Carbon Dioxide Reduction Targets of Hot Water Showers for People in Hong Kong

: Improving water and energy efﬁciency in buildings is one of the best ways to reduce greenhouse gas emissions. This study examines various energy-related carbon dioxide (CO 2 ) reduction measures, including the use of water efﬁcient showerheads and shower drain water heat recovery, in order to distinguish the signiﬁcance of user inﬂuence on the water usage of a shower. The probability of taking a hot shower and the number of showers taken by an occupant per day, which can be evaluated from open literature data, are used as the parameters of user responses to water conservation measures in this study. A Monte Carlo model of water consumption and CO 2 reduction for showering is adopted to determine the contributions of user responses. The results demonstrate that the inﬂuence of users on CO 2 reduction is signiﬁcant and compatible to the inﬂuence of water efﬁcient showerheads. This study can be used as a reference to enhance water and energy incentives and to facilitate continuous improvement in building water systems. study examined various energy-related CO 2 reduction measures, including the use of water efﬁcient showerheads and shower drain water heat recovery, in order to distinguish the signiﬁcance of user inﬂuence on the water usage of a shower. The results demonstrated that the inﬂuence of users on CO 2 reduction is signiﬁcant (up to 22%) and compatible to the inﬂuence of water efﬁcient showerheads (up to 26%). In contrast, the CO 2 reduction is less signiﬁcant for heat recovery from hot showers in cities of hot climates (such as Hong Kong) (up to 14%) and water supply efﬁciency improvement in buildings (up to 2%). This study can be used as a reference to enhance water and energy incentives, and to facilitate continuous improvement in building water systems.


Introduction
Scientific understanding of global warming is increasing [1]. Climate model projections indicated that, during the 21st century, the global surface temperature is likely to rise further by 0.3 to 1.7 • C in the best case scenario and 2.6 to 4.8 • C in the worst case scenario [1]. The Paris Agreement adopted under the United Nations Framework Convention on Climate Change (UNFCCC) established a global framework for reducing carbon dioxide (CO 2 ) emissions and noted that global warming should be limited to 1.5 • C [2]. Studies have quantified the carbon reduction potential due to a reduction of potable water usage [3]. In the U.S., the CO 2 embedded in the nation's water represents 5% of all U.S. carbon emissions [4]. In Japan, residential water supply systems account for 5% of total CO 2 emissions and about 60% of those emissions are from hot water bathing [5]. In Australia, a study showed that the average energy consumption from hot showers ranged between 2.9 and 4.5 GJ ps −1 yr −1 , corresponding to CO 2 emissions ranging between 160 and 245 kg CO 2 ps −1 yr −1 [6]. In Hong Kong, over 40% of domestic water consumption is used for showers for bathing [7], while about 19% of residential energy consumption in 2013 was used to provide hot water for showers and baths [8].
The urban water cycle can reduce its carbon footprint in various ways; three key initiatives are: (1) better water delivery system designs, (2) water efficiency improvements, and (3) water conservation programmes [9]. Better water delivery system designs, such as employing energy efficient pumps and adopting effective maintenance and replacement schedules, are proven to reduce energy use and thus CO 2 emissions [10,11]. A study reported that energy consumed by many existing high-rise water supply systems could be reduced by up to 50% via water storage tank relocations [12].

Quantification for User Influence
The probability of taking a hot shower P sh and the number of showers taken by an occupant per day N s,j are the parameters of user responses to water conservation measures in this study. It is noted that the reduction of P sh resulted in a decrease in energy for water heating, while the reduction of N s,j resulted in a decrease in energy for both water heating and water supply and treatment.
A survey reported that all winter showers and over 90% of summer showers were hot showers [18]. Figure 1a shows the survey ratios P sh of having hot showers against the ambient temperature T a ≤ 21.5 • C. A linear relationship for fractional P sh,Ta at hypothetical T a = 35 • C with constants c 0 and c 1 (Table 1) was assumed.
The energy conserved by an occupant taking fewer hot showers without changing the frequency of showers can be mathematically expressed by P sh (=0.5-0.9) as shown in Figure 1a. All survey data was not less than P sh = 0.9.
According to the survey, all occupants would take at least one shower per day [17]. A total of 597 occupants were interviewed; 269, 289, 37, and 2 of them would take one, two, three, and four showers in the summer while 537, 57, 3, and none of them would take one, two, three, and four showers in the winter respectively. Figure 1b-d illustrate the ratios of an occupant having one to three showers per day (i.e., P s1 to P s3 ) against the mean ambient air temperature T a ( • C). The case averages are also shown (i.e., T sf = 0 • C). As the correlations of the case averages were insignificant (p > 0.05, t-test), a probabilistic approach was adopted. It was found that more showers were taken in summer than in winter (p < 0.01, t-test). On average, an occupant would take N s,j = 1.6 (standard deviation (SD) = 0.6) showers on a summer day (June-August) and 1.1 (SD = 0.3) showers on a winter day (December-February), giving an overall average of 1.4 (SD = 0.6) showers per day.
A behavioural response to water conservation is to have fewer daily hot showers. In this study, it is expressed by a temperature shift T sf (i.e., at an ambient air temperature T a + T sf ) as shown in Figure 1b-d and determined by Equation (2), where T a ( • C) is the ambient air temperature, i is the number of showers per capita per day, U is a utility function, and c 0 and c 1 are the constants as presented in Table 1.    Figure 2 graphs the expected number of showers per occupant per day determined by Equation (3). Averages (i.e., T sf = 0 • C) from a previous study are also shown for comparison. The figure shows that there is approximately a 1% reduction in the number of showers per day for each 1 • C increment in T sf .

Simulations
In this study, simulations were performed to obtain the confidence intervals for water and energy consumption and to determine the CO2 emissions associated with the consumption. Moreover, a Monte Carlo model of water consumption and CO2 reduction for showering was adopted to investigate the influence of a century-scale rise in the average temperature of the Earth's climate system and its related effects on water consumption and CO2 emissions from showers for bathing [16,19].
Higher ambient air temperatures as a result of climate change have a great impact on shower usage patterns, and thus a significant influence on subsequent energy used and CO2 produced. The ambient air temperatures of Hong Kong in the years 1986-2005 and the projected temperature changes up to year 2100 were used in this study to simulate the scenarios of average ambient air temperature change from +1 to +4 °C [21]. As compared with the average air temperature of 1986-2005, the temperature projection suggested that the ambient air temperature increase by 2100 would be 1.4 to 3.2 °C and 3.1 to 5.5 °C for the Representative Concentration Pathways (RCP) 4.5 and 8.5, respectively.
In the simulations, a uniformly distributed random number x  [0,1] was taken from a random number set generated by the prime modulus multiplicative linear congruential generator, and the input parameters described below (i.e., i = {ts,To,Ta,k,Ps,PL,Le}) were sampled from the defined distribution functions. The input value i,x of a parameter i was then determined from the descriptive Per capita annual CO2 emissions Mp (kg-CO2 ps −1 yr −1 ) from hot showers are linked with water consumption Vp (m 3 ps −1 yr −1 ) and energy consumption Ep (GJ ps −1 yr −1 ), where j is a day of a year, ρ (=1000 kg m −3 ) is the density of water, cp (=4.2 × 10 −6 GJ kg −1 K) is the specific heat capacity of water, α (=0.94 kg-CO2 m −3 ) and β (200 kg-CO2 GJ −1 ) are emission factors per unit water consumed and per unit energy consumed respectively, To (°C) is the expected shower 1

Simulations
In this study, simulations were performed to obtain the confidence intervals for water and energy consumption and to determine the CO 2 emissions associated with the consumption. Moreover, a Monte Carlo model of water consumption and CO 2 reduction for showering was adopted to investigate the influence of a century-scale rise in the average temperature of the Earth's climate system and its related effects on water consumption and CO 2 emissions from showers for bathing [16,19].
Higher ambient air temperatures as a result of climate change have a great impact on shower usage patterns, and thus a significant influence on subsequent energy used and CO 2 produced. The ambient air temperatures of Hong Kong in the years 1986-2005 and the projected temperature changes up to year 2100 were used in this study to simulate the scenarios of average ambient air temperature change from +1 to +4 • C [21]. As compared with the average air temperature of 1986-2005, the temperature projection suggested that the ambient air temperature increase by 2100 would be 1.4 to 3.2 • C and 3.1 to 5.5 • C for the Representative Concentration Pathways (RCP) 4.5 and 8.5, respectively.
In the simulations, a uniformly distributed random number x ∈ [0,1] was taken from a random number set generated by the prime modulus multiplicative linear congruential generator, and the input parameters described below (i.e., ζ i = {t s ,T o ,T a ,k,P s ,P L ,L e }) were sampled from the defined distribution functions. The input value ζ i,x of a parameter ζ i was then determined from the descriptive distribution function ζ i at percentile x.
Per capita annual CO 2 emissions M p (kg-CO 2 ps −1 yr −1 ) from hot showers are linked with water consumption V p (m 3 ps −1 yr −1 ) and energy consumption E p (GJ ps −1 yr −1 ), where j is a day of a year, ρ (=1000 kg m −3 ) is the density of water, c p (=4.2 × 10 −6 GJ kg −1 K) is the specific heat capacity of water, α (=0.94 kg-CO 2 m −3 ) and β (200 kg-CO 2 GJ −1 ) are emission factors per unit water consumed and per unit energy consumed respectively, T o ( • C) is the expected shower water temperature, t s is the expected showerhead operating time, and N s is the expected number of showers per occupant per day. The showerhead flow rate v (L min −1 ), which is subject to user adjustments and limited by the maximum water supply flow rate, is described by: The user preferred showerhead flow rate v * (L min −1 ) is given by a cumulative distribution and is expressed by a probabilistic user acceptance ϕ as given in Equation (7), where a probabilistic occupant acceptance range of 0.03-0.97 is within a showerhead flow rate range of 3-18 L min −1 [16]: The maximum showerhead flow rate v p (L min −1 ) available from the water supply system is determined by the showerhead water pressure P (kPa) and the showerhead resistance factor k (kPa min 2 L −2 ): The showerhead water pressure P (kPa) is given by the difference between the static pressure at the showerhead P s (kPa) (in the design range of 150-350 kPa for typical high-rise water supply systems) and the pressure drop along the water supply pipe P L (kPa), It is noted that for WELS rated showerheads with a standard deviation SD = 1.74 kPa min 2 L −2 in a resistance factor range of 0.81-9.04 kPa min 2 L −2 , the average resistance factor k is 3.8 kPa min 2 L −2 [16].
In a typical high-rise water supply system, a pipe pressure drop from P L,0 to P L,1 corresponding to a flow rate from v 0 to v 1 due to the number of showerheads connected can be approximated by Equation (10), where P L /L e = 0.1-0.5 kPa m −1 with an equivalent pipe length range L e = 100-300 m [22,23].
The expected showerhead operating time t s (s) is given by Equation (11), with the assumption of 99% confidence intervals CI 99% = 185-1093 s for a lognormal distribution [24], The cold water temperature T j ( • C) is given by the following expression, where T a ( • C) is the ambient air temperature: A higher shower temperature for maintaining user comfort was reported for showerheads with lower flow rates [25]. In a temperature range of 33.4-42.7 • C with SD = 2.6 • C, the expected shower water temperature T o ( • C) is expressed by [23]: Water 2017, 9, 576 6 of 11

Results and Discussion
Based on the 1986-2005 ambient temperature data and the existing shower usage patterns, the simulation results for water consumption, energy consumption, and CO 2 emissions are 35.6 m 3 ps −1 yr −1 , 2.16 GJ ps −1 yr −1 , and 465 kg-CO 2 ps −1 yr −1 , respectively. Figure 3, which illustrates the plotted results of V calculated from Equation (14) with a temperature shift T sf , shows the linear trend of the percentage change in water consumption %V against the change in ambient air temperature ∆T a for an average increment of 2.3% • C −1 . The outcome shows a linear upward trend of −1.6% • C −1 in warmer environments.

Results and Discussion
Based on the 1986-2005 ambient temperature data and the existing shower usage patterns, the simulation results for water consumption, energy consumption, and CO2 emissions are 35.6 m 3 ps −1 yr −1 , 2.16 GJ ps −1 yr −1 , and 465 kg-CO2 ps −1 yr −1 , respectively. Figure 3, which illustrates the plotted results of V calculated from Equation (14) with a temperature shift Tsf, shows the linear trend of the percentage change in water consumption %V against the change in ambient air temperature ∆Ta for an average increment of 2.3% °C −1 . The outcome shows a linear upward trend of 1.6% °C −1 in warmer environments.   Figure 4 exhibits the percentage change in heating energy consumption E against the change in ambient air temperature ∆T a . The results reveal that the heating energy required for additional water consumption is less dominating than the heating energy reduced in a warmer environment. Although there are variations of E in the simulations, a general downward trend against warmer environments is observed. As shown in Figure 4a,b, energy credits can be achieved, respectively, by taking fewer hot showers and by taking one more shower in a warmer period while adopting a positive temperature shift.

Results and Discussion
Based on the 1986-2005 ambient temperature data and the existing shower usage patterns, the simulation results for water consumption, energy consumption, and CO2 emissions are 35.6 m 3 ps −1 yr −1 , 2.16 GJ ps −1 yr −1 , and 465 kg-CO2 ps −1 yr −1 , respectively. Figure 3, which illustrates the plotted results of V calculated from Equation (14) with a temperature shift Tsf, shows the linear trend of the percentage change in water consumption %V against the change in ambient air temperature ∆Ta for an average increment of 2.3% °C −1 . The outcome shows a linear upward trend of 1.6% °C −1 in warmer environments.    Figure 4 exhibits the percentage change in heating energy consumption E against the change in ambient air temperature ∆Ta. The results reveal that the heating energy required for additional water consumption is less dominating than the heating energy reduced in a warmer environment. Although there are variations of E in the simulations, a general downward trend against warmer environments is observed. As shown in Figure 4a,b, energy credits can be achieved, respectively, by taking fewer hot showers and by taking one more shower in a warmer period while adopting a positive temperature shift.
The results also show that using 10% less hot shower water can save 1.7% energy, with additional savings of 0.5% °C −1 in warmer environments. An expression given by Equation (15) is shown in Figure 4a to illustrate the change in energy used E.  (15) By measuring the temperature shift, the gradients in Figure 4a indicate user behavioural changes. With a lessened energy burden, an average energy credit of 1.5% °C −1 is expected. Reportedly, there is a linear downward trend of 0.8% °C 1 in warmer environments. An expression given by Equation (16) is shown in Figure 4b to illustrate the change in energy used E.  Figure 5 presents the percentage changes in CO2 emissions for showering in warmer environments. It can be observed that the energy consumed for water heating is more significant than that for water supply and treatment. Despite variations in the simulation results, there is an overall downward trend. However, less energy savings can be seen in the figure as compared with Figure 4, because energy is required for more showers in warmer environments.
For every 10% reduction in the number of hot showers, it is expected to save 1.5% energy, with additional savings of 0.46% °C −1 in warmer environments. As shown in Figure 5a, the maximum CO2 emissions reductions are 14% and 20% at ∆Ta = 3 °C and 4 °C, respectively.
Regarding the temperature shift, a carbon credit of 1.5% °C −1 is expected. A linear downward trend of 0.8% °C −1 for hot showers is observed in warmer environments. As shown in Figure 5b, the maximum CO2 changes are 9.5% and 10% at ∆Ta = 3 °C and 4 °C, respectively.  The results also show that using 10% less hot shower water can save 1.7% energy, with additional savings of 0.5% • C −1 in warmer environments. An expression given by Equation (15) is shown in Figure 4a to illustrate the change in energy used E.
By measuring the temperature shift, the gradients in Figure 4a indicate user behavioural changes. With a lessened energy burden, an average energy credit of 1.5% • C −1 is expected. Reportedly, there is a linear downward trend of 0.8% • C −1 in warmer environments. An expression given by Equation (16) is shown in Figure 4b to illustrate the change in energy used E. Figure 5 presents the percentage changes in CO 2 emissions for showering in warmer environments. It can be observed that the energy consumed for water heating is more significant than that for water supply and treatment. Despite variations in the simulation results, there is an overall downward trend. However, less energy savings can be seen in the figure as compared with Figure 4, because energy is required for more showers in warmer environments.
For every 10% reduction in the number of hot showers, it is expected to save 1.5% energy, with additional savings of 0.46% • C −1 in warmer environments. As shown in Figure 5a, the maximum CO 2 emissions reductions are 14% and 20% at ∆T a = 3 • C and 4 • C, respectively.
Regarding the temperature shift, a carbon credit of 1.5% • C −1 is expected. A linear downward trend of 0.8% • C −1 for hot showers is observed in warmer environments. As shown in Figure 5b, the maximum CO 2 changes are 9.5% and 10% at ∆T a = 3 • C and 4 • C, respectively.
The changes in CO 2 emissions C as expressed by Equations (17) and (18) are shown in Figure 5a,b, respectively, for illustration. The changes in CO2 emissions C as expressed by Equations (17) and (18) are shown in Figure  5a,b, respectively, for illustration.  The CO2 emissions from the water supply system and water heater according to user influences can be determined by Equation (19), where Cα and Cβ are the changes in CO2 emissions due to the water supply system and water heater, respectively, while kα (=0.06) and kβ (=0.94) are the constants for CO2 emission fractions for water supply and treatment and water heating (approximately 1:15), respectively [16]. The CO 2 emissions from the water supply system and water heater according to user influences can be determined by Equation (19), where C α and C β are the changes in CO 2 emissions due to the water supply system and water heater, respectively, while k α (=0.06) and k β (=0.94) are the constants for CO 2 emission fractions for water supply and treatment and water heating (approximately 1:15), respectively [16]. Figure 6 exhibits various target CO 2 reductions based on user behavioural changes for P sh,35 ≥ 0.5 and T sf ≤ 5 • C. The maximum CO 2 reduction shown in the figure is 22% for ∆T a ≤ 3 • C, where C α and C β are −9.5% and −24.3%, respectively.  Table 2 summarizes the maximum CO2 reduction estimates from various measures, including water conservation programmes that target Psh,35 ≥ 0.5 and Tsf ≤ 5 °C, water efficient products, shower drain water heat recovery, and energy efficiency improvements for water supply systems [11,12,16,17]. The influence of users on CO2 reduction is found to be significant and compatible to that of water efficient showerheads. The contributions from heat recovery systems can also be significant. The maximum CO2 reduction calculated from all of the measures listed in Table 2 using Equation (19) is estimated to be 52%.  Table 2 summarizes the maximum CO 2 reduction estimates from various measures, including water conservation programmes that target P sh,35 ≥ 0.5 and T sf ≤ 5 • C, water efficient products, shower drain water heat recovery, and energy efficiency improvements for water supply systems [11,12,16,17]. The influence of users on CO 2 reduction is found to be significant and compatible to that of water efficient showerheads. The contributions from heat recovery systems can also be significant. The maximum CO 2 reduction calculated from all of the measures listed in Table 2 using Equation (19) is estimated to be 52%.

Conclusions
Improving water and energy efficiency in buildings is one of the best ways to reduce greenhouse gas emissions. It is necessary to identify the most significant measures to achieve the target. This study examined various energy-related CO 2 reduction measures, including the use of water efficient showerheads and shower drain water heat recovery, in order to distinguish the significance of user influence on the water usage of a shower. The results demonstrated that the influence of users on CO 2 reduction is significant (up to 22%) and compatible to the influence of water efficient showerheads (up to 26%). In contrast, the CO 2 reduction is less significant for heat recovery from hot showers in cities of hot climates (such as Hong Kong) (up to 14%) and water supply efficiency improvement in buildings (up to 2%). This study can be used as a reference to enhance water and energy incentives, and to facilitate continuous improvement in building water systems.