А new model for solving the shallow water equations, sediment transport andmorphological changes in natural watercourses, using the lattice Boltzmannmethod (LBM) has been formulated and produced by this doctoraldissertation. The depth averaged shallow water equations (SWE) have beenused to reach the flow pattern, the advection-diffusion equation (ADE) wasexploited to determine sediment concentration in the water, bed load wasdetermined by the active layer mass conservation equation (ALMC), while themorphological changes of the river bed were determined by the global activelayer mass conservation equation (GALMC). All equations are linked byadditional terms describing the exchange of materials by erosion anddeposition, formulated separately for each granulometric interval. Thisapproach enables presentation of the non-uniform grain size composition,often characteristic to natural mixtures, by size intervals, thus providingopportunity for considering the behavior of fractions, defined by characteristicgrains of certain size, separately. In addition, the model enables exchange ofmaterial between the layers of the river bed, applying the principle of theactive layer. The SWE are solved by the multiple-relaxation-time lattice Boltzmann method, (MRT-LBM), while the single-relaxation-time (SRTLBM)approach has been used for solving the ADE, ALMC and GALMC.The dissertation has two main goals, namely: application of the LBM forsolving the flow pattern in complex natural watercourses, and providing a newmathematical formulation for solving sediment related processes, itsimplementation into the model and testing the model. For this purpose, thecalibration and verification of the model for solving the flow pattern wasperformed on three examples of real, natural watercourses, while the modelfor sediment processes and morphological changes has been checked on onenatural watercourse. In all examples, calibration has been achieved bycomparison of the results produced by the proposed LBM model to the resultsgained by the finite difference method, and by measurements.