(more details frederic.chome++at++oma.be )
The complete version of this paper with figures is downloadable from: ftp://ftpserver.oma.be/pub/meteo/fchome/alanl0599.doc
NDLR:
There is currently a new burden of interest for the much debated challenge : strong stretching versus LAM, and the associated problem of the optimal coupling strategy. Frederic Chome, a PhD student at the Belgium Met'Office, focuses on predictability properties with very simplified models (no physics, no orography). His first results are summarized hereafter, a more complete paper is available on his ftp. In the meantime, in Toulouse, Eric Bazile reran the "Vaison-la-Romaine" case, a reference situation with very strong convective precipitations. He compared the operational ARPEGE/ALADIN-France couple and ARPEGE with a stronger stretching factor (6.3 instead of 3.5). This choice ensured a similar computational cost for both configurations. In this case, forecasts were better with ALADIN, which was not what Eric expected. A summary of these experiments (presented at the recent HIRLAM workshop on high resolution modelling in Norrkopping) will be put on the ALADIN web site very soon.
Introduction
In the vast majority of regional forecasting models, the high-resolution part of interest is nested within a low-resolution global forecasting model. The latter is integrated over time independently of the nested part, and the outcome of this integration provides a boundary forcing constantly acting on the limited area under investigation.
The objective of the present work is to relax this constraint by viewing the evolution laws in the entire space under consideration as a single dynamical system rather than as two dynamical systems one of which is embedded in the other. This will be achieved by building an autonomous continuous variable-mesh model (VMM) and by examining its dynamical and predictability properties versus those of the nested limited area one (NLAM).
The particular context in which this comparative study will be carried out is the loss of stability of plane-wave solutions toward inhomogeneous long wavelength fluctuations known to occur in thermal convection, one of the processes at the basis of mesoscale atmospheric variability. It can be shown that near the instability threshold this type of dynamics can be cast in a universal form known as the complex Landau-Ginzburg equation. It generates spatio-temporal chaos and therefore exhibits sensitivity to initial conditions which, as well known, is one of the main factors limiting predictability.
The intrinsic simplicity of our model, capable of generating complex behavior sharing, in addition, key features of atmospheric variability while being amenable to a detailed numerical and statistical analysis, will enable us to delineate the role of various factors in the observed behavior. In particular it will allow for a comprehensive analysis of the probabilistic properties since integrations over a large number of samples starting from different initial conditions can here be carried out at a reasonably low computational cost. This will in turn be a necessary prerequisite for a detailed predictability analysis of the fields of interest generated by the models.
Statistical results
We are interested in the quality of representation of the relevant variables in a statistical sense by the VMM and the NLAM as compared to the values provided by an "exact" solution in which the entire space is filled by the fine grid (the reference model). We shall focus on the statistical properties of the field at a particular gridpoint chosen here to be the centre of the limited-area grid that is by construction the centre of the global model.
The probability density displays a symmetry around the mean, where the densities for both the NLAM and VMM are nearly indistinguishable from the reference model. However in the NLAM case sizeable deviations are apparent as one moves to the extremes values of P as well as around the most probable events. In contrast, the P(x) obtained from the VMM is closer to the reference system, the improvement reaching a factor 10 as compared to the NLAM for the most probable events.
Interestingly, these properties depend on the length LN of the nested domain of interest for the NLAM. The mean deviations of each model from the reference one clearly indicates zones where the mean error for the NLAM is considerably reduced, showing two optimal lengths for the nested fine-scale domain for which the performance is higher than the globally coarse model, the errors being practically negligible (less than 3%). It appears therefore that a judicious choice of the size of the nested model may provide statistics of enhanced quality. The dependence of the probability distribution as obtained from the VMM on LN is practically negligible, its mean being of very high quality (lower than 1%).
In the spatial power spectra, we observe that for the short scales the agreement is in general satisfactory for both regional models, but for large scales the spectrum of the NLAM deviates form the reference model in that it presents a number of equally spaced spurious peaks. Varying the length of the nested model reveals again the existence of an optimal length (LN=200 LU) for which the large-scale oscillation disappears in the NLAM spectrum. The VMM results in a perfect agreement at all scales for every LN, the disappearance of the spurious large scale oscillations being presumably due to the natural continuity of the fields from the global grid toward the fine scale one, resulting in a unique self-consistent dynamics. On the other hand, the spurious oscillation over the low wavenumbers in NLAM spectrum is presumably due to the nesting procedure, which forces the fine-scale limited-area dynamics to readjust artificially at regular timesteps to the behavior of the large scale fields provided by the global coarser model.
Predictability properties
The main interest in analysing the growth of initially small errors between each regional model and the reference one will be to assess whether the replacement of the boundary forcing of the NLAM by the purely dynamical description adopted in the VMM brings about noticeable improvement and, if so, whether this improvement can be optimised by appropriate choices of the parameters.
In order to identify errors associated to the modelling of the nesting procedure, we first considered the ideal case of exact initial conditions in the regional domain. It turned out that the continuous variable-mesh model was by far more efficient than the nested limited-area one, since the errors reach the saturation level after 100 time units for the VMM, which is to be compared with 15 T.U. and 20 T.U. for the NLAM and the globally coarse model, respectively.
This tendency holds when adding small initial errors arising from the uncertainty to the initial state of the system. The mean error decreases for short times and subsequently grows with similar rates for the global and the nested limited-area model, whereas a smaller rate of increase is apparent for the VMM. It is worth mentioning however that although the NLAM turns out to be of lower predictive quality than the VMM, it still performs better than a globally coarse large-scale model, at least for short-term forecasts.
Once again, the forecasting ability of the VMM is evident as compared to the NLAM. Note however that the VMM presents a stronger sensitivity arising from the uncertainty to the initial conditions, suggesting that in this case only the use of appropriate data assimilation techniques could improve substantially the predictive skill of those continuous regional models.
Our study highlights the complexity of the dynamics of limited-area models. In particular, the influence of model errors in the degradation of the quality of forecasts reflects the importance and intricacy of the coupling procedure of fine-grid and the surrounding coarse parts for the nested model, suggesting strongly the intensive use of VMM to describe and forecasts small scale fields over zones of limited extension.
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