Abstract
A new parameter optimization and uncertainty assessment procedure using the Bayesian inference with an adaptive Metropolis-Hastings (AM-H) algorithm is presented for extreme rainfall frequency modeling. An efficient Markov chain Monte Carlo sampler is adopted to explore the posterior distribution of parameters and calculate their uncertainty intervals associated with the magnitude of estimated rainfall depth quantiles. Also, the efficiency of AM-H and conventional maximum likelihood estimation (MLE) in parameter estimation and uncertainty quantification are compared. And the procedure was implemented and discussed for the case of Chaohu city, China. Results of our work reveal that: (i) the adaptive Bayesian method, especially for return level associated to large return period, shows better estimated effect when compared with MLE; it should be noted that the implementation of MLE often produces overy optimistic results in the case of Chaohu city; (ii) AM-H algorithm is more reliable than MLE in terms of uncertainty quantification, and yields relatively narrow credible intervals for the quantile estimates to be instrumental in risk assessment of urban storm drainage planning.
Highlights
Effective urban hydrologic engineering planning, design and operation are very much dependent on reliable rainfall frequency modeling, such as intensity/depth-duration-frequency (IDF/DDF) curves or rainfall intensity formulae, which can summarize the return levels of extreme rainfall for the continuum of durations (e.g., 5 min to 24 h) and specified return periods (e.g., Chow et al ; Cheng & AghaKouchak ; Sarhadi & Soulis ; Parvez & Inayathulla )
When the recorded rainfall series are long enough, IDF/ DDF curves or rainfall intensity formulae can generally be determined via frequency analysis of extreme rainfall (Porras & Porras )
This study presents two innovative aspects. (i) The application of adaptive Metropolis–Hastings (AM-H) algorithm is relatively novel in extreme rainfall frequency modeling. (ii) The uncertainties of probability distribution parameters were often not taken into consideration for the conventional rainfall frequency modeling algorithms including maximum likelihood estimation (MLE)
Summary
Effective urban hydrologic engineering planning, design and operation are very much dependent on reliable rainfall frequency modeling, such as intensity/depth-duration-frequency (IDF/DDF) curves or rainfall intensity (or depth) formulae, which can summarize the return levels (i.e., intensities and depths) of extreme rainfall for the continuum of durations (e.g., 5 min to 24 h) and specified return periods (e.g., Chow et al ; Cheng & AghaKouchak ; Sarhadi & Soulis ; Parvez & Inayathulla ). Coles et al ( ) reiterated that conventional technologies (e.g., MLE) do not fully consider the uncertainties of models and predictions, and are confined to produce overly optimistic appraisals of future extreme events They pointed out that Bayesian methods have theoretical and technical advantages in the evaluation of uncertainties. The study area and rainfall data used are briefly introduced, followed by a section revealing characteristics of the distribution of the maximum daily rainfall by comparing the fitting results of six candidate distribution models in detail This is followed by the section ‘Daily rainfall depth formula for Chaohu city’, in which the performance of the AM-H is compared to the MLE with a quadratic approximation in the two aspects of parameters estimation and uncertainty quantification. The main findings on advantages of the AM-H and limitations of the MLE are summarized
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
