The article discusses territorial and structural changes in the productivity of grain and leguminous crops in the districts of the Republic of Belarus, as well as differences in the doses of mineral fertilisers for certain types from 2014 to 2018. The aim of the study is to determine the degree of influence of fertilisers on the dynamics of productivity for the studied period and to analyse the reasons for changes in the level of yields of grain and leguminous crops in the regions of the country. The work is based on statistical research methods – correlation and regression analysis of the relationship between mineral fertilisers and productivity were carried out. Correlation analysis showed a significant inverse linear dependence of the yield dynamics on the fertility score (correlation coefficient – 0.66), proving that more fertile soils lose in harvests of grain and leguminous crops are almost 2 times in comparison with less suitable land. Regression analysis confirmed the significant effect of mineral fertilisers (determination coefficient 56 %) on the final harvests of grain and leguminous crops. The novelty of the research lies in the mathematical formalisation of the stochastic dependence of the yield of grain and leguminous crops on the level of application of certain types of mineral fertilisers and the establishment of its linear character. With the help of GIS technologies, territorial differences in the effectiveness of the use of fertilisers for grain and leguminous crops in the administrative regions of the Republic of Belarus were established and three clusters of productivity in the country were identified – highly productive south-west (Grodno Region, Brest Region and adjacent districts of Minsk Region), productive south-east (Gomel Region and Mogilev Region with border areas of neighbouring regions) and low-productive north (Vitebsk Region with northern regions of Minsk Region and Grodno Region).
The article presents one of the possible options for improving the methodology for identifying zones of potential soil fertility. The necessity of using areal interpolation as the only method of geostatistical analysis that takes into account the area of input objects is proved. To check the data for a Gaussian normal distribution, it is necessary to use several verification methods, since when evaluating only statistical parameters, significant (in the case of phosphorus, abnormal) deviations were found, however, when evaluating histograms and quartile-quartile plots, it is necessary to bring the data to a normal distribution was relevant only for humus and phosphorus. The main advantages and disadvantages of the areal interpolation method are shown. With a significant deviation from the normal distribution, in the absence of built-in functions for automated reduction of data to the Gaussian distribution, one of the few ways can be the logarithm of the data. After zoning, it is necessary to perform a reverse translation to the original values for a representative visualization of the results. As a result of the selection of theoretical semivariograms-deconvolutions, the degrees of spatial dependence and optimal distances for the studied properties are determined. It is clear that the lag of acidity and potassium content is 1000 m and 1050 m, respectively. For phosphorus, it is 1300 m. For the humus content, the lag is much lower—440 m. The maximum autocorrelation distance is typical for potassium and humus—2330 and 1528 m; the minimum for phosphorus is 637. The reliability of the cartograms of agrochemical properties is confirmed by the calculated root-mean-square errors. The deviations of pH values are in the range of up to 0.15 units. The highest mean square error of interpolation is observed in weakly acidic soils. The error in the interpolated values of humus from the initial data is inherent in anthropogenically transformed soils. The root-mean-square error of phosphorus values can be estimated as insignificant. The largest errors in K2O—in isolated cases, they reach 120 mg/ha in the central and eastern parts of the region. The resulting map of potential soil fertility was used to determine the relationship with the granulometric composition of soils. A low level is observed on sandy and sandy loam soils, a high level—on loams. Also, the productivity is affected by the relief of the territory—in the dissected areas, productivity is lower than on the plains.
Gaussian geostatistical modeling by the Geostatistical Analyst tools of ArcGIS ArcMap using, stochastic modeling and a comprehensive spatial assessment of the variability of a number of soil properties in a key area were performed. According to the parameters of the third (asymmetry) and fourth (excess) orders, the normality of the distribution of acidity indicators, the content of mobile phosphorus compounds, moisture and specific surface of soils is proved. According to the sharpness of the distribution of data, the need for their conversion by indicators of phosphorus content and specific surface area is revealed. According to the quartile-quartile type charts, points are identified that are knocked out of the general sample for exclusion during further analysis. The analysis showed the presence of global trends in acidity and phosphorus content, described by polynomials of the 2nd and 1st orders, which indicates the presence of a determinate component in the general heterogeneity of properties, which was removed when selecting a mathematical model (semivariogram) and will be automatically taken into account when constructing the final cartograms. A large proportion of the total heterogeneity falls on the random spatially correlated mesocomponent, which is described by variography methods. When using the developed models in precision farming technologies, it is possible to take into account up to 85 % of the heterogeneity in humidity and up to 100 % in the phosphorus content. The existence of significant differences between the use of classical geostatistics and Gauss modeling, which allows smoothing and eliminating statistical heterogeneity, is proved. It is shown that standard deviation cartograms can be representative tools for developing monitoring networks and determining the need for an additional sampling point. Based on the parameters of the absolute values of the indicator, the location of the initial reference points, the lag value and standard deviation, a total monitoring network of 100 points was obtained.
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