACGIH, Threshold Limit Values (TLVs) and Biological Exposure Indices (BEIs), 2012. doi:10.1073/pnas.0703993104.