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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.

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.

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.

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.

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.

Возрастающий спрос на сельскохозяйственную продукцию обычно приводит ко все большему применению удобрений. Азот, содержащийся в удобрениях и не усвоенный сельскохозяйственными культурами, может поступать в атмосферу в виде парниковых газов либо попадать в почвенные воды, приводя к экологическим последствиям. Наряду с применением азотных удобрений необходимы альтернативные источники азота для создания более устойчивых систем в сельском хозяйстве. Бобовые культуры обладают потенциалом для реализации такой потребности благодаря своей уникальной биологической способности фиксировать азот из атмосферы, что благоприятно воздействует не только на сами бобовые, но и на культуры в севообороте. Исследуются и сравниваются факторы окружающей среды, влияющие на сложный процесс биологической азотфиксации бобовых культур: температуру, содержание влаги, концентрацию азота, рН в корнеобитаемом слое почвы, питание растений, включая субстраты углерода (С) и азота (N) в корнях, и генетическую вариацию потенциальной способности бобовых культур к азотфиксации. Конечная цель исследования – разработка модели симбиотической азотфиксации бобовыми культурами. Задача же данного раздела сфокусирована на том, как азотфиксация бобовых культур реагирует на условия окружающей среды и на содержание субстратов углерода и азота в растениях.DOI 10.14258/izvasu(2015)1.1-33, Increasing demand for agricultural production typically results in greater fertilizer application. Nitrogen (N) in fertilizers or manures which is not taken up by crops can be released into the atmosphere as nitrogenous greenhouse gases or leached into ground water, with resulting environmental implications. Rather than relying purely on application of N fertilizer, alternative N sources are needed to help develop more sustainable farming systems. Legumes have the potential to fulfil this requirement due to their unique ability to fix N biologically from the atmosphere, benefiting not only the legumes themselves, but also the intercropped or subsequent crops. In this paper, we explore and compare the environmental conditions influencing complex process of legume biological nitrogen fixation such as temperature, water content, N concentration, root zone рН, plant nutrient status including C and N substrates in roots, and a genetic variation in potential N fixation capacity. The ultimate goal of the research is to develop a model of legume biological nitrogen fixation. In this section, we focus only on how legume biological nitrogen fixation responds to environmental conditions and plant C and N substrates.DOI 10.14258/izvasu(2015)1.1-33

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.

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

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.

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.