UBC Undergraduate Research

Roof Solar Potential at UBC : Assessing Suitability of Campus’ Building Roofs for Solar Energy Capture Nicoletti, Leonardo 2018-06-20

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UBC Social Ecological Economic Development Studies (SEEDS) Sustainability Program  Student Research Report          Roof Solar Potential at UBC: Assessing Suitability of Campus’ Building Roofs  for Solar Energy Capture Leonardo Nicoletti University of British Columbia UFOR 401 Energy, Buildings, Climate June 20, 2018      Disclaimer: “UBC SEEDS Sustainability Program provides students with the opportunity to share the findings of their studies, as well as their opinions, conclusions and recommendations with the UBC community. The reader should bear in mind that this is a student research project/report and is not an official document of UBC. Furthermore, readers should bear in mind that these reports may not reflect the current status of activities at UBC. We urge you to contact the research persons mentioned in a report or the SEEDS Sustainability Program representative about the current status of the subject matter of a project/report”. ROOF SOLAR POTENTIAL AT UBCAssessing Suitability of Campus’ Building Roofs for Solar Energy CaptureLeonardo NicolettiInformation has been redacted from this report to protect personal privacy. If you require further information, you can make an FOI request to the Office of University Council. Table of Contents1. Executive Summary2. Context3. Methodology3.1. Roof Suitability Analysis3.2. Solar Suitability Study4. Results5. Discussion and Recommendations6. Appendix 1: Area Solar Radiation Tool7. Appendix 2: Yearly Solar Radiation Statistics and Solar Suitability Index for UBC Buildings Rooftops8. Bibliography1. Executive SummaryWhen implemented in the right location, solar energy provides many benefits. UBC, Vancouver campus, has extensive roof area that could be used for implementation of solar energy facilities such as Photovoltaic solar arrays. However, whether it is beneficial to implement these facilities depends on a variety of influencing factors. This study provides an assessment of UBC campus and its spatial, architectural, and geographical attributes to determine the suitability of UBC rooftops for implementation of solar energy capture facilities. The first part of this study, the roof suitability study, provides a brief analysis of suitability of UBC roofs for PV solar arrays by taking into consideration the urban form of UBC campus only. The second part of the study, the solar suitability study, consists of a simulation of the sun’s behavior over UBC in generally clear sky conditions, calculating solar radiation for each m2 of campus area for the year of 2018. UBC’s urban form, its geographical location and geoclimatic zone, atmospheric conditions, and monthly changes in the sun’s behavior are taken into consideration. Solar radiation maps are provided as well as estimates of total yearly solar radiation that could potentially be captured by UBC’s roof area. Finally, the study provides a solar suitability in-dex, ranking all 537 UBC roofs from most suitable for solar energy facilities to least suitable for solar energy facilities.2. ContextIn recent years, UBC has made significant efforts to meet sustainability standards. This is reflected by several of UBC’s campus policies and guidelines such as the Energy Management Plan, the Green Building Plan (anticipated to be com-pleted in Fall 2018), and Climate Action Plan (UBC Campus + Community Planning, 2010). In 2010, UBC identified clear targets for its emission reductions: 67% emission reductions by 2020, and 100% reductions by 2050 (UBC Campus + Community Planning, 2010).  In order to meet these targets UBC campus will have to implement more environmental-ly-friendly, low-emissions technologies to source its energy and fuel its vibrant student life. One type of renewable en-ergy source that UBC has yet to implement at a larger scale are photovoltaic (PV) solar panel arrays. Implementation of solar power on UBC campus is attractive for two reasons: cost of solar energy is decreasing fast; solar energy provides long-term pay off and requires little maintenance (International Energy Agency, 2017). The purpose of this project is to evaluate the technical potential of solar energy on UBC campus, given the total available rooftop area. In this context, the study aims at providing a better understanding of which rooftop areas are most relevant and suitable for imple-mentation of PV solar panel arrays; and an estimate of how much energy can be captured by those areas. 3. MethodologyThe study consisted of a spatial analysis of UBC Campus focusing on how urban form, geographical location, and atmospheric conditions affect solar potential. It was done in two parts: a roof suitability analysis, and a solar suitability study. In this study, LiDAR point cloud datasets of UBC campus for 2015, and a shapefile of UBC’s building footprints from 2015 were used. These datasets are described in Table 1.Table 1. Data used for study of solar potentialData SourceUBC LiDAR datasets for 2015http://dvn.library.ubc.ca.ezproxy.library.ubc.caUBC building footprints shapefilehttp://dvn.library.ubc.ca.ezproxy.library.ubc.ca3.1. Roof Suitability AnalysisA number of PV Solar Panel requirements were taken into consideration. • First, suitable roof surfaces must be at an angle that is between 0° and 49°, the latter being equal to the lati-tude of Vancouver’s geographical location (49.2827° N) (Brakels, 2018).• Second, suitable roof surfaces must not be North facing, and South facing surfaces must be considered opti-mal. Though less relevant, East and West facing surfaces must be considered as well (EnergySage, 2018).• Third, suitable roof surfaces must be at least 100m2. This zone represents the area required for a 10kW solarPV system, which is the average minimum installed capacity for commercial buildings (Hong et al., 2016; Hois,2013, SunergySystems, 2018).These requirements were used for the roof suitability analysis, the first phase in evaluating technical potential of solar energy on UBC campus. This was an initial sweep intended at providing a general idea of solar suitability at UBC con-sidering building form only. Using ESRI’s ArcMap’s model builder and a Digital Surface Model (DSM), created from the LiDAR datasets, slope and aspect raster datasets were derived. These were computed using the “Slope” (Data management toolbox), and “Aspect” (Data management toolbox) tools. Using the “Reclassify” tool and “Raster Calculator” tool, all south, east and west facing surfaces were extracted and ranked. South facing surfaces were ranked as class 1, and East/West facing surfaces as class 2. Similarly, all the surfaces falling between 0° and 50° angles, were extracted and ranked. Surfaces at angles between 25° and 50° were ranked as class 1 and lower angles as class two. Apart the efficiency decrease mentioned above, another reason why flat and low angle roofs were ranked as class 2 is that although PV solar panels can be mounted on tilted frames on flat roofs, this solution has downsides. Mainly, costs increase by around 200$ to 300$ per system, and fewer panels can be fitted on roof space if they are tilted. This is because they have to be mounted with more space between panels, in order to avoid one row casting a shadow on the row below it (Brakels 2018; Ibrahim, 2015).From the buildings footprints shapefile, all roof areas greater or equal to 100m2 were extracted. Finally, using the “Ras-ter Calculator” tool, ranked aspect, ranked slope, and minimum required roof areas were combined together to create a final roof solar potential suitability map (Figure 1).Figure 1. Aspect Classification, Slope Classification, and Roof Selection.3.2. Solar Suitability Study The second part of the analysis, the Solar Suitability Study, was intended at providing a much more extensive analysis of solar energy potential on campus. It consisted of simulating the trajectory of the sun over UBC campus for each month of the year (Figure 6). This was done using the “Area Solar Radiation” tool in ArcMap. For a given day of the year and hourly interval, and with the Digital Surface Model (DSM) as an input, “Global Radiation” (a combination of direct, diffuse, and global insolation) is calculated in Wh/m2, across the UBC campus geographical area. This tool uses Meth-ods from the hemispherical viewshed algorithm developed by Rich et al. (1994), and returns “global radiation” as the total amount of radiation calculated for a specific geographical area. “Global radiation (Globaltot) is calculated as the sum of direct (Dirtot) and diffuse (Diftot) radiation of all sun map and sky map sectors, respectively:Globaltot = Dirtot + DiftotSee appendix 1 for a detailed description of the “Area solar radiation” tool. “Area solar radiation” has been widely used to calculate solar energy in a number of instances. For example, the “Min-• =• / =• =• ˚ ˚=• ˚ ˚=• =0 0.51 1.50.25Kmnesota Solar Suitability Analysis” was an ambitious project completed by students at University of Minnesota in which the entire state of Minnesota was mapped for solar suitability using the “area solar radiation” tool in ArcGIS (University of Minnesota, 2010). At UBC, former PhD student Rory Tooke used this tool to map solar suitability for the Metro Van-couver area, and created the online interactive map “Community Energy Explorer” (CALP, 2010). For estimating solar potential on UBC campus, the “area solar radiation” tool was run for the 15th of each month of 2018 at 1 hour intervals, during the interval representing hours of sunlight for each of those days. These intervals were taken from timeanddate.com predictions (TimeAndDate, 2018) and can be viewed in Table 2. For each of those inter-vals, global solar radiation in Wh/m2 was obtained for each hour of sunlight as a raster. Next, using the “raster calcu-lator” tool, each of those rasters representing 1 hour worth of solar radiation were added together to calculate daily solar irradiance in Wh/m2 as a raster layer. This process was repeated for the 15th of each month. Finally, each 15th day raster layer was multiplied by the number of day in each given month using the “raster calculator” to estimate monthly solar irradiance as a raster dataset. All raster datasets representing a month’s worth of solar radiation were then added together using “raster calculator” to obtain a final raster representing yearly solar irradiance in Wh/m2 (Figure 2). These values were divided by 1000 to convert them into kWh/m2.Table 2. Sunlight intervals used for each day, from timeanddate.com (TimeAndDate, 2018).Below are the equations used for calculation of solar radiation. For each month:SolarDaily = ∑ solar radiation1st hour of sunlight, n hour of sunlightWhere n = # of hours of sunlightSolarMonthly = SolarDaily  * (# of days/month)For estimation of yearly solar radiation:SolarYearly = ∑ SolarMonthly (january, december)Where solar radiation is measured in Wh/m2.Using the “raster calculator” tool, the yearly solar radiation raster was multiplied by the UBC roofs layer. This allowed to quantify solar radiation for UBC roofs at a yearly scale (Figure 7). The “Zonal statistics as table” tool was used to calcu-late the total potential amount of solar radiation reaching UBC roofs yearly. Considering average efficiency of 15% for PV solar cells (Green et al., 2011; Solar by Empire, 2018; Murmson, 2017), the potential total amount of primary energy was multiplied by 0.15 to estimate the potential total amount of secondary energy convertable by PV solar cells from UBC roofs. Finally, this number was converted to GJ using the kWh to GJ conversion factor of 0.0036 as shown below: 1 kWh = 0.0036 GJAdditionally, the “Zonal Statistics as Table” tool was used to combine building data from the UBC buildings footprints shapefile and solar radiation data from the yearly solar radiation raster. This process allowed to generate a variety of solar radiation statistics (min; max; mean; range; standard deviation; sum) for each UBC building. Using the “table to excel” tool, these statistics were exported to Microsoft Excel format and were used to calculate the potential total amount of primary energy reaching UBC roofs.  In Excel, a Suitability Index was created by assigning a suitability rating to each building between 0 and 1. This rating was calculated by the following equation:Suitability = (Yi - Ymin)/(Ymax - Ymin) * (Xi - Xmin)/(Xmax - Xmin)Where:• Y — Roof area in m2• X — Average solar radiation in kWh/m2• i — A given UBC buildingFigure 2. Solar simulation mapping workflow.4. Results Figure 3 illustrates the result of the roof suitability analysis. As observed, several roofs seem to be suitable for solar energy in terms of their aspect, slope and size. Out of 642,211 m2 of roof area, 47% meets the slope, size, and aspect suitability requirements described in “Section 1: Methodology” (Figure 3). January 2018December 2018Yearly Solar Radiation (kWh/m2)High : 1134.03Low : 0.0316493Figure 3. Roof Suitability Map.Total yearly solar radiation for UBC and UBC roofs in kWh/m2 can be observed in Figure 4. For UBC’s total roof area of 642,211 m2, the total yearly solar radiation potential, in generally clear sky conditions, is of 490,707,543 kWh. UBC’s total roof area receives on average 767 kWh/m2 of solar radiation yearly, with radiation values ranging from 0.03 kWh/m2 to 1134 kWh/m2. Monthly averages in solar radiation greatly vary between seasons, with highest monthly average in June of 132 kWh/m2 and lowest monthly average in December of 5.5 kWh/m2.Suitability ClassesNot SuitableVery SuitableSuitableSomewhat Suitable0 0.5 1 1.50.25KmFigure 4. UBC Yearly Solar Radiation (left), UBC Roof Yearly Solar Radiation (right) Maps.Zonal statistics performed on yearly solar radiation at UBC revealed results indicative of solar potential for each indi-vidual building. Of UBC’s 537 buildings, the 20 buildings with highest yearly total solar radiation potential (kWh) are shown in Figure 5. Among those, the Forest Sciences Center has the potential of receiving 6.8 Million kWh worth of solar radiation yearly, and the Doug Mitchell Thunderbird Sport Center has the potential of receiving 12.2 Million kWh worth of solar radiation yearly. While these buildings’ rooftops receive very high amounts of solar radiation, installing PV cells on them is not necessarily the most efficient solution. This is because they may have a large roof surface area but a low solar energy to roof area ratio (kWh/m2). For example, “Hampton Place Lot 3 - Thames Court” has the poten-tial of receiving 3.8 Million kWh worth of solar radiation yearly. However, on average, “Hampton Place Lot 3 - Thames Court” only receives 710 kWh of solar radiation per m2. This indicates that a portion of the roof area on “Hampton Place Lot 3 - Thames Court” is likely characterized by less optimal conditions for solar radiation collection.Figure 5. Top 20 Buildings with Highest Yearly Total Solar Radiation Potential (kWh).Yearly Solar Radiation (kWh/m2)High : 1134.03Low : 0.031649302,000,0004,000,0006,000,0008,000,00010,000,00012,000,00014,000,000Roof Solar Radiation Potential (kWh)Top 20 Buildings with Highest Total Yearly Solar Radiation (kWh)Figure 6. Top 20 Buildings with Highest Yearly Total Solar Radiation Potential (kWh).In this light, Figure 6 illustrates the 20 buildings with highest ratio of solar radiation per roof area (kWh/m2) at UBC (Figure 6). Among these buildings, the “Robert F. Osborne Centre - Unit 1” building has the potential of receiving 2.3 Million kWh worth of solar radiation at 942 kWh/m2. While these buildings may have very high ratio of solar radiation per roof area (kWh/m2), the installation of PV solar arrays on them is not necessarily the most impactful solution either. In fact, kWh of solar radiation per m2 is not the sole indicator of solar energy potential. If a roof has a high kWh of solar radiation per m2 but a small surface area, installation of PV solar arrays may not translate into significant energy pro-duction.Figure 7. Average Solar Radiation (kWh/m2) and Roof Area (m2)The distribution of roof sizes (m2) and solar radiation per roof area (kWh/m2) is illustrated in Figure 7. As depicted in Figure 7, UBC has a large quantity of small roofs that are intervariable in kWh of solar radiation per m2 potential. Figure 7 also indicates that UBC has a significant quantity of medium sized roofs with a generally high potential of kWh of solar radiation per m2. Lastly, Figure 7 illustrates that UBC has a small amount of very large roofs with high potential of solar radiation per roof area (kWh/m2). Roofs located within the upper right quadrant of Figure 7 are the most ideal roofs for implementation of PV solar arrays, for they would allow the harnessing of maximum solar energy with highest efficiency. Conversely, roofs located within the lower left quadrant of Figure 7 are the least ideal roofs for 01002003004005006007008009001,000010020030040050060070080090010000 2000 4000 6000 8000 10000 12000 14000 16000kWh/m2Roof AreaAverage Solar Radiation (kWh/m2) and Roof Area (m2)870880890900910920930940950Solar radiation per roof area (kWh/m2)Top 20 Buildings with Highest Ratio of Solar Radiation per Roof Area (kWh/m2)implementation of PV solar arrays, for they would allow the harnessing of minimal amounts of solar energy with low efficiency.As both roof area (m2) and solar radiation per roof area (kWh/m2)) must be high for good suitability, the solar suitability index combines both these parameters for each roof, and ranks all UBC roofs from most suitable to least suitable for solar energy capture. The 40 most suitable buildings for solar energy capture can be observed in Figure 8 (see Appen-dix 2 for the entire suitability index). Together, rooftops for those 40 buildings account for 37% of all solar radiation reaching UBC roofs (Table 10). The top 5 buildings that scored the highest on the solar suitability index are the Doug Mitchell Thunderbird Sports Centre, the Thunderbird Parkade, the TRIUMF - Accelerator and Experimental Building, the Life Sciences Centre, and the Forest Science Center (Figure 8). Please see Figure 9 for a 1:800 solar map of each of these buildings, and Table 10 for a summary of the results from this study.Figure 8. Top 40 Buildings with Highest Suitability for Solar Energy Capture0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Suitability RatingTop 40 Buildings with Highest Suitability for Solar Energy CaptureFigure 9. Top 5 Buildings with Highest Suitability for Solar Energy CaptureThunderbird Parkade Life Sciences CenterDoug Mitchell Thunderbird Sports CentreTRIUMF - Accelerator and Experimental BuildingForest Sciences CenterYearly Solar Radiation (kWh/m2)High : 1134.03Low : 0.0316493Building footprintTable 10. Results Summary (Yearly)5. Discussion and RecommendationsAs reported on the “UBC Vancouver Campus – 2016 Greenhouse Gas Emissions Inventory”, UBC is emitting about 40,536 tCO2e of greenhouse gas (GHG) emissions yearly and consuming 145,313,732 kWh of high voltage electricity purchased from BC hydro (University of British Columbia, 2016). As seen previously, the potential yearly total solar radiation reaching UBC roofs in generally clear sky conditions is 490,707,543 kWh (Figure 10). At 15% efficiency, UBC rooftops coupled with PV solar arrays have the potential of producing 73,606,131 kWh in electricity, which is slightly more than half the total consumption of electricity at UBC. Thus, solar energy could be used to replace a significant portion of purchased electricity from BC hydro. However, while electricity savings would be substantial, carbon emis-sion reductions would be less important given the low emission factor of BC hydro electricity (BC Hydro, 2015; Univer-sity of British Columbia, 2016; Table 10). In this scenario, it would be difficult to make a convincing business case for switching to solar energy at UBC, for little money would be saved on offset costs.Instead, solar energy at UBC could be used to replace other types of energy consumption that account for more sub-stantial amounts of GHG emissions. More than half of UBC’s carbon emissions originate from the burning of natural gas dedicated to district energy usage (University of British Columbia, 2016). If electricity from solar energy could be used for solar water heating at the building level, high GHG emission reductions could result from district energy us-age (Table 10)(Solar Water Heaters, 2018). Converting potential energy produced from solar into GJ yields 264,982 GJ. This represents 62% of UBC’s current usage for district energy of 424,697 GJ, and a potential GHG emissions reduction of more than half the current levels (University of British Columbia, 2016; Table 10). Thus, it seems that the argument for solar energy at UBC rests upon the possibility of transitioning from other forms of energy consumption to solar produced electricity. Future research could look at the feasibility of such scenario, and the associated net benefits of a solar energy transition.While this study provides an appropriate assessment of atmospheric, geographic, spatial, and architectural character-istics that influence PV solar array implementation potential on UBC Vancouver campus, it does not consider a num-ber of elements which fall outside of the scope of this study. These include, but are not limited to, structural integrity, accessibility of roofs, presence of other mechanical equipment on roofs, and type of roof material. The suitability index provided in this study is intended to be used as a tool for identifying roofs that would be most suitable in terms of energy production and production efficiency from solar. Before starting a solar project, experts must further assess other roof conditions such as those suggested above. Regarding the data used for this study, one limitation must be highlighted. The most recently available LiDAR datasets were of 2015, which imposed some constraints on the study. Many buildings that were under construction in 2015 could not be included as part of the study, and technical poten-tial for solar energy on those buildings could not be estimated. In addition, the study assumes that no trees have been removed from UBC campus since 2015. If trees have been removed, the calculation of solar roof radiation and the results of the solar suitability analysis could be affected.If UBC wishes to implement PV solar arrays on select buildings, it is recommended to refer to the solar suitability index provided by this study (Appendix 2). Highly suitable buildings in this index have the potential to provide maximum returns in energy production and highest conversion efficiency from solar. Focusing on buildings with highest suitabil-ity ratings (see 40 buildings identified in Figure 8) for implementation of PV solar arrays would provide the maximum benefits in terms of solar energy efficiency.Finally, it is important to consider that the solar study was carried out simulating generally clear sky conditions. The main reason for this limitation was the timeframe provided to complete the study. Solar radiation values are thus likely to be most accurate for spring and summer months, and inflated for the winter and fall months. Given Vancouver’s typical overcast conditions in the winter, it is highly recommended that this study is repeated simulating realistic cloud cover in winter and fall months. This additional research would prove crucial and necessary to be combined with the results of this study. Such extension of this study would improve the utility of the solar suitability index for buildings on UBC campus.6. Appendix 1: Area Solar Radiation ToolThe solar radiation analysis tools calculate insolation across a landscape or for specific locations, based on methods from the hemispherical viewshed algorithm developed by Rich et al. (Rich 1990, Rich et al. 1994) and further devel-oped by Fu and Rich (2000, 2002).The total amount of radiation calculated for a particular location or area is given as global radiation. The calculation of direct, diffuse, and global insolation are repeated for each feature location or every location on the topographic surface, producing insolation maps for an entire geographic area.Solar radiation equationSGlobal radiation calculationGlobal radiation (Globaltot) is calculated as the sum of direct (Dirtot) and diffuse (Diftot) radiation of all sun map and sky map sectors, respectively.Globaltot = Dirtot + DiftotDirect solar radiationTotal direct insolation (Dirtot) for a given location is the sum of the direct insolation (Dirθ,α) from all sun map sectors: Dirtot = Σ Dirθ,α    (1)The direct insolation from the sun map sector (Dirθ,α) with a centroid at zenith angle (θ) and azimuth angle (α) is calcu-lated using the following equation:Dirθ,α = SConst * βm(θ) * SunDurθ,α * SunGapθ,α * cos(AngInθ,α)    (2)where:• SConst — The solar flux outside the atmosphere at the mean earth-sun distance, known as solar constant. The solarconstant used in the analysis is 1367 W/m2. This is consistent with the World Radiation Center (WRC) solar con-stant.• β — The transmissivity of the atmosphere (averaged over all wavelengths) for the shortest path (in the direction ofthe zenith).• m(θ) — The relative optical path length, measured as a proportion relative to the zenith path length (see equation3 below).• SunDurθ,α — The time duration represented by the sky sector. For most sectors, it is equal to the day interval (forexample, a month) multiplied by the hour interval (for example, a half hour). For partial sectors (near the horizon),the duration is calculated using spherical geometry.• SunGapθ,α — The gap fraction for the sun map sector.• AngInθ,α — The angle of incidence between the centroid of the sky sector and the axis normal to the surface (seeequation 4 below).Relative optical length, m(θ), is determined by the solar zenith angle and elevation above sea level. For zenith angles less than 80°, it can be calculated using the following equation:m(θ) = EXP(-0.000118 * Elev - 1.638*10-9 * Elev2) / cos(θ)    (3)where:• θ — The solar zenith angle.• Elev — The elevation above sea level in meters.The effect of surface orientation is taken into account by multiplying by the cosine of the angle of incidence. Angle of incidence (AngInSkyθ,α) between the intercepting surface and a given sky sector with a centroid at zenith angle and azimuth angle is calculated using the following equation: AngInθ,α = acos( Cos(θ) * Cos(Gz) + Sin(θ) * Sin(Gz) * Cos(α-Ga) )    (4)where:• Gz — The surface zenith angle.Note that for zenith angles greater than 80°, refraction is important.• Ga — The surface azimuth angle.Diffuse radiation calculationFor each sky sector, the diffuse radiation at its centroid (Dif ) is calculated, integrated over the time interval, and cor-rected by the gap fraction and angle of incidence using the following equation:Difθ,α = Rglb * Pdif * Dur * SkyGapθ,α * Weightθ,α * cos(AngInθ,α)    (5)where:• Rglb — The global normal radiation (see equation 6 below).• Pdif — The proportion of global normal radiation flux that is diffused. Typically it is approximately 0.2 for very clearsky conditions and 0.7 for very cloudy sky conditions.• Dur — The time interval for analysis.• SkyGapθ,α — The gap fraction (proportion of visible sky) for the sky sector.• Weightθ,α — The proportion of diffuse radiation originating in a given sky sector relative to all sectors (see equa-tions 7 and 8 below).• AngInθ,α — The angle of incidence between the centroid of the sky sector and the intercepting surface.The global normal radiation (Rglb) can be calculated by summing the direct radiation from every sector (including obstructed sectors) without correction for angle of incidence, then correcting for proportion of direct radiation, which equals 1-Pdif:Rglb = (SConst Σ(βm(θ))) / (1 - Pdif)    (6)For the uniform sky diffuse model, Weightθ,α is calculated as follows:Weightθ,α = (cosθ2- cosθ1) / Divazi    (7)where:• θ1 and θ2 — The bounding zenith angles of the sky sector.• Divazi — The number of azimuthal divisions in the sky map.For the standard overcast sky model, Weightθ,α is calculated as follows:Weightθ,α = (2cosθ2 + cos2θ2 - 2cosθ1 - cos2θ1) / 4 * Divazi    (8)Total diffuse solar radiation for the location (Diftot) is calculated as the sum of the diffuse solar radiation (Dif ) from all the sky map sectors:Diftot = Σ Difθ,α    (9)(ESRI, 2018).7. Appendix 2: Yearly Solar Radiation Statistics and Solar Suitability Index for UBC Buildings Rooftops8. BibliographyBC Hydro (2015). Greenhouse Gas Intensities. Retrieved from https://www.bchydro.com/content/dam/BCHydro/customer-portal/documents/corporate/environment-sustainability/environmental-reports/ghg-intensi-ties-2007-2015.pdfCollaborative for Advanced Landscape Planning - CALP (2010). Explore Community Energy. Retrieved from http://ener-gyexplorer.ca/Energy Sage (2018). What’s the best angle for my solar panels? Retrieved from https://www.energysage.com/so-lar/101/impact-of-roof-angle/ESRI (2018). Area Solar Radiation. ArcGIS Resources. Retrieved from http://resources.arcgis.com/en/help/main/10.1/index.html#/How_solar_radiation_is_calculated/009z000000tm000000/Fu, P. 2000. A Geometric Solar Radiation Model with Applications in Landscape Ecology. Ph.D. Thesis, Department of Geography, University of Kansas, Lawrence, Kansas, USA.Fu, P., and P. M. Rich. 2000. The Solar Analyst 1.0 Manual. Helios Environmental Modeling Institute (HEMI), USA.Fu, P., and P. M. Rich. 2002. “A Geometric Solar Radiation Model with Applications in Agriculture and Forestry.” Comput-ers and Electronics in Agriculture 37:25–35.Green, A., Emery, K., Hishikawa,. Y., Warta, W. (2011). Solar cell efficiency tables (version 37). Progress in Photovoltaics. Retrieved from <https://onlinelibrary.wiley.com/doi/full/10.1002/pip.1088> Hong, T., Minhyun, L., Choongwan, K., Jimin, K., Kwangbok, J. (2016). Estimation of the Available Rooftop Area for Installing the Rooftop Solar Photovoltaic (PV) System by Analyzing the Building Shadow Using Hillshade Analysis. Energy Procedia. Retrieved from https://www.sciencedirect.com/scienceHois, E. (2013). Selecting the Size of Your Solar PV System. Solar Reviews. Retrieved from https://www.solarreviews.com/news/selecting-the-size-of-your-solar-pv-system/Ibrahim, A. (2011). Effect of Shadow and Dust on the Performance of Silicon Solar Cell. Journal of Basic and Applied Scientific Research. Retrieved from https://www.researchgate.net/publication/267971484International Energy Agency. Solar leads the charge in another record year for renewables. Retrieved April 1, 2018, from https://www.iea.org/publications/renewables2017/ Murmson, S. (2017). The Average Photovoltaic System Efficiency. Sciencing. Retrieved from https://sciencing.com/aver-age-photovoltaic-system-efficiency-7092.htmlRich, P. M., R. Dubayah, W. A. Hetrick, and S. C. Saving. 1994. “Using Viewshed Models to Calculate Intercepted Solar Radiation: Applications in Ecology. American Society for Photogrammetry and Remote Sensing Technical Papers, 524–529.Rich, P. M., and P. Fu. 2000. “Topoclimatic Habitat Models.” Proceedings of the Fourth International Conference on Inte-grating GIS and Environmental Modeling.Solar by Empire (2018). Is Solar Power Worth the Investment? Retrieved from http://solarbyempire.com/why-solar/so-lar-panel-efficiencySunergy Systems (2018). Commercial Solar FAQ. Retrieved from https://www.sunergysystems.com/commercial-solar/faqTimeAndDate (2018). Vancouver, British Columbia, 2018. Retrieved from https://www.timeanddate.com/sun/canada/vancouverUBC Campus + Community Planning (March, 2010). UBC Vancouver Campus Climate Action Plan.University of Minnesota (2017 FIND). Minnesota Solar Suitability Analysis. Retrieved from http://solar.maps.umn.edu/app/?lat=46.62125618098712&long=-94.01071581249535University of British Columbia (2016). UBC Vancouver Campus – 2016 Greenhouse Gas Emissions Inventory. Retrieved from https://sustain.ubc.ca/sites/sustain.ubc.ca/files/uploads/CampusSustainability/CS_PDFs/ClimateEner-gy/UBCGHGInventory_2016.pdf(2018). Solar Water Heaters. Energy. Retrieved from https://www.energy.gov/energysaver/water-heating/solar-wa-ter-heater

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