Efficient Conservative Global Transport Schemes for Climate and Atmospheric Chemistry Models

Ramachandran D. Nair Department of Marine, Earth and Atmospheric Sciences and Department of Mathematics, North Carolina State University, Raleigh, North Carolina

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Jeffrey S. Scroggs Department of Mathematics, North Carolina State University, Raleigh, North Carolina

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Fredrick H. M. Semazzi Department of Marine, Earth and Atmospheric Sciences and Department of Mathematics, North Carolina State University, Raleigh, North Carolina

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Abstract

A computationally efficient mass-conservative transport scheme over the sphere is proposed and tested. The scheme combines a conservative finite-volume method with an efficient semi-Lagrangian scheme based on the dimension splitting “cascade” method. In the regions near the poles where the conservative cascade procedure breaks down, a globally conservative, but locally approximate scheme is used. This procedure is currently restricted to polar meridional Courant numbers less than one. The resulting conservative cascade scheme is evaluated using a solid-body rotation test and deformational flow test, and found to be both accurate and efficient. Compared to the traditional semi-Lagrangian scheme employing a bicubic-Lagrange interpolator, the proposed scheme is considerably more accurate and almost twice as fast while conserving mass exactly.

Corresponding author address: Dr. Jeffrey S. Scroggs, Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695-8205. Email: scroggs@unity.ncsu.edu

Abstract

A computationally efficient mass-conservative transport scheme over the sphere is proposed and tested. The scheme combines a conservative finite-volume method with an efficient semi-Lagrangian scheme based on the dimension splitting “cascade” method. In the regions near the poles where the conservative cascade procedure breaks down, a globally conservative, but locally approximate scheme is used. This procedure is currently restricted to polar meridional Courant numbers less than one. The resulting conservative cascade scheme is evaluated using a solid-body rotation test and deformational flow test, and found to be both accurate and efficient. Compared to the traditional semi-Lagrangian scheme employing a bicubic-Lagrange interpolator, the proposed scheme is considerably more accurate and almost twice as fast while conserving mass exactly.

Corresponding author address: Dr. Jeffrey S. Scroggs, Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695-8205. Email: scroggs@unity.ncsu.edu

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