In this work, we consider discretization of the linearized shallow water equations on a reduced latitude-longitude grid with an analogue of Arakawa C-type variables staggering. The resulting schemes are based on the use of longitudinal interpolation procedures and can be of arbitrary order of accuracy. We also present the analysis of conservation and wave propagation properties of these schemes for the linearized shallow water model. This analysis reveals constraints on the interpolation procedures that ensure mass and total energy conservation. The presented approach for construction and analysis of the schemes is also applicable for the unstaggered reduced latitude-longitude grid case.

在这项工作中，我们考虑将线性化的浅水方程式离散化，使其在经纬度简化的网格上类似于Arakawa C型变量的交错形式。所得方案基于纵向插值过程的使用，并且可以具有任意精度级别。我们还对线性浅水模型的这些方案的守恒和波传播特性进行了分析。该分析揭示了对插值过程的约束，以确保质量和总能量守恒。所提出的用于方案构造和分析的方法也适用于无交错的经纬度减小的网格情况。