Traditionally civil infrastructure designs were rendered using rainfall data from dated historical records. However, recent studies have shown that the magnitude and intensity of historical precipitation events do not exhibit the extreme nature of precipitation events that are projected to occur in the future. Increasing extreme rainfall trends have already been documented in Canada. Therefore there are growing concerns that the aging infrastructure in southern Ontario will be unable to function effectively and as a result the frequency of floods is expected to increase. Updating intensity-duration-frequency (IDF) curves to account for extreme precipitation events is vital to ensure that the consequences of floods are mitigated. This study first reviewed the most robust techniques for updating IDF curves, and applied a select set of approaches to create IDF curves for stations within southern Ontario. Three robust techniques – the at-site method, the regional frequency analysis method, and a future IDF curve development technique – were compared with one another to determine which technique was most suitable for updating IDF curves in southern Ontario. Results showed that the difference between the at-site method and the regional frequency analysis method was marginal for short return periods, however for larger return periods larger differences were observed. Future IDF statistic results showed that for the 2050s there were minor differences in the increases in rainfall intensities when comparing with the at-site and the regional frequency analysis method. For the 2100s there were larger increases in rainfall intensities compared to the at-site and the regional frequency analysis method, especially for larger return periods. These results suggest that it is worthwhile for regions within southern Ontario to update their IDF curves using the future IDF curve technique, however it is recommended that additional climate models, emission scenarios and downscaling techniques involved in future IDF curve construction are explored. / Thesis / Master of Science (MSc)

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Intensity-Duration-Frequency (IDF) curves are among the standard design tools for various engineering applications, such as storm water management systems. The current practice is to use IDF curves based on historical extreme precipitation quantiles. A warming climate, however, might change the extreme precipitation quantiles represented by the IDF curves, emphasizing the need for updating the IDF curves used for the design of urban storm water management systems in different parts of the world, including Canada. This study attempts to construct the future IDF curves for Saskatoon, Canada, under possible climate change scenarios. For this purpose, LARS-WG, a stochastic weather generator, is used to spatially downscale the daily precipitation projected by Global Climate Models (GCMs) from coarse grid resolution to the local point scale. The stochastically downscaled daily precipitation realizations were further disaggregated into ensemble hourly and sub-hourly (as fine as 5-minute) precipitation series, using a disaggregation scheme developed using the K-nearest neighbor (K-NN) technique. This two-stage modeling framework (downscaling to daily, then disaggregating to finer resolutions) is applied to construct the future IDF curves in the city of Saskatoon. The sensitivity of the K-NN disaggregation model to the number of nearest neighbors (i.e. window size) is evaluated during the baseline period (1961-1990). The optimal window size is assigned based on the performance in reproducing the historical IDF curves by the K-NN disaggregation models. Two optimal window sizes are selected for the K-NN hourly and sub-hourly disaggregation models that would be appropriate for the hydrological system of Saskatoon. By using the simulated hourly and sub-hourly precipitation series and the Generalized Extreme Value (GEV) distribution, future changes in the IDF curves and associated uncertainties are quantified using a large ensemble of projections obtained for the Canadian and British GCMs (CanESM2 and HadGEM2-ES) based on three Representative Concentration Pathways; RCP2.6, RCP4.5, and RCP8.5 available from CMIP5 – the most recent product of the Intergovernmental Panel on Climate Change (IPCC). The constructed IDF curves are then compared with the ones constructed using another method based on a genetic programming technique. The results show that the sign and the magnitude of future variations in extreme precipitation quantiles are sensitive to the selection of GCMs and/or RCPs, and the variations seem to become intensified towards the end of the 21st century. Generally, the relative change in precipitation intensities with respect to the historical intensities for CMIP5 climate models (e.g., CanESM2: RCP4.5) is less than those for CMIP3 climate models (e.g., CGCM3.1: B1), which may be due to the inclusion of climate policies (i.e., adaptation and mitigation) in CMIP5 climate models. The two-stage downscaling-disaggregation method enables quantification of uncertainty due to natural internal variability of precipitation, various GCMs and RCPs, and downscaling methods. In general, uncertainty in the projections of future extreme precipitation quantiles increases for short durations and for long return periods. The two-stage method adopted in this study and the GP method reconstruct the historical IDF curves quite successfully during the baseline period (1961-1990); this suggests that these methods can be applied to efficiently construct IDF curves at the local scale under future climate scenarios. The most notable precipitation intensification in Saskatoon is projected to occur with shorter storm duration, up to one hour, and longer return periods of more than 25 years.

Urbanisation alters the hydrologic response of a catchment, resulting in increased runoff rates and volumes, and loss of infiltration and base flow. Quantification of uncertainties is important in hydrologic designs of urban infrastructure. Major sources of uncertainty in the Intensity Duration Frequency (IDF) relationships are due to insufficient quantity and quality of data leading to parameter uncertainty and, in the case of projections of future IDF relationships under climate change, uncertainty arising from use of multiple General Circulation Models (GCMs) and scenarios. The work presented in the thesis presents methodologies to quantify the uncertainties arising from parameters of the distribution fitted to data and the multiple GCMs using a Bayesian approach. High uncertainties in GEV parameters and return levels are observed at shorter durations for Bangalore City. Twenty six GCMs from the CMIP5 datasets, along with four RCP scenarios are considered for studying the effects of climate change. It is observed that the uncertainty in short duration rainfall return levels is high when compared to the longer durations. Further it is observed that parameter uncertainty is large compared to the model uncertainty. Disaggregation of precipitation extremes from larger time scales to smaller time scales when the extremes are modeled with the GPD is burdened with difficulties arising from varying thresholds for different durations. In this study, the scale invariance theory is used to develop a disaggregation model for precipitation extremes exceeding specified thresholds. A scaling relationship is developed for a range of thresholds obtained from a set of quantiles of non-zero precipitation of different durations. The disaggregation model is applied to precipitation datasets of Berlin City, Germany and Bangalore City, India. From both the applications, it is observed that the uncertainty in the scaling exponent has a considerable effect on uncertainty in scaled parameters and return levels of shorter durations. A Bayesian hierarchical model is used to obtain spatial distribution of return levels of precipitation extremes in urban areas and quantify the associated uncertainty. Applicability of the methodology is demonstrated with data from 19 telemetric rain gauge stations in Bangalore City, India. For this case study, it is inferred that the elevation and mean monsoon precipitation are the predominant covariates for annual maximum precipitation. For the monsoon maximum precipitation, it is observed that the geographic covariates dominate while for the summer maximum precipitation, elevation and mean summer precipitation are the predominant covariates. In this work, variation in the dependence structure of extreme precipitation within an urban area and its surrounding non-urban areas at various durations is studied. The Berlin City, Germany, with surrounding non-urban area is considered to demonstrate the methodology. For this case study, the hourly precipitation shows independence within the city even at small distances, whereas the daily precipitation shows a high degree of dependence. This dependence structure of the daily precipitation gets masked as more and more surrounding non-urban areas are included in the analysis. The geographical covariates are seen to be predominant within the city and the climatological covariates prevail when non-urban areas are added. These results suggest the importance of quantification of dependence structure of spatial precipitation at the sub-daily timescales, as well as the need to more precisely model spatial extremes within the urban areas. The work presented in this thesis thus contributes to quantification of uncertainty in precipitation extremes through developing methodologies for generating probabilistic future IDF relationships under climate change, spatial mapping of probabilistic return levels and modeling dependence structure of extreme precipitation in urban areas at fine resolutions.

Increasing global mean temperature or global warming has the potential to affect the hydrologic cycle. In the 21st century, according to the UN Intergovernmental Panel on Climate Change (IPCC), alterations in the frequency and magnitude of high intensity rainfall events are very likely. Increasing trend of urbanization across the globe is also noticeable, simultaneously. These changes will have a great impact on water infrastructure as well as environment in urban areas. One of the impacts may be the increase in frequency and extent of flooding. India, in the recent years, has witnessed a number of urban floods that have resulted in huge economic losses, an instance being the flooding of Mumbai in July, 2005. To prevent catastrophic damages due to floods, it has become increasingly important to understand the likely changes in extreme rainfall in future, its effect on the urban drainage system, and the measures that can be taken to prevent or reduce the damage due to floods. Reliable estimation of future design rainfall intensity accounting for uncertainties due to climate change is an important research issue. In this context, rainfall intensity-duration-frequency (IDF) relationships are one of the most extensively used hydrologic tools in planning, design and operation of various drainage related infrastructures in urban areas. There is, thus, a need for a study that investigates the potential effects of climate change on IDF relationships. The main aim of the research reported in this thesis is to investigate the effect of climate change on Intensity-Duration-Frequency relationship in an urban area. The rainfall in Bangalore City is used as a case study to demonstrate the applications of the methodologies developed in the research Ahead of studying the future changes, it is essential to investigate the signature of changes in the observed hydrological and climatological data series. Initially, the yearly mean temperature records are studied to find out the signature of global warming. It is observed that the temperature of Bangalore City shows an evidence of warming trend at a statistical confidence level of 99.9 %, and that warming effect is visible in terms of increase of minimum temperature at a rate higher than that of maximum temperature. Interdependence studies between temperature and extreme rainfall reveal that up to a certain range, increase in temperature intensifies short term rainfall intensities at a rate more than the average rainfall. From these two findings, it is clear that short duration rainfall intensities may intensify in the future due to global warming and urban heat island effect. The possible urbanization signatures in the extreme rainfall in terms of intensification in the evening and weekends are also inferred, although inconclusively. The IDF relationships are developed with historical data and changes in the long term daily rainfall extreme characteristics are studied. Multidecedal oscillations in the daily rainfall extreme series are also examined. Further, non-parametric trend analyses of various indices of extreme rainfall are carried out to confirm that there is a trend of increase in extreme rainfall amount and frequency, and therefore it is essential to the study the effects of climate change on the IDF relationships of the Bangalore City. Estimation of future changes in rainfall at hydrological scale generally relies on simulations of future climate provided by Global Climate Models (GCMs). Due to spatial and temporal resolution mismatch, GCM results need to be downscaled to get the information at station scale and at time resolutions necessary in the context of urban flooding. The downscaling of extreme rainfall characteristics in an urban station scale pose the following challenges: (1) downscaling methodology should be efficient enough to simulate rainfall at the tail of rainfall distribution (e.g., annual maximum rainfall), (2) downscaling at hourly or up to a few minutes temporal resolution is required, and (3) various uncertainties such as GCM uncertainties, future scenario uncertainties and uncertainties due to various statistical methodologies need to be addressed. For overcoming the first challenge, a stochastic rainfall generator is developed for spatial downscaling of GCM precipitation flux information to station scale to get the daily annual maximum rainfall series (AMRS). Although Regional Climate Models (RCMs) are meant to simulate precipitation at regional scales, they fail to simulate extreme events accurately. Transfer function based methods and weather typing techniques are also generally inefficient in simulating the extreme events. Due to its stochastic nature, rainfall generator is better suited for extreme event generation. An algorithm for stochastic simulation of rainfall, which simulates both the mean and extreme rainfall satisfactorily, is developed in the thesis and used for future projection of rainfall by perturbing the parameters of the rainfall generator for the future time periods. In this study, instead of using the customary two states (rain/dry) Markov chain, a three state hybrid Markov chain is developed. The three states used in the Markov chain are: dry day, moderate rain day and heavy rain day. The model first decides whether a day is dry or rainy, like the traditional weather generator (WGEN) using two transition probabilities, probabilities of a rain day following a dry day (P01), and a rain day following a rain day (P11). Then, the state of a rain day is further classified as a moderate rain day or a heavy rain day. For this purpose, rainfall above 90th percentile value of the non-zero precipitation distribution is termed as a heavy rain day. The state of a day is assigned based on transition probabilities (probabilities of a rain day following a dry day (P01), and a rain day following a rain day (P11)) and a uniform random number. The rainfall amount is generated by Monte Carlo method for the moderate and heavy rain days separately. Two different gamma distributions are fitted for the moderate and heavy rain days. Segregating the rain days into two different classes improves the process of generation of extreme rainfall. For overcoming the second challenge, i.e. requirement of temporal scales, the daily scale IDF ordinates are disaggregated into hourly and sub-hourly durations. Disaggregating continuous rainfall time series at sub-hourly scale requires continuous rainfall data at a fine scale (15 minute), which is not available for most of the Indian rain gauge stations. Hence, scale invariance properties of extreme rainfall time series over various rainfall durations are investigated through scaling behavior of the non-central moments (NCMs) of generalized extreme value (GEV) distribution. The scale invariance properties of extreme rainfall time series are then used to disaggregate the distributional properties of daily rainfall to hourly and sub-hourly scale. Assuming the scaling relationships as stationary, future sub-hourly and hourly IDF relationships are developed. Uncertainties associated with the climate change impacts arise due to existence of several GCMs developed by different institutes across the globe, climate simulations available for different representative concentration pathway (RCP) scenarios, and the diverse statistical techniques available for downscaling. Downscaled output from a single GCM with a single emission scenario represents only a single trajectory of all possible future climate realizations and cannot be representative of the full extent of climate change. Therefore, a comprehensive assessment of future projections should use the collective information from an ensemble of GCM simulations. In this study, 26 different GCMs and 4 RCP scenarios are taken into account to come up with a range of IDF curves at different future time periods. Reliability ensemble averaging (REA) method is used for obtaining weighted average from the ensemble of projections. Scenario uncertainty is not addressed in this study. Two different downscaling techniques (viz., delta change and stochastic rainfall generator) are used to assess the uncertainty due to downscaling techniques. From the results, it can be concluded that the delta change method under-estimated the extreme rainfall compared to the rainfall generator approach. This study also confirms that the delta change method is not suitable for impact studies related to changes in extreme events, similar to some earlier studies. Thus, mean IDF relationships for three different future extreme events, similar to some earlier studies. Thus, mean IDF relationships for three different future periods and four RCP scenarios are simulated using rainfall generator, scaling GEV method, and REA method. The results suggest that the shorter duration rainfall will invigorate more due to climate change. The change is likely to be in the range of 20% to 80%, in the rainfall intensities across all durations. Finally, future projected rainfall intensities are used to investigate the possible impact of climate change in the existing drainage system of the Challaghatta valley in the Bangalore City by running the Storm Water Management Model (SWMM) for historical period, and the best and the worst case scenario for three future time period of 2021–2050, 2051–2080 and 2071–2100. The results indicate that the existing drainage is inadequate for current condition as well as for future scenarios. The number of nodes flooded will increase as the time period increases, and a huge change in runoff volume is projected. The modifications of the drainage system are suggested by providing storage pond for storing the excess high speed runoff in order to restrict the width of the drain The main research contribution of this thesis thus comes from an analysis of trends of extreme rainfall in an urban area followed by projecting changes in the IDF relationships under climate change scenarios and quantifying uncertainties in the projections.

Extreme rainfall statistics are important for the design and management of the water resource infrastructure. The standard approach for extreme rainfall event severity assessment is the Intensity-Duration-Frequency (IDF) method. However, this approach does not consider the spatial context of rainfall and consequently does not properly describe rainfall storm severity, nor rarity. This study provides a critical account of the current standard practice and presents an approach that takes into consideration both the spatial context of rainfall storms, and indirectly incorporates runoff to produce a representative approach to assessing urban rainfall storm severity in terms of flood potential. A stepwise regression analysis was performed on a dataset of individual rainfall storm characteristics to best represent documented basement floodings in the City of Edmonton. Finally, the urban rainfall storm flood severity index was shown to be most representative of the documented basement floodings' severity when compared to that of the IDF method.

Extreme rainfall statistics are important for the design and management of the water resource infrastructure. The standard approach for extreme rainfall event severity assessment is the Intensity-Duration-Frequency (IDF) method. However, this approach does not consider the spatial context of rainfall and consequently does not properly describe rainfall storm severity, nor rarity. This study provides a critical account of the current standard practice and presents an approach that takes into consideration both the spatial context of rainfall storms, and indirectly incorporates runoff to produce a representative approach to assessing urban rainfall storm severity in terms of flood potential. A stepwise regression analysis was performed on a dataset of individual rainfall storm characteristics to best represent documented basement floodings in the City of Edmonton. Finally, the urban rainfall storm flood severity index was shown to be most representative of the documented basement floodings' severity when compared to that of the IDF method.