A Synoptic Weather-Typing Approach to Project Future Daily Rainfall and Extremes at Local Scale in Ontario, Canada

15 JULY 2011 C H E N G E T A L . 3667

CHAD SHOUQUAN CHENG,GUILONG LI, AND QIAN LI Atmospheric Science and Applications Unit, Meteorological Service of Canada Branch, Environment Canada, Toronto, Ontario, Canada

HEATHER AULD Adaptation and Impacts Research Section, Atmospheric Science and Technology Directorate, Science and Technology Branch, Environment Canada, Toronto, Ontario, Canada

(Manuscript received 1 April 2010, in ﬁnal form 20 December 2010)

ABSTRACT

This paper attempts to project possible changes in the frequency of daily rainfall events late in this century for four selected river basins (i.e., Grand, Humber, Rideau, and Upper Thames) in Ontario, Canada. To achieve this goal, automated synoptic weather typing as well as cumulative logit and nonlinear regression methods was employed to develop within-weather-type daily rainfall simulation models. In addition, regression-based downscaling was applied to downscale four general circulation model (GCM) simulations to three meteorological stations (i.e., London, Ottawa, and Toronto) within the river basins for all meteorological variables (except rainfall) used in the study. Using downscaled GCM hourly climate data, discriminant function analysis was employed to allocate each future day for two windows of time (2046–65, 2081–2100) into one of the weather types. Future daily rainfall and its extremes were projected by applying within-weather-type rainfall simulation models together with downscaled future GCM climate data. A ver- iﬁcation process of model results has been built into the whole exercise (i.e., statistical downscaling, synoptic weather typing, and daily rainfall simulation modeling) to ascertain whether the methods are stable for projection of changes in frequency of future daily rainfall events. Two independent approaches were used to project changes in frequency of daily rainfall events: method I—comparing future and historical frequencies of rainfall-related weather types, and method II—applying daily rainfall simulation models with downscaled future climate information. The increases of future daily rainfall event frequencies and seasonal rainfall totals (April–November) projected by method II are usually greater than those derived by method I. The increase in frequency of future daily heavy rainfall events greater than or equal to 25 mm, derived from both methods, is likely to be greater than that of future daily rainfall events greater than or equal to 0.2 mm: 35%–50% versus 10%–25% over the period 2081–2100 derived from method II. In addition, the return values of annual maximum 3-day accumulated rainfall totals are projected to increase by 20%–50%, 30%–55%, and 25%–60% for the periods 2001–50, 2026–75, and 2051–2100, respectively. Inter-GCM and interscenario uncertainties of future rainfall projections were quantitatively assessed. The intermodel uncertainties are similar to the interscenario uncertainties, for both method I and method II. However, the uncertainties are generally much smaller than the projection of percentage increases in the frequency of future seasonal rain days and future seasonal rainfall totals. The overall mean projected percentage increases are about 2.6 times greater than overall mean intermodel and interscenario uncertainties from method I; the corresponding projected increases from method II are 2.2–3.7 times greater than overall mean uncertainties.

1. Introduction Corresponding author address: Dr. Chad Shouquan Cheng, At- Heavy precipitation events are likely to increase al- mospheric Science and Applications Unit, Meteorological Service of Canada Branch, Environment Canada, 4905 Dufferin St., Tor- most everywhere over the globe owing to a changing onto ON M3H 5T4, Canada. climate (e.g., Cubasch et al. 1995; Zwiers and Kharin E-mail: [email protected] 1998; Kharin and Zwiers 2005; Tebaldi et al. 2006; Meehl

DOI: 10.1175/2011JCLI3764.1

Unauthenticated | Downloaded 10/03/21 02:21 PM UTC 3668 JOURNAL OF CLIMATE VOLUME 24 et al. 2007). The Fourth Assessment Report (AR4) of like precipitation, with a nonnormal distribution. To the Intergovernmental Panel on Climate Change (IPCC) overcome this problem, alternative techniques that can has indicated that precipitation intensity is projected to cater for nonnormal distributed data should be em- very likely increase over the world late this century un- ployed to downscale daily precipitation. To achieve this, der global warming (Alley et al. 2007). Many studies a number of studies (e.g., Buishand et al. 2004; Abaurrea have specifically focused on projecting changes in future and Asıń 2005; Fealy and Sweeney 2007) have con- annual mean precipitation and frequency of heavy structed the downscaling transfer functions of daily rainfall events, using general circulation model (GCM) precipitation by employing logistic regression as an oc- projections. For example, using a six-GCM-model en- currence model and generalized linear modeling (GLM) semble, Emori and Brown (2005) showed that annual approach as a quantity model. The results obtained from mean precipitation is projected to increase by 20%–50% these studies have shown that use of both logistic re- at high latitudes (i.e., poleward of 508N/S) by the end of gression and GLM offers a significant improvement over this century. Tebaldi et al. (2006) employed simulations multiple linear regression. However, some of the studies from nine IPCC AR4 GCMs to assess changes in future indicated that these daily rainfall downscaling transfer precipitation extremes and found that in the high latitudes functions still possess low model R2s (Buishand et al. of the Northern Hemisphere there are the most coherent 2004) and have difficulties with predicting extreme pre- regional patterns of significant increases in the intensity of cipitation events (Fealy and Sweeney 2007). Haylock precipitation extremes. Other studies (e.g., Zwiers and et al. (2006) have employed six statistical downscaling Kharin 1998; Kharin and Zwiers 2005) have determined methods to downscale daily precipitation over the United thattheincreaseinmagnitudeoffutureprojectedextreme Kingdom. Of the six methods examined, four employed precipitation is greater than that of annual mean preci- artificial neural networks, one used canonical correlation pitation. As pointed out by Kharin and Zwiers (2005), analysis, and another one is the regression-based statis- while the globally averaged annual mean precipitation tical downscaling method—SDSM developed by Wilby rate is projected by the Canadian Centre for Climate et al. (2002). The results revealed that ‘‘the inter-model Modelling and Analysis (CCCma) Coupled General Cir- differences between the future changes in the downscaled culation Model (CGCM1 A2) to increase by less than 3% precipitation indices were at least as large as the differ- by the end of this century, the corresponding increase in the ences between the emission scenarios for a single model’’ 20-yr return values of annual extremes of 24-h precipitation (Haylock et al. 2006). This implies that when projecting rates is projected to be more than 12%. future local-scale precipitation information, different However, large-scale GCM simulations are not suit- types of downscaling methods should be considered. able for local-scale climate change impact analysis. To Atmospheric circulation-type classifications, such as sea overcome the discrepancy between two scales, down- level air pressure patterns, have also been employed to scaling methodologies are widely used to derive local- or construct their relationships with daily rainfall, which can station-scale future rainfall information. One of the be applied to derive local-scale/station-scale future daily leading techniques for doing this is statistical (empirical) rainfall information from large-scale GCM simulations downscaling (Wilby and Wigley 1997). Many statistical (e.g., Goodess and Palutikof 1998; Kostopoulou and Jones techniques have been used to develop downscaling 2007a,b). An alternative approach—automated synoptic transfer functions, as reviewed by Fowler et al. (2007). weather typing (or air mass typing)—has been employed The statistical downscaling methods are generally di- in evaluation of climate impacts on a number of environ- vided into three major groups: regression-based models, mental issues (Cheng et al. 2010). The synoptic weather weather-typing schemes, and weather generators. typing is able to characterize a complex set of meteoro- Previous multiple regression approaches to develop logical variables as a coherent index (Kalkstein 1979; Perry precipitation downscaling transfer functions had diffi- 1983), using not only hourly sea level air pressure but also culty with simulating statistical properties of daily pre- hourly surface and upper-air observations of temperature, cipitation processes. For example, Nguyen et al. (2006) dewpoint, u wind, y wind, and total cloud cover. applied the statistical downscaling model (SDSM) built However, to date, it appears that the automatic syn- by the multiple regression method to downscale daily optic weather typing has not been employed to downscale precipitation in Montreal region (Quebec, Canada); the future daily rainfall climate information from large-scale coefficients of determination R2 after calibration of the GCM simulations in Canada. The current study employs downscaling transfer functions are very low, ranging the synoptic weather typing and a number of linear and from 0.062 to 0.098. One of the major reasons for this nonlinear regression techniques to downscale future daily weak regression result is that multiple regression ap- rainfall from large-scale GCM simulations to the selected proaches are not suitable for some weather variables, river basins in Ontario, Canada. This method is dependent

Unauthenticated | Downloaded 10/03/21 02:21 PM UTC 15 JULY 2011 C H E N G E T A L . 3669 on the stationarity of the past 50-yr predictor–predictand this current study. The warm season (April–November) relationships under future climate conditions. The down- was selected since most of the extreme rainfall events in scaling scheme is built upon the previous studies (i.e., the study area occur during this period. These observa- Cheng et al. 2008, 2010), which is made up of a three- tions include hourly surface meteorological data and U.S. step process. First, within-weather-type daily rainfall National Centers for Environmental Prediction (NCEP) simulation models were developed and validated using six-hourly upper-air reanalysis weather data. These data synoptic weather typing with cumulative logit regression consist of air temperature, dewpoint temperature, sea and nonlinear regression procedures (Cheng et al. 2010). level air pressure, total cloud cover, south–north and As demonstrated in the study by Cheng et al. (2010), the west–east wind speed. In addition to hourly meteoro- results obtained imply that it is necessary to perform syn- logical data, daily rainfall data observed at the climate optic weather typing prior to the development of daily stations within each of four selected river basins (Fig. 1) rainfall simulation models. Furthermore, for development were used to calculate daily river basin–average rainfall of daily rainfall simulation models, the study has used quantities, representing average rainfall conditions for the a number of the atmospheric stability indices in addition to catchment. A number of climate stations (13, 12, 13, and 9 the standard meteorological variables (commonly used in for Grand, Humber, Rideau, and Upper Thames River most of the previous downscaling papers). Second, re- basins, respectively) were selected for the analysis. As gression-based downscaling transfer functions developed described in the study by Cheng et al. (2010), one of the by Cheng et al. (2008) are adapted to project station-scale major reasons for using river basin–average daily rainfall future hourly meteorological variables (except rainfall) is that it is suitable for simulation of rainfall-related that were used in development of daily rainfall simulation streamﬂow volumes, as part of the project. models. Hourly meteorological variables include air tem- In addition to historical observations, daily climate perature, dewpoint temperature, sea level air pressure, change simulations from three GCMs and two emission total cloud cover, and south–north and west–east wind scenarios were used in the study, summarized in Table 1. speed. Future hourly climate projections were derived These models and scenarios include the following: one from temporal downscaling transfer functions (i.e., rela- Canadian GCM—CGCM2 [IPCC Special Report on tionships between hourly and daily weather variables Emissions Scenarios (SRES) A2 and B2]; one U.S. derived from observations). Third, using downscaled fu- GCM—Geophysical Fluid Dynamics Laboratory Cli- ture hourly climate projections, future daily synoptic mate Model version 2.0 (GFDL CM2.0; IPCC SRES weather types and then future daily rainfall quantities A2); and one German GCM—ECHAM5–Max Planck can be projected by applying synoptic weather typing Institute Ocean Model (MPI-OM; IPCC SRES A2). A2 and within-weather-type rainfall simulation models. and B2 scenarios considered different assumptions of This paper is organized as follows. In section 2, data future greenhouse gas (GHG) emissions derived from a sources and their treatments are described. Section 3 distinctly different direction for future population growth, summarizes within-weather-type daily rainfall simulation economic development, and technological change. From modeling and statistical downscaling developed from re- Environment Canada’s Web site (Environment Canada cent studies (Cheng et al. 2008, 2010) since methods and 2006), it is seen that the scenario A2 is similar to the IPCC results from both studies are used in the current analysis. ‘‘business-as-usual’’ scenario. Compared to scenario A2, Section 4 presents the analysis techniques as applied to the scenario B2 produces much lower GHG emissions and projection of future weather types and assessment of cli- aerosol loadings in the future and projects less future mate change impacts on daily rainfall: method I and warming, especially in the second half of this century. method II. Section 5 includes the results and discussion on Both scenarios were used in the study to generate a range future rainfall-related weather types, robustness of rain- of projections of possible climate change impacts on fu- fall simulation models, changes in frequency of future ture daily rainfall events. From the GCM experiments of daily rainfall events and seasonal rainfall totals, changes in stationary simulations for the speciﬁed time slices, daily future return-period values of extreme rainfall events, and data for all used surface weather variables (i.e., maximum uncertainty of the study. The conclusions and recom- and minimum temperatures, sea level air pressure, and mendations from the study are summarized in section 6. west–east and south–north wind speed) were included in the study. In addition to surface climate information, daily upper-air GCM simulations of temperature and west–east 2. Data sources and south–north winds on standard atmospheric levels Historical observations for the period April–November (i.e., 925, 850 700, 600, and 500 hPa) were used in the 1958–2002 used in the study by Cheng et al. (2010) to analysis. For these GCM simulations, the three time develop daily rainfall simulation models were also used in windows (1961–2000, 2046–65, 2081–2100) were used in

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FIG. 1. Study area and location of four selected river basins in Ontario, Canada. Dots are climate stations having daily observations and stars are location of the cities with meteorological stations having hourly observations. the analysis because these data are only available from the were used in synoptic weather typing, which are hourly Web site of the Program for Climate Model Diagnosis and surface weather observations of six elements: air tem- Intercomparison (Program for Climate Model Diagnosis perature, dewpoint temperature, sea level air pressure, and Intercomparison 2006). Furthermore, for projections total cloud cover, and south–north and west–east wind of future return-period values of extreme rainfall events, speed. Using daily 13-component scores produced by two Canadian GCM transient model simulations for the PCA that explained 91% of the total variance, the a 100-yr period (2001–2100) were included (Table 1). average linkage clustering procedure and discriminant function analysis resulted in 24 major synoptic weather types for the study area. Of these weather types, 10 3. Summary of the previous studies synoptic weather types were identiﬁed over the 45-yr As part of this research, Cheng et al. (2010) have de- period as primary rainfall-related weather types. These veloped simulation models of daily rainfall quantities 10 weather types can capture 73%–77%, 92%–93%, and statistical downscaling transfer functions for stan- and 95%–98% of the rainfall events with daily rainfall dard meteorological variables (Cheng et al. 2008). Since greater than or equal to 0.2, 10, and 25 mm, respectively, both studies were used in this current paper to project across the selected river basins. changes in frequency of future daily rainfall events, it is As described in the study by Cheng et al. (2010), 10 necessary to outline major methods used in and results rainfall-related weather types are associated with syn- derived from both studies. optic weather patterns: cold front I, cold front II, cold front III, cold low, cyclone I, cyclone II, mesohigh, a. Summary of daily rainfall modeling quasi-stationary front, warm front I, and warm front II. A recent study by Cheng et al. (2010) employed an automated synoptic weather typing as well as stepwise cumulative logit and nonlinear regression analyses to TABLE 1. GCM simulations and scenarios used in the study. simulate the occurrence and quantity of daily rainfall GCM IPCC scenario Periods events. The synoptic weather typing was developed using principal components analysis (PCA), an average Canadian CGCM2 SRES A2 1961–2000, 2046–65, SRES B2 2081–2100; return linkage clustering procedure, and discriminant function period analysis: analysis to identify the weather types most likely to be 2001–2100 associated with daily rainfall events for the four selected German SRES A2 1961–2000, 2046–65, river basins in Ontario. The entire suite of 144 weather ECHAM5–MPI-OM 2081–2100 variables during the period April–November 1958–2002 U.S. GFDL-CM2.0 SRES A2

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FIG. 2. Monthly mean number of days occurring with each of 10 identiﬁed rainfall-related weather types or weather patterns in Thames River basin for the period 1958–2002.

The weather pattern was identiﬁed for each of the Within-weather-type daily rainfall simulation model- weather types, based on a subjective examination of ing comprises a two-step process: 1) cumulative logit a number of surface weather maps associated with heavy regression to predict the occurrence of daily rainfall rainfall events. As shown in Fig. 2, weather types or events, and 2) using probability of the logit regression, weather patterns occur in different seasons. The weather a nonlinear regression procedure to simulate daily rain- patterns labeled with ‘‘I’’ occur most frequently in the fall quantities. The 228 predictors used in development summer (June–August) and usually possess much warmer of daily rainfall event occurrence simulation models in- characteristics than do the same weather patterns labeled clude not only the standard meteorological variables but with ‘‘II,’’ which occur most often in the spring (April– also a number of the atmospheric stability indices (e.g., May) and fall (September–November). Cold front III was lifted index, Galway 1956; K-index, George 1960; total identiﬁed for the weather type that can occur through- totals index, Miller 1972). To avoid effects of multi- out all seasons and that typically has thermal conditions collinearity among explanatory variables, the PCA was between cold front I and cold front II. In addition, within- used once again to convert intercorrelated meteorolog- weather-type frequency of daily rainfall events and mean ical variables into uncorrelated principal component daily rainfall quantities in the Thames River basin for the scores, which were then used as predictors for the cu- period April–November 1958–2002 are shown in Table 2. mulative logit regression. In addition, to effectively dis- Similar results were also found for other selected river tinguish heavy rainfall events, the atmospheric stability basins but not shown owing to the limitations of space. indices were rearranged as dummy variables based on

TABLE 2. Within-weather-type daily mean rainfall amount and number of daily rainfall events in Thames River basin for the period April–November 1958–2002.

Synoptic weather type No. of daily rainfall events Weather pattern No. of days Daily mean rainfall (mm) $10 mm $25 mm Cyclone I 591 5.8 112 20 Cyclone II 516 6.9 129 26 Mesohigh 668 5.1 111 27 Cold low 569 5.4 107 20 Cold front I 739 3.4 70 15 Cold front II 304 3.8 26 4 Cold front III 316 6.9 76 13 Quasi-stationary front 636 4.1 96 18 Warm front I 253 9.3 97 17 Warm front II 296 5.4 60 6 Subtotala 4888 5.3 884 166 Other I (with rainfall)b 3086 0.9 55 3 Other II (no rainfall)c 2943 0.1 6 0 Totald 10 917 945 169 a The sum of 10 rainfall-related weather types. b Weather types with nonsigniﬁcant rainfall days (composed of seven major weather types and smaller ones). c Weather types with a little or no rainfall days (composed of seven major weather types and smaller ones). d The sum of all weather types.

Unauthenticated | Downloaded 10/03/21 02:21 PM UTC 3672 JOURNAL OF CLIMATE VOLUME 24 their relationships with daily rainfall quantities. Across TABLE 3. Criteria used to evaluate daily rainfall quantity simu- the four selected river basins, the daily-rainfall-event lation models. Diff is the absolute difference between observed and occurrence simulation models revealed that there are simulated rainfall and obs is the river basin–average daily observed rainfall. significant correlations between the occurrence of daily rainfall events and model simulations. As described Correctness Observed Observed in the study by Cheng et al. (2010), the models’ concor- level rainfall , 5mm rainfall $ 5mm dances, derived from cumulative logit regression, range Excellent Diff # 1.5 mm Diff # 30% of obs from 0.82 to 0.96 (a perfect model would have a con- Good 1.5 , Diff # 3.0 mm 30% of obs , Diff cordance value of 1.0). Of the total 40 simulation models # 60% of obs Fair 3.0 , Diff # 4.0 mm 60% of obs , Diff (10 models for each of the 4 selected river basins), 11, 19, # 80% of obs and 33 models possess concordances greater than 0.92, Poor Diff . 4.0 mm Diff . 80% of obs 0.90, and 0.87, respectively. To evaluate performance of daily rainfall quantity simulation models, the four correctness levels of ‘‘excellent,’’ ‘‘good,’’ ‘‘fair,’’ and ‘‘poor,’’ downscaling method developed by Cheng et al. (2008) asshowninTable3,weredefinedbasedontheabsolute was adapted for this current study. This downscaling difference between observed and simulated daily rainfall method comprises a two-step process: to spatially down- amounts. As described in the study by Cheng et al. (2010), scale daily GCM simulations to the selected weather the proportion of simulations on daily rainfall quantities stations in south-central Canada and then to temporally that fell into excellent and good categories was much downscale daily scenarios to hourly ones. higher than the proportion that fell into fair and poor The downscaling transfer functions were constructed categories. Cheng et al. (2010) have found that, across using different regression methods for different meteo- the four selected river basins, the percentage of excellent rological variables since a regression method is suitable and good daily rainfall simulations ranged from 62%– only for a certain kind of data with a specific distribution. 84%. In addition, it is noteworthy that the rainfall simu- A number of regression methods, such as multiple step- lation models are able to capture most of daily heavy wise regression, cumulative logit regression, orthogonal rainfall events (i.e., $32.5 mm) with the percentage of regression, and autocorrelation correction regression, excellent and good simulations: 62%, 68%, 70%, and 81% were used to develop downscaling transfer functions. for Grand, Thames, Humber, and Rideau River basins, Performance of the downscaling methods was evaluated respectively. by 1) analyzing model R2s of downscaling transfer func- The entire methodology used in the study by Cheng tions, 2) validating downscaling transfer functions using et al. (2010), which is comprised of synoptic weather a leave-one-year-out cross-validation scheme, and 3) typing and rainfall simulation modeling, was validated comparing data distributions, diurnal/seasonal varia- by randomly selecting one-fourth of the total years for tions, and extreme characteristics of the weather vari- the weather data. The remaining three-fourths of the ables derived from downscaled GCM historical runs total years were used for model development. The vali- with observations over a comparative time period of dation dataset is therefore independent from the data 1961–2000. The results showed that regression-based sample used in the development of the models. The downscaling methods performed very well in deriving validation results showed that the models were success- daily and hourly station-scale climate information for all ful at replicating occurrence and quantity of daily rainfall weather variables. The strong correlations between events with similar results to the model simulations station-scale predictands and GCM-scale predictors are outlined above (refer to Cheng et al. 2010 for details). similar between model calibrations and validations. Most of the daily downscaling transfer functions possess b. Statistical downscaling of meteorological model R2s greater than 0.9 for surface temperature, sea variables level air pressure, upper-air temperature, and winds; the To project future daily rainfall, downscaled future corresponding model R2s for daily surface winds are hourly climate information for the standard meteoro- generally greater than 0.8. The hourly downscaling logical variables (excluding rainfall) that were used in transfer functions for surface air temperatures, dew- development of daily rainfall simulation models is point, and sea level air pressure possess the highest needed. These meteorological variables include surface model R2 (.0.95) of the weather elements. The func- and upper-air temperature, dewpoint, west–east and tions for south–north wind speed (y wind) are the south–north winds, sea level air pressure, and total cloud weakest model (model R2s ranging from 0.69 to 0.92 cover. To derive future hourly station-scale climate infor- with half of them greater than 0.89). For total cloud mation from GCM-scale simulations, a regression-based cover, hourly downscaling transfer functions developed

Unauthenticated | Downloaded 10/03/21 02:21 PM UTC 15 JULY 2011 C H E N G E T A L . 3673 using the cumulative logit regression have concordances that ranged from 0.78 to 0.87 with over 75% greater than 0.8. Details of the daily and hourly downscaling methodologies as well as the results of downscaling transfer functions’ calibration and validation are not presented in this current paper owing to the limitations of space (refer to Cheng et al. 2008 for details).

4. Analysis techniques To project climate change impacts on frequency of future daily rainfall events, in addition to daily rainfall simulation models and future station-scale climate simulations, future synoptic weather types are required for this study. The principal methods and steps used in this study are summarized in Fig. 3. This section focuses FIG. 3. Flowchart of methodologies and steps used in the study. on methodological description for projection of future weather types and assessment of climate change impacts daily rainfall events and seasonal rainfall totals can be on rainfall. quantitatively projected. In this study, two independent a. Projection of future weather types approaches were used to assess climate change impacts on daily rainfall: method I—comparing future and his- Using downscaled future hourly climate simulations, torical frequencies of rainfall-related weather types—and discriminant function analysis is able to project future method II—applying daily rainfall simulation models con- daily weather types. To determine future weather types, structed in the study by Cheng et al. (2010), with the principal component scores for each of the future days downscaled future climate information. Method I de- were calculated by multiplying the posteigenvector pends on changes in the frequency of future rainfall- matrix by the standardized future climate data matrix. related weather types alone. The frequency of future The posteigenvector, derived from the developmental daily rainfall events and future seasonal rainfall totals dataset by PCA for synoptic weather typing (con- are assumed to be directly proportional to change in structed in the study, Cheng et al. 2010), was used, so frequency of future rainfall-related weather types. The that future component scores are comparable with the future seasonal rainfall totals or frequency of future postscores since both used the same set of eigenvectors. daily rainfall events (Rainf ) can be projected as follows: In addition, to more effectively compare component ! scores from both historical and future datasets as well as n Freqf to remove the GCM bias, future downscaled climate f 5 i 3 h Rain å h Raini , (1) data were standardized using the mean and standard i51 Freqi deviation of downscaled GCM historical runs (1961– 2000). Using the centroids of the predetermined weather where n is the number of all weather types (including h types derived from the observed data, discriminant 10 rainfall-related and other weather types), Freqi f function analysis can assign each of the future days into and Freqi are seasonal mean occurrences of the weather one of the predetermined weather types based on proxi- type i for historical and future periods, respectively, and h mate component scores. Since the synoptic weather types Raini is the historical seasonal rainfall totals or fre- and their respective characteristics have already been pre- quency of historical daily rainfall events, within the determined, discriminant function analysis is an appropri- weather type i. ate tool to assign each day of the future two time periods To support this assumption, the relationships between (2046–65 and 2081–2100) into one of the predetermined observed seasonal rainfall totals (or the number of sea- weather types (Klecka 1980; Lam and Cheng 1998). sonal total rain days) and seasonal frequency of 10 rainfall-related weather types were evaluated for the b. Assessment of climate change impacts on rainfall: period April–November 1958–2002, across the selected Method I river basins. For the 45 individual seasons, seasonal Using changes in the number of days within weather rainfall totals (or the number of seasonal total rain days) types and weather characteristics as a result of climate versus seasonal occurrence frequency of 10 rainfall- change, potential changes in the frequency of future related weather types were plotted to demonstrate the

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FIG. 4. Upward trends of the (a) number of seasonal rain days and (b) seasonal rainfall totals against seasonal occurrence frequency of 10 rainfall-related weather types for the period April–November 1958–2002 in Thames River basin. The solid line is a regression trend with slope b and p value. relationships. As shown in Fig. 4, in the Thames River addition, the future standard meteorological variables basin, seasonal rainfall totals and frequency of daily were converted into the principal component variables rainfall events greater than or equal to 0.2 mm signiﬁ- for each day of the future dataset by multiplying the cantly increase with an increase in the seasonal fre- posteigenvector matrix (using the historical model de- quency of the 10 rainfall-related weather types. Similar velopmental dataset) by the future downscaled climate results were found for other selected river basins but not data matrix. Similar to projection of future synoptic shown owing to limitations of space. Across the four weather types, the posteigenvector was used, so that selected river basins, seasonal rainfall totals increase by future component scores are comparable with the a range of 1.8 mm (Rideau) to 4.3 mm (Humber) (four- postscores since both used the same set of eigenvectors. river-basin nonweighted average: 3.4 mm) per one day Moreover, the future downscaled climate data were increase in frequency of 10 rainfall-related weather standardized using the mean and standard deviation of types. The corresponding increase quantity for the num- downscaled GCM historical runs (1961–2000) to more ber of seasonal rain days ranges from 0.6 (Rideau) to 1.0 effectively compare component scores from both his- (Grand) (four-river-basin average 5 0.8). torical and future datasets as well as to remove the GCM bias. Second, using the probability of future daily rainfall c. Assessment of climate change impacts on rainfall: occurrence, within-weather-type nonlinear daily rainfall Method II quantity simulation models were used to project future daily rainfall amounts. In addition to changes in the frequency of future In each of the selected river basins, there are 11 daily rainfall-related weather types considered in method I rainfall quantity simulation models involved. In addition for projecting changes in future daily rainfall events, to 10 simulation models for 10 rainfall-related weather method II also considered changes in future climate types described above, an extra simulation model was characteristics. Method II applies within-weather-type developed for the weather grouping other I. Other I daily rainfall simulation models (developed in the study, consists of the weather types associated with some Cheng et al. 2010) with downscaled future climate data rainfall events, which do not meet the selection criteria to project future daily rainfall quantities. To project for a ‘‘pure’’ rainfall-related weather types, The remainder future daily rainfall quantities, a two-step process of of the weather types are grouped into other II, which is daily rainfall simulation modeling was employed. First, relatedtodayswithnorainfall. Consequently, all future daily rainfall occurrence simulation models were em- days falling into the weather grouping other II were con- ployed to project probability of future daily rainfall sideredtohavenorainfall. occurrence. To more effectively apply daily rainfall occurrence simulation models, the 228 predictors used in development of the models, as described above, are 5. Results and discussions needed for the future dataset. The future atmospheric a. Future rainfall-related weather types stability indices were set up as the dummy variables according to the same criteria used for the historical Using downscaled hourly climate information, discrim- observations (refer to Cheng et al. 2010 for details). In inant function analysis is able to project future daily

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FIG. 5. Percentage occurrences of the 10 rainfall-related weather types as shown by observations (obs, 1961–2000) and downscaled 3-GCM A2 ensemble for three time periods (HR—historical run, 1961–2000; 2046–65; 2081–2100). weather types for two time periods: 2046–65 and 2081– and historical observations over the time period 1961– 2100 as well as a GCM historical run period: 1961–2000. 2000, respectively. The difference in occurrence fre- As discussed above, 10 weather types were identiﬁed quency of each rainfall-related weather type between over the period April–November 1958–2002 as the pri- downscaled GCM historical runs and observations is mary rainfall-related types. Percentage occurrences of consistent among the selected river basins. Overall, the 10 rainfall-related weather types are plotted in Fig. 5, across the study area, the combined occurrence fre- as shown by observations and downscaled 3-GCM A2 quency of 10 rainfall-related weather types derived from ensemble for three time periods (1961–2000, 2046–65, downscaled GCM historical runs is 4%–6% lower than 2081–2100). Percentage occurrences of the weather that derived from the observations. However, the dif- types have a good agreement between observations and ference of percentage occurrence varies from weather downscaled GCM historical runs over a comparative type to type, as shown in Table 4, on average of three time period 1961–2000 across the study area. This im- cities (London, Ottawa, and Toronto). For example, plies that the downscaling method is suitable to derive about 1%–2% adjustment was used to increase the pro- station-scaled future climate information, and discrimi- jections of future daily rainfall events for each of the four nant function analysis performs well in projecting future weather types (cyclone I, quasi-stationary front, meso- rainfall-related weather types. high, and cold Front II). Conversely, for cold front I and As shown in Fig. 5, the occurrence frequency of each cold low, the occurrence frequency derived from down- rainfall-related weather type derived from downscaled scaled GCM historical runs is about 0.5%–1% greater GCM historical runs is slightly different from that de- than the observations, which were used to decrease the rived from the observations, over a comparative time future projections. period (1961–2000). This difference should be taken into After considering such a difference, the three-site- account for each of GCM scenarios and each of the river averaged percentage occurrences of the future 10 rainfall- basins when evaluating climate change impacts on fre- related weather types are projected to be 49%–53% quency of future daily river basin–averaged rainfall across two future time periods (the current average of events by the following expression: 46%). Speciﬁcally for individual weather types and GCM scenarios, the changes might be different. Table 5 f f h HR Rainadjusted,i 5 Rainunadjusted,i 1 (Raini 2 Raini ), (2) shows percentage changes in the frequency of future rainfall-related weather types derived from downscaled f f where Rainadjusted,i and Rainunadjusted,i are adjusted and CGCM A2 and CGCM B2 on average of three cities unadjusted seasonal frequencies of future daily river (London, Ottawa, and Toronto). It is immediately basin–averaged rainfall events associated with the weather apparent that the warmer weather types occurred usu- HR h type i,andRaini and Raini represent the corresponding ally in summertime, such as cyclone I, cold front I, quasi- values derived from downscaled GCM historical runs stationary front, and warm front I, are projected to

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TABLE 4. Within-weather-type difference of percentage occur- future change rates between A2 and B2 scenarios are ex- rences between downscaled GCM historical runs and observations pected since B2 scenario projects less future warming than over a comparative time period (April–November 1961–2000) on A2 scenario, especially in the second half of this century. average of three cities (London, Ottawa, and Toronto). Negative percentage occurrence difference: to increase future rainfall pro- In addition to frequency of the weather types, the jections; positive percentage occurrence difference: to decrease within-weather-type meteorological characteristics de- future rainfall projections. rived from downscaled future climate information were evaluated to compare with historical observations. As Downscaled GCM subtracted from an example, hourly meteorological variables (tempera- observation ture, dewpoint, sea level air pressure, u wind, and y Weather types Observation 3-GCM A2 ensemble* wind) for observations and downscaled future CGCM2 Cyclone I 4.85 21.16 A2 climate information are displayed in quartile box Cold front I 6.88 0.92 plots for the 10 rainfall-related weather types in London Quasi-stationary front 5.82 21.94 (Fig. 6). Similar results were also found for other loca- Warm front I 2.56 20.53 tions and GCM simulations but not shown owing to the Mesohigh 6.86 21.17 Cyclone II 4.93 20.27 limitations of space. From Fig. 6, it is immediately ap- Cold low 5.75 0.52 parent that within-weather-type variances of the meteo- Cold front II 2.89 20.92 rological characteristics derived from downscaled future Cold front III 3.34 0.13 GCM climate information are very similar to the obser- Warm front II 2.44 20.50 vations. In addition, the characteristics of warm weather * The 3-GCM A2 ensemble: CGCM2 A2, GFDL-CM2.0 A2, and types (e.g., cyclone I, mesohigh, and cold Front I) are ECHAM5–MPI-OM A2. projected to be warmer and moister. These results further implied that the downscaling method is suitable to derive station-scaled future climate information and the dis- increase in the future. The colder weather types that criminant function analysis performed well in projecting usually occur in spring and autumn, such as cyclone II, future weather types using downscaled hourly climate cold low, cold front II, and cold front III, are projected to information. decrease in the future. In addition, the change magni- It is noteworthy that the projected increase in fre- tudes of projected future rainfall-related weather type quency of the warmer rainfall-related weather types occurrences also vary between the scenarios. The in- might be not only due to the higher future temperatures crease rates for the warmer weather types (especially for but also considering other weather elements. From Fig. cyclone I and quasi-stationary front), derived from down- 6, it can be seen that within-weather-type data distri- scaled B2 scenario for future two periods 2046–65 and butions for sea level air pressure and winds derived from 2081–2100, are usually projected to be smaller than those downscaled future GCM climate data are similar to the from downscaled A2 scenario. The corresponding pro- observations. Furthermore, future hottest days were jected decrease rates by the period 2081–2100 for the assigned by the synoptic weather typing to two other colder weather types (especially for cyclone II and cold hottest weather types that were merged into the weather low), derived from downscaled B2 scenarios, could also be grouping other II with no rainfall. On average of smaller than those from A2 scenario. The difference in downscaled 3-GCM A2 simulations, the frequencies of

TABLE 5. Percentage changes in the frequency of future rainfall-related weather types derived from downscaled CGCM2 A2 and CGCM2 B2 from the current conditions of April–November 1961–2000 on average of three cities (London, Ottawa, and Toronto).

2046–65 2081–2100 Weather types Observation period (1961–2000) CGCM2 A2 CGCM2 B2 CGCM2 A2 CGCM2 B2 Cyclone I 4.85 145 81 187 111 Cold front I 6.88 23 21 3 32 Quasi-stationary front 5.82 35 13 26 19 Warm front I 2.56 2 14 24 47 Mesohigh 6.86 16 2 220 7 Cyclone II 4.93 20.4 25 229 215 Cold low 5.75 224 22 246 232 Cold front II 2.89 23 214 23 216 Cold front III 3.34 225 223 240 235 Warm front II 2.44 5 21813

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these hottest and second hottest weather types for the period 2081–2100 in Toronto are projected to be over 9.0 and 3.6 times greater than the current conditions (1.7 and 6.5 days yr21 observed during 1961–2000), respectively. In addition, the projected decrease in frequency of the colder weather types might be partly due to the selected time period (April–November). As future temperature increases, as projected by the GCMs, the colder weather types that currently occur in April or November could, in the future, occur earlier, such as in March or occur later in December, respectively. How- ever, in this study, March and December are not included in the analysis.

b. Robustness of rainfall simulation models Before assessing changes in frequency of future daily rainfall events, it is necessary to ascertain whether the methods are suitable for future projection by comparing data distribution of daily rainfall driven by the downscaled GCM historical runs with observations over a comparative time period (1961–2000). Figure 7 shows quantile–quantile (Q–Q) plots of sorted daily rainfall data from both downscaled GCM historical runs and observations in the selected river basins. If both datasets come from the same distribution, the plot will be linear along with the 458 line. From Fig. 7, it is clear that data distributions of both datasets are similar; so that it can be concluded that the methods used in the study are suitable for projecting or downscaling future daily rainfall information on a local scale. Any small differences between both datasets were used to further adjust GCM biases for projections of changes in frequency of future daily rainfall events by Eq. (2). To quantitatively assess how much these differences affect projections of increase in frequency and intensity of future daily rainfall events, we have calculated mean relative absolute

differences (RAD) between observations Oi and downscaled GCM historical runs Di by the following expression:

N 1 O 2 D RAD 5 å i i , (3) N i51 Oi

where N is the number of total pairs of the data sample. The RAD was calculated for a variety of thresholds when daily rainfall greater than 5, 10, 20, 30, 40, and FIG. 6. Data distribution comparison between hourly observa- 50 mm, for each of downscaled GCM historical runs and tions (the ﬁrst quartile box plot, 1958–2002) and downscaled future each of four selected river basins. Then the mean RAD hourly CGCM2 A2 simulations (the next two box plots: 2046–65 for each of the thresholds was determined by pooling and 2081–2100) for each of 10 rainfall-related weather types in London. four downscaled GCM historical runs and four river basins. The results shown that for thresholds with daily

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FIG. 7. (a)–(d) Q–Q plots of daily rainfall quantities derived by simulation models using independent GCM historical runs vs observations over a comparative time period (April–November 1961–2000) in the four selected river basins. A 458 reference line suggests that both datasets come from populations with the same distribution. rainfall of 30 mm or less, the differences between down- simulation model was redeveloped using all days with- scaled GCM historical runs and observations affect the out synoptic weather typing. The same methods and future projections by about 1%. The corresponding ef- potential predictors used in the earlier rainfall simula- fects for thresholds with daily rainfall greater than 40 and tion modeling (Cheng et al. 2010) were employed to 50 mm are about 2% and 4%, respectively. develop rainfall simulation test model for each of the As described by Cheng et al. (2010), the robustness of river basins. These rainfall simulation models were rainfall simulation models was examined using historical tested with downscaled GCM historical runs to project observations of all days without synoptic weather typing. daily rainfall quantities for the period April–November It was concluded that it is better to perform synoptic 1961–2000. The resulted daily rainfall distribution is weather typing prior to the application of cumulative compared with observations, as shown in Q–Q plots logit and nonlinear regressions for development of daily (Fig. 8). It is seen that, from Fig. 8, the rainfall simulation rainfall simulation models. In this paper, the robustness models without weather typing usually underestimate of rainfall simulation models is examined once again to quantities of daily heavy rainfall events (e.g., daily ascertain this conclusion is still valid for projection of rainfall greater than 35 or 40 mm). This implies that it is future daily rainfall quantities. To achieve this, a rainfall necessary to perform synoptic weather typing altogether

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FIG. 8. As in Fig. 7, but using the different rainfall simulation models developed using all days without synoptic weather typing. with daily rainfall simulation modeling for development days and future seasonal rainfall totals projected by two of daily rainfall downscaling transfer functions. methods versus historical observations are graphically illustrated in Figs. 9 and 10. Method II usually projects c. Changes in frequency of future daily rainfall events greater increases in the frequency of future daily rainfall and seasonal rainfall totals events and seasonal rainfall totals (April–November) Following the determination of weather types for than method I. In addition, the rainfall projections were future days based on downscaled GCM climate data, evaluated by comparing differences in the number of changes in the frequency of future daily rainfall events seasonal rain days and seasonal rainfall totals derived and seasonal rainfall totals could be quantitatively pro- from downscaled historical runs and observations jected. In this study, to consider using different down- during a comparative time period 1961–2000. As shown scaling methods for local climate change impact analysis in Figs. 9 and 10, the values from both datasets are very (Haylock et al. 2006), two independent methods de- similar for both method I and method II. This implies scribed above were employed: method I—comparing that both daily rainfall downscaling methods are suit- frequencies of historical and future rainfall-related able to be used for projecting changes in the number of weather types—and method II—applying daily rainfall future seasonal rain days and future seasonal rainfall simulation models. The number of future seasonal rain totals.

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FIG. 9. Method I (based on changes in frequency of future rainfall-related weather types): the number of future seasonal rain days [(a) $0.2, (b) $15, and (c) $25 mm] and (d) future seasonal rainfall totals vs the observed values during the period April–November 1961–2002. The shaded bar is for observations, and the following three bars represent 3-GCMA2–averaged values for future three time periods; in order from left to right: 1961–2000, 2046–65, and 2081–2100.

To more clearly present changes in the frequency of relative increases are presented by CGCM2 B2 and future daily rainfall events and seasonal rainfall totals, 3-CGM A2 averages with the range across GCMs. The four river basin average relative increases from the projections of relative increases in the frequency of fu- current conditions of April–November 1961–2002, de- ture daily rainfall events and seasonal rainfall totals vary rived from both methods, are shown in Table 6. The across GCMs and across scenarios. Across three GCMs,

FIG. 10. As in Fig. 9, but using method II (based on daily rainfall simulation models).

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TABLE 6. Four river basin–average percentage increases in the frequency of future seasonal rain days ($0.2, $15, and $25 mm) and future seasonal rainfall totals from the current conditions of April–November 1961–2002, presented by 3-GCM A2 ensemble and CGCM2 B2.

Current Method I* Method II** Rainfall events conditions Period 3-GCM A2 CGCM2 B2 3-GCM A2 CGCM2 B2 Seasonal rain 105 2046–65 8 (6–11) 8 12 (7–17) 23 days ($0.2 mm) 2081–2100 7 (5–8) 10 15 (12–17) 22 Seasonal rain 10.5 2046–65 15 (11–20) 15 23 (9–37) 43 days ($15 mm) 2081–2100 15 (12–17) 21 27 (22–32) 53 Seasonal rain 3.2 2046–65 17 (13–24) 18 23 (10–35) 46 days ($25 mm) 2081–2100 21 (16–23) 25 40 (24–52) 61 Seasonal rainfall 608 2046–65 12 (9–17) 12 20 (8–34) 35 totals (mm) 2081–2100 12 (9–13) 17 30 (28–34) 41 Overall mean 13 16 24 41

* Based on changes in frequency of future rainfall-related weather types. ** Based on daily rainfall simulation models. lower and upper boundaries of the range derived from likelihood of events such as heavy rainfall of a certain method I for the period 2046–65 shown in Table 6 are intensity. Return values are thresholds that will be ex- projections derived from CGCM2 A2 and ECHAM5 ceeded on average once every return period. The design A2, respectively, and vise versa for the period 2081– criteria of stormwater infrastructure are constrained by 2100. For method II, lower and upper boundaries of the largest precipitation event anticipated during a fixed the range generally represent projections derived from design period (e.g., 20, 50, or 100 years). To take into ac- CGCM2 A2 and GFDL A2, respectively, for both future count climate change impacts on infrastructure, scientific time periods. Between scenarios A2 and B2, the relative information on changes in future return values of extreme increase rates for the period 2046–65, projected from rainfall events is needed for developing adaptation strat- CGCM2 A2, are slightly greater than those from CGCM2 egies and policies. B2, and vise versa for 2081–2100, with less than 10% Annual maxima of the river basin–average three-day difference. For method II, the relative increase rates for accumulated rainfall totals for the period 1961–2002 both future periods projected from CGCM2 B2 are were fitted to the Gumbel (extreme value type I) dis- greater than those from CGCM2 A2. For more detailed tribution for each of the selected river basins. The use of differences, regarding intermodel and interscenario un- three-day accumulated rainfall totals is arbitrary. Future certainties, refer to section 5e. projections of the river basin–average daily rainfall data, The results with respect to increases in frequencies of using two downscaled CGCM transient model simula- daily rainfall events and seasonal rainfall totals pre- tions (Table 1) for three 50-yr periods (2001–50, 2026–75, sented in this study are consistent with the findings of and 2051–2100), were used to project future return- previous studies (e.g., Zwiers and Kharin, 1998; Kharin period values for this century. As shown in Table 7, the and Zwiers, 2005; Haylock et al. 2006; Tebaldi et al. return values of three-day accumulated rainfall ex- 2006; Meehl et al. 2007). There are three possible rea- tremes for all evaluated return periods are projected to sons for increases in the frequency of future rainfall increase by about 20%–70% over the present century. events. First, a warmer and moister future climate is For example, in the Humber River basin, the 20-yr re- projected by the GCM scenarios. Second, the projected turn period values of three-day accumulated rainfall warmer future climate could bring about more frequent extremes for future three 50-yr periods are projected and vigorous atmospheric convection in the future. to increase by 50%, 63%, and 69%, respectively, from Third, the hydrological cycle under the projected future the observed value of 80 mm for the past 40 years. climate could be modified from the current condition. The percentage increase rates for longer return periods are usually greater than shorter return periods (except d. Changes in future return-period values of extreme Thames River basin). Between two downscaled CGCM2 rainfall events simulations, the projected percentage increases in the A return period analysis was employed to project return values are similar, usually with slightly greater changes in future return values of the extreme rainfall values derived from downscaled CGCM2 A2 than those events for a number of return periods. A return period from downscaled CGCM2 B2. The difference between known as a recurrence interval is an estimate of the the percentage increases derived from downscaled

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TABLE 7. Percentage increases in future three-day accumulated rainfall extremes for nine return periods (ensemble of two Canadian GCMs) from current observed values (95% confidence interval in parentheses). To effectively compare the 95% confidence intervals between observed and future projected return values as the same as the future projections, the 95% confidence intervals derived from observations are presented as percentages below or above the return values.

Return Thames River basin Grand River basin period (yr) Obs (mm) 2001–50 (%) 2026–75 (%) 2051–2100 (%) Obs (mm) 2001–50 (%) 2026–75 (%) 2051–2100 (%) 256(61.4) 33 (61.7) 28 (61.3) 31 (62.5) 55 (61.8) 46 (62.2) 45 (61.4) 48 (62.2) 570(61.4) 34 (61.7) 26 (61.3) 24 (62.5) 67 (61.9) 57 (62.2) 53 (61.4) 58 (62.2) 10 80 (61.8) 34 (62.0) 25 (61.6) 21 (63.0) 74 (62.3) 62 (62.7) 57 (61.7) 63 (62.7) 15 85 (61.9) 34 (62.2) 25 (61.7) 20 (63.2) 79 (62.5) 65 (63.0) 59 (61.9) 65 (62.9) 20 89 (62.0) 34 (62.3) 25 (61.8) 19 (63.4) 82 (62.7) 66 (63.2) 60 (62.0) 66 (63.1) 25 92 (62.1) 34 (62.4) 24 (61.9) 19 (63.6) 84 (62.9) 67 (63.3) 61 (62.1) 68 (63.3) 30 95 (62.1) 34 (62.5) 24 (62.0) 18 (63.7) 86 (63.0) 68 (63.4) 61 (62.2) 68 (63.4) 50 101 (62.3) 34 (62.7) 24 (62.1) 17 (64.0) 92 (63.3) 71 (63.7) 63 (62.4) 70 (63.7) 100 110 (62.5) 34 (62.9) 24 (62.3) 16 (64.3) 99 (63.5) 73 (64.1) 65 (62.6) 73 (64.0) Mean 34 (62.3) 25 (61.8) 21 (63.4) 64 (63.1) 58 (62.0) 64 (63.1)

Humber River basin Rideau River basin 250(61.8) 47 (61.7) 48 (62.8) 48 (63.0) 51 (61.6) 43 (61.6) 43 (61.1) 43 (61.2) 563(61.7) 49 (61.7) 56 (62.7) 60 (62.9) 63 (61.4) 37 (61.6) 43 (61.1) 42 (61.2) 10 71 (62.1) 49 (62.0) 60 (63.2) 65 (63.5) 72 (61.8) 35 (61.9) 43 (61.3) 42 (61.5) 15 76 (62.2) 49 (62.2) 62 (63.6) 68 (63.8) 76 (62.0) 34 (62.1) 43 (61.5) 42 (61.6) 20 80 (62.4) 50 (62.3) 63 (63.8) 69 (64.0) 80 (62.1) 33 (62.2) 43 (61.6) 41 (61.7) 25 82 (62.6) 50 (62.4) 64 (63.9) 70 (64.2) 82 (62.2) 33 (62.3) 42 (61.6) 41 (61.8) 30 85 (62.6) 50 (62.5) 64 (64.0) 71 (64.3) 84 (62.3) 32 (62.4) 42 (61.7) 41 (61.8) 50 91 (62.7) 50 (62.7) 66 (64.4) 73 (64.7) 90 (62.4) 31 (62.6) 42 (61.8) 41 (62.0) 100 99 (63.0) 50 (62.9) 67 (64.7) 76 (65.1) 98 (62.7) 30 (62.8) 42 (62.0) 41 (62.1) Mean 49 (62.3) 61 (63.7) 67 (63.9) 34 (62.2) 43 (61.5) 42 (61.7)

CGCM2 A2 and CGCM2 B2 on average of four river differences between rainfall simulations driven by down- basins, as shown in Table 8, is usually less than 10% for scaled historical runs and observations were considered future three 50-yr periods, with a few exemptions. To for further correction of future rainfall projections. more effectively account for differences, the ‘‘differ- However, conclusions made in this study about the ence’’ here represents the absolute difference between impacts of climate change on future rainfall still rely CGCM2 A2 and CGCM2 B2 to avoid negative values on GCM scenarios/projections and, as a result, there is canceling out positive values. In addition, from Table 7, it can be seen that the 95% conﬁdence interval for future projected return-period values is similar to the observed TABLE 8. Differences of percentage increases in return values of future three-day accumulated rainfall extremes between down- ones, which implies that the future projected return- scaled CGCM2 A2 and CGCM2 B2 on average of the four river period values are plausibly reliable. basins. The percentage increases in the return values derived from downscaled CGCM2 A2 are usually slightly greater than those from downscaled CGCM2 B2 with a few exceptions. To more ef- e. Uncertainty of the study fectively account for differences, the ‘‘difference’’ here represents the absolute difference between CGCM2 A2 and CGCM2 B2 to Considerable effort was made in this study to transfer avoid negative values canceling out positive values. GCM-scale model simulations to station-scale climate information using statistical downscaling transfer func- Return period tions. Through the downscaling process, the GCM bias (yr) 2001–50 2026–75 2051–2100 was removed using about 50-yr historical relationships 2 5.7 3.7 3.7 between regional-scale predictors and station-scale 5 7.1 4.4 2.0 weather elements (Katz 2002). As a result, the quality of 10 8.0 7.5 2.9 15 8.5 9.5 3.4 future GCM climate projections, following downscaling, 20 8.8 10.8 3.7 was much improved. For example, the data distribution 25 9.1 11.9 4.0 (including extreme events) of the downscaled GCM 30 9.3 12.8 4.2 historical runs was similar to that of observations over 50 9.9 15.2 5.2 a comparative time period 1961–2000. In addition, any 100 10.7 18.5 6.7

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TABLE 9. Four river basin–average intermodel and interscenario uncertainties of percentage increases in the frequency of future seasonal rain days ($0.2, $15, and $25 mm) and future seasonal rainfall totals from the current conditions of April–November 1961–2002.

Uncertainty (absolute difference in percentage increases) Method Ia Method IIb Current Mean 3- CGCM2 A2 2 Mean 3- CGCM2 A2 – Rainfall events conditions Period GCM A2c CGCM2 B2 GCM A2 CGCM2 B2 Seasonal rain 105 2046–65 4 3 7 5 days ($0.2 mm) 2081–2100 2 5 3 4 Seasonal rain 10.5 2046–65 6 5 13 6 days ($15 mm) 2081–2100 4 9 7 17 Seasonal rain 3.2 2046–65 7 6 12 15 days ($25 mm) 2081–2100 5 9 21 29 Seasonal rainfall 608 2046–65 6 4 15 2 totals (mm) 2081–2100 3 7 8 7 Overall mean 5 6 11 11 a Based on changes in frequency of future rainfall-related weather types. b Based on daily rainfall simulation models. c Mean 3-GCM A2 is average of absolute differences between pairs of three GCM A2 models. corresponding uncertainty about the study findings. One above, it was found that the models have difficulty of the most important sources of uncertainty in climate in capturing some summer localized convective rainfall change impact studies comes from GCMs (Katz 2002). events (Cheng et al. 2010). This model limitation is also Because of the model resolution and complexity, the reflected by simulation difficulty of summer localized GCMs must have inevitably omitted some factors convective cloud cover. As pointed out by Cheng et al. that affect climate; in turn, the GCMs are unable to re- (2008), total cloud cover downscaling transfer functions solve subgrid-scale processes and generate uncertainties performed better in the winter season than in the sum- through the model parameterizations. To quantitatively mer season since localized convective activities com- assess inter-GCM and interscenario uncertainties of monly occur in summer. Furthermore, this study has future rainfall projections, we have analyzed the four attempted to downscale the river basin–average daily river basin–average absolute difference between three rainfall information, which might underestimate the selected GCMs under the SRES A2 scenario as well as future extreme rainfall events at the individual stations. absolute difference between two selected scenarios It is likely that projections in frequency of future heavy (CGCM2 A2 versus CGCM2 B2). The absolute differ- rainfall events offered by this study will represent the ence used in analysis is to avoid negative values can- lower bound values for the study area. Therefore, southern celing out positive values. As shown in Table 9, overall, Ontario could in the future possibly receive more heavy the intermodel uncertainties of percentage increases in rainfall events than is currently projected by the study. the frequency of future seasonal rain days and seasonal In addition to uncertainty of GCM scenarios and rainfall totals are similar to the interscenario uncertainties, limitation of rainfall simulation models, the observed for both projection methods. Both intermodel and inter- data used in the study have their limitations. Hourly scenario uncertainties from method II, overall, are about meteorological data are essential to develop synoptic as twice as the uncertainties from method I with 11% weather typing and rainfall simulation models. How- versus 5%–6%. However, the uncertainties are generally ever, in the Grand River basin hourly meteorological much smaller than the projection of percentage increases observations are not available. For the Grand River, in the frequency of future seasonal rain days and future weather types classified using meteorological data gath- seasonal rainfall totals as shown in Table 6. The overall ered at London International Airport (located in Thames mean projected percentage increases are about 2.6 times River basin) were used to link with the river basin’s daily greater than overall mean intermodel and interscenario rainfall data. Furthermore, predictors (e.g., atmospheric uncertainties from method I; the corresponding projected stability indices) derived from weather data observed at increases from method II are about 2.2–3.7 times greater the London International Airport were used to simulate than overall mean uncertainties. daily rainfall quantities for the Grand River basin. Although the models developed from this study can Therefore, the rainfall simulation results derived for the simulate most of daily heavy rainfall events, as described Grand River basin were not as accurate as they might be

Unauthenticated | Downloaded 10/03/21 02:21 PM UTC 3684 JOURNAL OF CLIMATE VOLUME 24 were hourly meteorological data for the Grand River projection of future daily rainfall, which might over- basin available. come some of the limitations using GCM simulations. Rainfall intensity–duration–frequency (IDF) curves, which consider short-duration (usually less than one 6. Conclusions and future work day) rainfall intensity, are commonly used for hydro- The overall purpose of this study is to project possi- logical engineering design standards. Since future daily ble changes in the frequency of daily rainfall events late rainfall totals are projected in this study, it is difficult to this century for four selected river basins (i.e., Grand, incorporate the 24-h value-based results into the shorter Humber, Rideau, and Upper Thames) in Ontario, than 24-h-duration IDF curves. To more effectively in- Canada. To achieve this goal, automated synoptic clude projections of future rainfall in the design stan- weather typing as well as cumulative logit and nonlinear dard, future short-duration rainfall data are necessary. regression analyses was applied together with down- Since six-hourly NCEP reanalysis data are available for scaled GCM simulations to project future daily rainfall the past 50 years, the methods used in this study to quantities. A formal verification process of model re- project future daily rainfall have potential to be adapted sults has been built into the whole exercise, comprising to project six-hourly rainfall quantities as a step toward synoptic weather typing, rainfall simulation modeling, even finer-scale temporal projections. The results of and statistical downscaling. The results of the verifica- short-duration rainfall intensity analyses could be po- tion, based on historical observations of the outcome tentially used to develop more functional tools, in- variables simulated by the models, showed good agree- tegrating climate change with the building code design ment. As a result, a general conclusion from this study is standard using the IDF curves. that a combination of synoptic weather typing, cumu- Acknowledgments. This study was funded through the lative logit and nonlinear regression analyses, and re- Government of Canada’s Climate Change Impacts and gression-based downscaling can be useful to project Adaptation Program (CCIAP), which made this re- changes in frequency of future daily rainfall events. The search project (A901) possible. The authors gratefully authors believe that such daily rainfall downscaling acknowledge the suggestions made by the Project Ad- methods are useful to derive river basin–scale daily rain- visory Committee, which greatly improved the study. fall quantities for applications of hydrological and meteo- We also would like to thank two anonymous reviewers rological modeling. In addition, the modeled results from for providing detailed comments that significantly im- this study found that the frequency of future daily rainfall proved the original manuscript. events could increase late this century due to the changing climate projected by GCM scenarios. The implication of the increases should be taken into consideration when REFERENCES adjusting engineering infrastructure requirements and Abaurrea, J., and J. Asıń, 2005: Forecasting local daily pre- developing adaptation strategies and policies. cipitation patterns in a climate change scenario. 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