Volume 37, Issue 2

The paper is focused on the construction of a numerical stochastic model of the joint spatio-temporal fields of air temperature, wind speed vector with three-hour resolution, and semidiurnal precipitation amounts according to observation data at a group of weather stations located in the south of the Baikal natural territory. The model also takes into account the dependence of one-dimensional distributions on temporal and spatial coordinates. The heterogeneity of the field in spatial correlations and the periodical correlation in time are also taken into account. The results of calculations for verification of the model are presented. An example of using the developed model to study the properties of time series of the wind chill index is given.

We introduce discrete curvatures for planar curves based on the construction of sequences of pairs of mutually dual polylines. For piecewise-regular curves consisting of a finite number of fragments of regular generalized spirals with definite (positive or negative) curvatures our discrete curvatures approximate the exact averaged curvature from below and from above. In order to derive these estimates one should provide a distance function allowing to compute the closest point on the curve for an arbitrary point on the plane.With refinement of the polylines, the averaged curvature over refined curve segments converges to the pointwise values of the curvature and, thus, we obtain a good and stable local approximation of the curvature. For the important engineering case when the curve is approximated only by the inscribed (primal) polyline and the exact distance function is not available, we provide a comparative analysis for several techniques allowing to build dual polylines and discrete curvatures and evaluate their ability to create lower and upper estimates for the averaged curvature.

The problem of potential predictability of the temperature of the upper layer of the Arctic Ocean for the data of pre-industrial climate modelling run by the INM-CM5 Earth system model developed at the INM RAS is considered. The main attention is paid to the analysis of predictability of the phases of the dominant modes of low-frequency variability of the Arctic Ocean circulation. The initial estimate of its predictability is made by using the method of analogues and calculating the resonances of the invariant measure. Then this estimate is verified by direct ensemble calculations with the model. The results obtained indicate that the maximum predictability time interval reaches ten years for 15-year average values of heat content and corresponds to the states with maximum positive anomalies along the leading low-frequency variability modes.

The paper is devoted to the construction of optimal stochastic forcings for studying the sensitivity of linear dynamical systems to external perturbations. The optimal forcings are sought to maximize the Schatten norms of the response. As an example,we consider the problem of constructing the optimal stochastic forcing for the linear dynamical system arising from the analysis of large-scale structures in a stratified turbulent Couette flow.

Idealized numerical experiments with the INM RAS climate model are used to study the potential predictability of the temperature in the upper 300-meter layer of the Arctic Ocean. It is shown that the heat content can be predictable for up to 4–6 years. Positive anomalies of the temperature and salinity are preceded for several years by a state in which the influx of Atlantic water into the Arctic Ocean exceeds the average value. Surface fields, including temperature, salinity, concentration and mass of ice, are less predictable than the heat content in the layer of 0–300 meters.