Subgrid modeling to account for unresolved topography within the context of shallow water equations relies on the use of coarse grids for computational efficiency. However, excessively coarse grids can lead to artificial cross flows between hydrologically disconnected areas separated by physical barriers smaller than the grid size. An approach based on introducing cell and edge clones, consisting of connected groups of pixels in each cell, is able to systematically remove such artificial cross flows. Such an approach considers that the subgrid barriers permanently divide flow among clones and effectively restrict flow to a predetermined path. In this work, a simple algorithm, along with the use of an overtopping formula, is proposed to extend the clone approach to a scenario in which clones are allowed to be further split and merged as needed, depending on the surface elevation during a given runtime. The algorithm is intended for accommodating the possibility of the subgrid barriers being inundated and no-longer dividing the flow during an extreme event. The performance of the proposed algorithm is demonstrated through a series of idealized and more realistic test cases, showing considerable improvements over existing methodologies.

在浅水方程组中考虑未解决地形的子网格建模依赖于使用粗网格来提高计算效率。但是，过于粗糙的网格可能导致在水力隔离区域之间的人为错流，这些水力隔离区域之间的物理屏障小于网格大小。一种基于引入单元格和边缘克隆的方法，该方法由每个单元格中相连的像素组组成，能够系统地消除此类人为错流。这种方法认为，亚网格屏障可永久性地在克隆之间分配流量，并有效地将流量限制在预定路径上。在这项工作中，提出了一种简单的算法，并使用了覆盖规则，将克隆方法扩展到允许根据需要进一步拆分和合并克隆的情况下，取决于给定运行时的表面高度。该算法旨在适应极端情况下子网格屏障被淹没且不再分流的可能性。通过一系列理想化和更实际的测试用例证明了所提出算法的性能，与现有方法相比，显示出相当大的改进。