Evaluation of current and future hourly weather data intended for building designs: A Philadelphia case study

Energy & Buildings 199 (2019) 491–511

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Evaluation of current and future hourly weather data intended for building designs: A Philadelphia case study Hamed Yassaghi, Nariman Mostafavi, Simi Hoque∗ Department of Civil, Architectural, & Environmental Engineering, Drexel University, 3141 Chestnut Street, 251 Curtis Hall, Philadelphia, PA 19104, United States

a r t i c l e

i n f o

Article history: Received 19 February 2019 Revised 1 July 2019 Accepted 8 July 2019 Available online 10 July 2019 Keywords: Global warming Current and future weather files Correlation Weather parameters uncertainties

a b s t r a c t Global warming presents a critical grand challenge for 21st-century building design and operation. Today’s buildings are designed using reference year databases that represent past weather observations and do not account for future weather scenarios predicated on global and regional climate models. But these models lack the required spatial and temporal resolution to be utilized in dynamic building simulation tools. The present article reviews methods for generating current, as well as future weather files used in dynamic building simulation tools for the City of Philadelphia. Our findings suggest that current TMY files are not suitable to capture predicted trends of global warming. Running a statistical t-test revealed a tendency to underestimate key parameters such as dry bulb temperature of the weather files. A comparison between outputs of four different weather tools in generating future weather data indicates significant variance in predicting the dry bulb temperature range, and an overall increase in extreme and mean figures. The variations among the generators in predicting global horizontal irradiation and wind speed are small. However, the diffuse normal irradiation increases in all predictions through future time slices. A correlation analysis is conducted on the outputs of each weather generator in order to investigate bivariate correlations for both current and future weather data. The discrepancies and uncertainties among the weather files are identified and a process for addressing uncertainties is outlined. This investigation is intended to guide the development of weather data sets for building design, also address challenges regarding the generation and use of current and future weather data sets. © 2019 Published by Elsevier B.V.

1. Introduction The increasing surface, oceanic and atmospheric temperatures, as well as rising sea levels and melting glaciers, are indicators that the global climate is warming. Although changes might differ from one decade to another, surface temperatures have been on the rise since 1900 [4]. Global warming is primarily caused by increased Greenhouse Gas (GHG) emissions due to burning fossil fuels. Buildings, as major consumers of fossil fuel energy, contribute substantially to global warming. Given their lifespan, anticipating building performance under present and future climate conditions is essential [2,58]. Many simulation tools exist to analyze building energy performance, and they depend on input data such as weather files [42]. Average historical weather data, known as Typical Year (TY) files, are commonly used in building energy assessment tools. TY data is based on historical observations that are concatenated by month to best represent an average year of past weather trends

∗

Corresponding author. E-mail addresses: [email protected] (H. Yassaghi), [email protected] (N. Mostafavi), [email protected] (S. Hoque). https://doi.org/10.1016/j.enbuild.2019.07.016 0378-7788/© 2019 Published by Elsevier B.V.

[19]. The most common TYs used in North America are Example Weather Year (EWY), Typical Meteorological Year (TMY), Test Reference Year (TRY), Design Reference Year (DRY), Weather Year for Energy Calculations (WYEC) and Design Summer Year (DSY). Each TY uses a specific criterion in the selection of months, and their common purpose is to create a whole year that would best resemble past weather observations. However, TY data does not represent future weather conditions, and given the current trend of global warming, it is possible that the use of TY files in building energy assessments is no longer appropriate. Therefore, using weather data that considers future climate predictions for building energy assessment is necessary. The first step for climate prediction is defining future scenarios. Scenarios are information used to understand the future climate and its uncertainties [38]. The Intergovernmental Panel on Climate Change (IPCC) presents several climate emissions scenarios based on carbon emission trends [33]. Previous IPCC scenarios are the 1990 IPCC Scenario A in the First Assessment Report, the 1992 IPCC Scenarios in the Third Assessment Report (TAR) and the Special Report on Emissions Scenarios (SRES) in the Fourth Assessment Report (AR4). Fig. 1 shows a summary of the SRES scenarios. The A scenarios reflect a more economical future where there is less attention to the environment.

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H. Yassaghi, N. Mostafavi and S. Hoque / Energy & Buildings 199 (2019) 491–511 Table 1 Projected change in global mean surface temperature [33]. 2046–2065

Mean Surface Temperature Change (°C)

2081–2100

Scenario

Mean

Likely Range

Mean

Likely Range

RCP2.6 RCP4.5 RCP6.0 RCP8.5

1 1.4 1.3 2.0

0.4–1.6 0.9–2.0 0.8–1.8 1.4–2.6

1.0 1.8 2.2 3.7

0.3–1.7 1.1–2.6 1.4–3.1 2.6–4.8

Note: Numbers after the letters RCP present the radiative forcing in W/m2 in the year 2100 [33].

Fig. 1. IPCC fourth assessment report scenarios summary (adapted from IPCC 2007 [3]).

Fig. 2. Yearly mean temperatures for different GHG emissions scenarios [53].

The B scenarios refer to a safe environmental future. The number 1 is for a global scale and number 2 for a regional level [33]. The A1 scenario has three categories, which are based on the type of technologies used in the future. A1FI focuses on the use of fossil fuels. A1T represents a non-fossil fuel energy source future. And A1B is a balance across the sources. Fig. 2 shows the trends of the different emissions scenarios, projected to 2100. The reason why they are called projections is because no one method can predict the future climate and each presents a snapshot of what the future might look like, depending on the present conditions and possible changes in human behavior towards the environment. As Fig. 2 indicates, the differences between most emissions scenarios and the climate conditions are not expected to be significant prior to 2040, due to the inertia of the climate and the ∼100year lifespan of CO2 emissions. In other words, the effect of past and present CO2 emissions will become noticable, starting around 2040 [56]. In the last IPCC report (AR5) [54], four different scenarios called the Representative Concentration Pathways (RCPs), were introduced, for which Table 1 shows the global range and mean surface temperature. RCPs are scenarios with time series of emissions and concentration, representing four future possibilities that would yield the

radiative forcing specified (i.e. RCP2.6, RCP 4.5, RCP6.0 and RCP 8.5) [55]. Radiative forcing is the total change in downward radiation flux (in units of W/m2 ) in the atmosphere due to climate change drivers (such as CO2 concentration) (IPCC). Scenarios are used as input for General Circulation Models (GCMs) and Regional Circulation Models (RCMs), which facilitate understanding of climate behavior and forecast change [31]. GCMs simulate the evolution of the earth’s climate system over time and describe how components (such as atmosphere, ocean and land surface) interact with each other to create climate variability. They are too large in scale to be projected for local locations and the outputs are daily or monthly averages of meteorological parameters at different altitudes [1]. The RCM provides a more detailed vision of climate change. There are two main ways to produce a more detailed image of the climate as a result of the GCMs and RCMs. One is integrating the results from the GCMs or RCMs into weather generators, and the other is using statistical methods to downscale the results of the models [5,31]. In the following section, we present a review of the research on future weather files that are suitable for use in the majority of building simulation tools. There exists a rich body of research on methods to predict the built environment’s performance under future climate. Eames et al. [14,15] proposed probabilistic future weather years from the UK Climate Projections (UKCP09). They compared future weather data based on UKCIP02 and the morphing procedure with results from a weather generator developed by the University of Newcastle for three locations in the UK. Chan [7] merged GCM outputs of projected monthly parameters under two emissions scenarios for three periods into a TMY weather file using the morphing procedure. Jentsch et al. [35] compared future weather data produced using the RCM and morphed data from the GCM and applied them to a naturally ventilated building in the UK. They concluded that until the RCM becomes thoroughly available for all regions, the morphed procedure can be reliable for building energy performance assessment purposes. Kikumoto et al. [37] physically downscaled the results from the GCM using the Model for Interdisciplinary Research on Climate (MIROC) and the Weather Research and Forecasting (WRF) to predict future local climate. Chen et al. [8] studied the climate variables that influence building space heating and cooling energy consumption. Zhu et al. [60] presented an alternative method to create future weather data based on long-term regional data and short-term observations to predict mean monthly temperatures. To produce hourly weather data, a morphing procedure was applied to the model. Rastogi and Andersen [47,48] developed a new weather generator that produces synthetic weather time series for any location worldwide based on the IPCC AR5. Their weather generator produces hourly weather files containing temperature, humidity, solar radiation and wind speed. Watkins et al. [57] proposed a new DRY as a substitute for DSY that could suitably account for extreme weather conditions for both summer and winter. Chow and Levermore [10] presented a new algorithm for hourly temperature data for the UK called the Quarter Sin Method, which uses daily maximum and minimum and average temperatures to produce future hourly typical weather data. Their method downscales daily values to create hourly data

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that then can be applied to building energy simulation tools. Guan [24] reviewed methods to create future hourly weather data for the built environment, showing a sinusoidal and exponential variation for daytime and night-time temperature respectively. Bueno et al. [6] presented a MATLAB-based simulator to estimate hourly urban air temperature and humidity using data from local weather stations. Dickinson and Brannon [13] introduced a new weather generator which produces TMY files projected to several future time slices for two IPCC AR5 emissions scenarios to be used in building simulation tools. The next section focuses on different approaches used by weather generators to create future weather files based on GCM or RCM projections that are applicable to building simulation tools. The paper continues by showing the differences between the outputs of the generators. A correlation analysis is then conducted to analyze the bivariate correlations among the weather variables produced by the generators. Finally, an uncertainty analysis shows how the uncertainties are partitioned from the results of the downscaling tools. 2. Weather files and methods of generation The main weather variables influencing building energy performance are dry bulb temperature, wet bulb temperature/relative humidity, solar radiation and wind speed/direction. As described above, several methods and tools exist to generate the weather parameters needed for future building energy assessments. The focus of this paper is to investigate weather generators, which use variables with properties similar to historical observations and can simulate meteorological variables for different future time scales. Three widely used weather generators capable of providing sufficient temporal resolution required for dynamic building simulations are analysed. 2.1. The Advanced WEather GENerator The University of Michigan developed the Advanced WEather GENerator (AWE-GEN) that can produce hourly weather data [34,17]. This MATLAB-based tool can produce characteristics of meteorological parameters with low and high-frequency based upon observed climate patterns. The generator uses data from 10 airport meteorological stations in the USA obtained from Webmet meteorological resources center for Tucson, Muskegon, Albuquerque, Boston, Nashville, San Francisco, Chicago, Miami, Philadelphia and Atlanta and one station in Italy [18]. For Philadelphia, meteorological time series for the period of 1961–88 were used. AWE-GEN uses a stochastic downscaling procedure that derives distributions of factors of change for several climate statistics from outputs of the GCMs. It is an open-access program and output results provided by the AWE-GEN are .mat files containing variables such as precipitation, cloud cover, air temperature, global solar radiation, diffuse solar radiation, direct solar radiation, relative humidity, wind speed and atmospheric pressure. However, these outputs cannot be used directly in building energy tools and need to be converted to TMY files. AWE-GEN was used in this paper to produce climate data for Philadelphia, without considering emissions scenarios. 2.2. The CCWorldWeatherGen The CCWorldWeatherGen [35] is a Microsoft Excel-based weather generator developed by the University of Southampton that adapts the “morphing” technique presented by Belcher et al. [1]. Morphed weather data are constructed by “shifting” and “stretching” historical data using climate change projection factors. Shifting is a process in which the monthly averages of the weather variable are shifted with the variance remaining the same, where

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stretching (also known as fractional change or change in skewness) is the opposite and the variance of the variable changes while the average remains the same. When temperature is transformed, not only the mean is shifted, but also its diurnal changes are stretched and therefore a combination of shifting and stretching is applied. CCWorldWeatherGen uses the Hadley Center Coupled Model Version 3 (HadCM3) of the Atmospheric-Ocean GCMs datasets. Combining the HadCM3 model with the CCWorldWeatherGen allows the generation of future weather files that capture average weather conditions of climate scenarios while preserving realistic weather sequences for any location around the world. Climate scenarios are representatives of future climate conditions [41]. This tool transforms present day TMY2 or EnergyPlus Weather (EPW) format weather files into future projected weather files and can be directly used as input for most building energy performance tools. TMY files use data from 1952 to 1975, TMY2 files use data from 1961 to 1990, and TMY3 files use data from 1991 to 2005. In this paper, CCWorldWeatherGen was used to morph two sets of typical weather data obtained from the National Renewable Energy Laboratory (NREL), TMY and TMY3 weather files using the IPCC SRES A2 scenario for Philadelphia.

2.3. Meteonorm Meteonorm is a weather generator that generates typical weather files for two periods, 1981–90 and 1991–2010 worldwide [39]. It not only contains a climate data base, but is also a spatial interpolation tool with the capability of generating stochastic weather data. Meteonorm obtains its data from Global Energy Balance Archive (GEBA) for global radiation and World Meteorological Organization (WMO) and National Climate Data Center (NCDC) for all other meteorological parameters [49]. In addition, it uses three emissions scenarios (A1B, B1 and A2) from the IPCC fourth assessment report and produces outputs in various formats (i.e., TMY and EPW) for nine future time slices (from 2020 to 2100). It uses an average of all 18 climate models in the IPCC AR4, and with a combination of its data base, interpolation algorithms and the stochastic generation, typical future years are produced. The outputs of the software contain essential weather parameters for building energy performance calculations and creating of TMY files such as air temperature, humidity, precipitation, wind speed, wind direction and solar radiation. Meteonorm uses stochastic weather generators to create the scenarios and requires large datasets to train the model. In cases where the weather station lacks sufficient weather information, the software interpolates from nearby weather stations data. Fig. 3 shows the results produced by the generators, the AWE-GEN, the CCWorldWeatherGen following A2 scenario projecting a TMY3 file, and Meteonorm following A2 scenario in three time slices, 2020, 2050 and 2080 and for the months July and January and the annual values as average hourly values for Philadelphia. The vertical axis shows the temperature in °C and the horizontal axis indicates the time in hours. For all three cases and for all time slices, the AWE-GEN shows lower trends compared to others. This is mostly due to the nature of the generation used in this study which does not account for emissions scenarios. The morphed TMY3 shows higher values for July and for the annual trend shows close values to the data projected using Meteonorm. The Meteonorm shows an increase between 2020 and 2080 and both summer maximum and winters minimum figures increase. In addition, Meteonorm and the morphed TMY3 file show close high values for the annual results. Fig. 4 shows the mean, maximum and minimum temperature parameters for the three weather generators for three time slices. In Fig. 4(a), the temperature mean does not change significantly for the three time periods. The year 2080 shows the highest max

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Fig. 3. Results from Meteonorm using A2 scenario for three time scales for Philadelphia.

Fig. 4. Comparison between temperature parameters from the outputs of three weather generators projected to three future time slices. (a) AWE-GEN, (b) CCWorldWeatherGen, (d) Meteonorm.

and lowest min, which suggests extreme weather conditions for summer and winter. For every time slice, the morphed TMY3 file (Fig. 4(b)) shows higher mean and more extreme (cooler) minimum temperature compared to morphed TMY, but with lower maximum temperatures. The morphed TMY3 weather files for each time period yields higher temperatures than morphed TMY files. This is mainly because it uses a more updated database compared to TMY files. The stochastic weather generators and the morphing process are both capable of providing examples of future typical conditions for the fine spatial and temporal resolution needed in building design.

However, neither are known to contain examples of most extreme conditions. A description of their limitations can be found in Herrera et al. [31]. In the next section a detailed examination of all the weather parameters as well as a correlation analysis is presented for both current and future weather files. 3. Comparing the results The weather generators above use mathematical models to simulate weather variables for different time scales. Since historical

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Fig. 5. Comparison of weather parameters for the existing weather TMY files.

observations provide limited information regarding climate change, weather generators rely on statistical projections based on historical data. The challenge is that not enough historical weather data are available. However, enough data can be produced to enable assessing the probability of occurrence of each variable in the future by “downscaling” [31]. Downscaling involves measuring the difference between the GCMs for present and future weather and interpolating present weather data at the location under study [36]. In this section, results of several existing TMY files and weather generators for future scenarios are compared. Dry bulb temperature (DBT), relative humidity (RH), wind speed/direction (WS, WD) and solar radiation are analyzed, possible extreme conditions are identified, and finally, a statistical t-test is conducted for DBT 3.1. Current weather files Fig. 5 compares the DBT, RH, WS, Global Horizontal Irradiation (GHI), Direct Normal Irradiation (DNI) and the Diffuse Horizontal Irradiation (DHI) for the existing weather files. GHI is the amount of radiation striking a horizontal surface, and DNI is the radiation hitting a perpendicular plate to the sun excluding diffuse radiation. For the existing climate conditions, the results of the National Solar Radiation Data Base (NSRDB) and the NCDC TMY files, Meteonorm files, the European Commission of Energy Efficient Research (ECEER) typical year file and a single year TMY3 file produced by the System Advisor Model (SAM) are presented and variations among different methods for all main parameters are discussed. The existing TMY files consist of NCDC TMY (using data from 1952 to 1975), NSRDB TMY2 (using data from 1961 to 1990) and NSRDB TMY3 (using data from 1961 to 1990 and 1991 to 2005). The Meteonorm TMY files use the period of 1991–2010 which is a more updated TMY compared to the NREL database and is referred to in Fig. 5 as “Met”. The ECEER TMY file uses the period of 2005–2014 which is the most updated TMY file compared to the other files. Data for the ECEER TMY are obtained from the Satellite

Application Facility on Climate Monitoring (CM SAF) for solar radiation and European Centre for Medium-Range Weather Forecasts (ECMWF) for all other data and are built on 10 years historical observations. The “2010” column represents the single year TMY files which are based on the SAM TMY files for the year 2010. The SAM tool provides TMY files which are derived from the same source as the NSRDB TMY 2 and TMY3 for locations in the USA As shown in Fig. 5, Meteonorm and ECEER files have higher mean values for DBT suggesting an increase in DBT. The mean DBTs of the weather files increase as they use updated historical data. In general, weather files with similar historical period could still show discrepancies due to the source of their data. For instance, historical observations recorded at the Franklin institute center [20] differ from the ones recorded by the Philadelphia International Airport (KPHL) [46]. Although the variations may be small, they stilladd to uncertainty in the data. Here we do not account for the different sources of the TMY data and the focus is on the period of the recorded data and the climate trends. The single year 2010 TMY file shows the second highest maximum and lowest minimum DBT. The opposite trend can be seen in RH with Meteonorm and ECEER having lower RH compared to other files. However, the RH for 2010 is inconsistent with the typical weather files, showing much higher values. In fact, the single year TMY file contains extreme data points for both DBT and RH, that are not reflected in other TMY files representing past weather observation. This can be explained by the process of the TMY file data selection which does not account for extreme conditions, and in cases where these conditions need to be considered, the use of an extreme meteorological year would be more favorable. Crawley & Lawrie [11] provide a detailed explanation of the applications of extreme year weather files. The TMY2 file which uses a period of 1961–90 for the selection of representative months shows the lowest mean temperature, most likely due to the lower mean temperature observed in that period compared to other files. Fig. 6 shows the annual mean temperature from 1874 to 2017 with a

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Fig. 6. Historical records of annual mean temperature for Philadelphia (Franklin Institute Weather Data [45]).

mean of 12.4 °C, 12.3 °C and 13.4 °C for the periods 1952–1975 (TMY), 1961–1990 (TMY2) and 1991–2005 (TMY3) respectively. The single year TMY file also shows the lowest mean WS, with the highest mean RH. The complete current and future datasets of WS are presented in Appendix A, generated by the climate consultant tool developed by the University of California, Los Angeles [40]. The wind speed and direction are crucial for measuring infiltration rates especially for naturally ventilated buildings. There is also much higher discrepancies involved in predicting characteristics of wind compared to other weather parameters. This would exacerbate uncertainties in future weather files when they are projected from existing weather information. In addition, all existing TMY files generated a high number of outliers for WS which could lead to many unintended consequences when designing with building energy simulation tools. Most building energy tools require weather files and design day files to predict building energy consumption. Design days are used for the HVAC equipment sizing to describe periods with maximum conditions that HVAC systems are designed to accommodate by maintaining some desired indoor condition. Warm season design days are based on annual percentiles of 0.4 or 1.0% and cold season conditions based on 99.6 or 99% yearly percentiles [27]. The use of annual percentiles ensures that the design days maintain a similar probability of occurrence even with extreme seasonal conditions. Fig. 7 shows the GHI, DNI and DHI for the months January and July and the whole year. For solar radiation the results of Meteonorm show the highest mean GHI and DHI and the highest max for all solar radiation. GHI mean varies slightly among the files with increasing trends which use more recently updated data. For DNI, however, there is a considerable difference between the means, with the single year 2010 having the highest of all files. The trend changes for DHI and even though the changes are minimal between weather files, a decreasing pattern can be seen as the weather files are updated which complies with the historical solar radiation observations. GHI is higher than DNI for summer months, but lower for winters since DNI is calculated based on a plane that is normal to the incoming irradiation and can absorb more energy in the winter compared to a horizontal plane on the ground. The ratio of diffuse to direct radiation depends on cloud cover, which also varies with the altitude of the location. In general, locations with high altitudes have greater cloud cover. For Philadelphia, the DHI is generally lower than the DNI, throughout the year. Next, a statistical t-test is conducted to analyze whether the TMY files generated by different sources match past observations. The test is performed for temperature which has the most significant impact on building energy performance. Table 2 shows the results of the t-test. For this test, the theoretical values for temperature with a significance level of 5% were obtained from the annual historical records of the Franklin Institute from 1872 to 2017 for Philadelphia. The missing data were replaced with data from

Table 2 Results of the t-test on current weather files.

p-value t Null mean

TMY

TMY2

TMY3

Meteonorm

ECEER

0.727 −0.350 12.396

0.00101 −3.287 12.376

<0.0001 −5.903 13.393

0.760 −0.305 13.391

0.00076 −3.366 13.831

the KPHL weather station and the mean for the null were selected based on the period from which the typical weather file was generated. The Null Hypothesis (H0 ) would be the mean temperature generated for the TMY file by different sources matching the theoretical mean for the given confidence interval (alpha = 0.05). The Alternative Hypothesis (Ha ) is true when the mean of the files is different from the observed mean. From Table 2, the weather files TMY2, TMY3 and the ECEER files do not adequately represent the historical temperature means from which they were generated, for Philadelphia. The Meteonorm TMY file has the highest p-value of 0.76, followed by the TMY file with a p-value of 0.727. The t(observed) for all weather files is negative, indicating that all weather files have a tendency to underestimate the actual data from which they are derived. These results suggest that there is a need to update TMY file when working with building energy simulation tools. This is necessary f not only for capturing the best historical trends in the weather files, but also because it lends credence to our hypothesis that existing TMY weather files might not be appropriate for use in building energy studies. Furthermore, it was assumed that the results obtained from the Franklin Institute which were used as the null case adequately represent the true population. However, the results may differ if data from different sources are used. 3.2. Future weather files The next challenge is to determine which future scenario or probabilistic distribution to use given the uncertainties in the input variables, and how to generate weather files that would be acceptable for a dynamic building energy assessment. Fig. 8 shows an overview of the annual mean temperatures in Philadelphia for the past (from 1880 to 2018) and future up to 2100 for three emissions scenarios from IPCC SRES generated by Meteonorm. For the future climate conditions, results for the morphed NREL TMY/TMY2/TMY3, morphed Meteonorm base TMY3 (MetB), morphed ECEER TMY3, Meteonorm future weather file (Met) and the AWE-GEN weather generator are presented in Fig. 9 for three future time slices (2020, 2050, 2080) based on the IPCC SRES A2. All morphed weather files are generated using CCWorldWeatherGen tool. Fig. 9 shows details of the main weather parameters influencing building energy performance for years 2020, 2050 and 2080. The difference in the results of the weather variables may be due to the methods of generation by weather generators, emissions

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Fig. 7. Results of solar radiation for current TMY files.

Fig. 8. Annual mean temperatures for Philadelphia.

scenarios/climate models, time periods, baselines, or the source data from which the baselines are generated. In this research the impact of the different data sources is not analyzed, rather the discrepancies in the final results of the weather generators as a whole are assessed for different time series. The MetB weather file, which is a morphed weather file from the Meteonorm base TMY, has the highest mean and max for all periods and lowest min for periods 2020 and 2050. The AWE-GEN, which are results from a stochastic weather generator, show the lowest mean temperature compared to other weather files, because they do not account for emissions scenarios. The Morphed TMY files follow the similar trend observed in their base weather files with TMY2 having the lowest and TMY3 having the highest mean temperatures for all periods. However, the same trend is not seen for ECEER and MetB. The base weather files show higher mean values for ECEER files, but the morphed files generated based on the Meteonorm base file show a higher mean compared to the morphed ECEER. For dry bulb temperature, Meteonorm seems more aggressive in minimum temperature, but quite mild in maximum

temperature compared to the morphed data. Although the morphing procedure is known to overestimate extreme data [31], in this case, the Meteonorm produced lower minimum temperatures. This could be explained by the morphing procedure in the production of the typical files. For temperature, a shifting and stretching technique is applied to the base temperature, which not only changes the skewness, but also shifts the data to higher temperatures. The change in relative humidity also follows the same pattern. Among the existing weather files shown in Fig. 5, AWE-GEN has the highest relative humidity and lowest mean temperature. AWEGEN results for relative humidity contained many outliers. With regards to wind speed, the changes between mean values from different methods are very small among future weather files through different periods. However, all weather files produce a large number of outliers which, if not treated properly, can negatively affect the HVAC design process. Results for solar radiation show a small variation in GHI among future time slices, with the ECEER data having a higher value compared to other weather files which might be due to the capability

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Fig. 9. Comparison of the weather parameters for the projected TMY weather files.

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Fig. 10. Comparison between projected dry bulb temperature to 2020 with 10 years of historical data for Philadelphia.

of the morphing procedure. The same pattern emerges for DHI, although in this case, ECEER has the lowest DHI value of all files. The DNI, on the other hand, changes among weather files for every timeframe. Nevertheless, the change in the mean DNI is slight between different time periods for each weather file. For DNI, the ECEER yields the highest mean. DNI for the morphed weather files increases with the updated weather base. For instance, among the weather files that are projected to the future using the morphing process, the lowest DNI is associated with the TMY which uses a base file generated from a 1952 to 1975 period. The TMY2 files show higher DNI for all timeframes compared to TMY, while TMY3 has the highest DNI among all morphed TMY files. In other words, even though using an updated weather base file for generating future data might not influence DHI and GHI significantly, it still has a major impact on the DNI data. It is worth mentioning that GHI value is of particular interest to photovoltaic installations and DNI is specifically of interest to solar thermal systems. The results for hourly averages for the months January and July and the whole year for GHI, DNI and DHI for 2080 are presented in Appendix B which shows the same GHI and DNI ratios for warm and cold seasons as described in Fig. 7. However, the results from the morphed ECEER are inconsistent with the rest of the data with a high DNI for most of the months. Validating future weather data is not practical as the future is unknown. However, to understand how close we are to the predictions of the weather generators, a comparison has been made between future weather files projected to 2020 for the Meteonorm and morphed typical files with historical hourly weather data for the past 10 years for Philadelphia from 2009 to 2018 derived from the Pennsylvania State Climatologist (PSC), which is shown in Fig. 10. The reason for the selection of 10 years period is to better compare the results of the future TMY files to the existing conditions because TMY files are produced based on a series of historical weather data and not just a single year. From Fig. 10 the weather generators projected to 2020 for the A2 scenario produced a relatively good prediction for dry bulb temperature when comparing their results to the past 10 years. However, when comparing Fig. 10 to the current weather data (Fig. 5) it can be seen that most of the single year weather files have higher mean temperatures compared to the current Me-

teonorm file (updated to 2010) and current ECEER file (updated to 2014). 4. Correlations analysis Understanding the inter-relationships between weather variables is critical for building energy simulation purposes. Many scholars have studied these associations for actual synthetic weather generators and different regions [8,25,30,51]. We have carried out an inter-variable correlation analysis for both the current files and future generated TMY files. We use typical weather files since they are inputs to dynamic building design models and play an important role in performance projections. The current weather files include the NSRDB TMY, TMY2 and TMY3, two Meteonorm and two ECEER typical years based on different historical data and a single year typical file for the year 2010. The future weather files are the morphed files from the existing current typical files (morphed based on the A2 scenario), the Meteonorm database files for three emissions scenarios and the AWE-GEN weather data over three future time slices. The inter-variable correlations show the scale and direction of the climate parameters interdependencies, and therefore, cannot be ignored. For instance, solar radiation causes temperature variations, the air temperature controls water evaporation/air saturation and air pressure that impact air humidity, and wind speed/direction [24]. We have examined the Pearson correlation (RXY ) between weather variables (whether they are spurious or not) which is widely used as an easy to interpret method of measuring linear dependencies betwen two variables. RXY takes values between −1 and +1 while zero indicates no correlation [12]:

Pearson Correlation Coe f f icient (RXY )   n  ¯ ¯ SXY i=1 Xi − X Yi − Y =  =    2  n  2 n  SXX SY Y ¯ ¯ i=1 Xi − X i=1 Yi − Y

(1)

where S is the sum of squares for the difference between the two variables and n is the total number of data series which is a total of 8 for current and 33 for future bivariate correlations in this study. For this section, and in order to produce more interpretable graphs, we only consider hourly data during the daytime since otherwise, DNI is mostly zero. Fig. 11 shows the results of the

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Fig. 11. Bivariate Pearson’ correlations for current and future weather files.

correlation test for current and future files. There is no exact principle for determining what magnitude of R could be defined as strong. Depending on data size and variability, distribution, outliers and measurement errors, in addition to the linearity of the data, determination of the correlation coefficient may differ [23]. Here we rely on both strength and significance of the correlations for evaluating relationships, and consider absolute correlation coefficient values of 0.2 and greater, conditioned on the probability value, to be indicators of a notable relationships. The significance level of the calculated bivariate correlations for current and future weather files are presented in Appendix D. As shown in Fig. 11, the bivariate correlations between DB and RH; RH and DHI; WS and GHI; WS and DNI; WS and DHI are not strong for both current and future files. The p-value for DB and RH was found to be higher than 0.05 for future files but not for current weather files. For RH and DHI the p-value was below 0.05 for both current and future weather files. The p-value for WS with GHI, DHI for both current and future and for WS and DNI for current weather files was found to be higher than 0.05. The correlations between DB and GHI; DB and DHI; GHI and DNI; GHI and DHI are positive and relatively strong, while RH and GHI; RH and

DNI; RH and WS are negatively correlated in both current and future weather files. The DNI-DHI correlation has high variation between upper and lower quartiles, similar in both current and future files, and the DB-DNI correlation coefficient is smaller than 0.2 for the current files. However, this changes for future weather files and the bivariate relationship is predicted to be positive and relatively strong. To further examine our findings, one-sample and two-sample Kolmogorov–Smirnov (K–S) tests were used (Table 3) to determine the goodness of fit for the distribution and to compare each two distributions, respectively. The K–S test is a nonparametric, distribution free, outlier sensitive test and does not rely on normality assumption, which is applicable even for small sample sizes [16]:

Dn =

√ n sup |Fn (x ) − F (x )|

 Dn =

(2)

x

n1 n2 sup |Fn1 (x ) − Fn2 (x )| n1 + n2 x

(3)

where Dn is the test statistic, F is the theoretical cumulative distribution and Fn is the empirical cumulative distribution, and n1 and n2 are observations from two different samples. Prior to the

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Table 3 Summary of the parameter fitting test and the K–S comparison of distributions. Current (parameter fitting test)

DB-RH DB-WS DB-GHI DB-DNI DB-DHI RH-WS RH-GHI RH-DNI RH-DHI WS-GHI WS-DNI WS-DHI GHI-DNI GHI-DHI DNI-DHI

Future (parameter fitting test)

K–S comparison test

n

Distribution

D statistic

p-value

n

Distribution

D statistic

p-value

D statistic (Dα )

p-value

7 8 7 7 8 7 7 7 8 7 8 7 8 8 8

Logistic Normal Logistic Beta Lognormal Logistic Normal Logistic Logistic Logistic Logistic Logistic Lognormal Logistic Logistic

0.227 0.181 0.240 0.138 0.177 0.178 0.251 0.224 0.167 0.207 0.194 0.205 0.166 0.160 0.284

0.792 0.916 0.737 0.996 0.999 0.953 0.686 0.806 0.954 0.871 0.871 0.879 0.955 0.966 0.456

33 30 31 30 32 30 30 33 32 30 33 31 31 32 33

Logistic Logistic Logistic Normal Lognormal Logistic Logistic Normal Logistic Logistic Normal Logistic Logistic Logistic Logistic

0.163 0.235 0.062 0.084 0.107 0.125 0.091 0.152 0.130 0.166 0.167 0.159 0.165 0.069 0.223

0.313 0.060 0.999 0.973 0.823 0.687 0.945 0.393 0.609 0.339 0.282 0.377 0.333 0.995 0.064

0.368(0.565) 0.350(0.5412) 0.47(0.569) 0.724(0.57) 0.469(0.537) 0.448(0.57) 0.229(0.57) 0.442(0.565) 0.281(0.537) 0.405(0.57) 0.258(0.536) 0.488(0.569) 0.25(0.539) 0.313(0.537) 0.22(0.536)

0.415 0.422 0.160 0.005 0.120 0.205 0.928 0.210 0.692 0.310 0.786 0.131 0.822 0.560 0.915

test, possible outliers were removed from the correlation coefficients dataset. We relied on the box plots to determine outliers for current weather files correlation coefficient, since drawing a clear normal assumption was not easy due to the relatively low number of observations. However, for future weather files, outliers were determined based on a Z-test with a significance level of 0.05. In some cases, there were multiple suitable fits. For instance, DB-DNI correlation in the current data files, could also be explained by a logistic distribution, or for future data, a beta distribution could also have been used. Fig. 12 shows the probability density functions of the Pearson coefficient values for the bivariate correlations developed by applying the measured parameters from the fitting process. The vertical lines indicate upper and lower bounds of the Confidence Interval (CI) for the current and future distributions. Looking at the sign (positive or negative) of the correlations, ’the bivariate correlations between DB and RH; DNI and DHI; RH and DHI; WS and GHI; WS and DNI; WS and DHI reveal both positive and negative relationships. Although the correlation strength for the latter four is quite low, the graphs confirm the complexities in determining a clear association between certain variables, and how the uncertainties in the possible patterns of climate variables such as solar radiation and wind speed can exponentially intensify the complications. The case is different for DNI-DHI correlation where not only the sign of the correlation changes from the upper to lower bound of the CI, but also the correlation can be relatively strong depending on the observation. The negative correlation matches the expectation; however, we cannot give a clear explanation for the positive association since we only have considered certain weather variables and some parameters such as cloud cover and precipitation that could potentially have an influence on this relationship are not included in this analysis. DB-DHI, DB-GHI, GHI-DHI, GHI-DNI correlations are positive and relatively strong while RH-DNI and RH-GHI correlations are strong and negative. These results are solely for Philadelphia and may not be necessarily generalizable to another place. From the density plots, in many cases, besides the intra-variations within current and future data files, the shape of the distribution of the bivariate correlations seem to vary between current and future data. It is as such for DB-DHI, and DB-DNI correlations. The K–S comparison of distribution test has been applied to determine whether the differences between the current and future bivariate correlation distributions are significant. These results are also incorporated in Table 3 (the last columns to the right side) and the details of the parameters of the fitting process are presented in Appendix C. The critical value

of the one sample K–S test statistic (Dα ), for current data of a sample size 7 is 0.4834 and for a sample size of 8 is 0.4543. For future data, Dα for the sample size 33 is 0.2308, for a sample size of 32 is 0.2342, for a sample size of 31 is 0.2379 and for a sample size of 30 is 0.2417. The changes in the sample size (n) in Table 3 is due to the removal of outliers. The results of the K–S test for drawing a comparison between current and future bivariate correlation distributions indicate that although in some cases the difference between current and future distributions are not much, for DB-DNI, WS-DHI, DB-GHI, DB-DHI, RH-WS, RH-DNI and WS-GHI correlations the differences are major. However, it is only for the DB-DNI correlation that the difference rises to the statistically significant threshold. The model does not have enough power to confirm the significance of the variance between current and future bivariate correlation distributions, which can be attributed to the sample size. In other words, our results confirm meaningful difference between the DB-DNI correlation in current and future files and points at similar meaningful current-future variances for WS-DHI, DB-GHI, DB-DHI, RHWS, RH-DNI and WS-GHI correlations. This could be a red flag for simulating climate variables, suggesting that the generators involved in the study are possibly ignoring inter-variable dependencies. Our results indicatethat weather generators possibly do not take into account the DB-DNI correlation, which, considering the strong correlations between the two variables (and between many other weather variables) is by no means realistic. Inter-variable correlations need to be considered as model parameters in generating future data files, and projections should preferably draw upon joint distributions of more than just one variable. The discrepancies in the bivariate correlation matrices pertaining to current and future data highlight the complexity of selecting a proper weather file as well as all the uncertainties within weather generators, global climate models and regional scale weather files. In order to understand the discrepancies of the projected climate, an uncertainty analysis has been conducted, and is explained in detail in the following section. 5. Uncertainty Constructing future typical years for building simulation tools is necessary to predict how buildings will perform under changed climate conditions. The impacts of future climate conditions on energy performance get harder to predict once the consequences of building aging are added to the picture, raising the uncertainty level even further. With respect to projecting climate variables, the

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Fig. 12. Distribution of the bivariate correlation coefficients for the current and future weather files.

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Fig. 13. Layers of uncertainty due to climate change projections (adapted from Giorgi [21]).

main sources of uncertainty arise from the models and their initial conditions, emissions scenarios uncertainties, internal variability [59] and downscaling methods. Each of these factors contribute to a layer of uncertainty in the results. The arrows in Fig. 13 represent layers of uncertainty for future building operations. Uncertainty in weather files generated for future scenarios stems from approximations of an unknown reality [22]. This uncertainty increases when applying weather files for regional scales and hourly time periods to be used in building simulations [9]. Every climate model output, emissions scenario, and initial condition can produce a new scenario, and not one has higher probability of occurrence than others [43]. The IPCC scenarios consider a range of socio-economic factors including population, economic or technological developments. Initial conditions are often set as the preindustrial conditions, which represents a period before anthropogenic changes to the climate. However, there is scant information on climate variables during preindustrial times, and simulations to create arbitrary preindustrial initial conditions are referred to as control runs. Given the assumptions behind this method, various input conditions can be selected as a starting point in developing climate models [43]. Uncertainties of climate models can be treated by using output results from different GCM models. The final source of uncertainty is the natural climate variability. Uncertainties from these sources can be handled by taking into account more than one future emissions and climate scenario and applying probabilistic approaches to each one of them [22]. For instance, Eames et al. [14] created future probabilistic TMY and DSY files applicable to building performance simulation using pointwise intervals for mean monthly temperatures. Overall, the uncertainties need to be quantified and decomposed to their sources. Methods for uncertainty partitioning have been developed in projecting different climate parameters such as global mean air surface temperatures [28,44,59] and regional precipitation levels [29]. We will be using a similar approach to Yip et al. [59] for partitioning the uncertainties. First, we use global climate models and emissions scenarios to validate our approach compared to the literature (Fig. 16). Next, we will apply that method to results obtained from hourly generators for the three emissions scenarios (Fig. 19). In this section, different sources of uncertainty at a global and regional scale are analyzed for Surface Air Temperature (SAT). An Analysis of Variance (ANOVA) model is used to partition sources of uncertainty of SAT for three timeframes in global climate models as well as downscaled regional hourly weather data. SAT in the global models refers to the ambient temperature at 2 m elevation. This is because most meteorological centers collect SAT at 2 m above ground level.

503

Thirteen models are obtained from the IPCC Fourth Assessment Report (BCM2.0, CM3, Mk3.0, ECHAM5-OM, CM2.0, CM2.1, ER, CM3.0, CM4, MIROC3.2, CGCM2.3.2, CCSM3, HadCM3) over three emissions scenarios (A2, A1B, B1) for three time slices (2020, 2050, 2080) [32], and Meteonorm was used for the downscaled data. The climate models mainly differ by the region/institute in which they were developed, spatial and temporal resolution and coverage, variables availability, ensemble and control runs, and assumptions used in the development of the models. The global models are reported as monthly means over a coarse spatial resolution. We conducted the analysis for the region of Philadelphia with latitude of 39.95° N and longitude of 75.16° W. Data from the global models that were closest to the coordinates of Philadelphia were selected. When analyzing the global models, in addition to the 13 climate models, two extra data sets were included in the global model analysis. One is the mean of all models (MM) and the other is the monthly average values of the downscaled data. An uncertainty analysis in this context reflects what different sources of uncertainty are and the ratio attributed to each source compared to the total uncertainty. Fig. 14 shows the distribution of monthly values of SAT taking all 13 climate models with the additional data sets for all climate scenarios through three time slices. As shown in Fig. 14, the range of SAT is wider in cold months (N,D,J,F,M,A) and narrower in warm months (M,J,J,A,S,O) for 2020 and 2050, but for 2080 the maximum-minimum gap gets smaller for all warm and cold months compared to previous time slices. Based on the distributions, it could be concluded that for the given emissions scenarios, climate models and the location under study, the uncertainty for winter months is higher than summer months. To quantify this, a two factor ANOVA analysis has been conducted. Details of the test are as follows [12]:

ST = SSA + SSB + SSEI

SSA =

J I   

X¯ i. − X..

(4)

2

=

i=1 j=1

SSB =

J I   

X¯ . j − X..

J I    i=1 j=1

(5)

J 1 2 1 2 X. j − X.. I IJ

(6)

i=1

2

=

i=1 j=1

SST =

I 1 2 1 2 Xi. − X.. J IJ

j=1

Xi j − X..

2

=

J I   i=1 j=1

Xi j 2 −

1 2 X.. IJ

(7)

where in Eq. (4), SSA is the scenario sum of squares, SSB is the model sum of squares, SSEI is the sum of squares due to the internal variability and error term as one factor and SST is the total sum of squares. Internal variability is the random, natural internal fluctuations in the climate system [52] and the model error term is the random difference between the observed value and the expected value and is assumed to be normally distributed [12]. The letter I shows the total scenarios (in this case three) and J shows the total models (in this case sixteen). In Eq. (6) and (7) X¯ i. , X¯ . j and X.. are the average of measurements obtained when factor A is held at level i, the average of measurements obtained when factor B is held at level j, and the grand mean respectively. The variance of each factor would then be obtained by dividing the sum of squares by its degree of freedom. Results of the test for the monthly values are presented in Fig. 15. Overall, the total variance in warm months is smaller than cold months, suggesting that the total uncertainty of the climate models and emissions scenarios for the location under study are higher for winter and lower for summer when taking into account global climate models in our analysis. Fig. 15 shows the total variance of SAT in each month over all time slices. I + E is the internal variability and error term, and has

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Fig. 14. Distribution of monthly values of SAT for all scenarios and climate models.

Fig. 15. Total SAT variance of the models and scenarios for three time slices.

Fig. 16. Fraction of variance of the models and scenarios for SAT.

the lowest contribution among all factors, for all time periods. In 2020, the major contributing factor is model uncertainty which continues to be the dominant factor for 2050 and 2080, for most of the months. However, scenario uncertainty shows an increase for most months of 2050 and 2080, compared to 2020. These results present the uncertainties of the monthly SAT values of the climate models for the given scenarios and the area under study.

Changes to any of these factors may alter the absolute values, but the relative values are expected to follow the same trend. Fig. 16 shows the ratio of variances and how much each element (scenario, model, or internal variability) contributs to the total uncertainty of the SAT for the given time periods. As described before, building simulation tools require a detailed spatial and temporal resolution of projected weather, which

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Fig. 17. Distribution of monthly values of SAT for all scenarios and downscaled climate models.

Fig. 18. Total SAT variance of the downscaled models and scenarios for three time slices.

climate models do not provide. Generally, downscaling techniques are applied, adding a layer of uncertainty to the data. To analyze this uncertainty, a second test is conducted accounting for the hourly values for the location under study. Fig. 17 shows the monthly description for the SAT accounting for hourly weather values for all scenarios and for the three time slices. The difference between the maximum and minimum SAT is higher for most months in this test (accounting for hourly values) compared to the previous test, but the min-max gap does not vary significantly from warm to cold months. In this case, the model uncertainty is from the hourly weather values. Fig. 18 shows the total variance. As shown in Fig. 18 the total variance is very high for all months and in total compared to the previous case. As described in Part 1 (Fig. 2) emissions scenarios start to diverge significantly starting at the mid-century. In addition, global models only capture a coarse spatial and temporal resolution. Therefore, in the second case (Fig. 18), which is the results of the generators downscaled to a finer spatial and temporal resolution, higher variance compared to the global models is observed (Fig. 15). It also appears that the variance values are more stable for years 2020 and 2050 for all months and year 2080, except for August, compared to results in Fig. 15. This could be explained by the presence of more observations (hourly values) than the previous case (monthly values). In addition, the variance of the SAT at 2080 increases significantly compared to 2020 and 2050 due to the inertia of emissions described in Part 1. To better understand the contribution of each element, the fraction of variance of each factor is measured and

results are presented in Fig. 19. Here, the I + E term is significantly smaller than what is shown in Fig. 16 , but still notable in summer values for years 2020 and 2050 and the portion decreases to a very small value at year 2080 for all seasons. As more observations were included, the error term decreased. Also, in Fig. 19, for 2020, the major contributor to the uncertainty is the model itself. But this contribution decreases for 2050 and 2080. For 2080, the major contributor to uncertainty is the scenario. However, this does not mean that the absolute value of the model or the I + E variance decreases. It is the share of their contribution to overall uncertainty that decreases. These findings are in accordance with the findings of Hawkins et al. [28], Yip et al. [59], and San-Martín et al. [50]. The uncertainty analysis conducted here is focused only on SAT and results might differ for different weather variables (such as wind speed, precipitation, or solar irradiation). In addition, only 13 climate models were selected for the analysis and introducing more models with a different historical base would likely change the results. 6. Conclusion Buildings contribute to climate change. They consume a significant portion of the total energy generated in the US, and building energy use is directly linked to weather and climate conditions. In this article we presented the most common methods for the creation of weather data to be used in energy simulation tools. Several methods for creating typical weather data exist. Typical weather data reflect historical observations and are used as an input for building design. Our findings suggest that weather data used in building design need to be updated and current TMY files may not be suitable to capture predicted trends of climate change. In this Philadelphia case study, the main weather parameters influencing building energy performance produced by commonly used weather generators based on the IPCC A2 scenario for three future time slices (2020, 2050 and 2080) were analyzed and uncertainties among them were described. The predicted dry bulb temperature varied significantly across weather generators and showed an increase in extreme and mean conditions. Global horizontal irradiation and wind speed showed small variations across weather generators and through all periods. However, the diffuse normal irradiation demonstrated an increase through future time slices. Data produced for wind speed for all generators had many outliers which could result in overestimation of HVAC requirements. A statistical t-test was conducted based on the theoretical values obtained for the year from which the typical weather files

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Fig. 19. Fraction of variance for the downscaled models and scenarios for SAT.

were generated. We found that most of the weather files failed to comply with the null hypothesis. The t(observed) for all the weather files were negative, suggesting that all weather files have a tendency to underestimate the actual data from which they were derived. The single year TMY file contains extreme conditions for DBT and RH that are not reflected in other TMY files representing past observations. This can be explained by the process of the TMY file data selection which does not account for extreme conditions. In cases where these conditions need to be considered, the use of an extreme meteorological year would be appropriate. Future weather files also have limitations. The most significant limitations are the coarse resolution of global climate models and the high degree of uncertainty in predicting future weather conditions. In most building studies, dry bulb temperature is considered the driver of extreme conditions. A correlation analysis was conducted on the outputs of each weather generator for all parameters for current and future files. Our results show that weather generators possibly do not take into account the DB-DNI correlation, which, considering the strong relationship between the two variables (and between many other weather variables) is by no means realistic. Inter-variable correlations need to be considered as model parameters in generating future data files, and projections should preferably draw upon joint distributions of more than just one variable. Finally, an uncertainty analysis was conducted. The total uncertainty of surface air temperature was partitioned and the contribution of each element (i.e., climate model, emissions scenarios, and internal variability I + E) was calculated. We found that the ratio of uncertainty attributed to I + E was reduced for all time slices as additional observations were added to the test. Also, as the number of observations increased, the ratio of uncertainty stemming from the model decreased, while the ratio of uncertainty stemming from the scenario increased over time. This can be traced back to the uncertainty in the assumptions made in the scenarios’ generation. The importance of the scenario uncertainty is revealed over time.

As explained by Hallegatte [26], no method can eliminate this uncertainty since the level of GHG emissions that determine the climate change, cannot be predicted. In summary, given the trends presented by climate models, a single design solution for buildings may be insufficient to understand the complex relationship between climate and building energy consumption. Instead, we suggest that buildings be designed through a framework of possibilities and vulnerabilities to reflect a range of solutions that address best and worst case climate scenarios. This would better reflect the uncertainties associated with energy use and more effectively predict how buildings may perform under competing climate scenarios over their lifetime. Conflict of interest We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.enbuild.2019.07.016. Appendix A. Wind data for current and year 2080 climate conditions The outer layer shows the percentage of hours where wind occurs. The next two layers show the temperature and humidity of the wind coming from each direction respectively and the triangles in the center show the maximum, minimum and average velocity of the wind. In Appendix A and B, column (a) shows the annual changes, column (b) shows the changes in January and column (c) shows changes in July for Philadelphia.

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Appendix B. Solar radiation data for future climate files (projected to 2080)

Appendix C. Details of the K–S fitting test

Current

DB-RH DB-WS DB-GHI DB-DNI DB-DHI RH-WS RH-GHI RH-DNI RH-DHI WS-GHI WS-DNI WS-DHI GHI-DNI GHI-DHI DNI-DHI

Future

Distribution

Parameter1

Parameter2

Distribution

Parameter1

Parameter2

Logistic Normal Logistic Beta Lognormal Logistic Normal Logistic Logistic Logistic Logistic Logistic Lognormal Logistic Logistic

−0.019 −0.191 0.4 2.992 −1.055 −0.252 −0.464 −0.489 −0.069 0.058 0.075 −0.002 −0.38 0.494 −0.15

0.046 0.076 0.009 33.148 0.125 0.023 0.057 0.044 0.036 0.016 0.035 0.018 0.119 0.06 0.142

Logistic Logistic Logistic Normal Lognormal Logistic Logistic Normal Logistic Logistic Normal Logistic Logistic Logistic Logistic

−0.06 −0.14 0.416 0.189 −1.164 −0.22 −0.45 −0.443 −0.097 0.041 0.053 0.029 0.713 0.463 −0.171

0.037 0.048 0.012 0.064 0.136 0.03 0.019 0.08 0.026 0.019 0.076 0.022 0.057 0.043 0.118

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Appendix D. Significance level of the bivariate correlations for both current and future weather files

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