Toward a Fully Lagrangian Atmospheric Modeling System

An improved treatment of advection is essential for atmospheric transport and chemistry models. Eulerian treatments are generally plagued with instabilities, unrealistic negative constituent values, diffusion, and dispersion errors. A higher-order Eulerian model improves one error at significant cost but magnifies another error. The cost of semi-Lagrangian models is too high for many applications. Furthermore, traditional trajectory “Lagrangian” models do not solve both the dynamical and tracer equations simultaneously in the Lagrangian frame. A fully Lagrangian numerical model is, therefore, presented for calculating atmospheric flows. The model employs a Lagrangian mesh of particles to approximate the nonlinear advection processes for all dependent variables simultaneously. Verification results for simulating seabreeze circulations in a dry atmosphere are presented. Comparison with Defant’s analytical solution for the sea-breeze system enabled quantitative assessment of the model’s convergence and stability. An average of 20 particles in each cell of an 11 20 staggered grid system are required to predict the two-dimensional sea-breeze circulation, which accounts for a total of about 4400 particles in the Lagrangian mesh. Comparison with Eulerian and semi-Lagrangian models shows that the proposed fully Lagrangian model is more accurate for the sea-breeze circulation problem. Furthermore, the Lagrangian model is about 20 times as fast as the semi-Lagrangian model and about 2 times as fast as the Eulerian model. These results point toward the value of constructing an atmospheric model based on the fully Lagrangian approach.