5:15 PM - 7:15 PM
[MGI30-P07] The adjustment of the horizontal diffusion coefficient to changes in the resolution of a general circulation model of the atmosphere
Keywords:atmospheric general circulation model, resolution change, horizontal diffusion coefficient, kinetic energy dissipation
In atmospheric general circulation models (AGCMs) using the spectral transform method, it is common to introduce a hyper-viscosity term into the prognostic equations for variables such as wind velocity as a dissipation process. In this presentation, we report the results of an investigation into how the diffusion coefficient should be adjusted when the order of hyper-viscosity is fixed and the resolution of the numerical experiment is changed, from the perspective of kinetic energy dissipation, using a theoretical dimensional analysis, and idealized dry atmosphere simulations of Held and Suarez (1994) [HS94].
From dimensional analysis of the energy dissipation under simple assumptions (e.g., Iwayama et al. 2019) and the relationship between the viscosity coefficient and the e-folding time (the decay time) at the maximum wavenumber (the truncation wavenumber or resolution) (e.g., Jablonowski and Williamson 2011), it can be shown that when the truncation wavenumber is sufficiently larger than 1, the e-folding time should be multiplied by 2-2/3 ~ 1/1.6 when the truncation wavenumber is doubled, regardless of the order of the hyper-viscosity.
On the other hand, the viscosity coefficient from the HS94 experiments was adjusted so that the energy spectrum distribution obtained at the triangular truncation wave number of 170 or 341 is close to that obtained from aircraft observations by Nastrom and Gage (1985) [NG85], and then empirically adjusted by multiplying the e-folding time by 1/p or p when the truncation wave number is doubled or halved, respectively. The results were inconclusive. 1) Considering whether a kinetic energy spectrum distribution at high wavenumbers close to that of NG85 can be obtained at the triangular truncation wavenumbers of 170 and 341 in particular, it is recommended that p = 1.2 when the order of hyper-viscosity is 2, p = 1.6 when it is 4, p = 2. 0 when it is 6, and p = 2.4 when it is 8. 2) On the other hand, considering that the wavenumber at which the transition of the energy spectrum distribution between low and high wavenumbers occurs does not change much from 40-60, better results were obtained with p = 1.6 for all orders of hyper-viscosity. In 1) for the order of 4, and in 2) for all orders studied, the results are in agreement with the dimensional analysis, and the results of the realistic moist simulations by Takahashi et al. (2006).
Future work will include an extension to a moist model, and a method for adjusting the e-folding time when the order of the hyper-viscosity is changed with fixed resolution.
From dimensional analysis of the energy dissipation under simple assumptions (e.g., Iwayama et al. 2019) and the relationship between the viscosity coefficient and the e-folding time (the decay time) at the maximum wavenumber (the truncation wavenumber or resolution) (e.g., Jablonowski and Williamson 2011), it can be shown that when the truncation wavenumber is sufficiently larger than 1, the e-folding time should be multiplied by 2-2/3 ~ 1/1.6 when the truncation wavenumber is doubled, regardless of the order of the hyper-viscosity.
On the other hand, the viscosity coefficient from the HS94 experiments was adjusted so that the energy spectrum distribution obtained at the triangular truncation wave number of 170 or 341 is close to that obtained from aircraft observations by Nastrom and Gage (1985) [NG85], and then empirically adjusted by multiplying the e-folding time by 1/p or p when the truncation wave number is doubled or halved, respectively. The results were inconclusive. 1) Considering whether a kinetic energy spectrum distribution at high wavenumbers close to that of NG85 can be obtained at the triangular truncation wavenumbers of 170 and 341 in particular, it is recommended that p = 1.2 when the order of hyper-viscosity is 2, p = 1.6 when it is 4, p = 2. 0 when it is 6, and p = 2.4 when it is 8. 2) On the other hand, considering that the wavenumber at which the transition of the energy spectrum distribution between low and high wavenumbers occurs does not change much from 40-60, better results were obtained with p = 1.6 for all orders of hyper-viscosity. In 1) for the order of 4, and in 2) for all orders studied, the results are in agreement with the dimensional analysis, and the results of the realistic moist simulations by Takahashi et al. (2006).
Future work will include an extension to a moist model, and a method for adjusting the e-folding time when the order of the hyper-viscosity is changed with fixed resolution.