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Вероятностный анализ

About the illusions and the reality in the methods of probability analysis of vector hydrometeorological processes

Yu. Klevantsov, M. Mikalajunas, V. Rozhkov, K. Smirnov


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).


Распределение хлорофилла "а" в Балтийском море

Ю.П. Клеванцов, В.А. Рожков, К. Г. Смирнов (СПО ГУ "ГОИН")

("Известия РГО". 2007. Т. 139. Вып.4)


В работе проанализированы спутниковые данные концентрации хлорофилла с 1998 по 2005 г. с дискретностью 8 суток и пространственным разрешением 9 км. Показано, что распределения вероятностей могут быть аппроксимированы гамма- и логнормальным распределениями, параметры которых изменяются по районам моря и сезонам; соотношения между производными плотности распределения по времени и пространству позволяют получить оценки параметров адвекции и диффузии концентрации хлорофилла.

The satellite data on chlorophyll concentration (1998-2005) with the discreteness 8 days and space resolution 9 km were analysed. It is shown that probability distributions are approximable by the gamma- and lognormal distributions; parameters of them are varied from region to region and from season to season; the relationships between time and space derivative of the distribution density allow to receive the estimates of advection and diffusion parameters for chlorophyll concentration.

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Физико-статистическая модель распределения хлорофилла в Балтийском море

Ю.П. Клеванцов, В.А. Рожков, К. Г. Смирнов (СПО ГУ "ГОИН")

("Труды ГОИН", Вып 211)


Приводятся результаты статистического анализа концентрации хлорофилла (КХ) и ее производных по времени и по пространству на основе данных спутниковых измерений (1998-2005) с дискретностью 8 суток и пространственным разрешением 9 км. Предложена физико-статистическая модель распределения хлорофилла, учитывающая изменение КХ за счет адвекции и диффузии, а также рождения и гибели органического вещества.

The results of statistical analysis of chlorophyll concentration and its derivatives in time and in space on a basis of satellite measurement data (1998-2005) with time discreteness 8 days and space step 9 km are presented. The physics-statistical model of chlorophyll distribution is offered; it takes into account the change of chlorophyll concentration at the expense of advection and diffusion, as well as birth and swarms of organic substance.

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Можно ли описать гидрометеорологические поля и процессы детерминистически.

В.А. Рожков

("Труды ГОИН", Вып 211)


Приводится обзор результатов исследований в области вероятностного анализа и моделирования океанологических процессов и полей за последние пять лет, дополняющие предшествующие публикации [1-3]. Обсуждаются проблемы описания гидрометеорологических процессов и полей на основе аналитических и численных решений детерминированных и стохастических дифференциальных уравнений, используемых в статистической гидрометеорологии. [7].