A hybrid coupled model of surface and subsurface flow for surface irrigation

• A hybrid coupling strategy is proposed for the coupled surface–subsurface flow model.
• The 1D complete hydrodynamic model is solved based on the improved hybrid numerical method.
• A high-order numerical method is proposed to solve the Richards equation.
• The proposed hybrid coupling strategy presents the satisfactory simulation performance.

SummaryIn surface irrigation, interaction between surface and subsurface water flows plays an important role, and this process can be effectively simulated by iterative coupled model of surface and subsurface water flows for surface irrigation. The water flow of surface irrigation exhibits a major characteristic which is the existence of wet-dry boundary. In numerical simulation, this wet-dry boundary of the surface flow can impact the stability of momentum conservation equation and reduce the simulation accuracy of iterative coupled models because of the anti-diffusion characteristic of the roughness term of the Saint–Venant equations. This study presents a hybrid coupling strategy by distinguishing the mass conservation and momentum conservation of surface flow and subsurface flow systems to reduce the iteration times of momentum conservation equation and then increase the simulation accuracy of coupled models. In the proposed coupling strategy, the mass conservation component of surface flow model and subsurface flow model are iteratively coupled at the same time step to obtain the convergence value of surface flow depth, and then the momentum conservation component of surface flow model is externally coupled based on the convergence value of both the surface flow depth and infiltration rate to update the surface flow velocity. In this hybrid coupling procedure, infiltration is used as the common internal boundary condition. The proposed coupling strategy is implemented by coupling a one-dimensional surface flow model that uses the complete hydrodynamic form of the Saint–Venant equation with a one-dimensional subsurface flow model on the basis of a numerical solution of the Richards equation. Solutions are numerically computed using an improved hybrid numerical method for surface flow model and a proposed numerical solution method with high-order accuracy for subsurface flow model. The proposed subsurface flow model has the satisfactory simulation accuracy, and presents a higher mass balance ratio and a higher convergence rate with third-order accuracy than the models solved by the finite-volume method and finite-difference method with second-order accuracy. Compared with the iterative coupling strategy usually implemented in the existing coupled models, the proposed hybrid coupling strategy exhibits better simulation accuracy, lower total volume balance error and 1.4-fold computational efficiency.