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Article describes a probabilistic model (stochastic generator) of spatial-temporal variability of sea ice concentration. Values of the ice concentration are generated at the nodes of the spatial grid with 10 km resolution; the model time step is one day. The change in ice concentration with time (temporal variability) is modeled on the basis of a matrix of transient probabilities (discrete Markov chain), each row of which is a distribution function of the conditional probability of changes in the ice concentration. Spatial variability is determined by empirical probability fields, with which the observed changes in fields of the ice concentration are associated with known conditional probability distribution functions. To identify the parameters of the stochastic generator, satellite data from the OSI SAF project for the period 1987–2019 were used. The generator takes into account seasonal, interannual and climatic variability. Interannual and climatic variability are determined on the basis of a stochastic model of changes in the types of ice coverage. In order to verify the developed stochastic generator, we compared the statistical indicators of observed and calculated ice fields. The results showed that the fieldaverage absolute error of statistical characteristics of the ice concentration (mean and standard deviation) does not exceed 3.3%. The discrepancy between the correlation intervals of ice coverage calculated from the model and measured ice concentration fields does not exceed 2 days. The variograms of the modeled and observed fields have a similar form and close values. As an example, we determined the duration of navigation of Arc4 ice class ships between the Barents and Kara Seas using synthetic fields of the ice concentration reproduced by the stochastic generator.

Russian and Turkish are the most frequently spoken and intensively investigated heritage languages in Germany, but contrastive research on their development in early childhood is still missing. This longitudinal study compares the trajectories of expressive lexicon development in Russian (n = 70) and Turkish (n = 79) heritage speakers and identifies predictors for their lexicon size at preschool age. Heritage lexicon size was tested with two comparable tests assessing the expressive lexicon at four test points between the mean ages of 3.3 (range: 25–49 months) and 5.6 (range: 54–78 months) years. The influence of language-related factors, such as input quantity, parents’ heritage language proficiency and age of onset (AoO) of German, and other potential predictors, i.e., intelligence and socio-economic status, is evaluated. Results show that the Turkish group’s abilities grow slower but are similar at the last test point. Common predictors for lexicon size are input quantity from siblings and AoO. Group-specific influences are parental input quantity in the Russian group and siblings’ proficiency in the Turkish group. Our findings emphasize the interplay of input quantity and society language AoO for heritage lexicon development. The relevance of our results for the usage-based theory of language acquisition is discussed.

This article is dedicated to applicability justification as well as advantages and disadvantages analysis of discrete models in population dynamics. Discretization is the process of transferring continuous functions, models, and equations into discrete counterparts. We consider how temporal, spatial and structural discretization can be applied for solving typical issues in mathematical ecology, and try to estimate corresponding models adequacy and applicability limitations.

Data on soil moisture reserves are the basis for decision-making in the agricultural boghara system, because it determines the development of agricultural crops potential, terms of top-dressing and additional fertilizing, and makes it possible to predict yield of agricultural crops. In this article the influence of relief morphometric characteristics on the distribution of precipitation over the territory was studied. The research area is the land of the eastern part of Klepininsky rural settlement of Krasnogvardeysky district, the central part of Crimean Peninsula. The article considers approaches, divided into 2 main categories (according to the type of data used), based on the use of GIS capabilities and remote sensing data, to analyze the soil water content (SWC) using the example of research area and relationship of this parameter to the terrain relief. It was established that the morphometric characteristics of relief affect the amount of soil moisture.

A functional description of the hydrophysical properties of the soil as a capillary-porous medium is presented. The described functions of water retention capacity and hydraulic conductivity of the soil have common parameters, which are interpreted within the framework of physical and statistical concepts. The practical significance of the proposed functions lies in the fact that the volume of labor-intensive field measurements necessary, for example, for modeling the dynamics of soil moisture, is significantly reduced. To identify the parameters of these functions, it is sufficient to use data only on the water retention capacity of the soil. The parameters identified in this way can be used to predict the ratio of the hydraulic conductivity of the soil to the moisture filtration coefficient. The presented system of the hydrophysical functions of the soil is compared with world analogues using literature data on soils of different texture.

Classical Chanter-Thornley model of mushroom growth has been modified and implemented in AnyLogic simulation environment by means of system dynamics, discrete-event and agent-based approaches. A numerical case study of the model is presented and the problem of optimum age at harvest, providing the maximum integral yield for all fruiting "waves" is solved.

At substantiating land amelioration and land management designs, as well as during periods of operation and reconstruction of water facilities, information support plays an important role in relation to the hydrophysical properties of soil. Effective implementation of this support faces a number of challenges. Such problems include the very high laboriousness of carrying out the corresponding engineering surveys and laboratory studies. In this regard, the methods of indirect estimating the hydrophysical properties, the measurement of which requires considerable labor, are very in demand for land amelioration and land management practices. An equally acute problem is the problem of the functional representation of the coefficients of the Richards equation, which is widely used in engineering-hydrological calculations. The paper suggests: 1) the original method for assessment of the ratio of the values of the hydraulic conductivity function of soil to the moisture filtration coefficient using data from direct measurements of the water-retention capacity of soil carried out according to the standard procedure; 2) the mathematical model describing the hydrophysical properties of soil, and the system of functions with interpreted parameters that physically adequately describe the coefficients of the Richards equation. In carrying out the study, data on soils of different texture were used. A sufficiently low error in the dot approximation (fitting-procedure) of the experimental data confirms the physical adequacy of the proposed system that includes the functions describing the coefficients of the Richards equation.

A description of five mathematical models of the water-retention capacity of soil is given, taking into account the hysteresis phenomena. A computational experiment was carried out with these models using data on sandy soil. The experiment consisted of: (i) tuning of the models (parameter identification) by the method of dot-approximation of experimental data on the main drying and wetting branches of the hysteresis loop using an optimizing algorithm; (ii) the predictive calculation of the scanning branches of the hysteresis loop; (iii) a comparison of the errors in tuning results and the predictive calculation using the Williams-Kloot criteria. The commensurate and sufficiently low errors in the adjustment of the models have been achieved. The differences in the calculation of the scanning hysteresis branches are revealed. The practical significance of the mathematical models presented is to ensure the calculation of precision irrigation rates. The application of such rates in irrigation farming will help to prevent excess moisture from flowing beyond the root layer of the soil under the influence of gravity and, thus, to minimize the losses (unproductive consumption) of irrigation water, fertilizers, meliorants and plant protection products, and also reduce the risk of groundwater contamination with agrochemicals and eutrophication of water bodies.

Für die Ableitung von Klimatrends aus langjährigen meteorologischen Datenreihen wird eine Methodik für ein nichtlineares Approximationsverfahren zufallsverteilter Ausgangsprozesse mathematisch hergeleitet. Bei der Verfahrenslösung wird dabei unter anderem auf die Spline-Approximation, die Greensche Funktion und die Spektralübergangsfunktion des Cauchyschen Problems zurückgegriffen. Über ein Diskretisierungsverfahren wird die für allgemein gehaltene Problemstellungen hergeleitete Methodik auf die speziellen Anwendungsbedingungen für Klimatrendberechnungen zugeschnitten. Die vorgestellte Methodik wird hinsichtlich ihrer Anwendung und der erzielten Ergebnisse auf der Grundlage unterschiedlich langer meteorologischer Datenreihen (40.. . 228 Jahre) zu Temperatur und Niederschlag von einem australischen und fünf europäischen Standorten überprüft und im Vergleich mit Literaturaussagen zum Klimatrendverhalten diskutiert.