A Synoptic Weather Typing Approach to Simulate Daily Rainfall and Extremes in Ontario, Canada: Potential for Climate Change Projections

Chad Shouquan Cheng Atmospheric Science and Applications Unit, Meteorological Service of Canada Branch, Environment Canada, Toronto, Ontario, Canada

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Guilong Li Atmospheric Science and Applications Unit, Meteorological Service of Canada Branch, Environment Canada, Toronto, Ontario, Canada

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Qian Li Atmospheric Science and Applications Unit, Meteorological Service of Canada Branch, Environment Canada, Toronto, Ontario, Canada

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Heather Auld Adaptation and Impacts Research Section, Science and Technology Branch, Environment Canada, Toronto, Ontario, Canada

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Abstract

An automated synoptic weather typing and stepwise cumulative logit/nonlinear regression analyses were employed to simulate the occurrence and quantity of daily rainfall events. The synoptic weather typing was developed using principal component analysis, an average linkage clustering procedure, and discriminant function analysis to identify the weather types most likely to be associated with daily rainfall events for the four selected river basins in Ontario. Within-weather-type daily rainfall simulation models comprise a two-step process: (i) cumulative logit regression to predict the occurrence of daily rainfall events, and (ii) using probability of the logit regression, a nonlinear regression procedure to simulate daily rainfall quantities. The rainfall simulation models were validated using an independent dataset, and the results showed that the models were successful at replicating the occurrence and quantity of daily rainfall events. For example, the relative operating characteristics score is greater than 0.97 for rainfall events with daily rainfall ≥10 or ≥25 mm, for both model development and validation. For evaluation of daily rainfall quantity simulation models, four correctness classifications of excellent, good, fair, and poor were defined, based on the difference between daily rainfall observations and model simulations. Across four selected river basins, the percentage of excellent and good simulations for model development ranged from 62% to 84% (of 20 individuals, 16 cases ≥ 70%, 7 cases ≥ 80%); the corresponding percentage for model validation ranged from 50% to 76% (of 20 individuals, 15 cases ≥ 60%, 6 cases ≥ 70%).

Corresponding author address: Dr. Chad Shouquan Cheng, Atmospheric Science and Applications Unit, Meteorological Service of Canada Branch, Environment Canada, 4905 Dufferin Street, Toronto ON M3H 5T4, Canada. Email: shouquan.cheng@ec.gc.ca

Abstract

An automated synoptic weather typing and stepwise cumulative logit/nonlinear regression analyses were employed to simulate the occurrence and quantity of daily rainfall events. The synoptic weather typing was developed using principal component analysis, an average linkage clustering procedure, and discriminant function analysis to identify the weather types most likely to be associated with daily rainfall events for the four selected river basins in Ontario. Within-weather-type daily rainfall simulation models comprise a two-step process: (i) cumulative logit regression to predict the occurrence of daily rainfall events, and (ii) using probability of the logit regression, a nonlinear regression procedure to simulate daily rainfall quantities. The rainfall simulation models were validated using an independent dataset, and the results showed that the models were successful at replicating the occurrence and quantity of daily rainfall events. For example, the relative operating characteristics score is greater than 0.97 for rainfall events with daily rainfall ≥10 or ≥25 mm, for both model development and validation. For evaluation of daily rainfall quantity simulation models, four correctness classifications of excellent, good, fair, and poor were defined, based on the difference between daily rainfall observations and model simulations. Across four selected river basins, the percentage of excellent and good simulations for model development ranged from 62% to 84% (of 20 individuals, 16 cases ≥ 70%, 7 cases ≥ 80%); the corresponding percentage for model validation ranged from 50% to 76% (of 20 individuals, 15 cases ≥ 60%, 6 cases ≥ 70%).

Corresponding author address: Dr. Chad Shouquan Cheng, Atmospheric Science and Applications Unit, Meteorological Service of Canada Branch, Environment Canada, 4905 Dufferin Street, Toronto ON M3H 5T4, Canada. Email: shouquan.cheng@ec.gc.ca

1. Introduction

It has become widely recognized that heavy precipitation events are projected to increase almost everywhere over the globe because of a changing climate (e.g., Cubasch et al. 1995; Zwiers and Kharin 1998; Kharin and Zwiers 2005; Tebaldi et al. 2006; Meehl et al. 2007). It is also likely that climate change could increase the heavy rainfall–related flooding risks. The Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) has indicated that the severity and frequency of extreme events such as floods and droughts could be expected to increase in the twenty-first century under global warming (Alley et al. 2007). In light of these concerns, Environment Canada, in partnerships with Conservation Ontario, the Ontario Ministry of Natural Resources, and CGI Insurance, has completed a 3-yr research project, which sought to investigate climate change and extreme rainfall–related flooding risks in southern Ontario, Canada. The current paper focuses on the development of daily rainfall simulation models, which will be used in another publication to project changes in frequency and magnitude of future daily rainfall events.

This paper describes the background to the development of quantitative rainfall simulation models, applying an automatic synoptic weather typing with stepwise cumulative logit and nonlinear regression analyses. To quantitatively simulate daily rainfall events, a number of previous studies have employed statistical methods to determine the relationships that exist between weather conditions and rainfall events. For example, a number of statistical procedures, such as linear regression, discriminant function analysis, logistic regression, neural network, and classifier system using a generic algorithm, have previously been employed for probabilistic quantitative precipitation forecast (QPF) (e.g., Ross 1987; Hall et al. 1999; Koizumi 1999; Wilson and Vallée 2002, 2003). Applequist et al. (2002) have compared these statistical methodologies for probabilistic QPF and concluded that logistic regression techniques performed best among all the methodologies studied. Most notable is that the predictive skill of logistic regression was significantly better at the 99% confidence limits than was that of linear regression; this finding is particularly helpful for predicting heavy rainfall events. A number of other studies (e.g., Buishand et al. 2004; Abaurrea and Asín 2005; Fealy and Sweeney 2007) have used logistic regression to simulate the occurrence of daily rainfall events and a generalized linear modeling (GLM) approach to simulate daily rainfall quantities. The results obtained from these studies have shown that the use of both logistic regression and GLM offers a significant improvement over multiple linear regression. However, some of the studies indicated that the daily rainfall simulation models still possess low model R2s (Buishand et al. 2004) and have difficulties with predicting extreme precipitation events (Fealy and Sweeney 2007).

In most of these previous studies, rainfall simulation models were developed using all days, combining non rain days and all types of precipitation-related weather patterns. In fact, some predictors may significantly contribute to the prediction of rainfall for one weather type but not for others, because of the multiscale nature of the atmospheric processes in rainfall formation over space and time. When all days are used to develop a rainfall simulation model, these predictors might not be significantly useful. It is also demonstrated by the current study that predictor thresholds of atmospheric stability indices that indicate the occurrence of precipitation vary from weather type to weather type, time to time, and place to place (refer to section 3 for detailed information). To overcome this shortcoming, a number of studies have applied atmospheric circulation classifications, such as sea level pressure types, to determine relationships between weather patterns and daily rainfall, which offers great potential to daily rainfall downscaling (e.g., Goodess and Palutikof 1998; Kostopoulou and Jones 2007a,b).

Over the past two decades, automated synoptic weather typing approaches have become popular for the evaluation of climate impacts on a number of environmental issues, such as air quality (Kalkstein and Corrigan 1986; Cheng et al. 2007a,b), human health (Kalkstein 1991; McGregor 1999; Cheng et al. 2008a,b), and freezing rain (Cheng et al. 2004, 2007c), particularly since these methodologies can characterize a complex set of meteorological variables as a coherent index (Kalkstein 1979; Perry 1983). Most of these studies have applied two different methods separately: (i) the hierarchical method–clustering procedure (e.g., Kalkstein 1991; Kalkstein and Corrigan 1986; McGregor 1999) or (ii) nonhierarchical method–discriminant function analysis (e.g., Kalkstein et al. 1996, 1998; Sheridan 2002). Some studies (e.g., DeGaetano 1996; Cheng et al. 2007a,b,c, 2008a,b) have attempted to combine both methods, resulting in better classification results with smaller within-cluster variances and larger between-cluster variances than using either method alone (refer to section 3a for further discussion).

To date, it appears that the automatic synoptic weather typing (or airmass typing) has not been employed for the assessment or projection of climate change impacts on future rainfall–heavy rainfall events in Canada. To effectively project future river basin–scale rainfall data from large-scale GCM outputs, the historical analysis is essential for us to build a science foundation that is able to reproduce historical rainfall–heavy rainfall events. The purpose of this study, then, is to develop within-weather-type daily rainfall simulation models using synoptic weather typing (combining both hierarchical and nonhierarchical methods) together with cumulative logit and nonlinear regression procedures. These daily rainfall simulation models have the potential to be used to project changes in frequency and magnitude of future daily rainfall–heavy rainfall events.

This paper is organized as follows: in section 2, data sources and their treatments are described. Section 3 presents the analysis techniques as applied to 1) automated synoptic weather typing, 2) synoptic weather types associated with daily rainfall events, 3) development of simulation models for daily rainfall quantity, and 4) validation of rainfall simulation models. Section 4 includes the results and discussion on 1) rainfall-related weather types, 2) simulation of daily rainfall event occurrence, 3) simulation of daily rainfall quantity, and 4) robustness of rainfall simulation models. The conclusions and recommendations from the study are summarized in section 5.

2. Data sources and treatment

The study area and locations of the four selected watersheds in southern Ontario (i.e., Grand, Humber, Rideau, and Upper Thames River basins) are shown in Fig. 1. Within each of the river basins, hourly and daily observed and reanalysis weather data for the period from April to November for each year of 1958–2002 used in the study are summarized in Table 1. There are a couple of reasons for the selection of the warm season (April–November). First, this study is part of the project focusing on investigation of climate change impacts on extreme rainfall–related flooding risks, of which snowmelt or ice jam flooding events were not considered. Second, the extreme rainfall events mostly occur in the study area during the warm season. Of the dataset, about 0.4%, 1.1%, and 0.8% of the total days have missing data for at least one weather element and require missing data interpolation for London (United Kingdom), Ottawa, and Toronto (Canada), respectively. With the exception of rainfall, missing data of hourly surface observations retrieved from the three airport weather stations were interpolated using a temporal linear method in cases where the data were missing for three consecutive hours or less; days with data missing for four or more consecutive hours were excluded from the analysis. After interpolation, the dataset was over 99.4% complete (63, 14, and 12 days with missing data for London, Ottawa, and Toronto, respectively).

In addition to hourly meteorological data, daily rainfall data observed at climate stations were used in the study. A number of climate stations, which are nearly evenly distributed within each of the river basins, were selected for the analysis (Table 1). The climate stations were selected based on the length of the available data record (e.g., >25 yr). The selected climate stations and an airport weather station in each river basin were used to calculate mean daily rainfall totals representing average rainfall conditions for the catchment as a whole, which were used in the analysis. The river basin average daily rainfall totals were set as zero when the value is less than 0.2 mm. These average rainfall data were used to develop daily rainfall simulation models for the prediction of daily river basin average rainfall quantities; however, the methods used in this study can also be applied to individual station series. There are a couple of reasons for using daily river basin average rainfall in the study. First, although some extreme events at individual stations were smoothed out from the river basin average daily rainfall series, the river basin average rainfall conditions are suitable to analyze rainfall-related streamflow volumes, as part of the project. Second, the computational time/cost using the river basin averaged data was much less than that when the daily simulation models were developed for each of the climate stations within a river basin. To use data from both climate and weather stations altogether, a “day” for the weather stations needs to be redefined to match that of the climate stations. The period of a day in observations of climate stations is defined as 24 h, from 0800 local standard time (LST) to 0800 the following day. At airport weather stations, in addition to the hourly automatic rainfall measurements, there are 6-hourly manual observations made using the same standard rain gauge as used at the climate stations. To maintain consistency in the method for daily rainfall measurements between the weather and climate stations, six-hourly rainfall totals ending at 1300, 1900, 0100, and 0700 LST observed from the airport weather stations were summed for the daily rainfall totals.

The 6-hourly upper-air reanalysis gridpoint weather data (Kalnay et al. 1996; Kistler et al. 2001) at 0700, 1300, 1900, and 0100 LST for the period April–November 1958–2002 were also used in the study (Table 1). Data from five pressure levels (925, 850, 700, 600, and 500 hPa) were used in this study since the atmospheric parameters needed to determine both production and type of precipitation are primarily confined to levels below 500 hPa (Cheng et al. 2004). To combine the gridded reanalysis data with the surface weather observations, the reanalysis data from a surrounding 4-grid domain field were interpolated to the three selected airport weather stations using the inverse-distance method (Shen et al. 2001). Two other domain sizes (i.e., 16-grid and 36-grid) were tested to ascertain if the selected domain field was suitable for interpolation of the reanalysis data, comparing with radiosonde data observed at Buffalo, New York (near the study area). The correlation (R2) between radiosonde and four-grid interpolated data for upper-air temperature, dewpoint, U wind, and V wind, averaged across the five pressure levels and two time observations (0700 and 1900 LST), is 0.93, 0.72, 0.87, and 0.88, respectively. The interpolation results from 16- and 36-grid domain fields are lower than the 4-grid interpolation with R2 decreasing by 9%–14%, 7%–13%, and 4%–7% for dewpoint, U wind, and V wind, respectively, although the corresponding interpolations for temperature are slightly better than 4-grid interpolation (R2 increasing by only 2%–4%).

3. Analysis techniques

The principal methods and steps used in this study are summarized in Fig. 2. Overall, this study is composed of four major parts: (i) automatic synoptic weather typing, (ii) identification of weather types associated with rainfall events, (iii) development of within-weather-type rainfall simulation models, and (iv) validation of the rainfall simulation models using an independent dataset. The detailed methodology for each of the aspects–steps is described in the following subsections.

a. Automated synoptic weather typing

The synoptic weather typing procedure used in the study is composed of (i) the correlation matrix-based principal component analysis (PCA), (ii) a hierarchical agglomerative cluster method—an average linkage clustering procedure, and (iii) a nonhierarchical method—discriminant function analysis. The weather typing, based primarily on differentiation and similarity of airmass characteristics, is able to assign every day to a distinctive weather type. In the weather typing, the entire suite of 144 weather variables was used, which are hourly (0800–0700 LST) surface weather observations of six elements: air temperature, dewpoint temperature, sea level pressure, total cloud cover, and south–north and west–east wind speed. To keep seasonal differences in characteristics of air masses within weather types, weather variables were standardized by mean and standard deviation of the dataset instead of removing seasonality, as part of the PCA. The PCA is employed to the 144 weather variables for all days within the dataset for three weather stations, producing a 13-component solution that explains 91% of the total variance within the dataset. The remainders of the components with eigenvalues less than one were discarded. Daily component scores rather than meteorological variables were used in the synoptic weather typing since days with similar meteorological situations tend to exhibit approximately similar component scores. Using daily 13-component scores, the average linkage clustering procedure results in 24 major synoptic weather types for the study area. The determination of the classification solution was based upon statistical diagnostics generated by the clustering procedure, attempting to minimize the within-cluster variance and to maximize the between-cluster variance (refer to Cheng et al. 2007a for details). Following the hierarchical classification, discriminant function analysis was used to reclassify all days within the dataset using the centroids of the hierarchical weather types as seeds. It has been demonstrated that the cluster structure resulting from nonhierarchical reclassification is better than that from hierarchical classification alone, with smaller within-cluster variances and larger between-cluster variances (e.g., DeGaetano 1996; Cheng et al. 2007a).

To obtain a classification solution that can more effectively capture heavy rainfall events within fewer weather types, the synoptic weather typing approach was repeated for each of the four datasets. The four datasets are (i) surface meteorological data alone, mentioned above, (ii) surface and upper-air meteorological data combined, (iii) surface meteorological data and atmospheric stability indices combined, and (iv) atmospheric stability indices alone. The upper-air data include 6-hourly National Centers for Environmental Prediction (NCEP) reanalysis data of air temperature, dewpoint temperature, and south–north and west–east wind speed at the five atmospheric levels of 925, 850, 700, 600, and 500 hPa. Atmospheric stability indices can indicate the likelihood of occurrence of severe thunderstorms and convective rainfall. Three stability indices, Lifted index (L; Galway 1956), K index (K; George 1960), and total totals index (TT; Miller 1972), were calculated at 6-hourly intervals from the surface meteorological observations and upper-air NCEP reanalysis data. These indices are commonly evaluated by meteorologists when operationally forecasting the potential for heavy rainfall and severe weather events (thunderstorms and possible tornadoes). The synoptic weather typing solution resulting from dataset (i) captures heavy rainfall events (e.g., ≥25 mm day−1) within the least number of weather types (i.e., 10 weather types); however, other classifications using datasets (ii)–(iv) result in more weather types being needed to capture heavy rainfall events (e.g., ∼15 types). This does not mean that upper-air data and atmospheric stability indices are not important in identifying rainfall-related synoptic weather types or patterns since the vertical thermodynamic profiles from the surface to 500 hPa are usually needed to determine production and type of precipitation (Cheng et al. 2004). These variables were used when developing daily rainfall simulation models (refer to section 3c).

b. Synoptic weather types associated with rainfall events

Since each of the weather types represents a distinctive air mass and synoptic signature, a specific regime of rainfall should be related to each. The daily average rainfall data within each of the selected river basins were assigned to the synoptic weather type occurring on that day for each of the within–river basin airport weather stations. The Thames River basin paired with London International Airport, the Humber River with Toronto International Airport, and the Rideau River with Ottawa International Airport. In the Grand River watershed, there is no hourly weather station available; therefore London and Toronto weather types were tested to ascertain which weather typing could be used. It was found that the linkage between London weather types and rainfall in the Grand River basin is closer than the linkage using Toronto weather types, based on proportion to the total rainfall events captured by rainfall-related weather types. For example, London’s rainfall-related weather types captured 99% of the total days with rainfall ≥25 mm for the Grand River basin (April–November 1958–2002). The corresponding percentage derived from Toronto’s weather types is 94%.

To identify the synoptic types most highly associated with rainfall events, in addition to within-weather-type daily mean rainfall amount, a frequency ratio of within-weather-type rainfall events was calculated. The frequency ratio compares the percentage frequency of days with rainfall events (actual frequency) to the percentage frequency of the weather type within the entire record (expected frequency). If a weather type possesses a frequency ratio >1.0, it is overrepresented for rainfall events and is selected as a rainfall-related weather type. A χ2 test was employed to ascertain whether the observed frequencies of rainfall cases were significantly different from their expected occurrences (χ2-test significance level of 0.001). A variety of rainfall events, based on daily rainfall amounts (i.e., ≥0.2, ≥10, ≥25, ≥50 mm), were included in the analysis. The thresholds used to define heavier rainfall events (i.e., 25 and 50 mm) are currently used by Environment Canada for issuing heavy rainfall warnings when the threshold is expected to be reached or exceeded within a certain time period (e.g., 12 or 24 h).

c. Development of simulation models for daily rainfall quantity

The rainfall prediction approach used in the study comprises a two-step process: (i) stepwise cumulative logit regression to predict the occurrence of daily rainfall events, and (ii) using probability of the logit regression, a nonlinear regression approach to simulate daily rainfall quantity. In cumulative logit regression, the predictand—the daily mean rainfall amount within the watershed—was set to three categories as 0, 1, and 2 when daily rainfall is <0.2, between 0.2 and 10, and ≥10 mm, respectively. More than three categories, based on daily rainfall amount (e.g., <0.2, 0.2–5, 5–10, 10–20, 20–30, ≥30 mm), were tested in the logit regression. The results showed that a model using a predictand with more than three categories was not suitable since some of the categories could not be identified by the logit regression, as the characteristics of predictors between adjacent categories (e.g., 10–20 and 20–30 mm) are not clearly distinguished.

The 228 predictors used in stepwise logit regression, derived from hourly surface observations and 6-hourly upper-air reanalysis data, are described in Table 2. These predictors were selected based on analyses of relationships between rainfall and predictors as well as results of previous studies (e.g., Djurić 1994; Glickman 2000). Atmospheric convective instability that has the potential for convective storm activity is assessed using derived indices. The L, K, and TT were the atmospheric stability indices used for rainfall prediction in this study. Other indices, such as the severe weather threat (SWEAT) index, convective inhibition (CIN), and convective available potential energy (CAPE), were excluded from the study because of a weak relation with rainfall based on the analysis and much larger variations than the three indices used in the study.

A certain threshold level of these stability indices can be an indicator of atmospheric instability and conditions that are suitable for the potential development of convective precipitation. For example, Glickman (2000) pointed out that as K increases from a value of approximately 20, the likelihood of showers and thunderstorms is expected to increase. Showers and thunderstorms become likely when the TT value is about 30 or more; when TT values reach 50 or more, severe thunderstorms can be considered likely. Environment Canada (2006) has used a K value of >30 and precipitable water >25 mm as two indicators of conditions favorable for the production of heavy rainfall events.

However, when examining relationships between daily rainfall amounts and the values of the indices, we found that thresholds of the indices vary from time to time, weather type to weather type, and place to place. To effectively apply the indices for predicting the occurrence of daily rainfall events using cumulative logit regression, the indices were visually set up as dummy variables for each of the locations, each of the weather types, and each of four times per day (0100, 0700, 1300, 1900 LST), from the scatterplots of relationships between daily rainfall amounts and the index values. A sample of dummy variable settings for a weather type, mesohigh, is shown in Fig. 3. For example, when the K is <14 or >27, the variable is set to 0 or 2, respectively; otherwise, the variable is set to 1. When surface dewpoint depression is <1°C, the variable is set to 1; otherwise, the variable is set to 0. The major purpose of the dummy variable settings is to enable the rainfall prediction models to more effectively identify the occurrence of heavy rainfall events.

The surface wind direction index (WDI) was used in the regression analysis instead of the wind direction angle, as the wind direction angle is discontinuous at 360°. The WDI is defined differently for the individual weather types, as the wind direction associated with daily rainfall events tends to vary among weather types and locations. The WDI was defined as follows:
i1558-8432-49-5-845-e1
where θ and φ are the wind direction angle and constant expressed in radians, respectively. This index ensures that the WDI attains its maximum value of two and minimum value of zero when the wind directions correspond to the highest and lowest frequencies of daily rainfall events, respectively; this can be controlled by the constant φ. For example, if southerly winds within a weather type are most frequently associated with daily rainfall events, the constant φ is equal to −90° so that the WDI attends its maximum value. In an effort to determine relationships between wind direction and rainfall events, the frequency of daily rainfall events was plotted as a function of the corresponding surface hourly wind direction at 0800, 1400, 2000, 0200, and 0700 LST. The results showed that the wind direction most often associated with daily rainfall events varies among weather types. For example, across the study area within the weather type “warm front,” rainfall events are most frequently associated with southerly surface winds; within the weather type “cold front,” rainfall events are most frequently associated with westerly-northwesterly winds.
Once the occurrence of daily rainfall events has been predicted, logit regression probability is used to develop prediction models for daily rainfall quantity. The cumulative logit regression theoretically provides one probability for each of three daily rainfall categories described above: <0.2, between 0.2 and 10, and ≥10 mm. Since the three probabilities are highly correlated, it is more appropriate to use one of them for the simulation of daily rainfall amount. The relationship between each set of probabilities and daily rainfall amounts was examined. The results showed that a higher probability for the category with daily rainfall ≥10 mm is usually associated with a heavier daily rainfall event. For the category with daily rainfall <0.2 mm, the corresponding relationship is usually reversed. For the category with daily rainfall between 0.2 and 10 mm, both higher and lower probabilities are associated with the heavier rainfall events. As a result, the probability for the category with daily rainfall ≥10 mm is most suitable for predicting daily rainfall quantity. To better capture nonlinear relationships between the probability and daily rainfall quantity, the probability is transferred by the following expression:
i1558-8432-49-5-845-e2
Then, the polynomial function was applied, using the probability index, to develop nonlinear prediction models to simulate daily rainfall quantities.

d. Validation of rainfall simulation models

The entire methodology used in this study, which is composed of synoptic weather typing and rainfall simulation models, was validated by randomly selecting one-fourth of the total years for the weather data. The remaining three-fourths of the total years were used for model development. The validation dataset is therefore independent from the data sample used in the development of the models. The 11 yr randomly selected from the period 1958–2002 to validate the models for all selected watersheds are 1964, 1971, 1972, 1975, 1979, 1981, 1983, 1989, 1990, 1994, and 1998.

The validation is divided into two steps: (i) weather type verification and (ii) validation of rainfall simulation models. For weather-type verification, component scores for each day of the validation dataset were determined by multiplying the posteigenvector matrix (deriving from the model developmental dataset) by the validation data matrix. The new component scores were comparable with the postscores since both used the same set of eigenvectors. Based on the new component scores, discriminant function analysis was used to assign each day within the validation dataset into one of the predetermined weather types using the centroids of the weather types as seeds. Since the number of weather types and their respective characteristics have been predetermined, discriminant function analysis is an appropriate tool for verification of weather types (Klecka 1980). Within-weather-type meteorological characteristics of all weather elements that were used in synoptic weather typing should be similar between both developmental and validation datasets.

This verification method of the weather typing approach, using centroids of predetermined weather types as seeds, is useful for forecasting on arrival the rainfall-related weather types for the future, with inputs of hourly climate data derived from a numerical weather prediction model or downscaled from a GCM output. However, one question that arises from the weather type verification analysis is whether the rainfall-related weather types identified in the calibration stage represent “typical” types for the region. To more effectively answer this question, the same procedures that were used for weather typing calibration were employed for the validation dataset for London International Airport to test the synoptic weather typing without prior seeding of the clusters. The new weather types were compared to the original ones derived from the validation method using seeding of the clusters. It was found that both weather types have the similar meteorological characteristics, especially for the rainfall-related weather types. About 77% of the total days within the rainfall-related weather types verified from the original validation were reclassified into the weather types possessing similar meteorological characteristics. The corresponding percentages for daily rainfall ≥10- and ≥25-mm cases are about 80% and 85%, respectively. As a result, it can be concluded that the rainfall-related weather types identified in the calibration stage represent typical types for the region.

Following determination of the weather type for each day of the validation dataset, the within-weather-type rainfall simulation models were used to verify the occurrence of daily rainfall events and daily rainfall quantities for all days in the validation dataset. These results were then compared with actual daily rainfall observations within the validation dataset to assess the performance of the rainfall simulation models (see section 4 for validation results).

4. Results and discussion

a. Rainfall-related weather types and associated weather patterns

Based on the within-weather-type frequency ratio of the actual frequency of daily rainfall events to the expected frequency, 10 synoptic weather types were identified over the 45-yr period as the primary rainfall-related weather types. Figure 4 illustrates the archetypical surface weather patterns associated with the 10 rainfall-related weather types. These 10 rainfall-related weather types are associated with 6 standard meteorological weather patterns: cyclone, mesohigh, cold low, cold front, quasi-stationary front, and warm front, occurring in different seasons (e.g., cold front I, II, and III). The weather patterns labeled with I occur most frequently in the summer (June–August) and usually possess much warmer characteristics than do the same weather patterns labeled with II, which occur most often in the spring (April–May) and fall (September–November). The cold front III is the weather type that can occur throughout all seasons and that typically can have temperature conditions between those of cold fronts I and II. The weather pattern was identified for each of the weather types, based on a subjective examination of a number of surface weather maps associated with heavy rainfall events. The maps illustrated in Fig. 4 are a combination of the digital weather maps retrieved from the Unisys Weather Map Archive (http://weather.unisys.com/archive/index.html) and the frontal positions that were manually copied from the scanned surface weather maps of the Ontario Storm Prediction Centre, Environment Canada.

The resulting ratios of the actual frequency of daily rainfall events to the expected frequency derived from the developmental dataset for each of the weather types are provided in Table 3 for the Thames River basin; similar results are found for other basins. For example, for synoptic type 1.1 in London, the expected frequency of daily rainfall events should be approximately 5.4%, based on the expected occurrence frequency of the weather type within the entire record. However, the actual frequency of the rainfall events with daily rainfall amount ≥25 mm is 14%, or about 2.6 times what might otherwise be expected. These 10 rainfall-related synoptic weather types, combining developmental and validation datasets, represent about 45%–48% of the total number of days during the period April–November 1958–2002, across the selected cities (Fig. 5). The percentage occurrence of each weather type is fairly consistent across the cities, although there is some spatial variation. These 10 weather types accounted for 73%–77%, 92%–93%, and 95%–98% of the rainfall events with daily rainfall ≥0.2, ≥10, and ≥25 mm, respectively, across the selected river basins.

Table 3 shows that in addition to the 10 rainfall-related weather types, there are two combined weather groupings: Other I and Other II. Other I consists of seven major weather types and some smaller ones associated with some rainfall events, which do not meet the selection criteria for a “pure” rainfall-related weather type. Other II comprises seven other major weather types and some lesser ones that are each usually related to days with no rainfall. The daily mean rainfall amount within Other I and Other II is usually <1 mm, which is much less than that in any of the identified rainfall-related weather types.

The validation of synoptic weather typing, using the independent randomly selected dataset, was examined through comparing (i) within-weather-type mean meteorological characteristics and (ii) the frequency of daily rainfall events, between developmental and validation datasets. To measure the similarities and differentiations between the two data sample means and variances within a weather type, t and F tests were applied; no significant difference was detected. In addition to evaluating within-weather-type mean characteristics of meteorological variables, the within-weather-type frequency of daily rainfall events between developmental and validation datasets was examined to validate the weather typing procedure. The within-synoptic-type frequency of daily rainfall events derived from the validation dataset for the Thames River basin is shown in Table 4. Comparing Tables 3 and 4, it can be seen that within-weather-type percentage frequencies of daily rainfall events for both the developmental and validation datasets are similar, except for heavy rainfall events due to the small number of the cases. These results implied that the discriminant function analysis performed well in identifying the weather types most highly associated with daily rainfall events.

b. Simulation of daily rainfall event occurrence

A stepwise cumulative logit regression procedure was performed on all days of the developmental dataset within each of the 10 rainfall-related weather types for each of the selected river basins (refer to section 3c). Table 5 lists the explanatory predictors to simulate the occurrence of daily rainfall events for the weather type (cold low) as an example; the predictors were identified using the stepwise cumulative logit regression model with an entry and retention significance level of 0.05. Generally, the predictors identified by logit regression procedure across the study area include surface and upper-air temperatures, sea level pressure, six-hourly pressure change, atmospheric stability indices, dewpoint depression, cloud cover, and winds. These predictors are consistent with the physical processes typically associated with rainfall events.

A daily rainfall event occurrence simulation model was developed for each of the 10 rainfall-related weather types in each of river basins. Across the four selected river basins, the simulation models reveal that there are significant correlations between the occurrence of rainfall events and model simulations. The models’ concordances range from 0.82 to 0.96 (a perfect model would have a concordance value of 1.0). Of the total 40 simulation models (10 models for each of the four selected river basins), 11, 19, and 33 models possess concordances greater than 0.92, 0.90, and 0.87 (arbitrary thresholds), respectively. The models are able to correctly identify most daily rainfall events with a high probability of detection (POD), while yielding a small false alarm rate (FAR). For example, in the Thames River basin, the models can produce a prediction result with a POD of 86%, 96%, and 99% for ≥10-mm event probability equal to or greater than 0.95, 0.8, and 0.6, respectively, with a corresponding FAR of 0.7%, 2.8%, and 5.8%. The corresponding quantities derived from the validation dataset are similar to those of model development. Similar results are also found for other river basins.

To more effectively evaluate the performance of simulation models of daily rainfall event occurrence, the relative operating characteristic (ROC) and reliability diagram, which are suitable to evaluate probabilistic prediction results (Mason 1982; Stanski et al. 1989; Wilks 1995; Mason and Graham 1999), were used in the study. In these model performance evaluations, not only rainfall occurrence simulation models for the 10 rainfall-related weather types but also two models developed for weather groupings Other I and Other II were included in the analysis. The ROC can graphically display the relationship between the POD and FAR transformed from probabilistic forecasts. As shown in Fig. 6, a point in the ROC paradigm is defined by the FAR value on the x axis and POD value on the y axis. The upper left corner of the ROC diagram represents a perfect forecast system with only hits (i.e., no false alarms). The closer the ROC curve is to this corner, the higher the model prediction skill. In reality, there is no perfect model with its values on a long convex curve pointing to the upper-left corner. The area between the ROC curve and the x axis and the x = 100% axis measures the skill of the model forecasts, which is commonly used as the ROC score. A skillful model should possess an ROC score greater than 0.5 when the POD exceeds FAR; in other words, the ROC curve lies above the no-skill line (the 45° line from the origin). From Fig. 6, it is seen that the logit regression procedure was successful at identifying daily rainfall event occurrence, and had a very high ROC score for all daily rainfall events (i.e., ≥0.2, ≥10, and ≥25 mm). The ROC scores to identify daily heavier rainfall events (≥10 or ≥25 mm) are greater than 0.97 for both model development and validation, across the selected river basins. The corresponding score for daily rainfall events (≥0.2 mm) is greater than 0.87 for all basins.

In addition to the ROC paradigm, an attribute diagram was used to evaluate the reliability of the rainfall occurrence simulation model in terms of evaluating the frequency bias of various probability categories (Stanski et al. 1989; Wilks 1995). For each of the logit regression probability deciles of 10%, 20%, and so on, the frequency of occurrence of a rainfall event with daily rainfall ≥0.2 mm was calculated. The observed frequencies were then plotted against the set of forecast probability categories. The diagonal line from the origin, as shown in Fig. 7, represents perfect model reliability. For example, if a probability forecast of 70% is given, the rainfall event should also be observed 70% of the time for the prediction model to be considered reliable. As a result, reliability of the model is indicated by the proximity of the plotted curve to the diagonal line. If the curve lies below or above the diagonal line, this indicates overforecasting or underforecasting, respectively. As shown in Fig. 7, the results of the rainfall occurrence simulation models derived from both the developmental and validation datasets indicate that the models are reasonably reliable. The reliability is usually higher for daily rainfall events with a higher forecast probability (e.g., >0.6). This high-probability proportion is more important than the low-probability proportion since heavy rainfall events usually occur with a higher forecast probability. For a lower forecast probability (e.g., <0.3), the model simulation mostly predicts nonrainfall events.

When using logit models, overdispersion or underdispersion might be a problem if the model does not fit, which is indicated when the deviance and Pearson chi-square statistic exceed or are below the degrees of freedom. As Allison (1999) pointed out, there are two possible causes for overdispersion or underdispersion: (i) an incorrectly specified model: more interactions and/or nonlinearities are needed in the model, and (ii) lack of independence of the observations. The logistic–logit regression analysis attempts to account for these dispersions. The SAS logistic–logit procedure (SAS Institute 1999a) employs two ratios to define overdispersion or underdispersion: (i) the Pearson chi-square statistic and (ii) the deviance, to their degrees of freedom. Both ratios should be approximately equal to one; otherwise, if a ratio is significantly greater than or smaller than one, the assumption of binomial–multinomial variability may not be valid and the data are said to exhibit overdispersion or underdispersion. All logit regression models developed in this study for the simulation of rainfall event occurrence have been checked; none of the ratios was significantly greater than or smaller than one. As a result, overdispersion or underdispersion is not considered an issue in the present study.

c. Simulation of daily rainfall quantity

Following simulation of occurrence of daily rainfall events, the cumulative logit regression probability can be used to develop simulation models for daily rainfall quantity. A ranking procedure was used to regroup the data for each of the 10 rainfall-related weather types and two other weather groupings (Other I and Other II). The data within each of the weather types–groupings, combining daily rainfall amount and the probability index, were sorted by the probability index expressed in Eq. (2) from lowest to highest. Then the days were put into the ranking groups with a roughly equal number of days in each group. The SAS Rank procedure (SAS Institute 1999b) was used to determine how many ranking groups were suitable for developing simulation models of daily rainfall quantity. Twenty-one different rankings (50, 55, … , 145, 150 groups, in intervals of 5) were tested for each of the weather types; the model with the greatest model R2 was used in the analysis. As an example, the results of the group-ranking daily rainfall quantity simulation models in four selected river basins for the weather type (cold low) are summarized in Fig. 8. Similar results were discovered for the other weather types as well. The models shown in Fig. 8 were constructed based upon 150 ranking groups (2–3 members in each group) for the Thames and Grand River basins, 105 groups (4–5 members) for Humber River, and 100 groups (5–6 members) for Rideau River. The model R2 of the total 40 group-ranking daily rainfall quantity simulation models (10 models for each basin) range from 0.70 to 0.94; about 58%, 35%, and 20% of the models possess an R2 of at least 0.80, 0.85, and 0.90, respectively.

Following the development of the group-ranking daily rainfall quantity simulation models, a within-weather-type model was applied to each individual day within the weather type for both developmental and validation datasets to calculate daily rainfall totals. To effectively evaluate performance of daily rainfall simulation models, the evaluation structure as shown in Table 6 was used. It should be noted that all references to the four correctness classifications of excellent, good, fair, and poor as defined in Table 6 are based on four subjectively selected difference levels between daily observed and simulated rainfall amounts. The results of the model performance evaluation for each of the river basins are summarized in Fig. 9. The observed daily rainfall data were divided into five categories based on daily rainfall amount: 1) <7.5 mm, 2) 7.5–12.5 mm, 3) 12.5–17.5 mm, 4) 17.5–32.5 mm, and 5) ≥32.5 mm. Some of these rainfall categories (e.g., 7.5–12.5 and 17.5–32.5 mm) were selected to correspond with and represent the rainfall thresholds (10 and 25 mm) used in the study. It was observed that the proportion of the simulations that fell into the excellent and good categories was greater than the proportion that fell into the fair and poor categories. Across the four selected river basins, the percentage of excellent and good simulations among the rainfall categories for model development ranged from 62% to 84% [of 20 individuals (5 rainfall categories and 4 river basins), 16 cases ≥ 70% and 7 cases ≥ 80%]; the corresponding percentage for model validation ranged from 50% to 76% (of 20 individuals, 15 cases ≥ 60% and 6 cases ≥ 70%). It is noteworthy that most of the heavy rainfall events (≥32.5 mm) that the daily rainfall simulation models cannot capture are summer localized convective storms.

The results of rainfall simulation model development and validation suggest that the models have the potential for downscaling of daily rainfall quantity under a changing climate. It is noteworthy that to achieve this goal, the rainfall simulation models in this study were developed in a stagewise procedure: to classify weather types without any knowledge of the rainfall events first, and then to develop within-weather-type rainfall simulation models. Otherwise, if rainfall information is included in the synoptic weather typing, the future weather type cannot be identified without rainfall information; in turn, the within-weather-type rainfall simulation model is unable to be used as a downscaling transfer function to project future daily rainfall information. In contrast, some of the previous studies (e.g., Bellone et al. 2000) have used a nonhomogeneous hidden Markov model to simultaneously identify the hidden weather states and simulate the precipitation quantities. However, this hidden Markov model can simulate only the distribution of daily precipitation quantities but cannot be used to predict precipitation for a specific day.

d. Robustness of rainfall simulation models

In this section, the robustness of the developed rainfall simulation models is examined using all days without synoptic weather typing. This study applied both synoptic weather typing and cumulative logit/nonlinear regressions altogether for the development of daily rainfall simulation models. To determine whether it was necessary to perform synoptic weather typing prior to the application of a regression model, the rainfall simulation model was redeveloped using all days without synoptic weather typing. The same methods used in the earlier rainfall simulation modeling and the same potential predictors (as shown in Table 2) for all days from developmental and validation datasets were employed to develop and validate the rainfall simulation test model for each of the river basins. Figure 10 illustrates evaluation of the daily rainfall simulation test model (using all days without synoptic weather typing) performance. To effectively compare the test models to the original ones (using synoptic weather typing), both model results derived from the same size of data sample should be used. As shown in Figs. 9 and 10, the original models perform better than the test models for both model development and validation, especially for heavy rainfall events. For example, for the events with daily rainfall ≥32.5 mm, the percentage of excellent and good simulations identified from the original models is about 14% greater than that from the test models, for model calibration. The corresponding percentage difference for model validation is about 11%. In addition, daily rainfall observations were compared with the model predictions from both test and original models to calculate model R2s and root-mean-square errors (RMSE), resulting in the fact that the overall model R2 and RMSE from the original models are about 15% greater and 5% less, respectively, than those from the test models. Specifically, the difference magnitude between both models varies from weather type to weather type. For example, for the weather type Warm front II in the Humber River basin, the model R2 is 0.64 and RMSE is 3.34 mm; the corresponding values for the test model are 0.51 and 3.90. These results imply that the synoptic weather typing prior to the application of cumulative logit–nonlinear regressions improves the results of daily rainfall simulations.

5. Conclusions and recommendations

An automated synoptic weather typing approach, consisting of principal component analysis, an average linkage clustering procedure, and discriminant function analysis, was used together with cumulative logit and nonlinear regression procedures to develop daily rainfall simulation models for four selected river basins in Ontario, Canada. Ten synoptic weather types were identified as being the most highly associated with historical rainfall events at the river basins. The within-weather-type rainfall simulation models demonstrated significant skill in the discrimination and prediction of the occurrence and quantity of daily rainfall events with a few exceptions of localized summer convective storms. A formal verification process of model results has been built into the whole exercise, such as synoptic weather typing and rainfall simulation modeling. The results of the verification, based on historical observations of the outcome variables predicted by the models, showed good agreement. In addition, the robustness of the developed rainfall simulation models using all days without synoptic weather typing was examined to ascertain that it is necessary to perform synoptic weather typing prior to the application of a regression model.

In this study, the weather typing structure and rainfall simulation models are site-specific since they can capture the synoptic and topographical influences specific to the selected river basins. Therefore, to apply these models at other locations, they have to be recreated each time using locally measured data. However, the methods, including weather typing and cumulative logit/nonlinear regression procedures, can be applied to any location influenced by a variety of topographic and other factors to build a new rainfall simulation model.

The results from this study showed that a combination of synoptic weather typing and cumulative logit–nonlinear regression procedures can be useful to simulate historical daily rainfall occurrence and quantity. Therefore, a general conclusion from this study is that the methods used in the study are suitable to assess changes in frequency and intensity of future daily rainfall events at a local scale. To achieve this, the future research work should include three aspects. First, the statistical downscaling method will be applied to downscale future GCM climate data to the selected meteorological stations for deriving future hourly climate data that were used in the synoptic weather typing and rainfall simulation modeling. Second, using future hourly station-scale climate data, the synoptic weather typing is able to project future daily weather types. Third, future daily rainfall will be projected by applying within-weather-type rainfall simulation models with downscaled future GCM climate data.

Acknowledgments

This study was funded through the Government of Canada’s Climate Change Impacts and Adaptation Program (CCIAP), administered by Natural Resources Canada, which made this research project (A901) possible. The authors gratefully acknowledge the suggestions made by the Project Advisory Committee, which greatly improved the study. The authors thank Dr. Rowan Fealy and two anonymous reviewers for providing detailed comments that significantly improved the original manuscript.

REFERENCES

  • Abaurrea, J., and J. Asín, 2005: Forecasting local daily precipitation patterns in a climate change scenario. Climate Res., 28 , 183197.

    • Search Google Scholar
    • Export Citation
  • Alley, R., and Coauthors, 2007: Summary for policymakers. Climate Change 2007: The Physical Science Basis, S. Solomon et al., Eds., Cambridge University Press, 1–18.

    • Search Google Scholar
    • Export Citation
  • Allison, P. D., 1999: Logistic Regression Using the SAS System: Theory and Application. SAS Institute, 288 pp.

  • Applequist, S., G. E. Gahrs, R. L. Pfeffer, and X. F. Niu, 2002: Comparison of methodologies for probabilistic quantitative precipitation forecasting. Wea. Forecasting, 17 , 783799.

    • Search Google Scholar
    • Export Citation
  • Bellone, E., J. P. Hughes, and P. Guttorp, 2000: A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts. Climate Res., 15 , 112.

    • Search Google Scholar
    • Export Citation
  • Buishand, T. A., M. V. Shabalova, and T. Brandsma, 2004: On the choice of the temporal aggregation level for statistical downscaling of precipitation. J. Climate, 17 , 18161827.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., H. Auld, G. Li, J. Klaassen, B. Tugwood, and Q. Li, 2004: An automated synoptic typing procedure to predict freezing rain: An application to Ottawa, Ontario. Wea. Forecasting, 19 , 751768.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., and Coauthors, 2007a: A synoptic climatological approach to assess climatic impact on air quality in south-central Canada. Part I: Historical analysis. Water Air Soil Pollut., 182 , 131148.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., and Coauthors, 2007b: A synoptic climatological approach to assess climatic impact on air quality in south-central Canada. Part II: Future estimates. Water Air Soil Pollut., 182 , 117130.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., H. Auld, G. Li, J. Klaassen, and Q. Li, 2007c: Possible impacts of climate change on freezing rain in south-central Canada using downscaled future climate scenarios. Nat. Hazards Earth Syst. Sci., 7 , 7187.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., and Coauthors, 2008a: Differential and combined impacts of extreme temperatures and air pollution on human mortality in south–central Canada. Part I: Historical analysis. Air Qual. Atmos. Health, 1 , 209222.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., and Coauthors, 2008b: Differential and combined impacts of extreme temperatures and air pollution on human mortality in south–central Canada. Part II: Future estimates. Air Qual. Atmos. Health, 1 , 223235.

    • Search Google Scholar
    • Export Citation
  • Cubasch, U., J. Waszkewitz, G. Hegerl, and J. Perlwitz, 1995: Regional climate changes as simulated time-slice experiments. Climatic Change, 31 , 273304.

    • Search Google Scholar
    • Export Citation
  • DeGaetano, A., 1996: Delineation of mesoscale climate zones in the northeastern United States using a novel approach to cluster analysis. J. Climate, 9 , 17651782.

    • Search Google Scholar
    • Export Citation
  • Djurić, D., 1994: Weather Analysis. Prentice-Hall, 304 pp.

  • Fealy, R., and J. Sweeney, 2007: Statistical downscaling of precipitation for a selection of sites in Ireland employing a generalised linear modelling approach. Int. J. Climatol., 27 , 20832094.

    • Search Google Scholar
    • Export Citation
  • Galway, J. G., 1956: The lifted index as a predictor of latent instability. Bull. Amer. Meteor. Soc., 37 , 528529.

  • George, J. J., 1960: Weather Forecasting for Aeronautics. Academic Press, 673 pp.

  • Glickman, T. S., 2000: Glossary of Meteorology. 2nd ed. Amer. Meteor. Soc., 855 pp.

  • Goodess, C. M., and J. P. Palutikof, 1998: Development of daily rainfall scenarios for southeast Spain using a circulation-type approach to downscaling. Int. J. Climatol., 18 , 10511083.

    • Search Google Scholar
    • Export Citation
  • Hall, T., H. E. Brooks, and C. D. Doswell, 1999: Precipitation forecasting using a neural network. Wea. Forecasting, 14 , 338345.

  • Kalkstein, L. S., 1979: A synoptic climatological approach for environmental analysis. Proc. Middle States Div. Assoc. Amer. Geogr., 13 , 6875.

    • Search Google Scholar
    • Export Citation
  • Kalkstein, L. S., 1991: A new approach to evaluate the impact of climate on human mortality. Environ. Health Perspect., 96 , 145150.

  • Kalkstein, L. S., and P. Corrigan, 1986: A synoptic climatological approach for geographical analysis: Assessment of sulfur dioxide concentrations. Ann. Assoc. Amer. Geogr., 76 , 381395.

    • Search Google Scholar
    • Export Citation
  • Kalkstein, L. S., M. C. Nichols, C. D. Barthel, and J. S. Greene, 1996: A new spatial synoptic classification: Application to air-mass analysis. Int. J. Climatol., 16 , 9831004.

    • Search Google Scholar
    • Export Citation
  • Kalkstein, L. S., S. C. Sheridan, and D. Y. Graybeal, 1998: A determination of character and frequency changes in air masses using a spatial synoptic classification. Int. J. Climatol., 18 , 12231236.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Kharin, V. V., and F. W. Zwiers, 2005: Estimating extremes in transient climate change simulations. J. Climate, 18 , 11561173.

  • Kistler, R., and Coauthors, 2001: The NCEP–NCAR 50-Year Reanalysis: Monthly means CD-ROM and documentation. Bull. Amer. Meteor. Soc., 82 , 247267.

    • Search Google Scholar
    • Export Citation
  • Klecka, W. R., 1980: Discriminant Analysis. Sage University Press, 71 pp.

  • Koizumi, K., 1999: An objective method to modify numerical model forecasts with newly given weather data using an artificial neural network. Wea. Forecasting, 14 , 109118.

    • Search Google Scholar
    • Export Citation
  • Kostopoulou, E., and P. D. Jones, 2007a: Comprehensive analysis of the climate variability in the eastern Mediterranean. Part I: Map-pattern classification. Int. J. Climatol., 27 , 11891214.

    • Search Google Scholar
    • Export Citation
  • Kostopoulou, E., and P. D. Jones, 2007b: Comprehensive analysis of the climate variability in the eastern Mediterranean. Part II: Relationships between atmospheric circulation patterns and surface climatic elements. Int. J. Climatol., 27 , 13511371.

    • Search Google Scholar
    • Export Citation
  • Mason, I., 1982: A model for assessment of weather forecasts. Aust. Meteor. Mag., 30 , 291303.

  • Mason, S. J., and N. E. Graham, 1999: Conditional probabilities, relative operating characteristics, and relative operating levels. Wea. Forecasting, 14 , 713725.

    • Search Google Scholar
    • Export Citation
  • McGregor, G. R., 1999: Winter ischaemic heart disease deaths in Birmingham, United Kingdom: A synoptic climatological analysis. Climate Res., 13 , 1731.

    • Search Google Scholar
    • Export Citation
  • Meehl, G. A., C. Covey, T. Delworth, M. Latif, B. McAvaney, J. F. B. Mitchell, R. J. Stouffer, and K. E. Taylor, 2007: The WCRP CMIP3 multimodel dataset: A new era in climate change research. Bull. Amer. Meteor. Soc., 88 , 13831394.

    • Search Google Scholar
    • Export Citation
  • Miller, R. C., 1972: Notes on analysis and severe storm forecasting procedures of the Air Force Global Weather Central. Tech. Rep. 200(R), Headquarters, Air Weather Service, USAF, 190 pp.

    • Search Google Scholar
    • Export Citation
  • Perry, A., 1983: Growth points in synoptic climatology. Prog. Phys. Geogr., 7 , 9096.

  • Ross, G. H., 1987: An updateable model output statistics: scheme. Programme on Short- and Medium Range Weather Prediction, PSMP Report Series, Vol. 25, World Meteorological Organization, 45–48.

    • Search Google Scholar
    • Export Citation
  • SAS Institute, 1999a: SAS/STAT User’s Guide, Version 8. SAS Institute, 3809 pp.

  • SAS Institute, 1999b: SAS Procedure Guide, Version 8. SAS Institute, 1563 pp.

  • Shen, S. S. P., P. Dzikowski, G. Li, and D. Griffith, 2001: Interpolation of 1961–97 daily temperature and precipitation data onto Alberta polygons of ecodistrict and soil landscapes of Canada. J. Appl. Meteor., 40 , 21622177.

    • Search Google Scholar
    • Export Citation
  • Sheridan, S. C., 2002: The redevelopment of a weather-type classification scheme for North America. Int. J. Climatol., 22 , 5168.

  • Stanski, H. R., L. J. Wilson, and W. R. Burrows, 1989: Survey of common verification methods in meteorology. 2nd ed. Environment Canada Research Rep. 89-5, 114 pp.

    • Search Google Scholar
    • Export Citation
  • Tebaldi, C., K. Hayhoe, J. M. Arblaster, and G. A. Meehl, 2006: Going to the extremes: An intercomparison of model-simulated historical and future changes in extreme events. Climatic Change, 79 , 185211.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.

  • Wilson, L. J., and M. Vallée, 2002: The Canadian Updateable Model Output Statistics (UMOS) system: Design and development tests. Wea. Forecasting, 17 , 206222.

    • Search Google Scholar
    • Export Citation
  • Wilson, L. J., and M. Vallée, 2003: The Canadian Updateable Model Output Statistics (UMOS) system: Validation against perfect prog. Wea. Forecasting, 18 , 288302.

    • Search Google Scholar
    • Export Citation
  • Zwiers, F. W., and V. V. Kharin, 1998: Changes in the extremes of the climate simulated by CCC GCM2 under CO2 doubling. J. Climate, 11 , 22002222.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Study area and location of four selected watersheds in Ontario.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 2.
Fig. 2.

Flowchart of methodologies and steps used in the study.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 3.
Fig. 3.

Demonstration of dummy variable threshold settings for the weather type (mesohigh) in London.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 4.
Fig. 4.

Archetypical samples of surface synoptic weather patterns associated with the 10 identified rainfall-related weather types [weather maps: the Unisys Weather Map Archive (http://weather.unisys.com/archive/index.html); fronts: the scanned surface weather maps of Environment Canada’s Ontario Storm Prediction Centre].

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 5.
Fig. 5.

Percentage occurrence of the 10 rainfall-related weather types in the selected cities (April–November 1958–2002).

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 6.
Fig. 6.

The ROC curves for rainfall event occurrence identified by simulation models in the four river basins during the period April–November 1958–2002 (Dev = development; Val = validation).

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 7.
Fig. 7.

Reliability diagrams for probability of daily rainfall event occurrence identified by simulation models in the 4 river basins during the period April–November 1958–2002 (N = number of sample days; NRAIN = number of days with rainfall ≥0.2 mm).

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 8.
Fig. 8.

Group-ranking daily rainfall quantity simulation models for the weather type (cold low) at the four selected river basins.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 9.
Fig. 9.

Daily rainfall quantity simulation results for model development and validation within the 10 rainfall-related weather types in the four river basins (the x axis is rainfall category based on observations; Number is the number of days).

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Fig. 10.
Fig. 10.

As in Fig. 9, but using all days without synoptic weather typing, using the same size data sample as in Fig. 9, and pooling the datasets of the four river basins.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2010JAMC2016.1

Table 1.

Data for the period April–November 1958–2002 used in the study. Note: time is local standard time.

Table 1.
Table 2.

The 228 meteorological predictors used in stepwise cumulative logit regression. Note: time is local standard time.

Table 2.
Table 3.

Within-synoptic-type frequency of rainfall events in the Thames River basin (London synoptic weather type). Development datasets: April–November 1958–2002 except for 11-yr validation data. The labels (a)–(e) are used to identify particular columns.

Table 3.
Table 4.

As in Table 3, but for the validation dataset: randomly selected 11 yr from 1958 to 2002.

Table 4.
Table 5.

Summary of rainfall occurrence simulation models using stepwise cumulative logit regression for the weather type (cold low) at Thames River basin (concordance = 0.92). Note: Prin1 means the first principal component using the variables listed in Table 2, Prin4 the fourth principal component, and so on. Estimate is the coefficient of the algorithm. Minus sign (−) indicates a negative relationship between rainfall occurrence and the predictor. Time indicates local standard time.

Table 5.
Table 6.

Criteria used to evaluate daily rainfall simulation models. Note: diff = absolute difference between observed and simulated rainfall in mm; obs = river basin average daily observed rainfall in mm.

Table 6.
Save
  • Abaurrea, J., and J. Asín, 2005: Forecasting local daily precipitation patterns in a climate change scenario. Climate Res., 28 , 183197.

    • Search Google Scholar
    • Export Citation
  • Alley, R., and Coauthors, 2007: Summary for policymakers. Climate Change 2007: The Physical Science Basis, S. Solomon et al., Eds., Cambridge University Press, 1–18.

    • Search Google Scholar
    • Export Citation
  • Allison, P. D., 1999: Logistic Regression Using the SAS System: Theory and Application. SAS Institute, 288 pp.

  • Applequist, S., G. E. Gahrs, R. L. Pfeffer, and X. F. Niu, 2002: Comparison of methodologies for probabilistic quantitative precipitation forecasting. Wea. Forecasting, 17 , 783799.

    • Search Google Scholar
    • Export Citation
  • Bellone, E., J. P. Hughes, and P. Guttorp, 2000: A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts. Climate Res., 15 , 112.

    • Search Google Scholar
    • Export Citation
  • Buishand, T. A., M. V. Shabalova, and T. Brandsma, 2004: On the choice of the temporal aggregation level for statistical downscaling of precipitation. J. Climate, 17 , 18161827.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., H. Auld, G. Li, J. Klaassen, B. Tugwood, and Q. Li, 2004: An automated synoptic typing procedure to predict freezing rain: An application to Ottawa, Ontario. Wea. Forecasting, 19 , 751768.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., and Coauthors, 2007a: A synoptic climatological approach to assess climatic impact on air quality in south-central Canada. Part I: Historical analysis. Water Air Soil Pollut., 182 , 131148.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., and Coauthors, 2007b: A synoptic climatological approach to assess climatic impact on air quality in south-central Canada. Part II: Future estimates. Water Air Soil Pollut., 182 , 117130.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., H. Auld, G. Li, J. Klaassen, and Q. Li, 2007c: Possible impacts of climate change on freezing rain in south-central Canada using downscaled future climate scenarios. Nat. Hazards Earth Syst. Sci., 7 , 7187.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., and Coauthors, 2008a: Differential and combined impacts of extreme temperatures and air pollution on human mortality in south–central Canada. Part I: Historical analysis. Air Qual. Atmos. Health, 1 , 209222.

    • Search Google Scholar
    • Export Citation
  • Cheng, C. S., and Coauthors, 2008b: Differential and combined impacts of extreme temperatures and air pollution on human mortality in south–central Canada. Part II: Future estimates. Air Qual. Atmos. Health, 1 , 223235.

    • Search Google Scholar
    • Export Citation
  • Cubasch, U., J. Waszkewitz, G. Hegerl, and J. Perlwitz, 1995: Regional climate changes as simulated time-slice experiments. Climatic Change, 31 , 273304.

    • Search Google Scholar
    • Export Citation
  • DeGaetano, A., 1996: Delineation of mesoscale climate zones in the northeastern United States using a novel approach to cluster analysis. J. Climate, 9 , 17651782.

    • Search Google Scholar
    • Export Citation
  • Djurić, D., 1994: Weather Analysis. Prentice-Hall, 304 pp.

  • Fealy, R., and J. Sweeney, 2007: Statistical downscaling of precipitation for a selection of sites in Ireland employing a generalised linear modelling approach. Int. J. Climatol., 27 , 20832094.

    • Search Google Scholar
    • Export Citation
  • Galway, J. G., 1956: The lifted index as a predictor of latent instability. Bull. Amer. Meteor. Soc., 37 , 528529.

  • George, J. J., 1960: Weather Forecasting for Aeronautics. Academic Press, 673 pp.

  • Glickman, T. S., 2000: Glossary of Meteorology. 2nd ed. Amer. Meteor. Soc., 855 pp.

  • Goodess, C. M., and J. P. Palutikof, 1998: Development of daily rainfall scenarios for southeast Spain using a circulation-type approach to downscaling. Int. J. Climatol., 18 , 10511083.

    • Search Google Scholar
    • Export Citation
  • Hall, T., H. E. Brooks, and C. D. Doswell, 1999: Precipitation forecasting using a neural network. Wea. Forecasting, 14 , 338345.

  • Kalkstein, L. S., 1979: A synoptic climatological approach for environmental analysis. Proc. Middle States Div. Assoc. Amer. Geogr., 13 , 6875.

    • Search Google Scholar
    • Export Citation
  • Kalkstein, L. S., 1991: A new approach to evaluate the impact of climate on human mortality. Environ. Health Perspect., 96 , 145150.

  • Kalkstein, L. S., and P. Corrigan, 1986: A synoptic climatological approach for geographical analysis: Assessment of sulfur dioxide concentrations. Ann. Assoc. Amer. Geogr., 76 , 381395.

    • Search Google Scholar
    • Export Citation
  • Kalkstein, L. S., M. C. Nichols, C. D. Barthel, and J. S. Greene, 1996: A new spatial synoptic classification: Application to air-mass analysis. Int. J. Climatol., 16 , 9831004.

    • Search Google Scholar
    • Export Citation
  • Kalkstein, L. S., S. C. Sheridan, and D. Y. Graybeal, 1998: A determination of character and frequency changes in air masses using a spatial synoptic classification. Int. J. Climatol., 18 , 12231236.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Kharin, V. V., and F. W. Zwiers, 2005: Estimating extremes in transient climate change simulations. J. Climate, 18 , 11561173.

  • Kistler, R., and Coauthors, 2001: The NCEP–NCAR 50-Year Reanalysis: Monthly means CD-ROM and documentation. Bull. Amer. Meteor. Soc., 82 , 247267.

    • Search Google Scholar
    • Export Citation
  • Klecka, W. R., 1980: Discriminant Analysis. Sage University Press, 71 pp.

  • Koizumi, K., 1999: An objective method to modify numerical model forecasts with newly given weather data using an artificial neural network. Wea. Forecasting, 14 , 109118.

    • Search Google Scholar
    • Export Citation
  • Kostopoulou, E., and P. D. Jones, 2007a: Comprehensive analysis of the climate variability in the eastern Mediterranean. Part I: Map-pattern classification. Int. J. Climatol., 27 , 11891214.

    • Search Google Scholar
    • Export Citation
  • Kostopoulou, E., and P. D. Jones, 2007b: Comprehensive analysis of the climate variability in the eastern Mediterranean. Part II: Relationships between atmospheric circulation patterns and surface climatic elements. Int. J. Climatol., 27 , 13511371.

    • Search Google Scholar
    • Export Citation
  • Mason, I., 1982: A model for assessment of weather forecasts. Aust. Meteor. Mag., 30 , 291303.

  • Mason, S. J., and N. E. Graham, 1999: Conditional probabilities, relative operating characteristics, and relative operating levels. Wea. Forecasting, 14 , 713725.

    • Search Google Scholar
    • Export Citation
  • McGregor, G. R., 1999: Winter ischaemic heart disease deaths in Birmingham, United Kingdom: A synoptic climatological analysis. Climate Res., 13 , 1731.

    • Search Google Scholar
    • Export Citation
  • Meehl, G. A., C. Covey, T. Delworth, M. Latif, B. McAvaney, J. F. B. Mitchell, R. J. Stouffer, and K. E. Taylor, 2007: The WCRP CMIP3 multimodel dataset: A new era in climate change research. Bull. Amer. Meteor. Soc., 88 , 13831394.

    • Search Google Scholar
    • Export Citation
  • Miller, R. C., 1972: Notes on analysis and severe storm forecasting procedures of the Air Force Global Weather Central. Tech. Rep. 200(R), Headquarters, Air Weather Service, USAF, 190 pp.

    • Search Google Scholar
    • Export Citation
  • Perry, A., 1983: Growth points in synoptic climatology. Prog. Phys. Geogr., 7 , 9096.

  • Ross, G. H., 1987: An updateable model output statistics: scheme. Programme on Short- and Medium Range Weather Prediction, PSMP Report Series, Vol. 25, World Meteorological Organization, 45–48.

    • Search Google Scholar
    • Export Citation
  • SAS Institute, 1999a: SAS/STAT User’s Guide, Version 8. SAS Institute, 3809 pp.

  • SAS Institute, 1999b: SAS Procedure Guide, Version 8. SAS Institute, 1563 pp.

  • Shen, S. S. P., P. Dzikowski, G. Li, and D. Griffith, 2001: Interpolation of 1961–97 daily temperature and precipitation data onto Alberta polygons of ecodistrict and soil landscapes of Canada. J. Appl. Meteor., 40 , 21622177.

    • Search Google Scholar
    • Export Citation
  • Sheridan, S. C., 2002: The redevelopment of a weather-type classification scheme for North America. Int. J. Climatol., 22 , 5168.

  • Stanski, H. R., L. J. Wilson, and W. R. Burrows, 1989: Survey of common verification methods in meteorology. 2nd ed. Environment Canada Research Rep. 89-5, 114 pp.

    • Search Google Scholar
    • Export Citation
  • Tebaldi, C., K. Hayhoe, J. M. Arblaster, and G. A. Meehl, 2006: Going to the extremes: An intercomparison of model-simulated historical and future changes in extreme events. Climatic Change, 79 , 185211.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.

  • Wilson, L. J., and M. Vallée, 2002: The Canadian Updateable Model Output Statistics (UMOS) system: Design and development tests. Wea. Forecasting, 17 , 206222.

    • Search Google Scholar
    • Export Citation
  • Wilson, L. J., and M. Vallée, 2003: The Canadian Updateable Model Output Statistics (UMOS) system: Validation against perfect prog. Wea. Forecasting, 18 , 288302.

    • Search Google Scholar
    • Export Citation
  • Zwiers, F. W., and V. V. Kharin, 1998: Changes in the extremes of the climate simulated by CCC GCM2 under CO2 doubling. J. Climate, 11 , 22002222.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Study area and location of four selected watersheds in Ontario.

  • Fig. 2.

    Flowchart of methodologies and steps used in the study.

  • Fig. 3.

    Demonstration of dummy variable threshold settings for the weather type (mesohigh) in London.

  • Fig. 4.

    Archetypical samples of surface synoptic weather patterns associated with the 10 identified rainfall-related weather types [weather maps: the Unisys Weather Map Archive (http://weather.unisys.com/archive/index.html); fronts: the scanned surface weather maps of Environment Canada’s Ontario Storm Prediction Centre].

  • Fig. 5.

    Percentage occurrence of the 10 rainfall-related weather types in the selected cities (April–November 1958–2002).

  • Fig. 6.

    The ROC curves for rainfall event occurrence identified by simulation models in the four river basins during the period April–November 1958–2002 (Dev = development; Val = validation).

  • Fig. 7.

    Reliability diagrams for probability of daily rainfall event occurrence identified by simulation models in the 4 river basins during the period April–November 1958–2002 (N = number of sample days; NRAIN = number of days with rainfall ≥0.2 mm).

  • Fig. 8.

    Group-ranking daily rainfall quantity simulation models for the weather type (cold low) at the four selected river basins.

  • Fig. 9.

    Daily rainfall quantity simulation results for model development and validation within the 10 rainfall-related weather types in the four river basins (the x axis is rainfall category based on observations; Number is the number of days).

  • Fig. 10.

    As in Fig. 9, but using all days without synoptic weather typing, using the same size data sample as in Fig. 9, and pooling the datasets of the four river basins.

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