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Light gray forest soils (Eutric Retisols (Loamic, Cutanic, Ochric)) were studied under a 20–25-yr-old fallow at the stage of overgrowing by meadow vegetation, pine, and birch. The studied area plot was confined to one element of topography, without morphological evidences of erosion processes, and with relatively homogenous soil texture. To assess the influence of fallow vegetation on the formation of soil organic matter (SOM), the plant cover was zoned according to vegetation indices calculated on the basis of remote sensing data. The k -means algorithms and the Random Forest method were used for this purpose. It was shown that there were statistically significant differences between the types of land cover in terms of the SOM stocks in the upper layer of the old-arable horizon with the specification of three and four clusters. The specification of three classes of vegetation on the fallow—coniferous woody vegetation, deciduous woody vegetation, and herbaceous vegetation—proved to be the most expedient; the correctness of their allocation was confirmed by the geobotanical survey of the territory. The results of a pairwise comparison of sites occupied by different types of fallow vegetation indicated that they significantly differ in the SOM stocks only in the uppermost 5-cm-thick layer of the old-arable horizon and only for the pair of coniferous woody and herbaceous vegetation. Differences in the accumulated humus stocks in the layer of 0–10 cm were statistically significant for the soils under deciduous and coniferous woody vegetation and under herbaceous and coniferous woody vegetation. There was no significant difference in this indicator between the soils under deciduous woody vegetation and herbaceous vegetation.

To create maps of the available forms of nutrients in arable land for implementation of systems of mineral fertilizers differential application, various approaches of interpolation by the ordinary kriging method were used. Maps of the availability were built according to the agrochemical analysis of mixed samples compiled from elementary plots of 5 ha. In the first case, the result of the agrochemical analysis was tied to the centroids of the elementary plots, and the interpolation was carried out using point ordinary kriging. In the second case, the indicator value was attached to blocks corresponding to the area of elementary sites. In this case, the interpolated cards were obtained using block kriging. It was shown that the application of various approaches to interpolation gives similar maps of spatial distribution. At the same time, maps obtained by ordinary point kriging are characterized by a more accurate forecast compared to maps obtained using block kriging. Therefore, the construction of interpolated maps of the availability of arable lands with nutrients based on the results of agrochemical analysis of mixed samples with data binding to the centroids of the sampling cells and compiling the combined samples is more preferable.

The differentiation of the old arable horizon (A p old ) by the content of mobile manganese (Mn) and copper (Cu) under fallow vegetation aged 15-20 years was studied. The accumulation of mobile Mn in the upper layer (0-10 cm), Cu in the 5-15 cm layer was observed. Linear modeling of the dependence of the content of Mn and Cu on alkali-soluble organic matter (OM P ) and pH showed the influence of only one significant predictor on each element. The content of Mn has a significant strong (R 2 adj.= 0.72) influence of OM P . The pH has a statistically significant, but weak (R 2 adj.= 0.19) effect on the Cu content. The difference in the patterns of differentiation is associated with the accumulation of mobile Mn by newly formed organic matter (OM) in fallows and the migration of mobile Cu with soluble fractions of OM in acidic soils. The study of changes in the mobility of heavy metals (HMs) in fallows is necessary to reduce environmental risks when changing land use, as well as to provide a realistic prediction of atmospheric carbon sequestration in fallow soils, taking into account changes in the level of toxicity of HMs. The relevance of these studies is associated with the fact that the removal of lands with heavy HM contamination from arable circulation in fallows is practiced more and more often.

The heterogeneous relief leads to an uneven distribution of nutrients in the redistribution of crop rotation fields, which creates the prerequisites for contamination of adjacent environments and introduces risks to the production of eco-products when applying mineral fertilizers calculated for the entire. Taking into account the uncertainty introduced by the relief into the spatial distribution of soil fertility indices increases the accuracy of the VRA maps. However, it is often moved beyond the interests of introducing precision farming technologies. In this work, using various methods of regression modeling, the characteristic of the variability of the properties of chernozem soils on two arable lands with different heterogeneous relief is given. In the area with heights from 80 to 140 m, the relief determines from 24 to 58% of the spatial variability of soil properties, and in the area with a flat relief (110-150 m), the proportion of the dispersion of soil parameters described by the relief is much lower and amounts to 13-30%. It is shown that, in areas with significant elevation differences, it is possible to use regression techniques to describe the spatial distribution of soil properties, while in leveled areas, regression models need to be supplemented with a geostatistical description of spatial heterogeneity.

The three most common techniques to interpolate soil properties at a field scale—ordinary kriging (OK), regression kriging with multiple linear regression drift model (RK + MLR), and regression kriging with principal component regression drift model (RK + PCR)—were examined. The results of the performed study were compiled into an algorithm of choosing the most appropriate soil mapping technique. Relief attributes were used as the auxiliary variables. When spatial dependence of a target variable was strong, the OK method showed more accurate interpolation results, and the inclusion of the auxiliary data resulted in an insignificant improvement in prediction accuracy. According to the algorithm, the RK + PCR method effectively eliminates multicollinearity of explanatory variables. However, if the number of predictors is less than ten, the probability of multicollinearity is reduced, and application of the PCR becomes irrational. In that case, the multiple linear regression should be used instead.

The concept of climate-optimized agriculture (COA) of the UN FAO implies the transformation of agriculture techniques in conditions of changing climate. It is important to implement a timely transition to the concept of COA and sustainable development of soil resources, accurate digital maps of spatial distribution of soils and soil properties are needed. Digital mapping of soil humus content was carried out on the territory of the national crop testing fields (NCTF) of the Republic of Tatarstan (Russian Federation) and the accuracy of the maps obtained was estimated.

Creating accurate digital maps of the agrochemical properties of soils on a field scale with a limited data set is a problem that slows down the introduction of precision farming. The use of machine learning methods based on the use of direct and indirect predictors of spatial changes in the agrochemical properties of soils is promising. Spectral indicators of open soil based on remote sensing data, as well as soil properties, were used to create digital maps of available forms of nitrogen, phosphorus, and potassium. It was shown that machine learning methods based on support vectors (SVMr) and random forest (RF) using spectral reflectance data are similarly accurate at spatial prediction. An acceptable prediction was obtained for available nitrogen and available potassium; the variability of available phosphorus was modeled less accurately. The coefficient of determination (R2) of the best model for nitrogen is R2SVMr = 0.90 (Landsat 8 OLI) and R2SVMr = 0.79 (Sentinel 2), for potassium—R2SVMr = 0.82 (Landsat 8 OLI) and R2SVMr = 0.77 (Sentinel 2), for phosphorus—R2SVMr = 0.68 (Landsat 8 OLI), R2SVMr = 0.64 (Sentinel 2). The models based on remote sensing data were refined when soil organic matter (SOC) and fractions of texture (Silt, Clay) were included as predictors. The SVMr models were the most accurate. For Landsat 8 OLI, the SVMr model has a R2 value: nitrogen—R2 = 0.95, potassium—R2 = 0.89 and phosphorus—R2 = 0.65. Based on Sentinel 2, nitrogen—R2 = 0.92, potassium—R2 = 0.88, phosphorus—R2 = 0.72. The spatial prediction of nitrogen content is influenced by SOC, potassium—by SOC and texture, phosphorus—by texture. The validation of the final models was carried out on an independent sample on soils from a chernozem zone. For nitrogen based on Landsat 8 OLI R2 = 0.88, for potassium R2 = 0.65, and for phosphorus R2 = 0.31. Based on Sentinel 2, for nitrogen R2 = 0.85, for potassium R2 = 0.62, and for phosphorus R2 = 0.71. The inclusion of SOC and texture in remote sensing-based machine learning models makes it possible to improve the spatial prediction of nitrogen, phosphorus and potassium availability of soils in chernozem zones and can potentially be widely used to create digital agrochemical maps on the scale of a single field.

Using the example of two crop rotation fields located in the chernozem zone of the Republic of Tatarstan, the spatial variability of soils agrochemical properties was assessed in terms of the application of precision farming technologies when applying mineral fertilizers. It is shown that the use of mixed samples of polygons with an area of 5 ha as an elementary sampling site is sufficient detail for a geostatistical description of the spatial heterogeneity of the agrochemical properties of chernozem soils.

This article describes the possibilities for applying the historical and biographical approaches during the blended physics courses taught by using the original electronic training courses. This article provides the original e-learning modules that were applied during the Pedagogical Education course at the Kazan Federal University in 2016-2017 and 2017-2018. The training process was based on several different thematic blocks. Survey was conducted after the success testing. This survey has revealed that the historical and biographical approaches to teaching physics by means of the MOODLE LMS allow the teachers to increase the interest not only to this course, but also to the history of its development. In percentage terms, 39.7% of students have noted an increased level of motivation for independent activity. The original online courses will come in handy to design new physics curricula for online teaching and learning in other countries.

A geochemical survey of lead contamination was conducted for soils of the Republic of Tatarstan. 1164 topsoil samples were collected from different soil types. The effect of land use type (natural, agricultural, urbanized) on lead content and mobility in the topsoil was evaluated. The method of regression trees was used to study the structure of interactions between lead and other soil factors (organic matter, physical clay, Fe, Mn, pH). The relative impacts of soil constituents on the content and mobility of lead in soils were assessed. The results showed that human activities were not the primary source of lead in the soils under natural and agricultural land use types. The correlations between content and mobility of lead and soil components are determined by the soil type and land use type