“…Conventionally, such a construction is referred to as layer‐averaged discretization, which was used by some isopycnal models (e.g., Bleck, ; Oberhuber, ) or the Arbitrarily Lagrangian Eulerian framework (e.g., Adcroft & Campin, ; Ringler et al, ) in the ocean modeling community. For atmospheric modeling, it is also convenient for some vertically Lagrangian models (e.g., Chen et al, ; Lin, ) or quasi‐Lagrangian models (e.g., Bleck et al ) to adopt such a construction. In a quasi‐Lagrangian approach, for example, an isentropic coordinate for the atmosphere, remains zero in the adiabatic condition so that no flux goes across the coordinate face.…”