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Yu. Klevantsov, M. Mikalajunas, V. Rozhkov, K. Smirnov About the illusions and the reality in the methods of probability analysis of vector hydrometeorological processes

In 1982 we have published in “Труды ГОИН” (“Transactions of the State Oceanographic Institute”, or SOI) the article: “A. Belyshev, Yu. Klevantsov, V. Rozhkov.  About the illusions and reality in the methods of sea current analysis” [4].

Nearly 30 years have passed, but we found no one article in foreign editions where the authors used the “vector-algebraic method” for vector process analysis (it was elaborated during 1974-1978 in Leningrad Branch of SOI and then published in 1983 (in Russian) in the monograph “Probabilistic analysis of sea currents” [5]). So we decided to repeat the publication of the basic ideas of that old article in English in the hope that somebody will read it with some interest and even will try to apply this method for the statistical analysis of his own vector data. It is difficult now for us to make the translation of the book [5] and to place it in our web-site; so we tried to adduce some interpretation of invariant characteristics of correlation and spectral functions of current or wind velocity (or gradients of scalar processes) very briefly; may be in future we’ll be able to translate and publish in more detail the peculiarities of this interpretation.

The data of long measurements of sea current or wind velocity are one  of the basic information source about the regularities of structure and dynamics of these processes. The data may be received in some fixed point or in several points (in particular on the polygon or in the model net).

For the obtaining of sea current or wind statistical regularities these data are considered as vector probabilistic process V(t);  its characteristics are the moment functions of the first and the second order . (Here and further we notice the vector (in contradistinction to the scalar) value, function or process by heavy-faced type).

The space-time characteristics of this process were computed on the base of auto- and cross-correlation and spectral analysis of velocity time series which were measured on the different horizons of one or several stations.

As a first approximation process V(t) is called two-dimensional (though the modern devices allow to receive three-dimensional data; the analysis of current velocity vertical component shows that it can have not so small values compared some time with horizontal component values, and we elaborated now the method of vector-algebraic analysis for such data).

In the applied works often uses the examination of two-dimensional vector as

-          well regulated number couple (abstract vector coordinates in some basis)  [21, 23];

-          complex number, real and imaginary parts of which coincide with Cartesian projections of  vector  [1, 23];

-          the value, which has a modulus, a direction and can be added with the same values by the “rule of parallelogram”.

For sea currents in oceanography are four approaches to the analysis of current velocity; call them

-          “component-wise”;

-          “complex-valued”   and  “method of rotary components”;

-          “vector-algebraic method”;

everyone of these three position may be correlated with three above-mentioned definitions of vector.

Two of them (“component-wise” and “vector-algebraic method”) are use now for wind velocity probabilistic analysis although (for example [8, 17, 21].
27 February 2012