Abstract: Hydrologic models are increasingly used as tools to
predict stormwater quantity and quality from urban catchments.
However, due to a range of practical issues, most models produce
gross errors in simulating complex hydraulic and hydrologic systems.
Difficulty in finding a robust approach for model calibration is one of
the main issues. Though automatic calibration techniques are
available, they are rarely used in common commercial hydraulic and
hydrologic modelling software e.g. MIKE URBAN. This is partly
due to the need for a large number of parameters and large datasets in
the calibration process. To overcome this practical issue, a
framework for automatic calibration of a hydrologic model was
developed in R platform and presented in this paper. The model was
developed based on the time-area conceptualization. Four calibration
parameters, including initial loss, reduction factor, time of
concentration and time-lag were considered as the primary set of
parameters. Using these parameters, automatic calibration was
performed using Approximate Bayesian Computation (ABC). ABC is
a simulation-based technique for performing Bayesian inference
when the likelihood is intractable or computationally expensive to
compute. To test the performance and usefulness, the technique was
used to simulate three small catchments in Gold Coast. For
comparison, simulation outcomes from the same three catchments
using commercial modelling software, MIKE URBAN were used.
The graphical comparison shows strong agreement of MIKE URBAN
result within the upper and lower 95% credible intervals of posterior
predictions as obtained via ABC. Statistical validation for posterior
predictions of runoff result using coefficient of determination (CD),
root mean square error (RMSE) and maximum error (ME) was found
reasonable for three study catchments. The main benefit of using
ABC over MIKE URBAN is that ABC provides a posterior
distribution for runoff flow prediction, and therefore associated
uncertainty in predictions can be obtained. In contrast, MIKE
URBAN just provides a point estimate. Based on the results of the
analysis, it appears as though ABC the developed framework
performs well for automatic calibration.
Abstract: A comprehensive Bayesian analysis has been carried out in the context of informative and non-informative priors for the shape parameter of the Burr type X distribution under different symmetric and asymmetric loss functions. Elicitation of hyperparameter through prior predictive approach is also discussed. Also we derive the expression for posterior predictive distributions, predictive intervals and the credible Intervals. As an illustration, comparisons of these estimators are made through simulation study.