A 2D Adaptive Mesh Refinement (AMR) technique on the sphere is applied to the so-called Lin-Rood advection algorithm which is built upon a conservative and oscillation-free finite-volume discretization in flux form. The AMR design is based on two modules, a block-structured data layout and a newly developed AMR grid library for parallel computer architectures. The latter defines and manages the adaptive blocks in spherical geometry, provides user interfaces for interpolation routines and supports the communication and load-balancing aspects for parallel applications. The adaptive grid simulations are guided by user-defined adaptation criteria. Both statically and dynamically adaptive setups are supported that start from a regular block-structured latitude-longitude grid. All blocks are logically rectangular, self-similar and independent data units that get split into four in the event of refinement requests, thereby doubling the horizontal resolution. Grid coarsenings reverse this re-finement principle that overall guarantees a uniform 2:1 mesh ratio at all fine-coarse grid interfaces. The adaptive advection model is tested using a standard shallow water test case which transports a cosine bell around the sphere. It is shown that the cosine bell is reli-ably detected and tracked with high-resolution grids that are steered by a geopotential-based threshold criterion. It is argued that the AMR design is a viable option for atmospheric transport schemes with further potential for non-linear atmospheric flow solvers. 1 1.
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grid points Resolution ∆x (km) at different positions ϕ level ∆λ, ∆ϕ lon x lat (full grid) Equator 60 ◦ N/S 75 ◦ N/S Near pole 0 5 ◦ 72 x 36 556.0 278.0 143.9 24.26 1 2.5 ◦ 144 x 72
– Max
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1
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error norms Final # Blocks # Time CPU resol. level l1 l2 l∞ α = 0 ◦ hmax h (m) min max steps time (s) 1.25 ◦ 0 0.0073 0.0078 0.0107 -0.0106 984.2 768 312 230 5 ◦ 0 0.1157 0.1001 0.0949 -0.0869 838.0 48 84 4 5 ◦ 1 0.0341 0.0301 0.0317 -0.0305 949.1 54 60 1
– Height
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