###### Abstract
To overcome the shortcomings of trial-and-error methods, many researchers developed intelligent optimization methods to calibrate the roughness ([PERSON] et al., 2018; [PERSON] et al., 2018). For example, [PERSON] et al. (2018) developed an automated calibration framework for estimating Manning's roughness coefficient using a genetic algorithm that was formulated as an optimization problem with a heuristic search procedure. The study suggested that multiobjective GA using pooled and balanced aggregated function statistics can be used to optimize multiple objectives. Additionally, a coupled optimization-simulation model that integrated the particle swarm optimization (PSO) algorithm and InfoWorks Integrated Catchment Modelling (ICM) software was established to solve the objective function and hydraulic process. The proposed method was applied to estimating the roughness values and showed better performance in model calibration ([PERSON] et al., 2018). The nature of these intelligent models makes them require a large amount of observational data, which may pose challenges in practical river measurement systems. Parameter-inversion models, on the other hand, can be less computationally intensive, as they use model calibration techniques to adjust the model parameters to better fit historical data, but require high-quality historical data for model calibration. The challenging task of identifying parameters in certain instances can be attributed to the ill-posed nature of the inverse problem ([PERSON] et al., 2018). This is because roughness inversion results could theoretically be influenced by initial conditions such as the starting values of the model parameters ([PERSON] et al., 2018), particularly for underdetermined inversion models, which refers to a common situation in which the amount of the observed data is insufficient to determine the number of the model parameters in practice. For complex river networks, insufficient hydrological observations and underdetermined inversion models often lead to model calculation failure, requiring manual intervention to ensure reasonable results. It is, thus, important to develop parameter-inversion models with high robustness to historical data in terms of quality and quantity. To provide a more accurate and reliable method for calibrating riverbed roughness, which is a critical parameter for hydraulic simulations, this study proposes a new inversion model of bed roughness based on historical data considering the regularization term for controlling the continuous variation in river roughness along the flow direction. The model is solved through an iterative process. A simulated river network with four levels of river channels is used for optimizing the model parameters through analyzing the impact of the number of measurement stations, the amount of the observed data, initial bed roughness, observational noise, and the weight of the regularization term on the accuracy of the inversed roughness. An experiment was carried out on a real river in North America using the model after parameter calibration, and its results were compared with those from the literature. The potential application of the model for hydraulic simulations is discussed. The outline of this study is as follows: In Section 2, we present the procedure for establishing the inversion model of bed roughness. In Section 3, we outline how we applied the inversion model in a simulated river network, and analyze the impact of various parameters on the accuracy of inversed roughness, including the number of measurement stations, the amount of the observed data, the initial bed roughness, observational noise, and the weight of the regularization term. Section 4 focuses on the calibration process of the inversion model established in this study, and compares the results with those from other researchers. Lastly, in Section 5, we provide a conclusion on the basis of our findings.