M. Bellus (SHMI) - J.-F. Geleyn (Météo-France)
1. Introduction
After several changes in the operational code of ARPEGE (change from CYCORA to CYCORA-bis package and afterwards CYCORA-ter parallel suite, decreasing of the horizontal diffusion in the assimilation cycle since September 2001 etc.), there were some model crashes in a rather short time period. It was important to investigate, whether those instabilities in the model were caused by the new modifications in the code or whether they were present (but hidden) in the past too and have been just woken up for instance by decreased horizontal diffusion. On the other hand we wanted to understand the mechanism, which creates such instabilities and to find some solutions in order to avoid them.
2. Investigation
One of the biggest crashes in the operational suite happened on the 10th of October 2001, while running ARPEGE T95 with Eulerian advection scheme (4d-var ARPEGE forecast). That crash was caused by the development of very big temperature gradients in horizontal as well as in vertical directions (see Fig. 2 - top, REF). From the geographical point of view, this temperature anomaly took place over Pacific ocean 40° N and 180° E. In principle, one can avoid this blowing by shortening of the time step or using semi-Lagrangian advection scheme instead of the Eulerian one. With the increased horizontal diffusion, which will smooth the temperature oscillations, we can also succeed.
Coming from CYCORA to CYCORA-bis package, we allow more moisture to be transported to the top of the cloud. This moisture is probably not consumed enough by downdraft and feeds the large scale precipitation (LSP). Afterwards, that water coming from the LSP is evaporating in a thin dry air layer where strong cooling takes part. The instability itself seems to have a numerical source. There is indeed a tendency of very quick cold air mass descent, which creates of course unrealistically strong vertical wind. Furthermore, the vertical CFL (Courant Friedrich Levy) condition is broken and numerical instability can creates such big vertical temperature oscillations (see Fig. 1 - bottom, REF). (This can even create, in some strange way, the better conditions for convection and some positive feedback may causes the further instability amplification.)
Inside CYCORA modifications there was the possibility to smooth the humidity turbulent diffusion tendency (LCVLIS=.TRUE.), but subtraction of a constant tendency everywhere would have a relative big impact in the upper atmosphere where the humidity is small, and small one in the lower troposphere. Therefore a scaling of humidity tendency by specific humidity at saturation was introduced with a coefficient (GCVPSI) allowing the continuous transition between the non-averaging state (local use of turbulent fluxes when GCVPSI=1.) to a complete smoothing (integral computation of turbulent fluxes when GCVPSI=0.).
Several tests aimed on moisture distribution in the cloud showed even negative impact to the Pacific case while there was no smoothing of turbulent fluxes in the turbulent diffusion tendency computation for both specific humidity and enthalpy (see Fig. 1 - bottom, T01). The other extreme, when turbulent fluxes of specific humidity and enthalpy were completely smoothed, was also worse than the reference (see Fig. 1 - bottom, T03). On the other hand, the return to the CYCORA situation (LCVLIS=.FALSE., GCVPSI=0. ) with the local treatment for q and complete smoothing for T, reduced dangerous temperature gradients significantly (see Fig. 1 - top, T06).
The experiments based on the differences between CYCORA and CYCORA-bis setups (we tested the impact of the parameter groups with the similar functionality) were most sensitive for the above mentioned smoothing of turbulent fluxes and to the group of parameters GCVNU, GCVALFA and ECMNP. Though, it did not cure the instability problem completely and quite big vertical oscillations of temperature tendency were still present. The combination of GCVNU, GCVALFA, ECMNP (CYCORA values) with the smoothing of temperature turbulent fluxes and local computation of specific humidity turbulent fluxes (LCVLIS=.FALSE., GCVPSI=0. ) did not bring any further improvement (see Fig. 1 - top, T11). But we have shown, that this group of parameters has bigger positive impact (concerning the instability curing) together with LCVLIS=.FALSE. rather then with LCVLIS=.TRUE. .
Changing the scaling parameter in the specific humidity tendency computation, where instead of specific humidity at saturation we used specific humidity, afterwards specific humidity of wet bulb temperature and finally specific humidity of the cloudy ascent, did not helped at all. But we found out that this Pacific case is very sensitive to the large scale evaporation and melting processes. Suppressing evaporation and melting (separately or together) helped to remove the instability, and vertical oscillations of temperature tendency were smoothed very well (see Fig. 1 - bottom and Fig. 2 - bottom, T04). (The same effect we found later also for the another similar problematic case from 28th December 1999, well known as Xmas storm - although it has nothing to do geographically with the Christmas storm now.)
If there is no evaporation, there is no possibility for enormous cooling by evaporating large scale precipitation. If we force downdraft in convection scheme to get rid of more moisture (just not to feed the LSP with it), one can suspect some improvement concerning the smaller cooling due to the LSP evaporation. But our experiences with the enhanced downdraft were quite different. Furthermore, on the other hand the experiments with suppressed downdraft had positive impact and helped to decrease big temperature oscillations along the vertical.
The problem is not only inside the convection scheme (instability in the model was still present even without convection scheme), but probably in the interaction between it and LSP. There was coded (but not used) a modification of enthalpy and specific humidity turbulent fluxes coming from vertical diffusion by additional fluxes coming from LSP to be used only inside convection scheme. This approach was not used, because of the inconsistency between specific humidity and enthalpy fluxes computations. But now, when the smoothing of specific humidity turbulent fluxes is implemented in the convection scheme, it seems to be logical to use it.
Above mentioned modification of the fluxes used inside convection scheme had positive impact to the Pacific case as well as to the other case from 28th December 1999. We have shown, that this modification can reduce the vertical oscillations of temperature tendency (although not so markedly than the test without evaporation can, see Fig. 1 - bottom and Fig. 2 - second line, 6REF) while it is not significantly touching the global scores (see Fig. 3 - top).
There was suspicion that this modification is responsible for amplification of convective activity oscillations in the tropics (visible on pseudo-satellite images), but we have shown that the problem with such oscillations between the time steps is present even in the operational model and with the same order of magnitude. To find the source of those oscillations we did several tests and found out the source of it inside the shallow convection scheme.
Afterwards, following the idea of Eric Bazile, we coded the smoothing of ZAUX parameter, which is a correction of Richardson number due to the shallow convection (computed inside the shallow convection scheme). Smoothed ZAUX parameter (using its values from the previous and actual time step, see Fig. 3 - bottom) applied in further stability computations, brought significant improvement concerning the convective activity oscillations. And what is more, this kind of smoothing had a positive impact also to the other fields, mainly to the temperature at the lowest model levels.
3. Conclusion
Modifications in the code of aplpar.F90 (enthalpy and specific humidity turbulent fluxes coming from vertical diffusion are expanded by fluxes coming from LSP and are used in the convection scheme) and in the code of accoefk.F90 (smoothing of the Richardson number correction due to the shallow convection) are worth to be implemented to the operational cycle.
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