Antibiotics are extensively applied in aquaculture for the treatment of microbial infections and to improve production. Among various antibiotics, sulfonamides (SA) are popular in fish farming, and SA residues in the aquatic environment have detrimental effects on both ecosystem and human health. Understanding the fate of SA in the aquatic environment is a basic necessity to provide an approach for solving the current problem. In this study, a two-dimensional lattice Boltzmann model was introduced to investigate the transport and occurrence of SA in Laizhou Bay, a prosperous aquaculture area in China. The model is based on the shallow-water equations and advection-diffusion equation with the Bhatnagaar–Gross–Krook scheme. Experimental data are used to verify the model after numerical simulations and the results illustrate the accuracy of the proposed model. This model provides a potential universal method for the simulation of the fate of antibiotics in the aquatic environment.

This study proposes a novel framework of the lattice Boltzmann model for multilayer shallow water equations, considering the mass and momentum exchanges between layers (LABMSWE+). Compared with the original LABMSWE model consisting of N two-dimensional lattice Boltzmann method for shallow water equation (LABSWE) models, the new model includes 1+N LABSWE models. The singular LABSWE model with unit relaxation time is introduced to update the total water depth, and thus, the layer water depths can be obtained explicitly through the fixed layer ratios. The N-layer LABSWE models with the multiple-relaxation-time operator evolve the layer velocities. These two modules are coupled by the total water depth and depth-averaged velocities. The constructed model avoids the freely variable layer thicknesses, which is considered as the main source of the instability. In addition, the mass exchanges enable this model to simulate vertical circulation flows, which are beyond the application of the LABMSWE model. Several numerical tests are then conducted to validate the proposed model. The results show that it exactly satisfies the C-property. In addition, the central difference scheme is more stable and accurate than the upwind and nonequilibrium schemes in the computing of the mass exchanges. The numerical results have an excellent agreement with analytical solutions and reference data, while some unstable and nonphysical results are obtained by the original LABMSWE model. Moreover, the computational time is about 40%–60% of that for the MIKE3, a finite volume solver for the three-dimensional shallow water equations by the Danish Hydraulic Institute.

Soil salinization poses a major threat to agricultural sustainability in arid regions worldwide, where it is intrinsically linked to irrigated agriculture. In these water-scarce environments, the equilibrium of the water and salt balance is easily disrupted, causing salts to accumulate in the root zone and directly constraining crop growth, thereby creating an urgent need for precise water and salt management strategies. While precise water and salt transport models are essential for prediction and control, their accuracy is often compromised by parameter uncertainty. To address this, we developed a lumped water–salt balance model for the Hetao Irrigation District (HID) in China, integrating farmland and non-farmland areas and vertically structured into root zone, transition layer, and aquifer. A novel calibration approach, combining random sampling with Kernel Density Estimation (KDE), was introduced to identify optimal parameter ranges rather than single values, thereby enhancing model robustness. The model was calibrated and validated using data from the Yichang sub-district. Results showed that the water balance module performed satisfactorily in simulating groundwater depth (R² = 0.79 for calibration, 0.65 for validation). The salt balance module effectively replicated the general trends of soil salinity dynamics, albeit with lower R² values, which reflects the challenges of high spatial variability and data scarcity. This method innovatively addresses the common challenge of parameter uncertainty in the model, narrows the parameter value ranges, enhances model reliability, and incorporates sensitivity analysis (SA) to identify key parameters in the water–salt model. This study not only provides a practical tool for managing water and salt dynamics in HID but also offers a methodological reference for addressing parameter uncertainty in hydrological modeling of other data-scarce regions.