In computational hydraulics models, predicting bed topography and bedload transport with sufficient accuracy remains a significant challenge. An accurate assessment of a river's sediment transport rate necessitates a prior understanding of its bed topography. Therefore, we designed a machine learning model to deduce bathymetry from cost-effective flow surface data, i.e., velocity fields. This model was applied to three case scenarios, especially at the confluence of the Kaskaskia River and Copper Slough in east-central Illinois, United States of America. The results demonstrated the model's effectiveness in gravel-bed river bathymetry estimation. Although the bed topography can be deduced with good accuracy using indirect approaches, predicting bedload transport still faces a high level of error. One accepted reason among scientists for such high errors is that bedload transport is a noise-driven process. The bedload transport depends on many non-linearly varying parameters with various time and space scales, and these parameters are interrelated. Additionally, the fluctuations in bedload transport significantly influence several aspects of morphodynamic variations, such as bedform and bank erosion. Hence, the spatio-temporal variability of the bedload transport rate is of great importance as an inherent characteristic of gravel-bed rivers. To account for these fluctuations, we developed and validated one- and two-dimensional stochastic bedload models. In the next step of this thesis, we aim to examine the one-dimensional stochastic bedload model through numerical simulation. To this end, bedform development and bedload transport rate in narrow gravel-bed flumes under supercritical flow regimes have been studied. This examination employs a numerical solver based on the one-dimensional depth-averaged Saint-Venant--Exner equations, integrated with a stochastic bedload model. In this work, we have proposed closure analytical formulas to parameterize the mass exchange rates between the flow and the bed. The numerical solver is implemented by the Finite Volume Method. While the stochastic numerical solver provides a single realization of reality, its key characteristics oscillate around mean values, allowing for meaningful comparisons between numerical outcomes and experimental datasets. The numerical studies concentrate on three key aspects: i. the rate of bedload transport; ii. the amplitude and wavelength of the antidunes; and iii. their migration velocity. These numerical predictions are examined by applying the solver to two laboratory datasets. Finally, the last aim is to develop a two-dimensional stochastic bedload model that incorporates fluctuations and computes the random time variations in particle activity. To achieve this, the one-dimensional morphodynamic model is generalized to two dimensions. A linear stability analysis was carried out based on the developed governing equations, yielding neutral curves that align with the experimental dataset drawn from the literature. Subsequently, a numerical solver is developed based on the Finite Volume Method. The two-dimensional depth-averaged solver was used to study alternate bar development. It has been applied to gravel-bed experiments conducted in a long and wide gravel-bed flume under steady-state flow conditions. The numerical outcomes successfully captured the bedload transport rate, bar formation, and their growth rates in line with experimental data.