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The relevance of the study is determined by the demand for a physically adequate mathematical description of the interactions of water in the soil to develop a model of soil moisture dynamics as the intellectual core of resource-saving technologies for precise irrigation farming. The aim of the work is theoretical substantiation and mathematical formulation of the hydrophysical functions of the soil, taking into account hysteresis. A description of three systems of soil hydrophysical functions is given. To verify and compare the systems, computational experiments were carried out using both the package of original software and “3305 Ida silt loam (> 15 cm)” soil data from the authoritative literary source – the Mualem catalogue. The parameters of the functions were identified by the method of point approximation of the experimental data on the main branches of the hysteretic water-retention capacity. Using these parameters, we calculated (i) predictive estimates for the values of the function of relative hydraulic conductivity; (ii) scanning branches of the hysteretic water-retention capacity; (iii) precise irrigation rate. The hysteresis phenomenon is not typical for the hydraulic conductivity as a function of the volumetric water content in the soil. The original functions of System 3 are recommended for use. The advantages of the proposed method for calculating the precise irrigation rate are shown. The benefit of each system is that the functions forming this system, namely the water-retention capacity and the relative hydraulic conductivity of the soil, have a common set of parameters. For the type of soil considered, in case of using the identical value of pre-irrigation soil moisture (179 [cm3 · cm-3]), both for calculating the precision irrigation rate and according to the “traditional” method, when moistening 50 cm soil layer, the total unproductive water consumption at irrigation rate 555 [m3 · ha-1] can reach 0.029 [cm3 · cm-3] or 140 [m3 · ha-1] in the calculated layer. At the same time, when applying precision standards, an excess of free moisture is not formed. It shows additional opportunities not only to save water during irrigation, especially in arid regions, but also to reduce the leaching of nutrients and agrochemicals outside the calculated soil layer and, accordingly, to reduce the additional environmental load on the surrounding area.

The aim of this study is to model the water-retention capacity and the relative hydraulic conductivity of the soil as a capillary-porous medium, as well as to verify the proposed models in comparison with the well-known world analogues. This aim is achieved by solving the following tasks: (1) description of the soil hydrophysical properties in the form of three systems of functions with corresponding sets of common parameters, (2) verification of these systems by evaluating the relative hydraulic conductivity and scanning branches of the water-retention capacity using parameters identified from the literature data on the main branches of the water-retention capacity hysteresis for the 3501 Rubicon sandy loam; (3) application of the equality of exponential parameter values in the calculations of the drying and wetting branches of hysteresis loop to eliminate the artificial “pump effect”; (4) study of the influence of the additive parameter on the errors of the point approximation of data on the main branches of the water-retention capacity, as well as on the errors of estimating the relative hydraulic conductivity and scanning branches of the water-retention capacity hysteresis; and (5) identification of significant differences between the errors of these estimates according to the Williams–Kloot criterion for choosing the best system of functions. Application of the proposed models seems to be preferable for solving the problems of irrigation farming, such as forecasting the water availability of crops and calculating precision irrigation rates.

The main aim of the current study was to present the abilities of widely used crop models to simulate four different field crops (winter wheat, spring barley, silage maize and winter oilseed rape). The 13 models were tested under Central European conditions represented by three locations in the Czech Republic, selected using temperature and precipitation gradients for the target crops in this region. Based on observed crop phenology and yield from 1991 to 2010, performances of individual models and their ensemble were analyzed. Modelling of anthesis and maturity was generally best simulated by the ensemble median (EnsMED) compared to the ensemble mean and individual models. The yield was better simulated by the best models than estimated by an ensemble. Higher accuracy was achieved for spring crops, with the best results for silage maize, while the lowest accuracy was for winter oilseed rape according to the index of agreement (IA). Based on EnsMED, the root mean square errors (RMSEs) for yield was 1365 kg/ha for winter wheat, 1105 kg/ha for spring barley, 1861 kg/ha for silage maize and 969 kg/ha for winter oilseed rape. The AQUACROP and EPIC models performed best in terms of spread around the line of best fit (RMSE, IA). In some cases, the individual models failed. For crop rotation simulations, only models with reasonable accuracy (i.e. without failures) across all included crops within the target environment should be selected. Application crop models ensemble is one way to increase the accuracy of predictions, but lower variability of ensemble outputs was confirmed.

Offshore development and growing prospects of commercial shipping in the Arctic pose the challenge of optimal ship routing in ice. Route selection in spatially distributed ice conditions significantly affects the voyage time and determines the efficiency of shipping. Most of the applied methods of ice routing solve the problem of a single vessel route selection without considering icebreaker support. At the same time, the real practice of ice navigation is closely connected with icebreaker assistance. It allows reducing the voyage time and fuel consumption, while having additional costs for icebreaker services. Such opposite trends set an optimization task that has not been studied in detail before. In this article, we presented the formulation of a Single Vessel and Icebreaker Assisted Ice Routing optimization problem in non-stationary ice conditions. We considered the icebreaker assistance as an integral part of the overall route optimization problem, and used the economic criterion to optimize both ship route and amount of icebreaker involvement. The article contains the adapted mathematical formulations of classical graph-based and wave-based routing problems in order to consider icebreaker assistance. To prove the practical applicability of these formulations, we developed special subject-oriented research software and implemented there both graph-based (Dijkstra, A*) and the wave-based ice routing methods. Using this developments, we conducted several case studies and made the analysis of strengthens and weaknesses of the alternative routing methods in case of ice operation. The results of the study may serve an additional step to the practical implementation of ice routing technologies and planning of icebreaker resources.

We developed a detailed simulation model of the Arctic marine transport system (MTS) for oil platform Prirazlomnaya. The model has a multidisciplinary nature and involves: sub-models of various transport and technological processes; stochastic weather generator to obtain time series of 15 environmental parameters; and contextual planning algorithm to build voyage plan considering several types of ships and cargoes. We used a significant amount of real operational data to identify model parameters and to prove its statistical reliability. Our main scientific task is to investigate the interaction of various processes of a different nature, while the practical aim is to find a set of measures to increase the efficiency of MTS. The results of the study reveal many examples of the mutual interaction of various processes that need to be considered at the design stage to avoid technical mistakes. The study formed a basis for making managerial decisions at the top level of Gazprom Neft Shelf Company.

An abnormal non-monotonic shape of production function (response of obtained yield to increasing rates of mineral nitrogen fertilizers) has been observed in experimental field trials. Often, the observed effect (an inflection point, or intermediate plateau or even local undershoot of the “yield-fertilization” curve) is treated as a test distortion and will be ignored or sorted out. This article presents the authors’ efforts to interpret and to explain similar phenomenon by means of investigating two mechanistic crop simulation models – AGROSIM and AGROTOOL. It is demonstrated that an imitation model can be used as a valuable tool of scientific research, allowing for the hypothesising of alternative understandings of non-trivial natural phenomena.

Investigation and management of the productivity of agricultural landscapes in regional scale play a significant role in solving the most important problems of sustainable development of the region under interest. A modern wide-distributed and powerful scientific tool for analysis, monitoring, and decision support in agronomy and agroecology is crop simulation modelling. At the same time, the simplest calculation methods (empirical regression models) are traditionally used for the predictive estimation of the productivity of agroecosystems over rather large areas (region-wide). The article intends to fill such gap, presenting the author’s view on the specifics of using dynamic models for regional (mesoscale) calculations. The issues of information support of models in the regional projects as well as the aspects of program implementation of the infrastructure of corresponding computer experiments are considered. We also discuss several prospective use cases for crop-model-based regional projects and propose the methods of processing and presentation the obtained results in a GIS-environment. The practical applicability of the described methodology is demonstrated on the example of calculations of spring barley production processes in the Republic of Crimea.

An agricultural landscape is a section of a region shaped by its natural landscape features primarily involving agricultural land use and land management. Intensive anthropogenic activities have left a permanent mark on agricultural landscapes, which have been developed over hundreds of years. Agricultural landscapes constitute a spatiotemporal structure. Hence they represent a complex system in which a large number of processes occur continuously that, due to their temporal dynamics, lead to constant changes in the state of the system. Traditional experiments are inappropriate for the impact assessment of anthropogenic and naturally occurring changes in agricultural landscapes. The only option here is to conduct virtual landscape experiments at the computer level. To this end, a relevant set of spatial, quantifiable landscape indicators is defined that can be used to map the landscape on the computer. Building on the extensive expertise in agricultural landscape research, indicators can be mapped using validated and robust models and their dynamics described involving temporal aspects. Various model types can be used in this process. Special simulation environments involving the use of spatial data and accounting for possible land use and global changes enable forward-looking scenario simulations to provide answers to the question of the sustainability of agricultural land use systems. Decision support systems (DSS) that exploit the latest possibilities offered by information technology, statistics and artificial intelligence provide the framework for integrating models, spatial data concerning the state of the landscape and scenario data, simulation techniques as well as tools for interpreting and visualising results. Such DSS are also the basis for quantifying the complex impact of site conditions, changes in land use or management, and of potential climate change on individual landscape parameters or landscape indicators. A number of examples show how indicator-based models of different types can be used to assess the impact and sustainability of land use systems on a landscape scale. As a prerequisite for the development and validation of integrated dynamic landscape models, more long-term ecological studies and monitoring systems are required. This also means that more resources are necessary to support these activities. The use of models and virtual simulation experiments within a DSS framework at the computer is a very promising way of finding suitable site-specific complex measures for the adaptation of agriculture to climate change.

Development of new offshore projects in the Arctic begins with comprehensive analysis of Marine Transport System’s (MTS) performance. At the same time researchers with different professional orientation (shipbuilders, logisticians, economists and managers etc.) are often have narrow view while making their investigations of MTS, focusing mostly at corresponding familiar sides of the system. It leads to specific “disproportional” description of MTS’s when some components considered in detail but other are out of investigation that in some cases may result in inaccurate conclusions. This makes authors sure that the only proper approach to investigate complex arctic MTS should be multidisciplinary. Article contains the description of integrated R&D project fulfilled at State Krylov Research Centre and devoted to realization of multidisciplinary methodology and corresponding software for arctic MTS design and analysis. Integrated software solution is based on object-oriented paradigm and combines such scientific areas as geographic information systems (GIS), shipbuilding disciplines, discrete event and agent-based simulation models. Theoretical base of the solution and its architecture envelops the following subject fields: ship design and fleet sizing, resistance and propulsion of ships including ice-going capabilities, vessel routing in ice, scheduling, downstream and upstream logistics, navigation process simulation, environment conditions stochastic modeling, operation research, queue theory, economy and management. Software has a modular structure with open and expansible architecture, which makes possible to add new functionality and upgrade existing program blocks in accordance with demands of specific project. Simulation model serve as the center of multidisciplinary integration because this technology allows reproducing behavior of different objects of MTS under dynamic conditions. Realized in AnyLogic ® framework simulation model replicates vessel operation process according to individual schedule generated by special planning component. Vessel’s activities simulated in modeled time with consideration of special aspects of operational planning and resolving accidents. Main model also includes specialized sub-models that provide opportunity to describe many local dynamic essences such as processes of offshore drilling and production, freeze-up of channel in fast ice, different ship interaction aspects, “weather windows” in ports etc. Number of instances are also given in the article, they allows to conclude that adequate and consistent model of MTS working in heavy ice-conditions or having complex organization scheme could be obtained only by means of simulation modeling under multidiscipline approach.

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.

Three systems of functions are used to describe the water-retention capacity and the ratio of the hydraulic conductivity of the soil to the moisture filtration coefficient (relative hydraulic conductivity of the soil). Each of the three systems uses an appropriate set of parameters. These parameters are common to each pair of functions that make up the corresponding system. The parameters of the first system of functions are formal in nature and are used in the Mualem-Van Genuchten method. The parameters of the second and third systems have a physics-statistical interpretation. The main purpose of the considered systems is to predictively evaluate the values of the relative hydraulic conductivity function using parameters identified by the point approximation of data on the water-retention capacity of the soil. Using the soil example «3304 Touchet silt loam» from the Mualem catalog, three systems of functions are compared. In order to identify significant differences between the errors of the compared function systems with respect to the point approximation of data on water-retention capacity, as well as for predictive estimates of the values of the function of the relative hydraulic conductivity of the soil, the Williams-Kloot test is used. The influence of the additive parameter describing the capillary pressure of the «air inlet» on the errors of the second and third systems is estimated. The results of the study indicate the advantages of the second and third systems over the first system, the functions of which are used in the Mualem-Van Genuchten method. The third system is formulated in the form of fairly simple relationships using elementary mathematical functions and is recommended for modeling the hydrophysical properties of the soil and solving problems of ameliorative farming.

The most important of the hydrophysical properties is the water-retention capacity of the soil. This property is formulated as a relationship between the volumetric moisture of the soil and the capillary pressure of soil moisture. Three hysteresis models of soil water-retention capacity are presented. The parameters were identified by point approximation of experimental data (from an authoritative literary source) on the main (boundary) drying and wetting branches of the soil «2003 Silt of Nave-Yaar» using the «SoilHysteresis-v.1.0» computer program developed by the authors. Applying the condition of equality of the values of the exponential parameter for the branches of draining and moistening eliminates the undesirable (methodical) «pump effect». A comparative analysis of hysteresis models based on the identification of significant differences between the errors of the point approximation of the experimental data by the Williams-Kloot test. The advantages of models in which an additional additive parameter is used are revealed. The use of physically justified models of hysteresis of the water-retention capacity of the soil has prospects in the development and application of resource-saving technologies in precision reclamation agriculture.

Purpose of research was to develop technological basis for obtaining related remote sensing data and ground-based observations of high-level accuracy and reliability with its subsequent introduction into the monitoring system of agricultural lands state. Introduction of digital technologies will improve the quality of agricultural lands monitoring and accuracy of criterion assessments of parameters of crop condition and fertility levels, including capacity to localize and map degraded soil processes. The prerequisites for the transition to digital technologies in agriculture were studied. Existing systems for monitoring and forecasting the condition of crops are considered. The structure of the system of digital agricultural production, its components and relations between them are determined.

A system of improved hydrophysical functions describing the water-retention capacity and hydraulic conductivity of the soil is presented. The mathematical description of the functions is based on the physical ideas about the structure of the pore space of the soil and the capillarity phenomenon. For both functions, the parameters are common. The advantages of the presented functions are described in comparison with the most well-known world analogues, which are used in the Mualem-Van Genuchten method. An example of estimation of the ratio of the hydraulic conductivity of a soil to the filtration coefficient of moisture according to the data on the water-retention capacity of a soil of sandy particle size distribution is given. The presented system of hydrophysical functions of the soil can be used to justify the development and resource-saving technologies in irrigation and drainage construction and irrigation agriculture. Practical application of applied models based on these functions will significantly reduce the energy intensity of the operation of irrigation and drainage systems and the production of agricultural products.

A new geological epoch has begun—the Anthropocene. Huge anthropogenic transformations of terrestrial landscapes over the past five decades have forced its declaration. Exploring of interaction of humans with nature in general, and with landscapes in particular, can be characterised properly by the terms ‘landscape research’ and ‘landscape science’. Landscape science has been a traditional scientific discipline of geography. This is the case in Russia, whilst the terms geo-ecology and landscape ecology have become established in the English-speaking scientific community. As landscapes are multifunctional, highly complex systems, landscape research is a platform for disciplinary, interdisciplinary and transdisciplinary research. Landscape research in the Anthropocene must aim to combine landscape sustainability with high quality and productivity. This mission is in accord with the Sustainable Development Goals of the United Nations and the provisions of the Landscape Convention of the European Council. It includes halting landscape degradation, developing cultural landscapes and maintaining semi-natural landscapes. Clean water and air, fertile and healthy soils for food and other ecosystem services and a green and biodiverse environment are attributes of landscapes for the survival and well-being of humans in coexistence with nature. Landscape research must generate knowledge, innovations and responsible decision rules for achieving these aims. Big data gathering and scenario modelling are important for knowledge generation in a globalised world. International long-term experiments, observatories and monitoring systems will deliver data for comprehensive ecosystem models and decision support systems. Technical innovations must be imbedded in cultural solutions for the evolvement of landscapes. Springer International’s new book series ‘Innovations in Landscape Research’ aims to support better understanding, monitoring and managing landscapes. It contains a multitude of approaches and data. Some focus is on technical innovations for agri-environmental monitoring, on land and water management and its implications for landscape sustainability. Authors present novel tools for ecosystem modelling and forecasting of landscape processes, and on creating knowledge, rules and approaches for handling the multifunctionality of landscapes. The coming book series may serve as a knowledge, data and communication basis for informed decisions regarding the development of landscapes. It will enlarge our horizon and field of action by building bridges between scientific communities, scientific disciplines, and researchers and citizens.

Requirements for the infrastructure and functionality of dynamic models of the production process of agricultural plants, which are necessary for building computer systems to support long-term solutions in agriculture and land management, are described. The extent to which domestic and foreign developments meet these requirements is shown.

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.

The improved method for estimating the effective supply of productive moisture in soil is based on soil-hydrological indices. The estimation is carried out using the software based on the mathematical model with physically interpreted parameters. The model is developed in the framework of the concepts of capillarity and lognormal distribution of effective pore radii and describes the main and scanning curves of the hysteresis of soil water-retention capacity. The presented example demonstrates the advantage of the improved method that enables minimizing water wastage at crop irrigation.

Basic principles of the multidisciplinary approach to arctic marine transport systems (MTS) design and analysis are described in the article. The main idea of the approach is to synthesize geographic information system (GIS) technologies, different shipbuilding disciplines, fleet planning instruments and agent-based dynamic simulation models in an integrated software framework on the basis of object-oriented programming. Vessel operation is described as the movement and interaction of independent ships in GIS environment within the framework of the simulation model. MTS operation combines vessel operation itself (routing, determination of speed and fuel consumption, icebreaker escort, etc.) with plenty of external entities (port infrastructure, ice channel freezing process, offshore platform operation, etc.) that could be described as systems with comprehensive logic and physical behavior. Such integration provides a new quality of MTS simulation that allows considering complex interconnection of various subsystems and all the important details of each MTS project. The outline of the program framework to realize such an approach is given, and two case studies are described to demonstrate its capabilities and feasibility.

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.

Some problems of decision support systems in computer aided agriculture are discussed. The main focus is made on collaborative model development, including model decomposition issues and implementation of generic frameworks for polyvariant model use. A current state and prospective ideas for improvement of modeling infrastructure suitable to perform multi-factor computer experiments with existing crop simulation models are presented.

A method is proposed to calculate water irrigation rates for crops that considers hysteresis in the volumetric water content (θ)-water pressure head (ψ) relations, including scanning paths, by the method of point approximation. Three θ(ψ) models are described and computational experiments were carried out using data from literary sources on the hydrophysical properties of soils with different textures. The error analysis of the point approximation of the main branches and the predictive calculation of the scanning branches of the hysteresis loop were carried out. The practical significance of the research lies in the possibility to calculate the precise irrigation rates for crops. The use of such standards minimizes unproductive spending of irrigation water, fertilizers, ameliorants and plant protection products, as well as prevents the pollution of natural waters with agrochemicals and reduces the risk of eutrophication of water sources.

Zusammenfassung Die Entwicklung der Mikroprozessoren und die damit einhergehende Massentauglichkeit der modernen Kommunikationsmedien haben dazu geführt, dass Individuen Gespräche vermehrt kulturübergreifend - und über Ländergrenzen hinweg - über das Internet führen können. Als moderne Kommunikationsform etabliert sich seit einigen Jahren immer weiter die Videokonferenz. Ihr didaktisches Potenzial wurde allerdings aus (fremd-)sprachwissenschaftlicher und (fremd-)sprachdidaktischer Sicht bislang verhältnismäßig wenig diskutiert.1 Wir wollen mit diesem Beitrag einen allgemeinen Überblick zur Forschungslage über den Nutzen von Videokonferenzen im Unterricht geben und der Frage nachgehen, ob Videokonferenzsoftware und Kontaktvermittlungsportale wie »Skype in the classroom« Möglichkeiten bieten, die kulturübergreifende Videokommunikation für den DaF-Bereich nutzbar zu machen.

Ведущая роль в балансе питательных веществ и сохранении плодородия почвы принадлежит биологическим факторам и в том числе – фиксации атмосферного азота симбиотическими и свободноживущими диазотрофами. Наиболее значимым для практики сельского хозяйства процессом является азотфиксация, осуществляемая клубеньковыми бактериями в симбиозе с бобовыми растениями. Создание специфических севооборотов с участием бобовых культур за счет использования бобово-ризобиальных систем составляет основу «биологического земледелия». Поэтому включение алгоритмов симбиотической азотфиксации в математические модели продукционного процесса бобовых культур, а следовательно, и в комплексные модели расчета системы сельскохозяйственных севооборотов с участием бобовых культур, представляется важной практической задачей. Исследуются и сравниваются методы моделирования процесса и количественной оценки биологической фиксации азота бобовыми, зернобобовыми и кормовыми культурами в полевых условиях, которые представлены в российской и зарубежной литературе. Сопоставляются различные схемы и функции, которые используются для моделирования реакции азотфиксации на биотические и абиотические факторы, выявляются их относительно сильные и слабые стороны. Кроме того, анализируются расхождения в существующих моделях и предлагается вариант усовершенствования модели биологической азотфиксации в комплексной модели продукционного процесса бобовых культур.DOI 10.14258/izvasu(2015)1.1-34, The leading role in balance of nutrients and preservation of soil fertility belongs to biological factors which includes fixation of atmospheric nitrogen by symbiotic and free-living diazotrophs. The most significant process for agricultural practice is the nitrogen fixation which is performed by nodule bacteria in symbiosis with bean plants. Specific crop rotations with participation of bean cultures due to use of bean rizobium systems make a basis of "biological agriculture". Therefore, inclusion of symbiotic nitrogen fixation algorithms in mathematical models of production process of bean cultures, and, therefore, and in complex models of calculation of agricultural crop rotations systems with participation of bean cultures, is an important practical task. In this article, we explore and compare methods of modeling and quantitative estimation of biological nitrogen fixation by grain and forage legumes in the field environment. Different schemes and functions used to simulate the response of nitrogen fixation to biotic and abiotic factors are compared and analyzed for their relative strengths and weaknesses. Besides, divergence in current models is analyzed, and an improvement of the biological nitrogen fixation model in a complex model of production process of bean cultures is proposed.DOI 10.14258/izvasu(2015)1.1-34

We consider the dynamics of a lattice of phase oscillators with a nearest-neighbor coupling. The clustering hierarchy is described for the case of linear distribution of natural frequencies. We demonstrate that for small couplings prior to the appearance of the first cluster the dynamics is quasi-Hamiltonian: the phase volume is conserved in average, and the spectrum of the Lyapunov exponents is symmetric. We explain this unexpected for a dissipative system phenomenon using the concept of reversibility. We show that for a certain coupling a smooth transition from the quasi-Hamiltonian to the dissipative dynamics occurs, which is a novel type of chaos–chaos transition.

A mathematical model of the hysteresis of the water-retention capacity of the soil is proposed. The parameters of the model are interpreted within the framework of physical concepts of the structure and capillary properties of soil pores. On the basis of the model, a computer program with an interface that allows for dialogue with the user is developed. The program has some of options: visualization of experimental data; identification of the model parameters with use of measured data by means of an optimizing algorithm; graphical presentation of the hysteresis loop with application of the assigned parameters. Using the program, computational experiments were carried out, which consisted in verifying the identifiability of the model parameters from data on the main branches, and also in testing the ability to predict the scanning branches of the hysteresis loop. For the experiments, literature data on two sandy soils were used. The absence of an "artificial pump effect" is proved. A sufficiently high accuracy of the prediction of the scanning branches of the hysteresis loop has been achieved in comparison with the three models of the precursors. The practical importance of the proposed model and computer program, which is developed on its basis, 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 and, thus, minimize the unproductive loss of irrigation water and agrochemicals, as well as reduce the risk of groundwater contamination and natural water eutrophication.

A method for nonlinear approximation of stochastic processes is derived for calculation of climatic trends of long-term meteorological data sets. The method mainly makes use of spline approximation, Green's function and spectral transfer function of the Chauchy problem. Generally applicable for a wider range of problems the method is specified for special conditions typical for meteorological and climatological data. The applicability of the method described is examined on the basis of long-term (40... 228 years) meteorological data sets for temperature and precipitation data from one Australian and five European locations. The results obtained are discussed in comparison with climate trend results from temperature and precipitation data taken from literature.

Typical use cases of the crop simulation models consist of such operations as parametric identification, yield forecast and optimization, analysis of different technologies etc. All these tasks relate to multiple running of the model with several variants of input parameters and can be automated by means of polyvariant crop simulation framework which allows performing the multiple running in the batch mode. Such framework has been developed in our laboratory. It makes it possible to register any crop simulation model in the database and to perform several typical operations with it. As a result we present the wide-functional computer system for planning and automation of multi-factor computer experiment with arbitrary dynamic crop models.

We analyze the bifurcation of an attractor in a system of multiplicatively coupled maps. It is shown that the phenomenon can be characterized by on-off intermittency and it is rigorously described by the on-off intermittency in the presence of noise through the concept of a virtually invariant manifold. Presenting numerical results which conform our claims, we elucidate the role of on-off intermittency in bifurcation phenomena.

We examine the influence of noise on the propagation of harmonic signals with two frequencies through discrete bistable media. We show that random fluctuations enhance propagation of this kind of signals for low coupling strengths, similarly to what happens with purely monochromatic signals. As a more relevant finding, we observe that the frequency being propagated with better efficiency can be selected by tuning the intensity of the noise, in such a way that for large noises the highest frequency is transmitted better than the lower one, whereas for small noises the reverse holds. Such a noise-induced frequency selection can be expected to exist for general multifrequency harmonic signals.

We consider the collective dynamics in an ensemble of globally coupled chaotic maps. The transition to the coherent state with a macroscopic mean field is analyzed in the framework of the linear response theory. The linear response function for the chaotic system is obtained using the perturbation approach to the Frobenius-Perron operator. The transition point is defined from this function by virtue of the self-excitation condition for the feedback loop. Analytical results for the coupled Bernoulli maps are confirmed by the numerics.