Quantification of uncertainties in urban precipitation extremes

Abstract

Urbanization alters the hydrologic response of a catchment, resulting in increased runoff rates and volumes, and loss of infiltration and base flow. In general, quick runoff response to precipitation extremes due to short times of concentration in urban areas, exacerbated by inadequate storm water drainage infrastructure, causes intense floods. Quantifying the short duration precipitation extremes is, therefore, crucial in hydrologic designs of urban infrastructure. Also, quantifying distributional behavior of extreme events is important due to the sparse data at fine resolutions. In addition, climatology of urban areas is, in general, different from that of their surroundings and the spatial variation of extreme precipitation within the city could be much higher, especially for short duration events. An understanding of such variation is also important for urban infrastructure design and operation. The work presented in this thesis attempts to quantify extreme precipitation and model the spatial distribution of extreme precipitation within an urban area and its non-urban surroundings.

The Intensity Duration Frequency (IDF) relationships are used extensively in engineering, especially in urban hydrology, to obtain return levels of extreme rainfall events for a specified return period and duration. Major sources of uncertainty in the IDF relationships are due to insufficient quantity and quality of data leading to parameter uncertainty (parameters of the distribution fitted to the data) and, in the case of projections of future IDF relationships under climate change, uncertainty arising from use of multiple General Circulation Models (GCM) and scenarios, referred to as model uncertainty. It is important to study these uncertainties and propagate them into the future for accurate assessment of return levels for the future. The work presented in the thesis presents methodologies to quantify the uncertainties arising from parameters of the distribution fitted to data and the multiple GCM models using a Bayesian approach. The Bayesian method upgrades uncertainty about parameters expressed in terms of prior distribution to posterior distribution using Bayes’ rule. The posterior distribution of parameters is transformed to obtain return levels, along with uncertainty, for a specified return period. The Markov Chain Monte Carlo (MCMC) method using the Metropolis Hastings algorithm is used to obtain the posterior distribution of parameters. Annual maximum precipitation series of Bangalore City at different durations are used to demonstrate the methodology. High uncertainties in GEV parameters and return levels are observed at shorter durations for the case study.

Climate change is likely to cause variations in intensity, duration, and frequency of extreme precipitation events. Quantifying the potential impacts of climate change and adapting to them is one way to reduce vulnerability. Therefore, it is essential to update the IDF relationships for future climatic conditions. Twenty-six GCMs from the CMIP5 (Coupled Model Intercomparison Project, Phase 5) datasets, along with four Representative Concentration Pathways (RCP) scenarios, are considered for studying the effects of climate change and to obtain projected IDF relationships for the case study of Bangalore City in India. GCM uncertainty due to the use of multiple GCMs is treated using the Reliability Ensemble Averaging (REA) technique along with the parameter uncertainty. Scale invariance theory is employed for obtaining short duration return levels from daily data. 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.

Precipitation extremes are often modeled considering either the annual maximum series or the peaks over threshold series. The Generalized Extreme Value (GEV) distribution is used to model maxima of finite-sized blocks (usually of annual extreme precipitation) based on Extreme Value (EV) theory. However, GEV models using only one maxima per year (i.e., annual extreme precipitation) disregard other extreme data that could provide additional information. Therefore, modeling extreme precipitation above a certain threshold following the Generalized Pareto Distribution (GPD) model is generally preferred. 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 GPD parameters and exceedance rate parameters are modeled by the Bayesian approach and the uncertainty in the scaling exponent is quantified. A quantile-based modification in the scaling relationships is proposed for obtaining the varying thresholds and exceedance rate parameters for shorter 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. It is also observed that the uncertainty in the scaling exponent increases as the threshold reduces and that the choice of prior for the shape parameter has a considerable effect on the return levels.

Variation of precipitation extremes over the relatively small spatial scales of urban areas could be significantly different from those over larger regions. An understanding of such variation is critical for urban infrastructure design and operation. Urban climatology and sparse spatial data lead to uncertainties in the estimates of spatial precipitation. A Bayesian hierarchical model is used to obtain spatial distribution of return levels of precipitation extremes in urban areas and quantify the associated uncertainty. The Generalized Extreme Value (GEV) distribution is used for modeling precipitation extremes. A spatial component is introduced in the parameters of the GEV through a latent spatial process by considering geographic and climatologic covariates. A Markov Chain Monte Carlo algorithm is used for sampling the parameters of the GEV distribution and the latent process model. 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. Variation of seasonal extremes is also examined in this study. 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. A significant variation in spatial return levels of extreme precipitation is observed over the city.

In the Bayesian hierarchical model, the precipitation is considered to be conditionally independent, spatially. However, there could be some spatial dependence among the observations, specifically at comparatively larger durations. Also, climatology of urban areas is, in general, different from that of their surroundings and the spatial variation of extreme precipitation within the city could be much higher, especially for short duration events. Therefore, 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 spatial dependence of precipitation is analyzed with three different measures for examining dependence, considering observations from pairs of stations. Further, the spatial precipitation extremes are modeled with the max-stable process to include the dependence structure of spatial extremes. 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. Further, the extreme precipitations at different durations are modeled considering max-stable process. Different geographical and climatological covariates are considered in the modeling of location and scale parameters of the Generalized Extreme Value distribution. 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 time scales, 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