Projection of Temperature and Precipitation Related Climatic Design Data Using CMIP5 Multi-Model Ensemble: A case study for Ontario, Canada under RCP 6.0
Ziwang Deng a, Jinliang Liu b, Xin Qiu c,Xiaolan Zhou a, Hamed Babazadeh a, Huaiping Zhu a
a Lamps, Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
b Department of Earth and Space Science and Engineering, York University, Toronto, ON M3J 1P3, Canada
c NOVUS Environmental, Guelph, ON N1G 4T2, Canada
The urban environment and its infrastructure are vulnerable to climate change and the impacts of climate change are mostly local and, thus, adaptation should be highly location specific. Sub-daily climate projections of temperature and precipitation are necessary to estimate the impacts. However, the highest temporal resolution of climate change projection data is at daily time scale. In this study, a novel method that combines the K-means clustering and the logistical regression is developed to generate hourly temperature, and a method that combines a stochastic weather generator and conditional cumulative distribution function is proposed to disaggregate precipitation. Using these methods, a 12-member ensemble of hourly temperature and rainfall is produced at 228 locations in Ontario for the period from 1981-2100. Based on the daily (the bias correction constructed analogs RCP6.0 data of CMIP5 GCMs) and the sub-daily data, eight temperature and precipitation related extreme climate indices are projected for the 2050s and 2080s. The results show that the three design temperature indices (Degree Days Below 18°C, 2.5% and 1% January temperatures) will increase significantly in the 2050s and 2080s relative to the 1990s; annual total precipitation and annual rainfall will also increase significantly in the 2050s and 2080s relative to the 1990s; though relative to 2050s, total rainfall could decrease in the 2080s at some locations. 50-year return period value of one-day maximum precipitation and 10-year return period value of maximum 15-minute rainfall will increase at most locations with large uncertainty at some locations. These projected changes in climatic design data may have substantial implications for the design and operation of infrastructures in Ontario, Canada.
Keywords: downscaling, temporal disaggregation, temperature, precipitation, climatic design data, extreme climate indices
The IPCC's Fifth Assessment Report (AR5) estimates that global mean surface temperature is likely to be in the range of 2.6 to 4.8°C for 2081-2100 relative to 1986-2005 based on the worst scenario RCP8.5 (Field et al., 2014). In this scenario, annual minimum of minimum temperature (TNn), maximum of maximum temperature (TXx) and the maximum 5-day precipitation (RX5day) are projected to increase by 6.7°C, 5.4°C and 20%, respectively, over global land by the end of the 21st century (Sillmann, Kharin, Zwiers, Zhang, & Bronaugh, 2013). The urban environment and its infrastructure will be significantly impacted by climate change and are identified as one of the specific sectors needing "priority planning" for adaptation (Auld et al., 2008). As a northern region, the province of Ontario in Canada could experience more significant changes in both mean and extreme climatic conditions than the global average. Recently, some projections have been generated for several variables to indicate the change in mean climate and moderate extreme climatic conditions (Deng et al., 2016). These projections have provided useful information to the public.
There is a need for more comprehensive research on potential impacts of climate change on infrastructure design. Typically, climatic design data are developed using historical climate data, assuming that the past climate conditions will still be representative over the future lifespan of the structure (Auld et al., 2008). While this assumption has worked in the past, it will become less valid as the climate changes. The recently updated climatic design values for 228 locations in Ontario (MMAH, 2015) were generated using observations from stations for a 25-year period up to 2006. These design values might be already altered in the past decade as well as the near future given the projected climate changes. However, very few studies have examined the potential effects of climate change on these design values. Several challenges need to be addressed in such a study. Unlike the above-mentioned IPCC AR5 average variables and indices defined with daily data, some design values demand hourly or sub-hourly data. However, global climate models (GCMs) don't provide hourly data. Projection of the design values needs not only to spatially downscale daily GCM data to local points, but also to temporally downscale daily data to hourly or even minute resolution. This combined temporal-spatial downscaling is extremely challenging. Furthermore, the climatic design values are usually thresholds of longer return period precipitation events (for example 5-year, 10-year or 50-year extreme events) or 1 and 2.5 percentiles of monthly temperatures. Some recent studies have provided a framework to deal with these issues. For example, the general extreme value theory (GEV, Castillo, 2012; De Haan & Ferreira, 2007; Hong & Ye, 2014) provided a framework for the threshold issue and some recently proposed temporal downscaling methodologies have been used to generate hourly rainfall, wind speed, and temperature (Ephrath, Goudriaan, & Marani, 1996; Hosmer, Lemeshow, & Sturdivant, 2013;Vrac et al., 2012; Maraun, 2013; Shrestha et al., 2015).
To address the need of the built environment and infrastructure sector in Ontario to adapt to the changing climate, this study explores a method to produce probabilistic projections for the 2050s and 2080s of the eight climatic design values associated with temperature and rainfall data. The projected eight climatic design values will be estimated at the 228 sites (see figure 1) listed in table 1 of the MMAH Supplementary Standard SB-1 Climatic and Seismic Data. They can provide valuable guidance to fill in the knowledge gaps in the climatic design data development to leverage the safety and confidence with respect to the uncertainty factors considered in the design of the current and future infrastructure. To achieve this goal, different temporal downscaling models are developed to generate hourly data from a spatially downscaled CMIP5 RCP6.0 GCM ensemble.
The paper continues in section 2 with brief descriptions of the downscaled daily data, reanalysis data, observations and the recently updated Ontario climatic design data which will be used in this study. In section 3, several methods of temporal downscaling and extreme value analysis are provided, followed by the results in section 4. The paper ends with the summary and conclusions in section 5.
2.1 Model Data
In this study, a 12-member ensemble of CMIP5 GCMs (IPCC, Field et al., 2014) under RCP6.0 (Moss et al., 2010) are used. The RCP 6.0 is chosen because it represents an intermediate emissions scenario, which is consistent with the application of a range of technologies and strategies for reducing greenhouse gas emissions. The downscaled data include daily precipitation (Pr), minimum temperature (Tn) and maximum temperature (Tx) from 1981 to 2100 at a spatial resolution of 0.125 degrees (ftp://gdo-dcp.ucllnl.org/pub/dcp/archive/cmip5/bcca/). It was generated using the Bias Correction and Constructed Analogs (BCCA) method. This procedure was introduced in Hidalgo, Dettinger, & Cayan (2008) and Maurer & Hidalgo (2008; 2014). The procedure of BCCA involves two-steps: Bias-Correction using a quantile mapping and Constructed Analogs. Both steps are based on daily GCM and observed values. Different than the BCSD approach that corrects the bias at each grid cell independently, the BCCA method is based on the linear regression of a collection of historically observed weather patterns that closely resemble the GCM weather pattern for each specific day, and therefore, is more dynamics-based (Hidalgo et al., 2008; Maurer & Hidalgo, 2014; Brekke, Thrasher, Maurer, & Pruitt, 2013). Therefore, this data is suitable to assess projected changes in variability of daily to multi-day precipitation events which could be relevant to flood control or other systems that are sensitive to daily precipitation variability. It also suits the assessment of projected changes in diurnal temperature range and multiday temperature extremes (Brekke et al., 2013; Gyawali, Garbrecht, & Zhang, 2016).
2.2 Station data
The raw data used in this study include the historical observations of daily and hourly temperature data at 27 stations, climate normal, and climate extremes (Environment Canada, 2012) at 151 stations as well as the engineering climate data (ftp://ftp.tor.ec.gc.ca/Pub/Engineering_Climate_Dataset/IDF/) at 133 stations. The IDF (Intensity-Duration-Frequency) data includes annual maximum for 15-minute to 24-hour and the return values. Hourly rainfall during May to November at these 133 IDF stations are provided by Environment and Climate Change Canada (ECCC). The observation periods at most of the 133 stations are short (less than 10 years). To increase the sample size of storms, hourly rainfall data at 12 stations in USA closest to Ontario (see figure 1), which have at least 10-year of complete data, are also used for developing the temporal disaggregation model to downscale daily rainfall to hourly rainfall on the storm days. Figure 1 shows the locations of these stations. It is observed that the 27 stations are among the 133 IDF stations and the 228 climatic design data sites.
2.3 Reanalysis Datasets
Reanalysis data is the best alternative to observed data sets (Dee at al., 2011). There are several high resolution reanalysis datasets available. These include gridded fields dataset (CRU TS3.10, Harris, Jones, Osborn, & Lister, 2014), ECMWF ERA-interim reanalysis climate data (Dee et al., 2015), NCEP North America Regional Reanalysis (NARR, Mesinger et al., 2004), and the NCEP climate forecast system reanalysis (CFSR, Saha et al., 2010, 2014). Compared with the station observation data in Ontario, it is found that the CFSR data is suitable for the sub-daily data analysis. Therefore, the CFSR data is used in this study (Deng, Liu and Qiu et al., 2018). The CFSR system assimilates many hydrological quantities from a parallel land surface model forced by NOAA's Climate Prediction Center (CPC) pentad merged analysis of precipitation and the CPC unified daily gauge analysis (Saha et al., 2014). The daily CFSR data has been widely used for verification of deterministic forecasts and validation of downscaling methods (Stefanova et al., 2011; Deng et al., 2016).
2.4 Current climatic design data
Recently updated climatic design data at 228 sites in Ontario is used as the reference data for model development and validation (MMAH, 2015). In this study, the following eight values are examined: Degree Days Below 18°C (also known as heating degree days, HDD), Annual Total Rainfall (RTot), Annual Total Precipitation(PrTot), 50-year return period values of One-day rainfall (RX1D), 2.5% (2.5%JanT) and 1% (1%JanT) January temperatures, 2.5% July temperature (2.5%JulT) and 10-year return period values of 15 min rainfall (R15min). These values are calculated based on historical observations before 2007 (MMAH, 2015).
3.1 Temporal disaggregation
Sub-daily (hourly and sub-hourly) data are required for projections of several design values, such as 2.5%JanT, 1%JanT, 2.5%JulT and R15min. In the following sub-sections, we will describe the techniques for the temporal disaggregation of temperature and rainfall.
3.1.1 Hourly temperature in January and July
A general location-independent algorithm for synthesis of correlated solar radiation and ambient temperature, which requires a few commonly well-known input parameters, has not been developed yet (Heinemann, Langer, & Schumacher, 1996). The diurnal air temperature curve was often described by the sine-exponential model or by a modification of this method (Ephrath et al., 1996) with minimum air temperature (Tn(j)), maximum air temperature (Tx(j)), the minimum air temperature of the next day (Tx(j+1)), and day length (DL). While this method is easy to implement, one of its obvious disadvantages is that it always generates similar daily cycles for all days at different stations. In this study, we developed a new method that combined the k-means clustering (Hartigan & Wong, 1979; Jiang, Qian, & Leung, 2016) and Logistic regression (Hosmer et al., 2013; Shrestha et al., 2015) to generate hourly temperature for January and July. The k-means clustering is applied to historical hourly temperature to obtain typical temporal varying patterns at each station for different months; and the Logistic regression model is used to predict the most possible pattern for a specific day at the corresponding station. Following is a detailed description of this procedure:
After conducting the clustering analysis, each day only belongs to one of the K clusters. A typical 24-hour temperature variation pattern for each of the K clusters could be obtained based on the corresponding sub-set of the data using the composite analysis method (Wilks, D.S, 1995; Welhouse, Lazzara, Keller, Tripoli, & Hitchman, 2016). For simplicity, we let K=2 for all the stations, let Y denotes a binary variable, which can take values of Y =0 corresponding to a cluster (cluster 1), or Y= 1 corresponding to another cluster (cluster 2). Figure 2 show two typical temporal variation patterns, cluster 1 (red), cluster 2 (blue) and the mean daily cycle (black) of the normalized hourly temperature (Left) in January at Pearson International Airport station. Using the same procedure, two typical patterns for each of the other 201 sites for January and July could be generated based on the hourly and daily temperatures interpolated from CFSR with the inverse distance weighting (Bartier & Keller, 1996). Afterwards, a binomial logistic regression model is constructed to forecast the cluster type of each day (Hosmer et al., 2013). The candidate predictors x include the five variables as follows: maximum and minimum temperatures of the day, maximum temperature of previous day, minimum temperature for the next day, and the cluster category of previous day:
where β (β0,β1) is a vector denotes the estimator of the six coefficients of the model.
(3) Generate hourly temperature data by rescaling the pattern thus its minimum (maximum) value equals the daily minimum (maximum) temperature.
3.1.2 Hourly rainfall during May-November
Sub-daily rainfall data is necessary for calculating the design values of 10-year return values of R15min. Because storms rarely happen in the cold seasons in Ontario, only daily rainfall amounts during May-November are temporally disaggregated to hourly data. A threshold of 10mm/day is used for identifying the storm days. When a daily rainfall is equal to or greater than 10mm, it is considered as a storm day and the daily rainfall is disaggregated to hourly rainfall. The modelling of rainfall amount is a complicated task because it combines a Bernoulli random variable corresponding to dry or wet events with a positive random variable corresponding to the rainfall intensity, therefore leading to a strong departure from the classical Gaussian framework (Ailliot, Allard, Monbet, & Naveau, 2015). The statistical rainfall disaggregation models can be classified broadly into the following four groups: two-part models, transition probability matrix models, re-sampling models, and time series models of the autoregressive moving average type (Srikanthan & McMahon, 2001). Because we are only interested in the maximum values of hourly precipitation, we do not consider the temporal auto-correlation of precipitation amount. Therefore, the two-part model method is used. This method is chosen because it is easy to implement and also meets the requirement of this study. The two-part model is a stochastic weather generator that aims at quickly simulating realistic random sequences of atmospheric variables (Wilks & Wilby, 1999; Ailliot et al., 2015; Kim, Rajagopalan, & Lee, 2016). This approach consists of two parts/models: a model for the occurrence of wet and dry hours and a model for the generation of rainfall amount at wet hours. To consider the seasonal variation in rainfall, a model is constructed for each of the months during the warm season. Following is a brief description of the procedure:
The model to identify wet and dry hours is constructed in the following steps:
After a threshold (R0) and the hourly rainfall (R) are given, the state of each hour is specified as "wet" (R>=R0) or "dry" (R<R0);
The fractions of wet hours in a day can be estimated (P1);
A relationship between the state of the current hour and the state of the preceding hours can be developed. Here, we denote P01 (or P11) as the probability of a wet hour conditioned on a preceding dry (or wet) hour, and P00 (or P10) as the probability of a dry hour conditioned on a preceding dry (or wet) hour, respectively. Based on the historical CFSR data, these frequencies can be easily estimated. In this study, we set R0=0.1mm/hour. For example, the result for the hourly August precipitation in the storm days at Pearson International Airport for the historical period (1981-2010) is as follows:
P1=0.6684, P00=0.8663, P01=0.1377, P10=0.0651, P11=0.9349.
Similar to the daily precipitation simulation procedure (Wilks & Wilby, 1999), a uniform random number u within the range of [0, 1] is generated for each simulated hour; whether the next hour in the sequence is wet or dry, it is determined by comparing the value of u and the conditional probabilities. If the previous hour (t-1) was dry, then hour t is simulated to be wet when u=<P01, otherwise it remains dry. If the previous hour was wet, then the current hour is simulated to be wet when u=<P11, and is dry otherwise. For the first hour, if u=<P1, it is simulated to be wet, and is dry otherwise.
The models used to generate daily rainfall amounts include the two-parameter Gamma distribution (Woolhiser & Roldan, 1982, Liu et al., 2011), combined with Exponential distribution (Woolhiser & Roldan, 1986), a skewed Normal distribution and a truncated power of Normal distribution (Hutchinson, Richardson, & Dykes, 1993). We examined more than twenty theoretical distributions to identify the best distribution, which can best simulate hourly rainfall in Ontario. The result shows that the Birnbaunsaunders and exponential probability density functions are the top two candidates. However, when using them to generate hourly rainfall, it is found that they couldn't produce suitable maximum values. Therefore, we used hourly rainfall at 133 IDF station in Ontario combined with hourly rainfall data of the 12 stations in USA, which are closest to Ontario, to construct the conditional cumulative distribution functions (CDFs). Using these CDFs, downscaled daily rainfall data and the quantile mapping method, wet hour rainfall in the future period could be generated. Since maximum hourly precipitations are generally greater than 10mm, we only focus on the days when daily rainfall amounts are greater than 10mm/day. Ideally, it is preferred to generate a cumulative distribution function (CDF) at each continuous value of daily rainfall for each station. However, this is impractical because we have no sufficient hourly data of storm days to construct robust conditional CDFs. At first, we categorized storm days (R>10mm/day) into nine categories according to the daily rainfall amounts. For each category, a conditional CDF is constructed (Figure 3). For example, the conditional CDF (F(x)/20mm<=Pr<25) is generated based on the rainfalls during wet hours on the days when daily rainfalls are between 20mm and 25mm (Figure 3c).
3.2 Extreme values analysis
There are several theoretical extreme value distribution functions (De Haan & Ferreira, 2007). The Gumbel distribution is used by Environment and Climate Change Canada (ECCC) to calculate the return period values listed in the MMAH Supplementary Standard SB-1 Climatic Data, including 10-year return period values of 15 min rainfall and 50-year return period value of one-day maximum precipitation. To be consistent with the industry standard in estimating these values, we used the Gumbel distribution to fit the projected data. The Gumbel distribution is (Castillo, 2012; Hong & Ye, 2014),
where a1, b1 and c1 are the parameters estimated by the available return period values such as 10-year return period values of 1-h, 2-h, 6-h, 12-h and 24-h maximum rainfall.
Based on the GCM projections from the 12-member ensemble and the methods mentioned above, the projections of these design values (defined in MMAH, 2015) for three 30-year period (1981-2010, 2041-2070 and 2071-2100) are developed. Following we will elaborate the procedure for each of the eight design values.
3.3.1 2.5% and 1% temperatures
The 1% and 2.5% January temperatures are the values used in the design of heating systems and the 2.5% percentile of July temperature is used in the design of cooling systems (MMAH, 2015). These temperature indicators are based on hourly temperatures generated by the methods described in 3.1. At each of the 228 locations, there are 22,320 hourly data (24-hours × 31-days × 30-years). The 2.5% and 1% of January temperatures are estimated using the 2.5th and 1st percentiles of the corresponding hourly temperatures. Similarly, the 2.5% July temperature is estimated using the 97.5th percentiles of the hourly temperatures.
3.3.2 Heating degree days(HDD)
HDD could be deemed as an indicator of building energy use in heating seasons. The calculation of HDD is straightforward. First, the downscaled high-resolution daily Tx and Tn (0.125° X 0.125°) are linearly interpolated on the 228 locations; Second, HDD is calculated with the approach provided in the handbook of the American Society of Heating, Refrigerating, and Air-conditioning Engineers (Handbook, 2009):
where N is the number of days in the year, T_18=18°C, is the reference temperature to which the degree-days are calculated, and T_i=(Tn+Tx)/2, is the mean daily temperature for the day. The superscript + indicates that only positive values of the bracketed quantity are taken into account in the HDD. Third, 30-year means of these values are calculated for each of the 12 models.
3.3.3 Annual Total Precipitation and Rainfall
Annual total precipitation and total rainfall of a year are calculated by adding all daily precipitations and rainfall in the year, respectively. Then, the annual values are spatially linearly interpolated on the 228 locations. Next, 30-year means of these values are calculated for each of the 12 ensemble members. Finally, the ensemble of PrTot and RTot are estimated.
3.3.4 Return Period Values
We calculated the return period values of RX1D and R15min, and used the median of the ensemble as the results.
4.1 January and July temperature change projection
Minimum temperature in January, maximum temperature in July, annual heating degree days (HDD) and cooling degree days (CDD) affect the design of heating system of buildings. Before analyzing these variables in details, we investigated their long term trend. The result shows that annual, January minimum and July maximum temperature steadily increased since 1980. As winter temperature continue increased, heating degree days significantly decreased since 1980 (not shown). Under RCP 6.0, temperatures and total precipitation are projected to significantly increase in Ontario (Zhu et al., 2017).
4.2 Indicators derived from daily data
As mentioned in section 3, Degree-days below 18°C (HDD), annual total precipitation (PrTot) and annual total rainfall (RTot) are directly estimated from the downscaled daily data. HDD is used as an indicator to measure the rate of consumption of fuel or energy to provide and maintain the thermal comfort for occupants of built environments. A difference of 1°C in the mean annual temperature will accumulate a difference of 250 to 350 °C day in HDD. PrTot is frequently used as a general indication of the wetness of a climate (MMAH, 2015). The three indicators (HDD, PrTot and RTot) are estimated in this study by comparing them with those in the updated climatic design data (MMAH, 2015). The result shows that the absolute error in HDD is less than 100°C (2.5% of averaged HDD) at most locations; errors in PrTot are less than 50mm (5-8%), and errors in RTot are less than 100mm (10-15%). These errors are within the reasonable ranges relative to the statistical properties (e.g. standard deviation, distribution, etc.) of these indicators. A further bias correction is conducted to the projections of future by subtracting the biases from the projected values in the individual models.
After the bias correction, the values in the base period (1990s) are the same as those in the recently updated codes (MMAH 2015). The values in the 2050s and 2080s are the projected data. Figure 4 shows the ensemble mean of HDD, PrTot and RTot for the three periods. It is observed that HDD may significantly decrease in the 2050s and 2080s relative to the values in the 1990s across all the 228 locations; PrTot and RTot may significantly increase in the 2050s and 2080s; relative to the 2050s, RTot may decrease in the 2080s at some locations.
Averaging over the 228 locations, HDD may decrease by 13.5% and 20.8% in the 2050s and 2080s, respectively; the decreasing amplitude varies across the province with a range of 450-800°C day in the 2050s and 700-1300°Cday in the 2080s. HDD could decrease more significantly in the northern regions.
PrTot may increase by 5.1% and 8.2%, and RTot may increase by 10.4% and 16.8% in the 2050s and 2080s, respectively. PrTot may increase more dramatically in the north than in the southern regions with a range of 30-60mm in the 2050s and 60-100mm in the 2080s. RTot may increase 50-100mm in the 2050s and 100-140mm in the 2080s, with larger increase in the southern Ontario.
4.3 Indicators derived from hourly temperature
The 1% and 2.5% January temperatures are the values used in the design of heating systems and the 2.5% percentile of July temperature is used in the design of cooling systems (MMAH, 2015). These three indicators are derived from the hourly temperatures which are generated using the equations (1--3). As an example, figure 2 shows two typical patterns of hourly temperature variation at the Pearson Airport weather station in January. It is observed that the average daily cycle of temperature (black) follows approximately a sine function. There are 61% of days, which are categorized as cluster-1, have a pattern similar to a sine function (red). The rest of the days are categorized as cluster-2 and follow a pattern (blue) significantly different from the sine function. Similarly, the two patterns are obtained for each of the 228 sites using the historical hourly data interpolated from the hourly CFSR temperature. The patterns vary with months (January and July) and locations (228 sites) in Ontario. Based on the patterns, the downscaled daily temperatures and the binomial logistic regression model (equation 3), hourly temperatures in January and July are generated at each of the 228 stations for each member of the ensemble for the period 1981-2100. Figure 5 shows the current (1990s) and projected (2050s and 2080s) values of 2.5% and 1% January temperatures, and 2.5% July temperature obtained using the method described in section 3.3.1. It is observed that these three design values will significantly increase in the future over all the locations. The 1% and 2.5% January temperatures may increase by 2-4°C and 4-7°C, and 2.5% July temperature may increase by 2-3°C and 4-5°C, in the 2050s and 2080s, respectively. Generally, the increases in the northern Ontario are more significant than in the southern parts of the province.
4.4 Indicators of extreme rainfall events
The 50-year return period values of rainfall for the 1990s, 2050s and 2080s are calculated by fitting the annual maximum one-day rainfall to the Gumbel extreme value distribution using the standard method described in section 3.2 (MMAH, 2015; Lowely & Nash, 1970). As well, the 15-minute values are estimated using the methods proposed in section 3.1.2, 3.2 and 3.3.4. The hourly rainfall data at the 12 USA stations are chosen to estimate the conditional CDFs, which are then used for the generation of rainfall amounts at wet hours. Although the hourly rainfall amounts of CFSR are not used to generate rainfall amount because they vary very smoothly and always underestimate extreme hourly rainfall, they are used to construct weather generators. As the observations at most of the 228 sites do not include complete datasets, the daily and hourly rainfall amounts from CFSR are used to construct the weather generators (WGs) at each site to predict the occurrence of wet and dry hours. Figure 3 shows that the conditional CDFs of hourly rainfall for the nine daily rainfall intervals. It is observed that the conditional CDFs of hourly rainfall amount (blue curves) are significantly different from the general CDF constructed based on all the hourly rainfall data (red line) of storm days; the differences are more significant for a heavier daily rainfall as it correlates with a higher probability of more intensive hourly rainfall. For example, the probability of >20mm/hour events is less than 0.5% on days when daily rainfall is between 20 and 25mm. However, this probability increases to 6% when daily rainfall is greater than 50mm. Combining the stochastic WGs for wet hour predictions and the conditional CDFs, hourly rainfall amounts on storm days during 1981-2100 are produced for each ensemble member.
Based on the IDF model proposed by Bernard (1932), the 10-year return period values of 15-minute rainfall could be indirectly estimated based on hourly rainfall. As an example, at Pearson International Airport station the model fits the return values of hourly rainfall very well with R2=0.96. There is a strong linear correlation between duration and rainfall intensity in the plot using a log-scaled vertical axis. Linear regression model fits the relation between durations for the 10-year return period values very well (not shown). Generally, there are stronger linear correlations among longer duration values. The correlation coefficients decrease with the length of durations. In Ontario, the correlation coefficient between the 10-year return period values of hourly and 15-minitue rainfall is 0.75, which represents a strong linear correlation. Using the 10-year return period values of 1-h, 2-h, 6-h, 12-h and 24-h maximum rainfall and equation (9), the 10-year return period values of 15-minitue rainfall are estimated at the 228 sites in this study. Figure 6 shows that the 50-year return period values of maximum daily rainfall and 10-year return period value of R15min may increase in the future at many locations. The intensity of RX1D may increase by about 5-15mm/day and 10-20mm/day at most locations in the 2050s and 2080s, respectively; and the intensity of R15min may increase by 1-5mm (or decrease by 1-2mm at some locations) in the 2050s and 2080s, respectively.
5. Summary and discussion
In this study, eight temperature and precipitation related climate indices are projected across the province of Ontario in Canada in the 2050s and 2080s based on an ensemble of downscaled CMIP5 data under the IPCC AR5 RCP6.0 scenario. These indices are often used as climate indicators in design of infrastructures. Four of them are based on daily data, and the other four indicators are based on sub-daily data.
To generate sub-daily data, a number of novel models are developed for temporally downscaling temperature and precipitation from daily to hourly scales, including clustering-logistic regression models to generate hourly temperature in January and July and weather generators to produce hourly rainfall on storm days from May to October. The hourly temperature data from all the members of the ensemble are then used to generate probabilistic distribution function and the percentiles (1% and 2.5%). Appling the extreme value theory to annual maximum of daily and hourly rainfall data, the return period values of rainfall events are calculated for the 2050s and 2080s.
The results show that as global warming continues, heating degree-days (HDD) may significantly decrease in the future; annual total precipitation amount may significantly increase in the 2050s, then remain stable or decrease at some locations in the 2080s. The three temperature percentile indicators may significantly increase in the future. January temperature percentiles (1% and 2.5%) may increase with a larger rate than July temperature (2.5%). The 50-year return period values of One-Day-Rainfall events may significantly increase across the province; while the 10-year return period values of 15-minutes rainfall may increase at most locations, they may remain stable after the 2050s only at some locations.
The projections of HDD provided in this study could set the stage for future research on building energy use projections in Ontario, as HDD could be deemed as an indicator of building energy use in heating seasons. However, drawing practical conclusions for building energy use would require us to pose more specific questions in conjunction with other energy/thermal performance indicators. For example, of many building properties, the type of building could play a significant role on how climate change might impact building energy use, demanding different climate change adaption strategy (Shen 2017). Among other energy/thermal performance indices, overheating hours should be also considered (Gupta & Gregg 2012) in tandem with HDD from not only energy use perspective but also thermal performance of building, which could adversely affect thermal comfort of occupants.
Despite the fact that climate models are helpful to estimate some climate extreme variables, quantifying the impact of climate change on the climatic design values is still an extremely challenging task. It is more challenging to estimate the precipitation related variables than temperature related variables. The uncertainty in projections of the extreme climatic values for climatic design data calculation may come from many different sources, such as the imperfection of GCM models, spatial-temporal downscaling models, approximation in extreme value theory, and the lack of long-term reliable high-resolution observation. Although great effort has been put in the development of the projections in this study using best available information to the authors, there is still plenty of room for further improvement. The results from this study should be used with caution and under guidance from climatic design data development professionals.
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