Analysis of correlations between time series with the use of the phase spectrum

In connection with the problem of revealing cause-effect relations among different climatic characteristics, methods for determining the dependence between time series on the basis of selected auto-and cross-covariance functions and periodograms expressed in terms of the Fourier coefficients of the initial series are discussed. Real time series do not always satisfy the conditions of statistical stationarity, so that their analysis requires a combination of statistical and deterministic approaches. The possibility of using the above numerical characteristics in relation to such series is considered. Characteristic features of describing finite segments of time series with the use of their Fourier coefficients is studied in detail. The main emphasis is on the determination of the time shifts (delays) at which the covariance between the series is maximal. The problems that appear during a practical implementation of the periodogram method for shift estimation are discussed. A previously unknown formula that is necessary for further studies and relates the Fourier transform of a selected correlation function to the periodogram of the series is derived.     

Water vapor in the atmosphere over the northern Tien Shan

Refined data of systematic measurements of total water vapor in the atmosphere from May 1980 to April 2005 are presented. The data were obtained at the Issyk Kul atmospheric-monitoring station by the method of solar molecular-absorption spectroscopy. Over 25 years, the annual mean water-vapor content in the atmosphere increased by 4.5% at a mean rate of increase of 0.18% per year. However, the water-vapor content decreased in the last five years. The results of statistical processing of experimental data (general statistical characteristics, correlation coefficients, composite oscillations) are described. A refined model is proposed for forecasts of temporal variations in the monthly mean and annual mean water-vapor contents for the coming years. The model includes a linear trend and the sum of oscillations with periods close to the periods of a number of well-known geophysical phenomena. Regression equations are proposed to relate the water-vapor content in the atmospheric column to the surface temperature and absolute humidity.     

Methods of fitting the Fisher-Tippett type 1 extreme value distribution

Methods are described for estimating the parameters of the Fisher-Tippet Type 1 extreme value distribution and associated return values from measured extremes, such as maximum wave height. A comparison of these methods, with simulated data, shows that those using Gumbel's plotting position are least satifactory. Maximum likelihood methods give the smallest mean square errors, but the very much simpler method of moments is nearly as good.     

Modelling of the spectral characteristics of the wind wave envelope

A method applied for the determination of the statistical characteristics of the wind wave envelope is considered. It is shown that the correlation function envelope for a normal random process defines the basic properties of the process envelope and it can be expressed through the spectrum width. No limitations are imposed on the form or the width of the spectrum. The model is effective for a developing and steady sea disturbance when the attenuation of the temporal correlation function can be approximated by an exponent. Numerical computations and experimental results for typical cases of sea disturbance are compared.Translated by Mikhail M. Trufanov.     

Relationship between the anomalies of temperature and air pressure over the ocean

This paper considers the relationship between multi-year air temperature and pressure fluctuations over the ocean, based on an approximate solution of the problem on the determination of large-scale seawater temperature anomalies from the conditions predominating at the sea surface. The dependence derived is numerically analysed using observations made in the North Atlantic. It is shown that the variability of annual mean air temperature anomalies is largely controlled by the air pressure field which has taken place during the preceding long-term period. The dependence derived may be applied to generate long-term forecasts of the ocean's hydrometeorological regime.Translated by Vladimir A. Puchkin.     

Some General Properties of Transverse Motions of the Geostrophic Front

Within the framework of the reduced-gravity model of the ocean taking into account the effect of friction in the Rayleigh form, we study the two-dimensional problem of nonlinear motions of a subsurface front of finite width. We consider the conservation laws and the character of motion of the center-of-mass of the cross section of the front and their variations caused by the losses of energy. For fields with special structure, the problem is reduced to the solution of a system of nonlinear ordinary differential equations. It is shown that the initially geostrophic frontal current decays with time according to a power law. The deviations of the initial state of the front from the state of geostrophic balance result in the generation of superinertial oscillations of the hydrodynamic fields.