Hierarchical Spatial Analysis of Extreme Precipitation in Urban Areas

Abstract:

Quantification of extreme precipitation is important for hydrologic designs. Due to lack of availability of extreme precipitation data for sufficiently large number of years, estimating the probability of extreme events is difficult and extrapolating the distributions to locations where observations are not available is challenging. In an urban setting, the spatial variation of precipitation can be high; the precipitation amounts and patterns often vary within short distances of less than 10 km. Therefore it is crucial to study the uncertainties in the spatial variation of precipitation in urban areas.

In this work, the extreme precipitation is modeled spatially using the Bayesian hierarchical spatial analysis and the spatial variation of return levels is studied. The analysis is carried out with both the Peak over Threshold (PoT) and the Block Maxima approaches for defining the extreme precipitation. The study area is Bangalore city, India. Daily data for seventeen stations in and around Bangalore city are considered in the study. The threshold exceedences are modeled using a Generalized Pareto (GP) distribution and the block maxima are modeled using Generalized Extreme Value (GEV) distribution. In the hierarchical analysis, the statistical model is specified in three layers. The data layer models the data (either block maxima or the threshold exceedences) at each station. In the process layer, the latent spatial process characterized by geographical and climatological covariates (lat-lon, elevation, mean temperature etc.) which drives the extreme precipitation is modeled and in the prior level, the prior distributions that govern the latent process are modeled. Markov Chain Monte Carlo (MCMC) algorithm is used to obtain the samples of parameters from the posterior distribution of parameters. The spatial maps of return levels for specified return periods, along with the associated uncertainties, are obtained. The results show that there is significant variation in return levels when the data is pooled compared with the return levels obtained at individual sites. Using the various covariates, the best fit model is selected using Deviance Information Criteria. The spatial maps of return levels thus generated are useful in storm water designs, adequacy analysis and identifying the vulnerable flooding areas.