The principal methods and steps involved in the projects are summarized in Table 2. Three major steps or analysis procedures were required to complete each study: (1) historical analysis and/or simulation modeling to verify the historical extreme weather events, (2) regression-based downscaling involving the projection of station-scale future hourly/daily climate information, and (3) future projections of changes in the frequency and intensity of daily extreme weather events under a changing climate. The methodologies of each part are briefly described as follows.
Transfer functions involved in future projections are typically used to relate historical climate variables to relevant outputs or impacts of interest to decision-makers. The historical analysis to obtain the transfer functions is comprised of: (1) an automated synoptic weather typing approach to classify daily weather types or air masses and (2) development of daily within-weather-type simulation models to verify historical extreme weather events. Synoptic weather typing approaches have become popular in evaluating the impacts of climate change on a variety of environmental problems. One of the reasons is its ability to categorize a complex set of meteorological variables as a coherent index (Yarnal 1993; Cheng and Kalkstein 1997), which facilitates climate change impacts analysis. The synoptic weather typing approaches include principal components analysis, average linkage clustering procedure, and discriminant function analysis (Table 2) and attempt to develop suitable classification solutions that minimize within-category variances and maximize between-category variances. Although the approaches of synoptic weather typing used in the studies are the same, the input data are different among the studies. For example, in the climate change and freezing rain study, hourly surface meteorological observations and six-hourly U.S. National Centers for Environmental Prediction (NCEP) upper-air reanalysis data listed in Table 1 were used to classify daily weather types (Cheng et al. 2004, 2007c, 2011b). However, for the heavy rainfall-related flooding project, only hourly surface observations were used (Cheng et al. 2010, 2011a). The climate change and human mortality project used six-hourly surface meteorological data observed at 03:00, 09:00, 15:00, and 21:00 local standard time (Cheng et al. 2007a, 2008a). The selection of hourly or six-hourly meteorological data used for a particular study was determined by the temporal resolution of the targeted weather events and verified using within-weather-type simulation models.
When developing statistical extreme-weather-event simulation and downscaling models, we have two key issues that need to be taken into consideration: (1) selection of appropriate regression methods and (2) selection of significant predictors and predicted variable(s) for decision-maker’s needs. A number of linear and nonlinear regression methods, listed in Table 2, were used to develop the simulation models for various extreme weather events. The different regression methods were employed for different meteorological variables since a given regression method is suitable only for a certain type of data with a specific distribution. For example, the cumulative logit regression approach is a more suitable analysis tool for use in developing a simulation model for ordered categorical data, such as total cloud cover (Allison 2000). On the other hand, when time-series data are used in developing a regression-based prediction model, autocorrelation correction regression should be used to take into consideration the serial correlation in the time-series data (SAS Institute Inc. 2006). In order to effectively select significant predictors, the modeling conceptualizations in meteorology and hydrology were carefully analyzed to identify the predictors with the most significant relationships with the predictand. For example, when developing daily rainfall simulation models, in addition to the standard meteorological variables, a number of the atmospheric stability indices were used (Cheng et al. 2010). A certain threshold level of these stability indices can be used as indicators of atmospheric instability and the conditions associated with the potential development of convective precipitation (Glickman 2000; Environment Canada 2002).
Two different kinds of the simulation models were developed to verify the occurrences of historical daily extreme weather events (e.g., freezing rain, Cheng et al. 2004, 2007c, 2011b) and to simulate the quantities of weather/environmental variables (e.g., daily streamflow volumes, air pollution concentrations, extreme temperature- and air pollution-related mortality, Cheng et al. 2007a, b, 2008a, b), separately in the studies. However, daily rainfall simulation modeling comprises both approaches altogether resulting in a two-step process: 1) cumulative logit regression to predict the occurrence of daily rainfall events and 2) using probability of the logit regression, a nonlinear regression procedure to simulate daily rainfall quantities (Cheng et al. 2010, 2011a). The 228 predictors used in development of daily rainfall event occurrence simulation models include not only the standard meteorological variables but also a number of the atmospheric stability indices. As described in the study by Cheng et al. (2010), the cumulative logit regression performed very well to verify historical daily rainfall events, with models’ concordances ranging from 0.82 to 0.96 (a perfect model would have a concordance value of 1.0). To effectively evaluate the performance of daily rainfall quantity simulation models, the four correctness levels of “excellent”, “good”, “fair” and “poor” were defined based on absolute difference between observed and simulated daily rainfall amounts. Cheng et al. (2010) have found that, across the four selected river basins shown in Fig. 1, the percentage of excellent and good daily rainfall simulations ranged from 62% to 84%. Further detailed information on the development of extreme-weather-event simulation models, including approaches for the selection of regression methods and predictors, can be found in publications by Cheng et al. (2004, 2007a, c, 2008a, 2010).
Approaches for projecting changes in the frequency and intensity of future extreme weather events require future hourly station-scale climate information of the standard meteorological variables used in synoptic weather typing and simulation modeling. These meteorological variables include surface and upper-air temperature, dew point temperature, west–east and south–north winds, sea-level air pressure, and total cloud cover. To derive future hourly station-scale climate data from GCM-scale simulations, Cheng et al. (2008c) developed a regression-based downscaling method. This downscaling method consisted of a two-step process: (1) spatially downscaling daily GCM simulations to the selected weather stations in south–central Canada and (2) temporally downscaling daily scenarios to hourly time steps. Similar to the development of extreme-weather-event simulation models, a number of linear and nonlinear regression methods, as listed in Table 2, were used to develop the downscaling “transfer functions”. Once again, the different regression methods were employed for different meteorological variables since a given regression method is suitable only for a certain type of data with a specific distribution.
As described in the study (Cheng et al. 2008c), the downscaling results showed that regression-based downscaling transfer functions performed very well in deriving daily and hourly station-scale climate information for all weather variables. For example, most of the daily downscaling transfer functions possess model R2s greater than 0.9 for surface air temperature, sea-level air pressure, upper-air temperature and winds; the corresponding model R2s for daily surface winds are generally greater than 0.8. The hourly downscaling transfer functions for surface air temperature, dew point temperature, and sea-level air pressure possess the highest model R2 (>0.95) of the weather elements. The functions for south–north wind component are the weakest model (model R2s ranging from 0.69 to 0.92 with half of them >0.89). For total cloud cover, hourly downscaling transfer functions developed using the cumulative logit regression have concordances ranging from 0.78 to 0.87 with over 75% >0.8. For more detailed information on the development and performance of downscaling transfer functions, refer to Cheng et al. (2008c).
Following downscaling of future hourly climate data, the synoptic weather typing and regression techniques were able to project changes in the frequency and intensity of future extreme weather events and their impacts. To achieve this, future daily weather types are needed and projected by applying synoptic weather typing methods using the downscaled future hourly climate data (Cheng et al. 2007b, c, 2008b, 2011a). To remove GCM model biases, future downscaled climate data were standardized using the mean and standard deviation of the downscaled GCM historical runs (1961–2000). As described by Cheng et al. (2008b, 2011a), the synoptic weather typing approach is appropriate for changing climate conditions since it can assign projected days with conditions above a threshold beyond the range of the historical observations into more extreme weather types. Using projections of daily synoptic weather types under a changing climate, the approach is able to project changes in the frequency and intensity of future extreme weather events and their impacts. As described in Table 2 and to reduce the uncertainties for decision-making, two independent methods were used in each study to project the possible impacts of climate change on extreme weather events. The first method was based on changes in the frequency of future extreme weather types relative to the historical weather types. The frequency and intensity of future daily extreme weather events were assumed to be directly proportional to change in frequency of future relevant weather types. The second method applied within-weather-type simulation models with downscaled future climate data to project changes in the frequency and intensity of future daily extreme weather events. Cheng et al. (2007b, c, 2008b, 2011a, b) provide more detailed information on these methodologies for projections of future extreme weather events and their impacts.
All steps and principal methods described above, namely synoptic weather typing, extreme-weather-event simulation modeling, and regression-based downscaling, were validated against an independent dataset to ensure the models performed well and were not over-fitted (e.g., could be duplicated with another dataset). To achieve this, as indicated in Table 2, two validation methods were employed: 1) randomly selecting one-fourth to one-third of the total years as an independent dataset and 2) apply a “leave-one-year-out” cross-validation scheme. For both methods, the validation dataset was independent from the data sample used in the development of synoptic weather typing, the simulation models of the extreme weather events, and downscaling transfer functions. The first validation method was used for verification of synoptic weather types and validation of within-weather-type simulation modeling in heavy rainfall, freezing rain, air quality, and human health studies. The second method was used for validation of impacts and related physical variables such as streamflow simulation models and downscaling transfer functions.
In these studies, the validation approaches were applied using synoptic weather typing and the simulation models to verify historical weather types and extreme weather events (Table 2). The results of the verification, based on historical observations of the outcome variables or impacts (e.g. mortality rates) simulated by the models, showed a very good agreement, which indicates that the methods used in the projects were appropriate in development of extreme-weather-event simulation models (Cheng et al. 2007a, c, 2008a, 2010, 2011a, b). In addition, as described in Table 2, the performance of the downscaling transfer functions was evaluated for the following aspects:
Validating downscaling transfer functions using a leave-one-year-out cross-validation scheme,
Analyzing model R2s of downscaling transfer functions for both development and validation datasets,
Comparing data distributions and diurnal/seasonal variations of downscaled GCM historical runs with observations over a comparative time period of 1961–2000,
Examining extreme characteristics of the weather variables derived from downscaled GCM historical runs with observations, and
Comparing against stakeholder’s expert judgement for consistency.
The results showed that regression-based downscaling methods performed very well in deriving future hourly station-scale climate information for all weather variables. For example, as shown in Table 3, the hourly downscaling transfer functions derived from both development and validation datasets possess model R2s >0.95 for surface air temperature, dew point temperature, and sea-level air pressure (Cheng et al. 2008b, c, 2011a).