Some limits to the variable-mesh solution and comparison with the nested-lam solution



The solution at high resolution of a global spectral model with a conformally-variable mesh, obtained through a stretched coordinate, is compared as fairly as possible to the ‘classical’ solution of a limited-area nested model. We compare the global, variable-mesh, ARPEGE model at hyper-stretched values (which is integrated operationally at Météo-France with a ‘low’ value of stretching) with its limited-area version, the ALADIN model. Having the same physics, the same grid-point dynamics and a high code-compatibility, they allow clean comparisons on real situations. to conclude on their efficiency and accuracy, comparisons are made choosing configurations of the two models having either the same resolution or the same computational price.

The limits of the variable-mesh strategy on the sphere are also investigated through a set of experiments with increasing stretching. We found that there is indeed a limit to the stretching factor in the interval [7, 9]: a stretching factor c = 7 keeps an accurate spectral solution and gives satisfying results, even when compared with the limited-area model at the same computational price. We show that the value c = 10.5 cannot be reached without paying the price of a spectral deformation of the fields which becomes too obvious. Additional tests showed the occurrence of this deformation, even if less pronounced, at the stretching value c = 8.75. At the same resolution ALADIN does not manifest any similar weakness.

Although the solution remains stable for at least 72 hours, its accuracy when increasing the stretching above the critical value becomes questionable. This problem seems to be due to a particular behaviour of the truncation error, which does not decrease with increasing resolution through stretching, thus leading to an energy accumulation in the tail of the spectra.

As a conclusion of this study, it follows that one can extend the idea of Courtier and Geleyn, currently used in operations at Météo-France for c = 3.5, to ‘medium’ stretched configurations up to c = 7 at least (at the current computer's power). Above a value found to be about c = 9, our results show that increasing the resolution does not produce any improvement and, hence, that the use of a limited-area model appears a better choice for very high resolutions.