Bringing realism into a dynamic copula-based non-stationary intensity-duration model

• Published in: Advances in water resources 2019-08, Vol.130, p.325-338
• Main Authors: Vinnarasi, R., Dhanya, C.T.
• Format: Article
• Language: English
• Subjects: Bayesian analysis; Bayesian inference; Climate change; Copula; Decision making; Distribution; Duration; Evolution; Evolutionary algorithms; Evolutionary computation; Extreme weather; Frequency analysis; Hydrology; Levels; Markov chains; Mathematical models; Non-stationarity; Parameters; Probability theory; Rain; Rainfall; Rainfall duration; Return level; Return period; Runoff; Statistical analysis; Sustainability; Urban areas; Water resources
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2019.06.009

•A novel approach is proposed to detect the non-stationarity in rainfall time series.•Developed a probabilistic time-dependent bivariate intensity-duration model.•Proposed approach checks for any signature of non-stationarity in the probabilistic distribution parameters and prunes off the insignificant (stationary) probabilistic distribution parameters, thus reducing the complexity and improving the computational efficiency of the model.•The present approach is superior to the stationary and traditional non-stationary approaches in avoiding any possible under/over-estimation of the return periods. Dynamic behavior of extreme rainfall characteristics heightened by the abrupt warming of the environment has affected the sustainability of the existing water resources systems and infrastructure, which were designed employing the traditional ‘stationary’ assumption. Here, we propose a realistic and efficient framework to detect non-stationarity in the observed hydrologic variables, to overcome a few limitations suffered by the traditional non-stationary approaches. The methodology is demonstrated over the short period rainfall series of four major metropolitan cities of India, where the intensity of the rainfall is reportedly increasing sharply accompanied by the changes in the pattern of rainfall. Since direct runoff is influenced by the intensity and duration of rainfall, it is important to study the joint characteristics of intensity and duration in the context of non-stationarity, especially in urban regions where the relationship is more distinct. Hence, we estimated the time-varying joint return period/return level of its extremes, utilizing a dynamic Bayesian copula. We have implemented time-varying multivariate probability frequency analysis to derive the time-varying Intensity-Duration relationship. Here we employed a Bayesian approach through Differential Evolution Markov Chain (DE–MC) algorithm to estimate the uncertainty bound of the time-varying return level. The results emphasize that the probabilistic distribution parameters vary both temporally and spatially, and recommend the incorporation of non-stationarity in the extreme event modeling, only if there is a change in the probabilistic distribution parameters. This non-stationary model can be seamlessly employed to compute return levels with better accuracy and reliability than traditional stationary/non-stationary methods. We observe that the short duration return level increases at a faster ra