CISL 2007 annual report banner

Adaptive-mesh grid techniques for climate modeling on millennial time scales

 
 
Advection of a slotted cylinder

Advection of a slotted cylinder with rotation angle α=30 and three refinement levels (0.625° x 0.625°) in the models SEM (left column) and FV (right column). The height field with h≥0.5 m is shaded in gray. (a,e) Initial height field (h=1000 m). (b,f) height field at day 6 (half a revolution). (c,g) day 9. (d,h) Cross section of h along the equator at day 12 (full revolution). The adapted spectral elements (SEM) and blocks (FV) are overlaid.
 
Barotropic wave comparison

Barotropic wave at day 6 in the models SEM (left column) and FV (right column) with uniform (non-adapted) grids at increasing resolutions as indicated above. The relative vorticity field ζ in the Northern Hemisphere is shown.
 
Barotropic wave evolution

Evolution of a growing barotropic wave in SEM (left column) and FV (right column) with four refinement levels (finest resolution is 0.3125° x 0.3125°). Snapshots of the relative vorticity field ζ at (a,e) day 3; (b,f) day 4; (c,g) day 5; and (d,h) day 6. The refinement criterion is |ζ|≥3x10E-5 s-1, the adapted spectral elements (SEM) and blocks (FV) are overlaid.
 
Error norms

Time traces of the normalized l2 geopotential height error norms for the flow over a mountain (test case 5). The adaptive simulations with three refinement levels (0.625° x 0.625° at the finest level) and several uniform-resolution runs are compared to a T426 spectral transform reference solution.
 

To provide a just comparison between non-conforming adaptive techniques in climate modeling, more testing was performed during FY2007. Two defects of the spectral element approach were pointed out by the new tests:

  • The cubed sphere mesh introduces a Rossby-Haurwitz number 4 wave into the simulation at low resolution.
  • Oscillations can drive a physically positive constant quantity to a negative value during the course of a simulation (the Gibb's phenomena).

 

In the second case, the error norms between the two techniques are comparable, but the lower-order method may have a more physically valid distribution of the error. When more grid points are added, the non-physical wave present for the cubed sphere mesh disappears, but no Fourier analysis was performed to demonstrate this. On the positive side, for the flow over a mountain test, the spectral element approach was doing much better than the finite-volumes method in terms of error norms. To demonstrate this, the high-resolution reference solution of the Deutscher Wetterdienst center was employed instead of the one from NCAR.

In FY2008, the combination of a more advanced time-stepping procedure will be studied for its suitability with AMR simulations to accelerate the time to solution.

This effort upholds NCAR's strategic priorities of "Conducting research in computer science, applied mathematics, statistics, and numerical methods," "Developing community models," and "Improving prediction of weather, climate, and other atmospheric phenomena." It will yield more efficient and accurate models, help reinforce NCAR's image as a leader in cutting-edge numerical methods, and may set the standard for next-generation climate and weather models. This project exploring adaptive-mesh grid techniques in spectral-element dynamical cores is supported by the NSF with awards 0222282, 0530845, and Core funding.