James Kent

Assessing Tracer Transport Algorithms and the Impact of Vertical Resolution in a Finite-Volume Dynamical Core

AbstractModeling the transport of trace gases is an essential part of any atmospheric model. The tracer transport scheme in the Community Atmosphere Model finite-volume dynamical core (CAM-FV), which is part of the National Center for Atmospheric Research’s (NCAR’s) Community Earth System Model (CESM1), is investigated using multidimensional idealized advection tests. CAM-FV’s tracer transport algorithm makes use of one-dimensional monotonic limiters. The Colella–Sekora limiter, which is applied to increase accuracy where the data are smooth, is implemented into the CAM-FV framework, and compared with the more traditional monotonic limiter of the piecewise parabolic method (the default limiter). For 2D flow, CAM-FV splits dimensions, allowing overshoots and undershoots, with the Colella–Sekora limiter producing larger overshoots than the default limiter.The impact of vertical resolution is also explored. A vertical Lagrangian coordinate is used in CAM-FV, and is periodically remapped back to a fixed Euler...

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

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.

An Idealised Test Case For Assessing The Linearization of Tracer Transport Schemes in NWP Models

The linearized version of a Numerical Weather Prediction (NWP) model, which consists of its tangent linear model (TLM) and adjoint, has a number of important applications in atmospheric modelling. As such it is important that the linearized version of the NWP model can provide an accurate representation of the perturbation growth that occurs in the nonlinear model and does not introduce spurious instability. A suite of test cases, built upon existing frameworks, are developed to assess the accuracy of the linearization of the tracer transport component of the NWP model. Deformation velocities are prescribed that return the tracer back to the initial conditions, thus providing an analytical solution. A selection of smooth and discontinuous tracers and tracer perturbations are used. Example results are shown using second-order and third-order tracer transport schemes, both with and without nonlinear flux limiters. Metrics are offered for assessing the skill of the linearization and predicting when problems will occur. For the example schemes used the results show that linearizations of the nonlinear flux-limited transport schemes behave poorly due to the presence of unstable modes. Some linearized model implementation strategies are offered for situations where the nonlinear scheme should not be linearized.