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Корреляционные функции метеополей: как их оценивать и какая от них польза
Homogeneous and isotropic with respect to horizontal variables random fields are useful for study of geophysical (in particular, meteorological) functions of spatial-temporal variables. The following horizontal scale (30 — 3000 km), which is induced by the spatial scale of the observing grid for the Earth’s atmosphere and by the power of modern computers for solutions of the system of hydrothermodynamics equations, which included water phase transformations etc, is important for the weather forecast problems.
The correlation functions (CFs) of the random fields may be applied for the following goals:
1) For the optimal interpolation of the meteorological information from the points of observation into the points of a regular finite-difference grid, as well as (for the checking of some observations by other ones) into another point of the observation.
2) For the models’ testing, if a climate model simulates adequately not only mean fields, but the fields of the relative dispersions and CFs, too, then we should consider the climate model as a certain one.
The CFs are evaluated by the global checked archive of meteorological observations by meteorological sounds. A special regularization procedure provides the strong positive definiteness of the CFs. The areas in the Earth atmosphere, where the isotropy hypothesis is essentially not fulfilled, were localized by a special algorithm.
Let us consider an algorithm, which can construct atmospheric fronts that separate so named homogeneous synoptic atmospheric volumes. Then we can evaluate separately CFs for the ensemble of the pairs of points, which are in a unite volume and CFs for the ensemble of the pairs of points, which are in a various volumes. We can see the difference between the different CFs. The difference will be more for a better algorithm. So, we obtain a quality criterion for such algorithms. The statistical approach given possibility to optimize the algorithm with respect to a lot of numerical parameters. The optimal algorithm was exploited in the operative regime in Hydrometeorological Center of Russia. The similar algorithms of numerical construction of boundaries between homogeneous volumes by a discrete set of observations can be realized for various physical media.