Investigating Spatiotemporal Variability of Water, Energy, and Carbon Flows: A Probabilistic Fuzzy Synthetic Evaluation Framework for Higher Education Institutions

: Higher education institutions (HEIs) consume signiﬁcant energy and water and contribute to greenhouse gas (GHG) emissions. HEIs are under pressure internally and externally to improve their overall performance on reducing GHG emissions within their boundaries. It is necessary to identify critical areas of high GHG emissions within a campus to help ﬁnd solutions to improve the overall sustainability performance of the campus. An integrated probabilistic-fuzzy framework is developed to help universities address the uncertainty associated with the reporting of water, energy, and carbon (WEC) ﬂows within a campus. The probabilistic assessment using Monte Carlo Simulations effectively addressed the aleatory uncertainties, due to the randomness in the variations of the recorded WEC usages, while the fuzzy synthetic evaluation addressed the epistemic uncertainties, due to vagueness in the linguistic variables associated with WEC benchmarks. The developed framework is applied to operational, academic, and residential buildings at the University of British Columbia (Okanagan Campus). Three scenarios are analyzed, allocating the partial preference to water, or energy, or carbon. Furthermore, nine temporal seasons are generated to assess the variability, due to occupancy and climate changes. Finally, the aggregation is completed for the assessed buildings. The study reveals that climatic and type of buildings signiﬁcantly affect the overall performance of a university. This study will help the sustainability centers and divisions in HEIs assess the spatiotemporal variability of WEC ﬂows and effectively address the uncertainties to cover a wide range of human judgment. The outcomes were then processed in a fuzzy synthetic system to accommodate the uncertainties in linguistic variables that are commonly used in benchmarking. A scenario analysis addressed the preferences to WEC. The fuzzy system consists of a fuzzy set and a fuzzy membership function. The analytical hierarchal process (AHP) accounts for the preference over the three indicators under three scenarios. Finally, the indicators were aggregated to determine the sustainability rank of the buildings in the University of British Columbia (Okanagan Campus).


Introduction
Benchmarks are set by many educational sectors to report energy consumption to communicate their performances. For example, typical energy consumption benchmarks for 320 educational buildings in Europe were reported to be 87 kWh/m 2 in Greece, 197 kWh/m 2 in Flanders, and 119 kWh/m 2 in Northern Ireland [1]. In the UK and Wales, educational buildings were found to be the most homogenous among all the non-domestic buildings, with a median of 46 kWh/m 2 for schools and 74 kWh/m 2 for HEIs [2]. Hernandez et al. (2008) benchmarked 88 non-domestic educational buildings in Ireland and ranked their performance in seven classes from (A-G) based on their energy performances [1]. Water benchmarks in educational buildings are less common than energy. The US educational buildings consume around 6% of the public sector's water usage, e.g., water consumption in nine large educational buildings is about 133 million m 3 per year which is equivalent to HEIs buildings were constructed before energy codes were applicable [41]. It is reported that 55% of commercial building (including HEI buildings) projects prior to the construction did not model energy in their design process, and do not adhere to any code compliance or green certification [30]. Therefore, monitoring, reporting, and continuous improvements are needed in HEIs.
Managing the adverse impacts associated with HEIs operations is necessary, due to the intrinsic role of HEIs in leading research, fostering talent, and creating safe and livable neighborhoods [64]. Emission estimation for educational buildings is challenging because energy demands in educational buildings are the least understood among the nonresidential buildings, due to their highly variable demand behaviors [10]. Some researchers highlighted the impact of occupancy behavior on energy consumption in buildings [65], while others have reported that the occupancy patterns do not significantly impact energy demand [34]. To promote energy conservation and sustainable use of energy, the European energy performance of building directive proposed reporting as means to effectively assess the institutions' performances. For example, the UK introduced laws to increase awareness in improving a buildings' energy performance, which require buildings to report and benchmark their energy consumption performances [66].
Reporting carbon emissions is a legal requirement for many HEIs, due to its role in calculating the carbon taxation imposition. However, HEIs do not consider carbon sequestration as means to mitigate the carbon released from their operations. Carbon sequestration includes both biological (in the form of plantation) and mechanical (in the form of carbon capture technologies) mechanisms and calculates the amount of carbon absorbed by the trees, shrubs, turfs, and soil in a campus. It is believed that carbon sequestration to have a significant impact at the community level [67]. A detailed carbon sequestration calculation involves both the type and area of vegetation.
Sustainability Reporting (SR) can be defined as the formal act of communicating the social, environmental, and financial performances of an organization [68]. The primary aim of the SR is to meet the demands of industrial growth, causing minimum impacts on the environment. This definition embodies the generalized theme of sustainable development (SD) stated by the Word Commission on Environment and Development as one that "meets the needs of the present without compromising the ability of future generations to meet their own needs [69]". The SR has become a normative practice among HEIs to meet sustainable development goals. Many reporting systems use indicators as the primary tool to make cross-institutional comparations (i.e., benchmarking) [53]. For instance, Martin (2005) stressed the need for developing techniques that can help in advancing SD in universities by using indicators and suggested that ecological footprint could be a useful approach for universities to report their performance [70].
The objective of this study is to propose a framework to assess the spatiotemporal variability in the sustainability of HEIs in terms of water use, energy use, and carbon emissions, incorporating probabilistic and linguistic uncertainties. This paper also proposes a method to estimate and include carbon sequestration by HEIs' greenery in a campus sustainability rating system for the first time. Figure 1 presents the developed probabilistic-fuzzy synthetic evaluation framework (PFSEF) to assess buildings' performance in terms of WEC flows. The framework consists of three modules, including Module 1: The selection and calculation of indicators, Module 2: Probabilistic assessment, and Module 3: Fuzzy synthetic evaluation assessment. Performance indicators are used to assess water use, energy use, and carbon emissions. The GHG emissions were calculated using the carbon equivalency of each source of energy. The biological carbon sequestration (negative emission) on campus was also estimated for the irrigation activities. The normalized WEC flows per building were then calculated. The probabilistic assessment addresses the aleatory uncertainties with the WEC data collection. The outcomes were then processed in a fuzzy synthetic system to accommodate the uncertainties in linguistic variables that are commonly used in benchmarking. A scenario analysis addressed the preferences to WEC. The fuzzy system consists of a fuzzy set and a fuzzy membership function. The analytical hierarchal process (AHP) accounts for the preference over the three indicators under three scenarios. Finally, the indicators were aggregated to determine the sustainability rank of the buildings in the University of British Columbia (Okanagan Campus).

Evaluation of Water, Energy, and Carbon Emissions
The biological carbon sequestration (negative emission) on campus was also esti the irrigation activities. The normalized WEC flows per building were then c The probabilistic assessment addresses the aleatory uncertainties with the WEC lection. The outcomes were then processed in a fuzzy synthetic system to acco the uncertainties in linguistic variables that are commonly used in benchmarkin nario analysis addressed the preferences to WEC. The fuzzy system consists of a and a fuzzy membership function. The analytical hierarchal process (AHP) acc the preference over the three indicators under three scenarios. Finally, the indica aggregated to determine the sustainability rank of the buildings in the Universi ish Columbia (Okanagan Campus).

Study Area
UBCO investigated in this case study is a branch of the University of Britis bia, located in the interior region of British Columbia. The campus has grown sig over recent years since 2005-the university started with 12 buildings and an a Hectares in 2005, and the campus now has 105 buildings within an overall ar Hectares in 2019 [71]. The growth in student enrollment has significantly incre the years. The growth since 2015 is shown in Figure A1 in Appendix A. The u operating budget also increased from $39 million in 2005/2006 to $175 m 2019/2020.

Study Area
UBCO investigated in this case study is a branch of the University of British Columbia, located in the interior region of British Columbia. The campus has grown significantly over recent years since 2005-the university started with 12 buildings and an area of 105 Hectares in 2005, and the campus now has 105 buildings within an overall area of 209 Hectares in 2019 [71]. The growth in student enrollment has significantly increased  Figure A1 in Appendix A. The university operating budget also increased from $39 million in 2005/2006 to $175 million in 2019/2020.
The campus is home to 10,708 full-time enrollment (FTE); 49% of the students are in arts and sciences, 18% in applied sciences, 12% in health and social development, 11% in creative and critical studies, 7% in management, and 3% in education. There are 46 buildings on the campus with an operating budget of $175 million in the fiscal year 2019/2020 [71]. Based on the campus FTE the campus may be considered a medium-size HEI [18].
The campus is located in a hemiboreal climate with long cold winters and warm summer [72]. Figure A2 in Appendix A shows the heating and cooling degree days (HDD and CDD) from 2013-2020. The average HDD is 3680.66 and subsequently 201.58 for the CDD [73]. The HDD and CDD measure the number of days where the outside temperature is below or above a set point temperature. It indicates the heating and cooling loads for a building [18,73].
This study investigates 23 buildings on the campus; two buildings are used for operational services and will be classified as operational buildings, while the rest includes 12 academic buildings and 9 residential buildings. The annotation for the buildings and their relative parameters is listed in Table A1 in Appendix A.

Evaluation of Water, Energy, and Carbon Emissions
The first step is the selection of performance indicators. In this study, reported water use and energy use were collected from the university. Carbon emissions were estimated using the carbon emission factors collected from the energy provider of the campus. These flows were then normalized by area as a common factor for comparability. This generates the performance indicators used in this study: water usage intensity (WUI), energy usage intensity (EUI), and carbon emission intensity (CEI). For parameters that were not reported on a building level, such as water utilization and carbon emissions, a proposed methodology is provided for this calculation.

Water
Water utilization data of the entire campus from April 2016 to January 2021 are provided by the university. Two approaches were taken to estimate each building's consumption of water. In the first approach, a water-to-area ratio was calculated, while in the second approach, water consumption per building was estimated using the Bonneville Environmental business water calculator is a webpage interface calculator. This calculator helps the business owners to estimate the closest approximation to water utilization, based on type and area, in their buildings, e.g., schools, office buildings, and health services, which is based on the type and area of the building [74]. The results yield the closest approximation to the actual reported water values are used.

Energy
Energy data is obtained from the energy facilities of the university from April 2016 to January 2021 as monthly data per source of energy. The amounts of energy generated from different sources are also provided. However, the energy used by water is missing, and to find this energy, this paper will adopt the method proposed by Chhipi- , since this study is carried out in closest approximation to Kelowna (i.e., where the campus is located) in terms of energy sources and water sources. Furthermore, both cities are located within the same geographic and climate factors. The ratios used by Chhipi-Shrestha (2017) will be used and derived from Equation (1) will be applied to estimate embodied energy (energy footprint) of necessary irrigation water.
By using the water-energy-carbon nexus model established by [75], the total energy required to deliver the volume of water is calculated: where the E w is the total energy required to deliver the volume of water, EE w is the embodied energy of supplied drinking water in kWh/m 3 and W v is the volume of water used in m 3 . This generates the amount of energy needed for that process in kWh. From this energy, the amount of carbon equivalent was calculated as given in the following section.
Area irrigation is irrigated area in hectares, and IR is the irrigation rate in L/ha/da, i.e., 977 L/m 2 /year for the Okanagan [76].

Carbon Emissions and Carbon Sequestration
The emissions covered in this study are Scope 1 and Scope 2 GHG emissions. Scope 1 emissions include the direct emissions released from the universities (i.e., primary source of energy), such as combusting the natural gas on-site to produce heat. Scope 2 emissions are the indirect emissions released by the electricity provider during the production of electricity (secondary source of energy). The distinction is usually referred to as the amount the university controls. Emissions are reported for the entire campus, including fleet transportation, emissions from electricity, and so on. The carbon emission factors are obtained from the BC Best Practices Methodology for Quantifying GHG Emissions [77]. This method has been used extensively to estimate emission factors for various sources of energy generation [5,18]. Since the UBCO uses natural gas and the local electricity grid as the energy sources, the GHG emission per building is calculated: where CE is the carbon emission in CO 2 e, CEF is the carbon emission factor for that source of energy CO 2 e/kWh, and EU is the energy use in kWh. The carbon sequestration is estimated based on the previous similar research [67,78] as follows: where C s is the total carbon sequestration it is measured in kg CO 2 /m 2 /year, SOC S is total the total landscape sequestration SOC it is measured in kg CO 2 /m 2 /year, ∆A i is the total landscaping area in m 2 [67], C st and C ss are total carbon sequestration by the trees and shrubs in kg CO 2 /m 2 or by the tree, and N t and N s are numbers of trees and shrubs, respectively [75]. The net carbon emission landscaping in a neighborhood can be estimated as, where C s is net carbon emission (kg CO 2 /year), C E is carbon emission and it is measured for each energy source in (CO 2 e), C s is total carbon sequestration by individual landscaping (kg CO 2 /m 2 /year), and n is a number of all landscaping with water supplied [75]. The area was calculated approximately using Google Earth.

Probabilistic Assessment
Probabilistic methods are used to address uncertainties that result from the randomness and stochastic nature of the data. These types of uncertainties are inherently common in data reporting [13,79]. Probabilistic uncertainties are a result of data selection, for instance using the average usage intensities on a yearly or monthly basis. Uncertainties may be a result of other factors, such as human behavior, occupancy uncertainties which all may affect the readings [16].
Monte Carlo simulation (MCS) is a common technique used to address model-parameter uncertainties. MCA assumes models are random, and it relies on computational representation in the provided data. The overall model can be generated in a probability-density function if "Y" is assumed to be a random variable, with probabilities should be less or equal to "y" for every unknown "Y", and is illustrated by [13], and if, Y is continuous, then, MCS was performed by assigning a probabilistic distribution for the flows that correspond to percentile values which were used as inputs in the following fuzzy synthetic evaluation. The 90th percentile of the distribution was used to perform the Monte Carlo simulation using 50,000 iterations of @RiskTM 8.1 (Palisade Corporation, Ithaca, NY, USA). A cumulative probability distribution is acquired to determine the corresponding percentiles of each indicator. Monte Carlo simulations propagate the distribution hundreds of times to account for random uncertainty in the data [80]. The outputs of the simulation can be used to determine the fuzzy classes.

Fuzzy-Based Assessment
Fuzzy-based techniques addressed the uncertainties caused by the vagueness and imprecise judgment in human insights [81]. A fuzzy set consists of a fuzzy number and a membership function. The assessment was done through the following steps:

Developing Membership Function and Fuzzification
A fuzzy set is presented as, where A(x) is the fuzzy set of X, and X is the universal set of variable x, and µ x A ranges between the normalized value of 0 and 1. A smaller µ x A indicates a less association between x and A. Furthermore, fuzzy sets can be illustrated in many shapes, and a common shape used is the triangular membership (a, m, b), as shown in Figure 2. The µ x A of x(x ∈ [a, b]) is the membership function calculated using Equation (9).
The fuzzy membership functions are developed to numerically transform linguistic variables. This can be achieved by using five linguistic variables: Very low (VL), low (L), medium (M), high (H), very high (VH), as shown in Appendix A, Figure A3. The outcomes of the probabilistic assessment are mapped into the membership function to extract fuzzy critical levels. Assuming that the red line in Figure 2 represents the probability of EU I 01 with a normalized value of 0.13, then the memberships to both "VL" and "L" levels are 0.5.

Weighting of Indicators
The AHP is commonly used in planning and multicriteria decision-mak ing both inductive and deductive reasoning to reach a synthesis [82]. AHP f archical structure that generally consists of a well-defined goal, followed b ends with an alternative or multiple levels of subcriteria as shown in Fig  commonly used in decision making, due to its ability to deal with comple simple pairwise comparison judgments, which are then used to develop the ities for ranking the alternatives ability to select the best set of numbers of alternatives with respect to multiple criteria [83]. The method is based on relative importance and could be obtained by several methods, such as mean [21], least square method, or the characteristic root method [84].

Weighting of Indicators
The AHP is commonly used in planning and multicriteria decision-making, addressing both inductive and deductive reasoning to reach a synthesis [82]. AHP follows a hierarchical structure that generally consists of a well-defined goal, followed by criteria, and ends with an alternative or multiple levels of subcriteria as shown in Figure 3. AHP is commonly used in decision making, due to its ability to deal with complex problems in simple pairwise comparison judgments, which are then used to develop the overall priorities for ranking the alternatives ability to select the best set of numbers of the evaluated alternatives with respect to multiple criteria [83]. The method is based on the pairwise relative importance and could be obtained by several methods, such as the geometric mean [21], least square method, or the characteristic root method [84].

Weighting of Indicators
The AHP is commonly used in planning and multicriteria decision-making, addressing both inductive and deductive reasoning to reach a synthesis [82]. AHP follows a hierarchical structure that generally consists of a well-defined goal, followed by criteria, and ends with an alternative or multiple levels of subcriteria as shown in Figure 3. AHP is commonly used in decision making, due to its ability to deal with complex problems in simple pairwise comparison judgments, which are then used to develop the overall priorities for ranking the alternatives ability to select the best set of numbers of the evaluated alternatives with respect to multiple criteria [83]. The method is based on the pairwise relative importance and could be obtained by several methods, such as the geometric mean [21], least square method, or the characteristic root method [84]. The steps needed to apply AHP to generate preferred weights [84,85]: The steps needed to apply AHP to generate preferred weights [84,85]: 1. Decompose a complex problem into a hierarchy of goals, criteria, and alternatives.

2.
Measurement methodology is used to create pairwise comparison priorities among the subcriteria and alternatives, by creating a n * m then derive the geometric mean for each criterion.

3.
Measurement theory to establish the relative importance of a parameter. This is calculated using:

4.
To verify the consistency, the following steps are taken: a.
Calculate the maximum eigenvalue λ max ; b.
Derive the consistency index CI and consistency ratio CR.
where RI is a given random index generated and can be referred to in [86]. If CR > 0.1, then it is inconsistent, the larger the CI implies that the judgment taken by a decision-maker is more inconsistent.
To assess pairwise comparison, Saaty (1980) developed a nine-point intensity scale (i.e., degree of preference) of importance between any pairs of criteria. The nine-point intensity scale and their internment points may be referred to Saaty (1980) [82].
The preference between the elements is conducted through a focus group, expert opinions, or several different and opposing scenarios. The AHP is commonly used in fuzzy synthetic evaluation to establish a set of preference weights based on the relative importance of each attribute using pairwise comparison. The set of preference weights is normalized to a sum of 1. This weighting method has been used to is commonly used in the literature [21,22,87]: Assume an importance matrixÂ is established where each elementÂ mn expresses the importance of the attributes m with respect to n. These preferences should be assigned based on expert opinions [21]: The weights can be obtained by taking the geometric mean of the weights vector and the normalization of the matrix.

Aggregation and Ranking
The step aggregates all the scopes with their respective weights and ranks them. Because the three criteria used are WEC, and they are not opposing, meaning that the more consumed of any parameter will result in a "worst" sustainability, therefore the higher the number is, the less sustainable it will be.

Defuzzification
The final step is defuzzification, there are many methods listed in the literature to defuzzify. The max method in Equation (17) will be used as means for defuzzification [88]. The score ranges will be between 0 and 1, the higher the numbers are, the worst the sustainability is.
x Water reporting is on a campus level, on type of buildings: Whether they are academic or residential per month. It is reported that the entire campus consumed a total of 797,968.8 m 3 during the period of April 2016-January 2021, with an average water use per year of 163,898.95 m 3 . In Appendix A, Figure A4 shows the average annual water use of different types of buildings.

Results and Discussion
In this study, raw water conveyance (from the extraction of water to treatment), water treatment, and water distribution are used to assess the energy for water use on campus, and consequently calculate the associated GHG emissions. Due to the lack of data, the embodied energy (upstream energy) of municipal water supply (potable water) is assumed to be the same as the nearby city (Penticton), which is 0.6053 kWh/m 3 [75]. Figure 4 presents the total volumes of water used over the years. Water consumption increases during May-Aug, due to irrigation. The water used for irrigation is included with each building's water consumption. Irrigation values alone are not metered. A recent commissioning report estimated that the campus uses an average amount of 55,781 m 3 of irrigation water per year which was based on the usage of Equation (2).
The final step is defuzzification, there are many methods listed in the literatu defuzzify. The max method in Equation (17) will be used as means for defuzzification The score ranges will be between 0 and 1, the higher the numbers are, the worst th tainability is. * = [ , , , , ]

Water Use
Water reporting is on a campus level, on type of buildings: Whether they ar demic or residential per month. It is reported that the entire campus consumed a to 797,968.8 m 3 during the period of April 2016-January 2021, with an average water u year of 163,898.95 m 3 . In Appendix A, Figure A4 shows the average annual water u different types of buildings.
In this study, raw water conveyance (from the extraction of water to treatment ter treatment, and water distribution are used to assess the energy for water use on pus, and consequently calculate the associated GHG emissions. Due to the lack of the embodied energy (upstream energy) of municipal water supply (potable water) sumed to be the same as the nearby city (Penticton), which is 0.6053 kWh/m 3 [75]. Figure 4 presents the total volumes of water used over the years. Water consum increases during May-Aug, due to irrigation. The water used for irrigation is inc with each building's water consumption. Irrigation values alone are not metered. A r commissioning report estimated that the campus uses an average amount of 55,781 irrigation water per year which was based on the usage of Equation (2). Water consumptions on campus have not been reported per building usage. To come this limitation, two approaches have been considered to estimate the water per building. First, a ratio-to-area approach, where the total reported campus wate divided into each building depending on each building's area. For instance, the CHP building has an area of 528 m 2 which is equivalent to 0.37% of the total buildings ass Year 2016 Year 2017 Year 2018 Year 2019 Year 2020 Water consumptions on campus have not been reported per building usage. To overcome this limitation, two approaches have been considered to estimate the water usage per building. First, a ratio-to-area approach, where the total reported campus water was divided into each building depending on each building's area. For instance, the CHP (O1) building has an area of 528 m 2 which is equivalent to 0.37% of the total buildings assessed in this study, and therefore, the corresponding water values are given in Appendix B. An average of six years was considered.
The second approach used the Bonneville Environmental business water calculator, which is based on building type and the area of the building [74]. Both the ratio-to-area and the BEF values are also reported in Appendix B. There is a significant difference between the two methods-for example, the mean of the ratio-to-area method is 6498 m 3 whereas, the mean for the BEF is 4570 m 3 and the standard deviation of the first method is 3661 and 2575, the standard error of the mean is 763 for the first method and 537 for the latter. Figure 5 shows the total water calculated by the first method is 149,444 m 3 and by the second 105,104 m 3 . The first method was found closer to the actual average reported water consumption of 163,898.95 m 3 . Water is then normalized by area, and the statistical summary and graph are illustrated in Appendix C.
in this study, and therefore, the corresponding water values are given in Appendix average of six years was considered.
The second approach used the Bonneville Environmental business water calcu which is based on building type and the area of the building [74]. Both the ratio-to and the BEF values are also reported in Appendix B. There is a significant differen tween the two methods-for example, the mean of the ratio-to-area method is 64 whereas, the mean for the BEF is 4570 m 3 and the standard deviation of the first m is 3661 and 2575, the standard error of the mean is 763 for the first method and 537 f latter. Figure 5 shows the total water calculated by the first method is 149,444 m 3 an the second 105,104 m 3 . The first method was found closer to the actual average rep water consumption of 163,898.95 m 3 . Water is then normalized by area, and the stat summary and graph are illustrated in Appendix C.

Energy Use
Monthly energy utilization data (kWh) for each building was obtained from th versity for the period between April 2016 and January 2021. The energy is being sup from two sources, electricity, and natural gas. The first source is connected with the tricity grid of FortisBC, which is predominantly powered by hydroelectricity [89]. W the campus, there are two operational buildings: A central heating plant and a geoth plant-both use natural gas to supply energy to each building. The central heating serves buildings A1, A2, A7, A8, A9, A11 through a low-temperature district energ tem (LDES). The geothermal plant serves academic buildings A1, A2, A3, A4, A5, A A8, A10, A11, A12 through a medium temperature district energy system (MDES) geothermal plant converts ambient temperature water to cold (7 °C) and hot water (4 Moreover, the geothermal plant was built to regulate surplus heat when the outside perature was lower than −2 °C and heating demand at outside temperatures of 15 °C higher. By recapturing the excess waste heat of buildings, the plant can achieve reduc in overall emissions [90].
The monthly energy per building is normalized by the area of that building. A plot is provided for energy comparison between the buildings in Figure 6, inclu monthly utilization from April 2016-January 2021. A statistical summary for the no ized energy usage intensity is provided in Appendix C. It is noted that, for instanc average monthly EUI of operational buildings is 52.99 kWh/m 2 and the monthly av for academic buildings is 30.21 kWh/m 2 , and finally, 11.45 kWh/m 2 for the resid buildings. It is important to note that these figures represent a monthly average o EUI. It is also noted that the energy used for the operational buildings is extensively h than that of other buildings, due to the nature of these two buildings, where they con vast amounts of energy to deliver heat, natural gas, and electricity to the other build

Energy Use
Monthly energy utilization data (kWh) for each building was obtained from the university for the period between April 2016 and January 2021. The energy is being supplied from two sources, electricity, and natural gas. The first source is connected with the electricity grid of FortisBC, which is predominantly powered by hydroelectricity [89]. Within the campus, there are two operational buildings: A central heating plant and a geothermal plant-both use natural gas to supply energy to each building. The central heating plant serves buildings A1, A2, A7, A8, A9, A11 through a low-temperature district energy system (LDES). The geothermal plant serves academic buildings A1, A2, A3, A4, A5, A6, A7, A8, A10, A11, A12 through a medium temperature district energy system (MDES). The geothermal plant converts ambient temperature water to cold (7 • C) and hot water (45 • C). Moreover, the geothermal plant was built to regulate surplus heat when the outside temperature was lower than −2 • C and heating demand at outside temperatures of 15 • C and higher. By recapturing the excess waste heat of buildings, the plant can achieve reductions in overall emissions [90].
The monthly energy per building is normalized by the area of that building. A box-plot is provided for energy comparison between the buildings in Figure 6, including monthly utilization from April 2016-January 2021. A statistical summary for the normalized energy usage intensity is provided in Appendix C. It is noted that, for instance, the average monthly EUI of operational buildings is 52.99 kWh/m 2 and the monthly average for academic buildings is 30.21 kWh/m 2 , and finally, 11.45 kWh/m 2 for the residential buildings. It is important to note that these figures represent a monthly average of the EUI. It is also noted that the energy used for the operational buildings is extensively higher than that of other buildings, due to the nature of these two buildings, where they consume vast amounts of energy to deliver heat, natural gas, and electricity to the other buildings.

Carbon Emissions
UBCO is mandated by law to submit a yearly GHG emission inventory repor emissions in this report include scope 1 and scope 2 GHG emissions and any offs emissions. These emissions include emissions from the energy used in buildings transportation, paper, and fugitives. A historic layout of the emission from UBCO is trated in Figure 7 [91]. Each building carbon emissions are calculated based on BC's best practices me ology as stated. The emissions factors for natural gas and electricity in Kelowna are 0 kg CO2e/kWh for natural gas and 0.0026 kg CO2e/kWh [77]. To illustrate an exam how the emissions are calculated, the Administration buildings Tables A5 and A6 i pendix C used in April 2016 226,933.9 kWh of energy from electricity and natura Natural gas accounts for 78,678.7 kWh, and electricity accounts for 148,255.1 kWh, fore by applying Equation (3), the overall emissions released by the building in Apri are estimated to be 14.5 tCO2e. Subsequently, the remaining emission for each build calculated. After that, the total emissions are divided by each building's area to atta carbon usage intensity per month. Figure 8 shows the box-plots for each building.

Carbon Emissions
UBCO is mandated by law to submit a yearly GHG emission inventory report. The emissions in this report include scope 1 and scope 2 GHG emissions and any offsetable emissions. These emissions include emissions from the energy used in buildings, fleet transportation, paper, and fugitives. A historic layout of the emission from UBCO is illustrated in Figure 7 [91].

Carbon Emissions
UBCO is mandated by law to submit a yearly GHG emission inventory report. The emissions in this report include scope 1 and scope 2 GHG emissions and any offsetabl emissions. These emissions include emissions from the energy used in buildings, flee transportation, paper, and fugitives. A historic layout of the emission from UBCO is illus trated in Figure 7   Each building carbon emissions are calculated based on BC's best practices method ology as stated. The emissions factors for natural gas and electricity in Kelowna are 0.1795 kg CO2e/kWh for natural gas and 0.0026 kg CO2e/kWh [77]. To illustrate an example o how the emissions are calculated, the Administration buildings Tables A5 and A6 in Ap pendix C used in April 2016 226,933.9 kWh of energy from electricity and natural gas Natural gas accounts for 78,678.7 kWh, and electricity accounts for 148,255.1 kWh, there fore by applying Equation (3), the overall emissions released by the building in April 2016 are estimated to be 14.5 tCO2e. Subsequently, the remaining emission for each building i calculated. After that, the total emissions are divided by each building's area to attain the carbon usage intensity per month. Figure 8 shows the box-plots for each building. Each building carbon emissions are calculated based on BC's best practices methodology as stated. The emissions factors for natural gas and electricity in Kelowna are 0.1795 kg CO 2 e/kWh for natural gas and 0.0026 kg CO 2 e/kWh [77]. To illustrate an example of how the emissions are calculated, the Administration buildings Tables A5 and A6 in Appendix C used in April 2016 226,933.9 kWh of energy from electricity and natural gas. Natural gas accounts for 78,678.7 kWh, and electricity accounts for 148,255.1 kWh, therefore by applying Equation (3), the overall emissions released by the building in April 2016 are estimated to be 14.5 tCO 2 e. Subsequently, the remaining emission for each building is calculated. After that, the total emissions are divided by each building's area to attain the carbon usage intensity per month. Figure 8 shows the box-plots for each building. A detailed statistical summary of the CEI is also calculated in Appendix C. The age CEI for the operational buildings is 0.19 tCO2e/m 2 , for academic buildings i tCO2e/m 2 and finally for the residential buildings 0.61 tCO2e/m 2 . Academic building average, produce 70% of the campus' entire GHG emissions.
Similar to water usage, GHG emissions are reported on the campus level. By the normalized average outputs in the literature. The total energy needed to convey, and distribute the estimated irrigation water of 55,781 m 3 on campus is estimated 33,764 kWh/year. Since the water facilities use the local electrical grid as an energy so the total carbon emitted, due to irrigation, is 87.79 kgCO2e/year using the carbon eq lency and by using Equation (3).
The energy from water usage in the first three stages proposed by [45] include water conveyance, water treatment, and water distribution use a total of 4172 MW energy to produce a water value of 6893 ML or 6.893 Mm 3 of water. This results in 0 kWh/m 3 of energy needed to meet the demand in the city of Penticton in the Okan Valley in BC. Therefore, to calculate the amount of energy used by the irrigation wa campus, the model in the graph will be used to assess the energy and consequent amount of carbon equivalent emitted. The total water consumption for the UBCO inc the water used in academic buildings, residential buildings, and the water used fo gation. The entire campus consumed 797,969 m 3 from April 2016-January 2021 by the ratio of 0.6053, as generated from Equation (1) from [75], the total energy requi 483,010.6 kWh, and since the water utility uses the electricity grid as a main sou energy, the corresponding GHG emissions are 1255.83 kgCO2e. Figure 9 illustrate box-plot graph of the energy and water nexus in the campus during the period from 2016 to January 2021.
Carbon is also sequestrated naturally through the growth of trees, vegetation shrubs. To calculate the total carbon sequestration from in the campus, as shown in tion (4). The parameters in the equation are listed in Table 1, which are modified from The total sequestration is around 13.879 tCO2e/year. The tree density in Kelowna sumed to be 150 stems/ha [92]. UBCO releases a vast amount of carbon, making t questration carry a minimal effect, if any, on the total performance. A detailed statistical summary of the CEI is also calculated in Appendix C. The average CEI for the operational buildings is 0.19 tCO 2 e/m 2 , for academic buildings is 1.85 tCO 2 e/m 2 and finally for the residential buildings 0.61 tCO 2 e/m 2 . Academic buildings, on average, produce 70% of the campus' entire GHG emissions.
Similar to water usage, GHG emissions are reported on the campus level. By using the normalized average outputs in the literature. The total energy needed to convey, treat, and distribute the estimated irrigation water of 55,781 m 3 on campus is estimated to be 33,764 kWh/year. Since the water facilities use the local electrical grid as an energy source, the total carbon emitted, due to irrigation, is 87.79 kgCO 2 e/year using the carbon equivalency and by using Equation (3).
The energy from water usage in the first three stages proposed by [45] includes raw water conveyance, water treatment, and water distribution use a total of 4172 MWh of energy to produce a water value of 6893 ML or 6.893 Mm 3 of water. This results in 0.6053 kWh/m 3 of energy needed to meet the demand in the city of Penticton in the Okanagan Valley in BC. Therefore, to calculate the amount of energy used by the irrigation water on campus, the model in the graph will be used to assess the energy and consequently the amount of carbon equivalent emitted. The total water consumption for the UBCO includes the water used in academic buildings, residential buildings, and the water used for irrigation. The entire campus consumed 797,969 m 3 from April 2016-January 2021 by using the ratio of 0.6053, as generated from Equation (1) from [75], the total energy required is 483,010.6 kWh, and since the water utility uses the electricity grid as a main source of energy, the corresponding GHG emissions are 1255.83 kgCO 2 e. Figure 9 illustrates the box-plot graph of the energy and water nexus in the campus during the period from April 2016 to January 2021.
Carbon is also sequestrated naturally through the growth of trees, vegetation, and shrubs. To calculate the total carbon sequestration from in the campus, as shown in Equation (4). The parameters in the equation are listed in Table 1, which are modified from [67]. The total sequestration is around 13.879 tCO 2 e/year. The tree density in Kelowna is assumed to be 150 stems/ha [92]. UBCO releases a vast amount of carbon, making the sequestration carry a minimal effect, if any, on the total performance. (c) Figure 9. Water-energy-carbon nexus of the supplied water at campus (a) water quantity, (b) energy from water usage, (c) carbon emission from the energy needed to use water at the campus level, and its corresponding energy use.

Probabilistic Assessment
The probabilistic distribution was generated using Monte Carlo simulation (MCS) with 50,000 iterations using @Risk TM 8.1 student version [93]. The probabilistic distributions of the three parameters are listed in Appendix D. The distribution of EUI is Gama, for CEI is Lognorm and for WUI is Uniform. The probabilistic assessment addressed uncertainties related to the randomness of data. The 5%, 25%, 50%, 75%, and 95% percentiles are used to generate the fuzzy numbers. For example, for the EUI, the 5% is 4.293; a lognormal is taken, and the corresponding 5% is 0.6328. Similarly, for CEI, it is 0.0278, and the log for it is −1.5560; for WUI it is 0.0841, and the log is −1.07534, as shown in Table 2.
These generated values were obtained from the Monte Carlo simulations to address the random uncertainties.⃒

Probabilistic Assessment
The probabilistic distribution was generated using Monte Carlo simulation (MCS) with 50,000 iterations using @Risk TM 8.1 student version [93]. The probabilistic distributions of the three parameters are listed in Appendix D. The distribution of EUI is Gama, for CEI is Lognorm and for WUI is Uniform. The probabilistic assessment addressed uncertainties related to the randomness of data. The 5%, 25%, 50%, 75%, and 95% percentiles are used to generate the fuzzy numbers. For example, for the EUI, the 5% is 4.293; a log-normal is taken, and the corresponding 5% is 0.6328. Similarly, for CEI, it is 0.0278, and the log for it is −1.5560; for WUI it is 0.0841, and the log is −1.07534, as shown in Table 2. These generated values were obtained from the Monte Carlo simulations to address the random uncertainties.

Fuzzy-Based Assessment
The fuzzy classes are then mapped onto their corresponding fuzzy sets, as shown in Appendix A, Figure A5, which will generate the corresponding membership for each building.

Scenario and Criteria Weights
AHP is used to assign weights for water, energy, and carbon emissions considering three scenarios, namely, water, energy, and carbon preferences. In the underwater preference scenario, water is strong importance (i.e., five) compared to the energy, and water is very strong (i.e., seven) compared to CUI. Table A2 in Appendix A shows the weights and consistency ratios. For the final two scenarios, because it is two parameters, so the consistency ratio is 0. Water is excluded because water values are not reported per building level, and in this study, a close approximation is used to estimate water (i.e., based on ratio); therefore, water value will hold a single class under any scenario and will not explain the variability in the buildings.
In all AHP scenarios, the CR is less than 0.1 making the weights consistent. Buildings will be benchmarked spatially and temporally. These seasons are selected at a time when occupancy in the university is at its peak during the winter season, and low in the summer, due to the limited enrollment in the summer programs. Winter is assumed to being from October till the end of April of the next year because it is when the corresponding HDD and CDD figures, shown in Appendix A, become dominant, while the summer averages are taken from May until the end of September, each year. Table 3 presents the seasons selected for this study and their duration. May 2020 September 2020 Summer 5 The aggregation is obtained by using Equation (16). Defuzzifiying is done by using Equation (17). Table 4 presents the defuzzifying results for all the three preference scenarios, including water preference, energy preference, and carbon preference. Table 4 includes all the collected data from April 2016 till the end of January 2021. This proposed type of benchmarking classifies buildings into five classes (VL, L, M, H, VH). It can be noted that Scenario 1 classifies all the buildings in the M class. This is due to the use of ratio-based calculation in the water in Section 4.1.1, and due to the highly emphasized weight on water in this scenario. Scenario 2: 65% of the buildings fall in the VL, L, and M class, and 35% fall in the H, VH class in an energy preference scenario. This means that 35% of the buildings fall behind in terms of performance. Finally, in scenario 3, 43% of the buildings fall in the VL, L, and M class, while 57% fall in the H and VH class. Thus, 57% of the buildings highly impact the HEIs goal towards carbon reductions in a carbon scenario. To gain a better understanding of the variability, a temporal analysis is completed by assuming nine seasons are proposed based on seasonality and occupancy load to understand their impact on the overall analysis. These seasons are associated with noticeably high HDD and or CDD. These nine seasons are shown in Table 3.  Table 5 shows the defuzzification results using Equation (17) for the energy preference scenarios proposed in Table 3. Table 6 shows the carbon preference scenarios based on the same seasonality proposed. It can be noted that buildings tend to underperform in the winter season, due to the increased use of heating which is often supplied via fossil fuels. A graphical presentation of the percentiles of each building in each class is presented in Figure 10a for the energy preference scenarios and for the carbon preference scenarios in Figure 10b. The percentage building in each class under each season. It can be noted that, as shown in Figure 10, during the summer 32% of the buildings fall in the VL class, on average. While in the winter season, none of the buildings is in the VL class. Figure 11 illustrates the two scenarios that considered energy preference and carbon preference weights for the entire data from April 2016 till January 2021. In the energy preference weighted scenario, none of the buildings fall in the VL class, and the majority of the L class buildings are residential buildings. While in the carbon preference weighted scenario, some of the residential buildings lie in the VL and L classes, due to their dependency on electricity which is generated by hydro sources in BC, and therefore, these buildings have low carbon footprints. These buildings are considered slightly impactful in the energy scenarios, indicating scope for improvements in the overall energy consumption in all buildings (also see Tables 5 and 6).
Spatiotemporal benchmarking results classify the buildings into five distinctive classes. To understand the performance at the building level, crisp defuzzification ranks the buildings based on the proposed WEC scenarios. Figure 12 shows the building type in the three primary scenarios. Academic buildings underperform residential buildings in all scenarios.

Season/Building S-1 W-1 S-2 W-2 S-3 W-3 S-4 W-4 S-5
Scenario S5 S7 S9 S11 S13 S15 S17 S19 S21  Environments 2021, 8, x FOR PEER REVIEW Figure 11 illustrates the two scenarios that considered energy preference preference weights for the entire data from April 2016 till January 2021. In preference weighted scenario, none of the buildings fall in the VL class, and t of the L class buildings are residential buildings. While in the carbon preferenc scenario, some of the residential buildings lie in the VL and L classes, due to th ency on electricity which is generated by hydro sources in BC, and therefore, t ings have low carbon footprints. These buildings are considered slightly impa energy scenarios, indicating scope for improvements in the overall energy co in all buildings (also see Tables 5 and 6). Spatiotemporal benchmarking results classify the buildings into five disti ses. To understand the performance at the building level, crisp defuzzificatio buildings based on the proposed WEC scenarios. Figure 12 shows the building three primary scenarios. Academic buildings underperform residential build scenarios. Spatiotemporal benchmarking results classify the buildings into five distinctive classes. To understand the performance at the building level, crisp defuzzification ranks the buildings based on the proposed WEC scenarios. Figure 12 shows the building type in the three primary scenarios. Academic buildings underperform residential buildings in all scenarios.

Ranking of Buildings
To rank individual buildings, crisp numbers were generated by assigning arbitrary weights to each membership, as proposed by Sadiq et al. (2004) [21]. Ideally, this would be set based on the goals, aspirations, and capabilities of each university. By using the order weighted aggregation [94], the assigned weights are (0.1, 0.15, 0.2, 0.25, 0.3). A risk index was developed for each building using Equation (18).
where RI is the risk index is an effective measure of quantifying the risk from a particular building with respect to the weights of importance in each fuzzy class. Table 7 shows the rank of the buildings based on water, energy, and carbon preferences of the buildings from most sustainable to the least. Ideally, these weights would be set by a group of experts in the HEIs with a proper understanding of their goals, limitation, budgets, and aspirations.
Occupancy ratios are one of the main limitations of this study, since student enrollment at a building is difficult to quantify, thus conclusions regarding occupancy influence on WEC consumption may not be derived. Furthermore, HEIs usually do not report the amount of water used per building, and even when this is done-it usually includes irrigation and out-of-building scope activities. Therefore, the extent of water performance on buildings and their impact between the building types may not be derived. HEIs need to aggressively pursue data collection to detect failures in the building or deteriorating appliances and address them before they are left unattended and may impact the university's overall efficiency and performance.

Conclusions
Currently, HEIs do not have a technical benchmarking tool that can undressing the two common types of uncertainties associated with benchmarking tools. This may be a result of two factors-firstly, it can be a result of assigning impartial weights to other attributes of sustainability, namely, social and economic aspects [5]. This is achieved through weight judgment uncertainties-as in the case by assigning a higher weight to other indicators in their reporting system, which is conveyed in a linguistic score associated with uncertainties. Secondly, this could be due to the nature of holistic systems' inability to address specific areas in their reporting systems [11]. This is not to undermine the importance of holistic systems in assessing multi-dimensional tasks, such as sustainability, on the contrary. Instead, this is to give attention to the set of considerations set in these options and to shed light on the need for examining the uncertainty inherent in these reporting systems. In addition, to a need to highlight more attention towards a reductionist approach to sustainability [8].
The proposed benchmarking method with both aspects, the spatial and temporal benchmarking approaches, are shown to illustrate how these two types of benchmarking systems can address the uncertainties and their ability to underpin underlying causes that affect HEIs performance. To improve on benchmarking and communicating performance. Twenty-one temporal scenarios are proposed to cover a wide range of judgments in human perception. Which can give a better understanding of the individual underperformer and the set of themes (i.e., climatic factors) that highly affect the university performance. Figure 12a-c shows the classification of each building by type in terms of the five classes. It can be noted that academic buildings hold a larger effect on the overall performance within the university compared to residential buildings.
By classifying the buildings in terms of the type of buildings (i.e., academic or residential), academic (which include operational buildings), and residential buildings as a separate class. It is noted that in academic buildings in Scenario 2, 43% of the buildings fall in the (VL, L, M) class, and 57% fall in the (H, VH) class. Similarly, for Scenario 3, 29% of the academic buildings are in the (VL, L, M) class, and 71% are falling behind in the carbon scenario. Residential buildings are less impactful, since all the residential buildings fall in the (VL, L, M) class with 0 buildings in the VL class, eight buildings in the L class, and one building in the M class. In the third scenario, 67% of residential buildings are better performers, and 33% have a considerable impact on the carbon scenario. In the energy preference scenario, two buildings are noted to have VH, which are an operational building and an academic building. These two buildings have high EUI, where O1 monthly average EUI is 77.17 kWh/m 2 and A11 reports 44.85 kWh/m 2 . Building A11 is reporting a VH class in both scenarios, which means this building is among the least performers in terms of energy and carbon scenarios.
This paper shows that heating requirements may be the main contributor to the energy and carbon impacts. Addressing these high-intensity areas in the buildings is a challenge for universities seeking to minimize their impact on the environment. Finally, this paper illustrated a proposal to the calculation method, based on system dynamic modeling of water-energy-carbon nexus and the carbon sequestration in HEIs. It also showed that, due to the intensive nature of academic buildings, biological sequestration may not be a viable option for universities to pursue-especially in regions where water resources are heavily dependent on fossil fuels.     Figure A2. Heating degree days and cooling degree days.         Scenario S4, S6, S8, S10, S12, S14, S16, S18, S20 Energy Preference Weight  Figure A6. Normalized water box-plot for any building. Figure A6. Normalized water box-plot for any building.   Figure A7. EUI results. Figure A8. EUI results. Table A10. Conditional distribution by class.