In this study the combined uncertainty of a two-dimensional (2D) hydraulic model expanded at 95% confidence level is estimated and the uncertainty budget for the model outputs is attempted to be constructed. It has been shown that many uncertainty sources in the inputs as well as the procedure applied have a significant impact on the accuracy of two-dimensional hydraulic modelling: the uncertainties in the model inputs due to variations in Manning's 'n' Coefficient assigned, the bridge modelling methods, the equation sets; Diffusion Wave and Full Momentum Equations employed and the geometric data sets for the same river system in the Black Sea Region of Turkey are assessed. To estimate an appropriate M'n'C and other model inputs of model for a river system with a wide 2D flow area is a daunting task. Therefore, any attempt to quantify uncertainties in the assigned values must be based on the samples large enough to obtain statistically significant results. To achieve this task, Monte Carlo Method is utilized to estimate the contribution of the likely variations of model inputs onto 'the combined expended uncertainty at 95% confidence level in two-dimensional hydraulic modelling'.

Laplace transform has been used for solving differential equations of fractional order either PDEs or ODEs. However, using the Laplace transform sometimes leads to solutions in Laplace space that are not readily invertible to the real domain by analytical techniques. Therefore, numerical inversion techniques are then used to convert the obtained solution from Laplace domain into time domain. Various famous methods for numerical inversion of Laplace transform are based on quadrature approximation of Bromwich integral. The key features are the contour deformation and the choice of the quadrature rule. In this work, the Gauss–Hermite quadrature method and the contour integration method based on the trapezoidal and midpoint rule are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability to different types of fractional differential equations, numerical accuracy, computational efficiency, and ease of programming and implementation. The performance and efficiency of the methods are demonstrated with the help of figures and tables. It is observed that the proposed methods converge rapidly with optimal accuracy without any time instability.

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