Novel Methods for Uncertainty Analysis of Hydrologic Models

Chen Changjun

March 2006

Abstract

The uncertainty in model output means that forecasts should be considered in a probabilistic way or using fuzzy logic. There are many examples in which deterministic approaches are not sufficient due to the stochastic nature of input variables, for example a deterministic forecast may fail when an extreme event occurs.

The aim of this study was to explore the resampling methods for uncertainty analysis of hydrologic models, including the Markov Chain Monte Carlo (MCMC) methodology, Metropolis algorithm in detail to estimate the uncertainties of simulated results. The limitations of this approach are investigated. Although this method does provide accurate results, the large number of simulations is required, and with a complex model requiring a lot of time even for one simulation, it takes a long time. This clearly indicates the requirement of time saving techniques, therefore, this study is also aimed to explore the methods of uncertainty analysis, so two algorithms, adaptive cluster covering (ACCO) and shuffled complex evolution metropolis (SCEM-UA) were investigated.

The investigation of MCMC method is grouped around the case studies: a known distribution case study, linear model case study and lumped conceptual rainfall-runoff tank model case study for the Bagmati catchment in Nepal. Firstly, a two-dimensional banana-shaped posterior distribution is simulated to test the code and investigate the applicability of the Metropolis-Hastings algorithm for assessment of parameter uncertainty for this two-dimensional highly nonlinear distribution. Secondly, linear model experiments are done, data sets with noise and without noise are applied to investigating the performance of Metropolis-Hastings (MH) algorithm, in order to understand the algorithm fully. ACCO and SCEM-UA are also used in these two cases. Thirdly, for Bagmati catchment case study, the mean daily data of hydrological station on the Bagmati river at Pandheradobhan is used and totally 2000 days data from Jan 1988 to June 1993 were collected to estimate the uncertainties of simulated results originating from both model parameters and all sources of uncertainty. ACCO was also investigated whether it can be used in uncertainty analysis and improve the simulation efficiency.

The results obtained demonstrate that ACCO can give reasonable parameter distributions for those parameters with steep shape and one peak, but it fails in other cases. MH can give the accurate results in most cases. It can be concluded that ACCO and SCEM-UA are more efficient than MH for calibration since they are able to obtain the best solution at much faster speed than MH, whereas the MH explores the entire parameter space and can produce more reliable results than the other two methods.

Keywords: uncertainty analysis, Markov Chain Monte Carlo simulation, Metropolis- Hastings, adaptive cluster covering, shuffled complex evolution, likelihood function, parameter ranges, confidence intervals

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