The march towards 3D-VAR in ALADIN

C. Fischer A. Dziedzic E. Gerard A. Horanyi W. Sadiki M. Siroka C. Soci

The ALADIN community develops a 3D-VAR analysis scheme, based on scientific and technological input from the ARPEGE/IFS system. The goal is to obtain an analysis system suitable for a mesoscale observation network and forecast model. A few scientific or technical constraints exist, which give a general guidance for the developments discussed below:

• since ALADIN is coupled with ARPEGE, and the ARPEGE 4D-VAR analysis and subsequent forecast are used as input for the initial and lateral conditions in ALADIN, do not "spoil" the fields from the large scale assimilation cycle while reanalyzing in the limited area model.
• as a consequence, search for a formulation where ARPEGE-resolved scales are not reanalyzed, and only the mesoscale ALADIN features are touched (this approach is called "decremental").
• the use of ARPEGE libraries as background, and the still limited manpower devoted to the developments of 3D-VAR, force the technical solutions to remain relatively close to those of the global model (definition of the control vector, modelization of Jb, ...). The present solutions can be viewed as a trade-off between the push towards the mesoscale and the closeness to the large scale system.

An important work is carried out in order to define a truely mesoscale background cost function Jb. The basic formulation of Jb is close to the one defined in ARPEGE/IFS, with an extra statistical balance relationship for specific humidity. The statistical relations are evaluated with the NMC method. The minimization is performed with the M1QN3 algorithm, in the space of the bi-Fourier spectral components.

Based on results of a previous work, which show that the forecast error variance in the large scales is controlled by the coupling data, an alternative NMC method is defined, by computing the statistics of 36h minus 12h forecasts and by using the same lateral boundary conditions in both forecasts (Siroka, 2000). This approach leads to a reduction of the large scale variance, and makes the Jb statistical model become much more mesoscale selective than with the traditional NMC method. This aspect is illustrated in fig. 2 and 3: the horizontal lengthscales are reduced in the case of constant LBC statistics, compared to the classical ones, by a factor of almost 2 (curves obtained from a 3 months winter 1999-2000 period with ALADIN/FRANCE).

1. Analysis increments

In the next step, first 3D-VAR experiments are carried out in order to assess the structure and the amplitude of the analysis increments. As seen on fig. 1, the analysis produces structures with mesoscale-sized decays from observation points. For specific humidity, the increments look like spots, but with only a local impact. It can also be noticed that the increments cross and overpass the mathematical extension zone of ALADIN. This behaviour can be damped by specifying very small background error variances in the E-zone, at the expense of small Gibbs waves in the analysis increments (not shown). These analyses are obtained by using conventional observations such as SYNOP, AIREP, TEMP, PILOT, SATOB, DRIBU. For the time being, some satellite observations are not treated (SATEM, TOVS). On the whole, about 16500 individual measurements are retained after the screening of observations, and enter the 3D-VAR minimization.

2. Ongoing developments

A number of questions are now being addressed, in order to define more precisely the formulation of the mesoscale analysis. Cycling aspects are not being considered for the time being. One question is the proper tuning of the background error variances. Indeed, with lagged NMC statistics, the replacement of the 12h old analysis by the coupling file, valid for the same time, but produced by the 36h old analysis, means that there is nomore any impact of refreshed data in the NMC statistics. As a consequence, the amplitudes of the error variances obtained with the lagged NMC statistics do not have any relationship with the actual forecast errors. The least one can do is to multiply the Jb variances by a scalar, which has to be tuned by some adjusting method.

Thus, investigations are now carried out in order to assess the suitable ratio between the background error cost function and the observation cost function (Jo / Jb). These studies involve the use of a posteriori evaluation of the consistency of the variational formulation. First results indicate that the ratio should be close to 1., but the method also exhibits a fairly poor sensitivity with respect to this ratio, so that a better fit is still needed, and new tests are under progress

Also, the impact of the digital filter initialization is now investigated, along with the strategy for choosing the most suitable first guess fields (tested data are interpolated analysis of the driving model, 6h ALADIN forecast or a mixture of both). These studies represent necessary steps in the way for real case studies and shed some light on the possible cycling mechanisms.

Future work will probably concentrate even more on the initialization aspects and then on the strategy for a genuine data assimilation cycle.

Figure 1: Analysis increments produced by the limited area 3D-VAR analysis from ALADIN at model level 20, for July, 15th 2000: (a) temperature, (b) specific humidity, (c) zonal wind, (d) meridional wind.

Figure 2: Horizontal lengthscales for temperature and log(ps).

Figure 3: Horizontal lengthscales for specific humidity.

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