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,

$c_4$ = .22475541,

$c_5$ = .00683783,

$c_6$ = .05481717,

$c_7$ = .00122874,

$c_8$ = .00085282,

$c_9$ = .00000199.

If the RH is less than 13% and the temperature is between 80 and 112 °F, then the following adjustment is subtracted from HI:

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

Otherwise, if the RH is greater than 85% and the temperature is between 80 and 87 °F, 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 80 °F. 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 and the result averaged with the temperature. If this heat index value is 80 °F 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 54 °F and 86 °F. 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-days and SET-hours are metrics to measure thermal safety and temperatures. The SET-days and SET-hours are degree-days and degree-hours in Celsius/Fahrenheit degrees based on the indoor SET.

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

• Cooling: Not to exceed 9 °F SET-days (216 °F SET-hours) above 86 °F for residential buildings. (SI Metric: Not to exceed 5 °C SET-days (120 °C SET-hours) above 30 °C SET for residential buildings.)

• Cooling: Not to exceed 18 °F SET-days (432 °F SET-hours) above 86 °F SET for non-residential buildings. (SI etric: Not to exceed 10 °C SET-days (240 °C SET-hours) above 30 °C SET for non-residential buildings.)

• Heating: Not to exceed 9 °F SET-days (216 °F SET-hours for all buildings. (SI Metric: Not to exceed 5 °C SET-days (120 °C SET-hours) below 12 °C SET-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 the SET-Hours and the SET-OccupantHours (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 (first occurrence if multiple time slots have the same duration).

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 [10].

$C{O}_2$ 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.