Predicting Water Consumption from Energy Data

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Accepted Manuscript Title: Predicting Water Consumption from Energy Data: Modeling the Residential Energy and Water Nexus in the Integrated Urban Metabolism Analysis Tool (IUMAT) Authors: Nariman Mostafavi, Fernanda Gandara, Simi Hoque PII: DOI: Reference:

S0378-7788(17)32997-3 https://doi.org/10.1016/j.enbuild.2017.12.005 ENB 8198

To appear in:

ENB

Received date: Revised date: Accepted date:

5-9-2017 1-12-2017 3-12-2017

Please cite this article as: Nariman Mostafavi, Fernanda Gandara, Simi Hoque, Predicting Water Consumption from Energy Data: Modeling the Residential Energy and Water Nexus in the Integrated Urban Metabolism Analysis Tool (IUMAT), Energy and Buildings https://doi.org/10.1016/j.enbuild.2017.12.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Predicting Water Consumption from Energy Data: Modeling the Residential Energy and Water Nexus in the Integrated Urban Metabolism Analysis Tool (IUMAT)

Nariman Mostafavi1, Fernanda Gandara2, Simi Hoque1,* 1

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Department of Civil, Architectural and Environmental Engineering, Drexel University, 3141 Chestnut Street, Curtis 251, Philadelphia PA 19104, USA; E-Mail: [email protected] 2 College of Education, University of Massachusetts Amherst, 813 North Pleasant Street, Amherst, MA 01003, USA; E-Mail: [email protected] *Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +1-215-895-2254; Fax: +1-215-895-1363 Highlights:

Residential energy use data can be used as a proxy for water consumption. Water heater characteristics are critical in calculating energy and water use. Renewable water heater industry needs more federal and utility incentive programs.

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This paper describes a method for residential water use modeling predicated on metered energy data. Actual measured hot water volumes for major indoor consumption are used to verify and adjust the outputs in gallons of hot water consumption based on climate variables, water heater technical features, and set-point and intake temperatures. Three independent datasets for residential energy (RECS 2009), water heater efficiency (Air-conditioning, Heating and Refrigeration Institute-AHRI), and end-use domestic water (Residential End Uses of Water, Version 2-REU II) are applied to identify specific demographic, built environment, and geographic factors that relate patterns of energy demand to water consumption. The proposed model acts within the broader Integrated Urban Metabolism Analysis Tool (IUMAT), a system-based analytical framework for evaluating the environmental performance of the built environment. The method described in this paper offers an alternative approach to residential water consumption modeling by implementing volume of hot water consumption as a proxy for indoor water use. It provides utilities with the potential to parse and prioritize energy and water conservation measures.

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Keywords: IUMAT; water energy nexus; hot water modeling; residential energy and water; urban water consumption 1. Introduction

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Water and energy are undeniably intertwined and their connection presents a complex framework that has yet to be unpacked (Siddiqi and Anadon 2011). Energy production requires water, and energy is needed for extraction, treatment, distribution, disposal and heating/cooling of water (Talebpour et al, 2014). The interlinkages between the two, especially in terms of resource dependencies, are commonly conceptualized and analyzed through the lens of water-energy nexus (Scott et al., 2011). In 2005, the United States consumed a total of 44.7 billion kWh of energy for water source/conveyance (18.7), treatment (23.4), and distribution (5.6) as well as 11.0 billion kWh for wastewater collection/treatment and 1.5 billion kWh for discharge (ACEEE 2014). A number of researchers (eg. Ackerman and Fisher, 2013;

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Bartos and Chester, 2014; Khan et al, 2017) have examined the synergetic impacts and relationships between energy and water use. In the residential sector, water related energy use is characterized by large groups of individual consumers to meet basic daily needs. For instance in the UK, 89% of total waterrelated emissions is attributed to residential use and mainly hot water provision, compared to 11% for public treatment and supply (Reffold et al., 2008). The amount of energy and GHG emissions associated with water use is influenced by many factors including climate conditions, pricing regimes, household makeup, appliances efficiency and behavioral parameters (Arbués et al., 2003).

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North American households consume between 44,000 and 175,000 gallons of water annually, 33.2% of which is hot water (averaging 45.5 gallons per household per day) (DeOreo et al., 2016). Water heating constitutes 17% of total residential energy use in the United States (compared to 25% in Europe) (EuroACE 2004; Ryan et al., 2010). Various US federal mandates have been established over the past three decades to control energy and water use by residential appliances. The U.S. Department of Energy (DOE) issued its first mandated standard for residential water heaters in 1990, which was last updated in 2010 (final rule 75 FR 20112) to raise minimum performance requirements. The Environmental Protection Agency’s (EPA) Energy Star Efficiency Program established in 1992, expanded a voluntary labeling initiative to residential cooling/heating and office equipment through 1995. The Energy Policy Act of 1992 (EPAct92) and 2005 (Pub.L. 109–58) required specific performance standards for residential and commercial appliances and fixtures. In 2006, Water Sense was launched by the EPA as a voluntarily partnership program between communities and manufacturers to encourage improvements beyond EPAct requirements. In 2016, an amendment (81 FR 63654) was added to the Energy Policy and Conservation Act (Pub.L. 94–163) to update energy labeling rules for consumer products towards improving water and energy efficiency of appliances such as refrigerators, furnaces, dishwashers and water heaters.

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Hot water demand modeling has been the focus of limited studies. Lutz et al., 1996 used multiple regression to forecast household daily structure of hot water demand throughout the day. deMonsabert and Liner 1998 introduced a synergetic spreadsheet model (WATERGY) to analyze energy savings associated with residential water conservation measures using engineering algorithms. Hendron and Burch 2007 used Accumulated Frequency Method within DHWcalc software (Jordan and Vajen 2001) to model hot water load profiles (duration and frequency of water use incidents, and number of daily drawoffs) for 6-minute time steps in one year based on mean flow rates. DOE’s Energy Efficiency and Renewable Energy Office (EERE) developed an analytical framework for water heating energy calculations (DOE 2009a), and supporting technical documents regarding energy-water use for commercial equipment and consumer products such as clothes washers (DOE 2012), furnace fans (DOE 2013), dishwashers (DOE 2014), and pool heaters (DOE 2015). The DOE tools apply Monte Carlo simulation techniques to generate heterogeneous households based on RECS 2005 data. Widén et al., 2009 employed time-use data to generate hourly personal hot water and electricity demand in apartments and detached houses. Shimoda et al., 2010 simulated the impact of introducing water heaters on energy and GHG emissions at city-level using occupant and building archetypes. Kenway et al., 2013 proposed a mathematical flow analysis method to investigate diurnal energy, water and emissions reduction potentials for a specific household. Abdallah and Rosenberg 2014 used linear regression methods to relate energy and water factors to household energy use based on disaggregated national energy and water datasets. Escriva-Bou et al., 2015 assumed probability distribution of hot water use for different appliances and tried to describe the variability in energy use among Monte Carlo generated households.

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These studies either do not fully integrate the water heating energy with the actual amount of water use, or disregard some major parameters behind the disparities in household consumption patterns. The existing models may emphasize energy use analysis (Widén et al., 2009), address peak loads to enable district heating equipment sizing (Hendron and Burch 2007), focus on conservation measures for homogenous household groups (deMonsabert and Liner 1998), investigate particular appliances (Sammer and Wüstenhagen, 2006), or concentrate on a specific region (Escriva-Bou et al., 2015). Aside from the cases where the specific analysis can serve a unique study goal, the limitations are usually forced by deterministic simulation of human behavior and scarcity of high resolution temporal and spatial datasets. A wide variety of technological, behavioral, geographic and demographic factors shape patterns of energy and water consumption among households (Suero et al., 2012; Jorgensen et al., 2009; Mostafavi et al., 2015) and overlooking any category of these variables undermines the models’ validity.

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Relating different categories of water consumption to physical and psychographic variables requires reliable end-use metering protocols. Overall, developing technologically advanced water use measurement methods have not gained the same traction from the planning community compared to energy metering, due to unmatched prices of water and energy. As an example, for residential water use, conventional water metering usually reports the annual water consumption based on two or four data points throughout the year (Britton et al., 2008). Quarterly recorded water use data not only fails to portray a complete description of weekly or monthly data, it does not enable breaking the aggregate figure that is usually in a unit of volume, into different end-use categories (such as showers, toilets, garden irrigation, dish washers and laundry). Smart metering technologies, in contrast, provide comprehensive insight into water-use patterns, and enable analyzing the influence of socio-economic parameters on various categories of water use. Also, reliable evaluation of the effectiveness of water reduction measures depends on availability of high quality data produced via automated sub-metering technologies and smart end-use analyses methods.

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Our study introduces a method for generating hot water load profiles for households from end-use energy data based on climatic, built environment and demographic variables. We use hot water energy consumption data obtained from Residential Energy Consumption Survey (RECS) 2009 and a survey of residential water heaters provided by Air-conditioning, Heating and Refrigeration Institute (AHRI). Furthermore, since detailed residential water data collection is scarce relative to energy data, especially due to high costs and limited availability of actual hot water sub-metering, we develop a method for generating hot and domestic water consumption profiles from energy data. Our long-term objective is to employ the outcomes within a broader urban metabolic core (Mostafavi et al., 2014a; Mostafavi et al., 2014b), while in this study, the model focuses on households’ water consumption in connection to energy and evaluating the impacts of behavioral change and technological improvements on residential resource efficiency. For validation, the method is applied to the Residential End Uses of Water Study Update, Version 2 (REU 2016) dataset that contains recorded hot water and domestic consumption information for 94 and 771 single family units in North America, respectively. This approach provides water and energy performance of household units disintegrated for various household activities (e.g. toilets, laundry machines, showers, refrigerators) and fuel types (e.g. oil, natural gas, electricity). 2. Methodology

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For large scale simulation of resource demand profiles, reliable datasets are required that cover geographic and demographic factors over wide geographical spreads. RECS 2009 provides the amount of energy use for different categories of residential end-use including water heating at the household level. Primarily an energy database, RECS nevertheless includes information on the number of storage/instantaneous water heaters, age and type/size of the heaters, and the fuel type/amount for domestic hot water. It also contains basic properties of dishwashers and clothes washers with their frequency of use in accordance to basic climate variables, housing type classification and socio-economic characteristics of the households such as household size, employment and income status.

Figure 1. Water heater fuel types in RECS 2009 and AHRI datasets.

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Over the past seven decades, storage electric and gas water heaters have dominated the market in the United States (CEC 2012). In the recent years, instantaneous water heaters that reduce or eliminate standby losses have become increasingly popular. In addition, solar, heat pump, and condensing gas water heaters have slowly penetrated the market, promoted as a result of federal tax credits, utility provided rebate incentives and growing environmental awareness. The Air-conditioning, Heating and Refrigeration Institute (AHRI) is a North American trade association with over 300 member companies manufacturing space heating, air-conditioning, commercial refrigeration and water heating equipment that account for over 90% of residential water heaters in the United States (AHRI 2016). In this analysis, we used a water heater directory maintained by AHRI that stores energy factor, recovery efficiency, first hour rating, power input and energy source for more than 2,750 active and discontinued models of storage, demand, heat pump and indirect water heaters. Figure 1 shows the share of different water heater fuel types in the RECS and AHRI data. The percentages are different since the AHRI dataset represents the diversity of the available models within fuel-source categories, while RECS data shows the popularity of water heaters by fuel type.

2.1. Estimating hot water consumption

Hot water consumption for households with storage water heaters can be calculated using a sum-up WHAM (Lutz et al., 1998) equation: 365 𝑎 ℎ𝑜𝑡,𝑎𝑛𝑛𝑢𝑎𝑙 𝑉𝑜𝑙𝑔𝑎𝑙

𝑏

= ∑∑∑

𝑅𝐸 ∗ (𝑄̇𝑖𝑛,𝑖,𝑗,𝑘 − 24 𝑈𝐴 (𝑇𝑡𝑎𝑛𝑘,𝑖 − 𝑇𝑎𝑚𝑏,𝑖 ))

𝑈𝐴𝑖 (𝑇𝑡𝑎𝑛𝑘,𝑖 − 𝑇𝑎𝑚𝑏,𝑖 ) 𝑖=1 𝑗=1 𝑘=1 𝜌 𝐶 (𝑇 ) 𝑝 𝑡𝑎𝑛𝑘,𝑖 − 𝑇𝑖𝑛,𝑖 ) ∗ (1 − 𝑃𝑜𝑛

(1)

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ℎ𝑜𝑡,𝑎𝑛𝑛𝑢𝑎𝑙 where 𝑉𝑜𝑙𝑔𝑎𝑙 is the amount of hot water drawn (gal/year), RE is the recovery efficiency (%), 𝜌 is water density (lb/gal), 𝑇𝑡𝑎𝑛𝑘 is daily hot water set-point temperature (⁰F), 𝐶𝑝 is the specific heat of water (Btu/lb ⁰F), 𝑇𝑖𝑛 is the inlet water temperature (⁰F), 𝑄̇𝑖𝑛 is the daily water heater energy flow (Btu/day), 𝑇𝑎𝑚𝑏 is the ambient temperature around the water heater, 𝑃𝑜𝑛 is the rated input power (Btu/h), 𝑎 and 𝑏 are appliances and occupants respectively, and 𝑈𝐴 is the standby heat loss coefficient (Btu/h ⁰F) that can be calculated using the following equation (DOE 2003; NREL 2013):

1 1 − 𝐸𝐹 𝑅𝐸 𝑈𝐴𝑖 = 24 1 ) (𝑇𝑡𝑎𝑛𝑘,𝑖 − 𝑇𝑎𝑚𝑏,𝑖 ) ∗ ( − 41,094 𝑅𝐸 ∗ 𝑃𝑜𝑛

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where EF is the efficiency factor. For tank-less water heaters, assuming no pilot input, gallons of hot water drawn throughout the year can be calculated as: 𝑏

= ∑∑∑

(3)

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𝑖=1 𝑗=1 𝑘=1

𝑄̇𝑖𝑛,𝑖.𝑗,𝑘 ∗ 𝑅𝐸 (1 + 𝑃𝐴) 𝜌 𝐶𝑝 (𝑇𝑡𝑎𝑛𝑘,𝑖 − 𝑇𝑖𝑛,𝑖 )

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365 𝑎 ℎ𝑜𝑡,𝑎𝑛𝑛𝑢𝑎𝑙 𝑉𝑜𝑙𝑔𝑎𝑙

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where PA is the performance adjustment factor. In order to improve the prediction by the model for both storage and instantaneous water heaters, as Figure 2 shows, inlet water temperature is estimated as a function of heating and cooling degree days. This is based on a dataset on cold water inlet temperature for U.S. locations (FTA 1995) using principal component analysis (PCA):

Figure 2. Principal component analysis to estimate tap water temperature from climate variables

𝑇𝑖𝑛 (0 F) = 66.38 − 2.33345𝑒 − 3 ∗ (𝐻𝐷𝐷 − 𝐶𝐷𝐷)

(4)

where HDD and CDD are heating and cooling degree days respectively. Accordingly, 𝑇𝑡𝑎𝑛𝑘 is estimated as:

𝑇𝑡𝑎𝑛𝑘 (0 F) = 129.40 − 1.2834𝑒 − 3 ∗ (𝐻𝐷𝐷 − 𝐶𝐷𝐷)

(5)

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RECS 2009 does not provide information on water heater location in the building, but climate indicators can be useful. For instance, it can be assumed that in extremely cold climates heat exchangers are very unlikely to be installed in unconditioned basements or garage spaces. Therefore, we assign households to three different climate HDD zones to estimate the location of water heater within the building. Following NEEA 2015, average annual 𝑇𝑎𝑚𝑏 can realistically be approximated at 64-70⁰F, 5068⁰F, 60-64⁰F and 52-62⁰F for conditioned indoor, un-ducted interior, basement and garage areas respectively, depending on the climate zone. In the absence of this information, the DOE uniform test method for measuring energy consumption of water heaters can be used as a viable alternative for ambient, supply and outlet temperatures (Tamb= 67.5±2.5 ⁰F, Tin= 58±2⁰F, Ttank= 125±5⁰F) (ECFR 2017).

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In order to estimate hot water consumption (equations 1 and 3) in the RECS data, AHRI and the RECS databases need to be connected. We can estimate the recovery efficiency, energy factor and power input for each household’s main water heater, even when the exact model of the surveyed water heater is unknown, by using information on the type, volume, and energy source that are provided in the RECS database. Using these variables and probabilistic methods, each housing unit in the RECS data is assigned a single water heater from the AHRI dataset. The assigned water heater is most likely to correspond to the housing unit, based on the variables aforementioned. Also, since not all brands are equally popular in the market, market sales share information on different manufacturing brands are used to weight the assignment of water heaters. To increase the robustness of the methodology, the process is repeated 100 times: 100 water heaters (with replacements) that match the corresponding type, size, and fuel type are assigned to each household. Using equations 1 through 5, and the information for each water heater (provided in AHRI), the hot water consumption is estimated for 100 water heater model scenarios, and the average value is taken as the final estimate for each house.

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Distribution functions for the variables of interest (recovery efficiency, energy efficiency, and power input) are not normal. Figure 3 shows density functions (based on 100 water heaters) for the desired water heater characteristics, for two houses selected as examples: first, a tank-less natural gas water heater and second, a storage natural gas heater with 50+ gallons capacity. The following figures also display the density of these characteristics in the whole set of water heaters, as provided in the AHRI dataset. As observed, the distributions for each case/example are slightly different from the corresponding “population” distributions as an effect of weighting.

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Figure 3. Energy factor, power input and recovery efficiency density functions for the one hundred market-shareweighted iterations (red line) and the entire set of available models (black line) for two separate cases: NG 50+ gallons storage (bottom) and NG tank-less (top).

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Figure 4 shows gallons of estimated hot water consumption using water heater characteristics and energy consumption information for more 10,399 units spread across the nation. Every data point is the average value obtained from one hundred simulated possible model scenarios.

Figure 4. Household daily hot water use (gal) calculated based on water heating energy use (MBtu)

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Figure 5 shows the possible range for annual hot water use for the two previously picked examples, under one hundred alternative scenarios. The wide range illustrates the significant impact of water heater choice on the magnitude of household water consumption.

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2.2. Major predictors of hot water consumption

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Figure 5. Annual hot water consumption (gal) density plots for hundred model scenario iterations for the example cases (red line is the average value)

A one parameter Box-Cox transformation , λ≠0

λ

ln 𝑌𝑖

, λ=0

(6)

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={

𝑌𝑖λ −1

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𝑌𝑖λ

𝑑𝑎𝑖𝑙𝑦

was applied to the estimated water use data (𝑉𝑜𝑙𝑔𝑎𝑙 ) in order to counter its non-normality (λ = 0.25),

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and then a hierarchical stepwise regression analysis is run to determine which factors are the major predictors of hot water consumption. The three sets of variables included in the hierarchical regression are the following: (a) variables related to the water heater (e.g. fuel type), (b) variables related to water consumption of the household (e.g. if there is a swimming pool, heated or not), and (c) demographic variables (e.g. income, household size/age). The order of each set of variables was prioritized by relevance (the first block is theoretically more relevant than the second, and both these blocks are theoretically more relevant than the third block). To account for scale problems, following the Box-Cox transformation, we multiplied the new DV (Box-Cox of the estimated hot water daily consumption) by 1000. Coefficients of the three fitted models with their corresponding R2 are presented in Table 1. The final selected model is Model 3, which shows that most variables included were significantly related to the DV. The only nonsignificant variables are hot tub use, family business at home, and educational attainment of the householders lower than a bachelor’s degree. All coefficients associated with other variables are significantly different than zero. Table 1. Coefficients and standard error estimates of the stepwise regression Model 1

Model 2

Model 3

Intercept

6041.5 (179.94)***

5539.08 (189.33)***

Natural Gas

958.66 (35.82)***

885.06 (37.55)***

770.342 (35.792)***

Oil

-319.72 (122.74)**

-409.94 (128.32)**

-589.658 (121.06)***

-47.81 (103.64) -1637.15 (188.07)***

-133.42 (109.03) -1462.65 (194.87)***

-285.675 (102.672)** -1142.437 (183.766)***

624.61 (27.26)***

575.87 (28.72)***

432.005 (27.61)***

Propane Type of heater (1=storage, 0=tank-less) Volume (0= no volume, 1= small, 2 = medium, 3=large) Age of the water heater (every 4 years; Last category is 20 years or more)

29.68 (12.66)*

18.85 (13.15)

32.432 (12.376)**

346.89 (54.67)***

208.233 (51.792)***

141.65 (81.02).

161.644 (76.665)*

79.96 (21.91)***

101.173 (21.636)***

262.33 (28.03)**

290.366 (26.404)***

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Pool (0=No Pool, 1=Pool, 2=Heated Pool)

4388.154 (189.114)***

Rec-bath (1= Uses hot tub, 0=Otherwise) Dish washer info (0= no dishwasher, 1 = dishwasher, 2 = efficient dishwasher) Clothes washer info (0= no clothes washer, 1 = clothes washer, 2 = efficient clothes washer) Employment status of householder (0=unemployed, 1=parttime, 2=full-time)

-67.867 (19.568)***

Business at home (1=yes, 0=no)

92.629 (61.655)

Number of members in the household

381.496 (11.736)***

High school

-42.456 (65.347)

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Income (every 25 K; last category, 100K or more) R2

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0.1244

-33.183 (67.91)

-60.562 (80.095) -158.605 (72.983)* -172.68 (83.476)* 18.519 (3.145)***

0.1349***

0.238***

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To interpret these coefficients, we need to back-transform the dependent variable. Also we cannot interpret the coefficients in isolation, because the relationships are not linear. Since the transformation can complicate the interpretation of coefficients, we elaborate briefly on the meaning of these numbers in Table 2, using eight cases that are each different in one parameter. For a household of four with an electric storage water heater, switching the fuel to natural gas leads to slightly more (less than 1 Kgal) hot water use on average throughout the year. This can result in lower rural water use per household, since the popularity of gas and electric water heaters is different in metropolitan and rural areas, probably due to less availability of gas outside of cities. Units with a medium-sized storage tank (30-50 gal), on average, use 2.3 Kgal less hot water compared to tank-less heaters. Within storage tank groups, every 20-gallon increase in tank size leads to a 3.1 Kgal increase in annual consumption per household (8.7 gal daily). This can be attributed to higher amounts of hot water available. Additionally, many small households have high volume storage tanks and oversized heaters waste a lot of energy and water if the system cannot play down to support low flow demand. Households with no employed adults use 1.0 Kgal compared to households with two employed adult members. This is most likely because unemployed adults spend longer hours at home. Income only affects hot water consumption among the highest income groups (more than $100K) as the results show they use 0.40 Kgal more compared to the bottom income category (less than $25K). Households with post-graduate education use 0.90 Kgal less than those with high-school level.

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Table 2. The impact of desired variables on annual gallons of hot water use Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

Case 8

4388.15 770.34 -589.66 -285.68 -1142.44

1 1 0 0 1

1 1 0 0 1

1 1 0 0 0

1 1 0 0 1

1 0 0 0 1

1 1 0 0 1

1 1 0 0 1

1 1 0 0 1

432.01

1

2

0

1

1

1

1

1

2 0 0

2 0 0

2 0 0

2 0 0

2 0 0

2 0 0

2 0 0

2 0 0

2

2

2

2

2

2

1

2

290.37

2

2

2

2

2

2

2

1

-67.87 92.63 381.50 -42.46 -33.18 -60.56 -158.61 -172.68

2 1 4 0 0 0 0 1

2 1 4 0 0 0 0 1

2 1 4 0 0 0 0 1

2 1 5 0 0 0 0 1

2 1 4 0 0 0 0 1

2 1 4 0 0 0 0 1

2 1 4 0 0 0 0 1

2 1 4 0 0 0 0 1

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32.43 208.23 161.64

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Annual Hot Water Use (gal)

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Coefficients

101.17

ED

Intercept Natural Gas Oil Propane Type of heater (1=storage, 0=tank-less) Volume (0= no volume, 1= small, 2 = medium, 3=large) Age of the water heater (every 4 years; last category is 20 years or more) Pool (0=no pool, 1=pool, 2=heated pool) Rec-bath (1= uses hot tub, 0=otherwise) Dish washer info (0= no dish-washer, 1 = efficient dish-washer, 2 = dish-washer) Clothes-washer info (0= no clothes-washer, 1 = efficient clothes-washer, 2 = Clotheswasher) Employment status of householder (0=unemployed, 1=part-time, 2=full-time) Business at home (1=yes, 0=no) Number of people in the household High school Some college Associate Bachelor’s Post-graduate or professional Income (every 25 K; last category, 100K or more)

18.52

4

4

4

4

4

1

4

4

18,552

21,740

24,003

21,348

19,751

18,169

17,859

16,615

2.3. Estimating total indoor water demand

0.66 𝑝 1−0.66 𝑝 ℎ𝑜𝑡 𝑤𝑎𝑡𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑑𝑜𝑜𝑟 𝑢𝑠𝑒

= 𝑒 −2.011175+0.011899𝑓+0.274011𝐸+0.266679𝑤

(7)

ratio, 𝑓 is frequency of daily faucet events, 𝐸 is employment factor (𝐸=0,1,2

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where 𝑝 is the

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Another dataset that was used is prepared by the Water Research Foundation (WaterRF). This dataset includes indoor, outdoor and hot water end-use breakdown for different fixtures and appliances. It is a representative randomly sampled database with details on demographics, landscape, water rates and building physical attributes for single family dwelling units. Residential End Uses of Water, Version 2 (REU II) includes information for 771 and 94 houses for indoor end-use and hot water respectively, obtained from nine utilities operating in the US and Canada. The hot water sample is admittedly relatively small (94 households), though it is worth mentioning that in the literature, either for simulation or model validation purposes, actual measured hot water data comes from small samples as well (e.g. Widén et al., 2009 and Lutz et al, 1996 use measured data on 60 and 110 households). Based on the REU II dataset, percentage of hot water in the total domestic water use mix, for each household, can be obtained through the following empirical correlation; and therefore, hot water can reliably be used as a proxy for indoor water use estimates, depending on the hot water appliances:

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for no, one, and two adults employed in order), and 𝑤 is a bath-dishwasher-laundry factor (𝑤= 0 or 1 (0 for no bathtub) + 0 or 1 (0 for no a dishwasher) + 0 or 1 (0 for no clothes-washer)). Subsequently, total 𝑎𝑛𝑛𝑢𝑎𝑙 indoor annual water use (𝑉𝑜𝑙𝑔𝑎𝑙 ) can be calculated as:

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ℎ𝑜𝑡,𝑎𝑛𝑛𝑢𝑎𝑙 𝑎𝑛𝑛𝑢𝑎𝑙 𝑉𝑜𝑙𝑔𝑎𝑙 = 𝑉𝑜𝑙𝑔𝑎𝑙 ∗ 𝑝−1

2.4. Validating the model

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The model is verified and adjusted by comparing the results for RECS single family houses (8,693 units) against REU II actual metered data for indoor use, since unlike RECS, REU II is a single family dataset. Quantile Regression (QR) of the water heating data in RECS 2009 confirms this validation as a reasonable measure because no correlation is found between the domestic hot water energy use and housing type for cases where separate units are not sharing a water heater (Mostafavi et al., 2017). Hot water energy use by multi-family units that share water heaters can be adjusted based on QR results. As shown in Figure 6, although energy use for hot water is highly correlated with household size, square footage, energy cost and income level, there is no relationship between the amount of water heater energy use and housing type, householder’s age, ownership of the house or climate variables (HDD and CDD). Although heating and cooling degree days may initially come across as major predictors of hot water energy consumption, as previously noted, in extreme weather conditions, it is very unlikely for the heater to be kept in nonconditioned spaces and therefore, HDD and CDD only minimally influence ambient temperature around the water heater. Unsurprisingly, the list of variables that impact the energy use for domestic hot water, is not identical to the inventory of the variables that drive the volume of hot water used by households. For instance, the type of fuel used by the water heater or its age are more likely than volume of water to impact water heating energy use. Similarly, multifamily housing has the potential to reduce the water heater energy use by 0.5 MWh for each unit (probably due to centralization of heating equipment and consequent distribution of standby heat losses), though it does not reduce the amount of hot water in gallons, since the demand for shower, laundry and dishwashers remains unchanged. The cost of energy does not seem to affect either the amount of water or water heating energy use. Table 3 summarizes the

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impact of different physical and socio-economic variables for different tiers of hot water energy use distribution (the results are contrasted against baseline groups with income