### Dynamical core model intercomparison project: Tracer transport test cases

"... Three-dimensional advection tests are required to assess the ability of transport schemes of dynamical cores to model tracer transport on the sphere accurately. A set of three tracer-transport test cases for three-dimensional flow is presented. The tests focus on the physical and numerical issues th ..."

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Three-dimensional advection tests are required to assess the ability of transport schemes of dynamical cores to model tracer transport on the sphere accurately. A set of three tracer-transport test cases for three-dimensional flow is presented. The tests focus on the physical and numerical issues that are relevant to three-dimensional tracer transport: positivity preservation, inter-tracer correlations, horizontal–vertical coupling, order of accuracy and choice of vertical coordinate. The first test is a three-dimensional deformational flow. The second test is a Hadley-like global circulation. The final test is a solid-body rotation test in the presence of rapidly varying orography. A variety of assessment metrics, such as error norms, convergence rates and mixing diagnostics, are used. The tests are designed for easy implementation within existing and developing dynamical cores and have been a cornerstone of the 2012 Dynamical Core Model Intercomparison Project (DCMIP). Example results are shown using the transport schemes in two dynamical cores: the Community Atmosphere Model finite-volume dynamical core (CAM-FV) and the cubed-sphere finite-volume MCore dynamical core. Key Words: advection; three-dimensional flow; spherical geometry; finite-volume methods

### © Author(s) 2010. CC Attribution 3.0 License. Atmospheric Chemistry and Physics

, 2010

"... doi:10.5194/acp-10-9451-2010 ..."

### Determining the effective resolution of advection schemes. Part II: Numerical testing

, 2014

"... Numerical models of fluid flows calculate the resolved flow at a given grid resolution. The smallest wave resolved by the numerical scheme is deemed the effective resolution. Advection schemes are an important part of the numerical models used for computational fluid dynamics. For example, in atmos ..."

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Numerical models of fluid flows calculate the resolved flow at a given grid resolution. The smallest wave resolved by the numerical scheme is deemed the effective resolution. Advection schemes are an important part of the numerical models used for computational fluid dynamics. For example, in atmospheric dynamical cores they control the transport of tracers. For linear schemes solving the advection equation, the effective resolution can be calculated analytically using dispersion analysis. Here, a numerical test is developed that can calculate the effective resolution of any scheme (linear or non-linear) for the advection equation. The tests are focused on the use of non-linear limiters for advection schemes. It is found that the effective resolution of such non-linear schemes is very dependent on the number of time steps. Initially, schemes with limiters introduce large errors. Therefore, their effective resolution is poor over a small number of time steps. As the number of time steps increases the error of non-linear schemes grows at a smaller rate than that of the linear schemes which improves their effective resolution considerably. The tests highlight that a scheme that produces large errors over one time step might not produce a large accumulated error over a number of time steps. The results show that, in terms of effective-resolution, there is little benefit in using higher than third-order numerical accuracy with traditional limiters. The use of weighted essentially non-oscillatory (WENO) schemes, or relaxed and quasi-monotonic limiters, which allow smooth extrema, can eliminate this reduction in effective resolution and enable higher than third-order accuracy.

### © Author(s) 2010. CC Attribution 3.0 License. Atmospheric Chemistry and Physics

"... doi:10.5194/acp-10-7017-2010 ..."

### unknown title

"... A flux-form version of the Conservative Semi-Lagrangian Multi-tracer transport scheme (CSLAM) on the cubed sphere grid ..."

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A flux-form version of the Conservative Semi-Lagrangian Multi-tracer transport scheme (CSLAM) on the cubed sphere grid

### unknown title

"... A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid ..."

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A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid

### unknown title

"... [1] A multimodel assessment of the performance of chemistry‐climate models (CCMs) in the extratropical upper troposphere/lower stratosphere (UTLS) is conducted for the first time. Process‐oriented diagnostics are used to validate dynamical and transport characteristics of 18 CCMs using meteorologica ..."

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[1] A multimodel assessment of the performance of chemistry‐climate models (CCMs) in the extratropical upper troposphere/lower stratosphere (UTLS) is conducted for the first time. Process‐oriented diagnostics are used to validate dynamical and transport characteristics of 18 CCMs using meteorological analyses and aircraft and satellite observations. The main dynamical and chemical climatological characteristics of the extratropical UTLS are generally well represented by the models, despite the limited horizontal and vertical resolution. The seasonal cycle of lowermost stratospheric mass is realistic, however with a wide spread in its mean value. A tropopause inversion layer is present in most models, although the maximum in static stability is located too high above the tropopause and is somewhat too weak, as expected from limited model resolution. Similar comments apply to the extratropical tropopause transition layer. The seasonality in lower stratospheric chemical tracers is consistent with the seasonality in the Brewer‐Dobson circulation. Both vertical and meridional tracer gradients are of similar strength to those found in observations.Models that perform less well tend to use a semi‐Lagrangian transport scheme and/or have a very low resolution. Two models, and the multimodel mean, score

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"... potential to narrow uncertainty in projections of stratospheric ozone over the 21st century ..."

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potential to narrow uncertainty in projections of stratospheric ozone over the 21st century