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UDC 631.474
USE GEOSTATISTICS TOOLS FOR EVALUATION THE SPATIAL DISTRIBUTION OF
ACID-SOLUBLE COPPER IN THE SOIL
T. N. MYSLYVA
УО «Белорусская государственная сельскохозяйственная академия», г. Горки, Республика Беларусь, 213407, e-mail: byrty41@yahoo.com
(Поступила в редакцию 17.03.2020)
This article reflects on the problem of the possibility of using geospatial statistics methods to assess the spatial distribution of acid-soluble copper in soil and applying geostatistical analysis methods to form management zones with different levels of acid-soluble copper in the soil within the land use of an agricultural enterprise. The results of assessing the nature of the spatial distribution of data on the content of acid-soluble copper in the soil by applying the functionality of the tools of the "Analysis of structural patterns" and "Calculation of clustering" modules of ArcGIS 10.5 are given. In particular, the data grouping analysis is performed using the k-means algorithm. The distance from which it is necessary to begin the analysis of spatial autocorrelation was 550 m, while the magnitude of the increment (lag), established empirically, is 250 m. The presence of reliable clustering of acid-soluble copper in the soil was established (the actual value of the global Moran index is 0.21802; p-value> 2.58). Three management zones with different Cu contents were identified, with an area of 2395.13 ha (average acid-soluble copper content 1.75 mg/kg), 3270.97 (average acid-soluble copper content 2.1 mg/kg) and 2540.31 ha (average the content of acid-soluble copper 2.52 mg/kg). The obtained information can be used to develop task maps for the differential application of mineral fertilizers during the introduction of precision farming. The presence of a reliable trend in increasing the copper content in the central part of land use for zone 1 was established; in a decrease in the copper content in the north-south direction for zone 2 and an increase in its content in the north-south and west-east for zone 3. The obtained information can be used to develop task maps for the differential application of micro-fertilizers during the introduction of precision farming.
Key words: acid-soluble copper, geospatial statistics, management zones, soil, clustering, Moran index, Getis-OrdGi, trend.
В статье рассматривается проблема возможности использования методов геопространственной статистики для оценки пространственного распределения кислоторастворимой меди в почве и применения методов геостатистического анализа для формирования менеджмент-зон c различным уровнем содержания в почве кислоторастворимой меди в пределах землепользования сельскохозяйственного предприятия. Приведены результаты оценки характера пространственного распределения данных о содержании в почве кислоторастворимой меди посредством применения функциональных возможностей инструментов модулей «Анализ структурных закономерностей» и «Расчет кластеризации» ArcGIS версии 10.5., в частности, выполнен анализ группирования данных с использованием алгоритма k-средних. Величина расстояния, с которого необходимо начать анализ пространственной автокорреляции, составила 550 м, тогда как величина приращения (лага), установленная эмпирическим путем, - 250 м. Величину лага рекомендуется использовать при создании мониторинговой сети наблюдений за содержанием Cu. Установлено наличие достоверной кластеризации содержания в почве кисло-торастворимой меди (фактическая величина глобального индекса Морана составляет 0,21802; р-значение > 2,58). Идентифицированы три менеджмент-зоны с различным содержанием Cu, площадью 2395,13 га (среднее содержание кислоторастворимой меди 1,75 мг/кг), 3270,97 (среднее содержание кислоторастворимой меди 2,1 мг/кг) и 2540,31 га (среднее содержание кислоторастворимой меди 2,52 мг/кг). Установлено наличие достоверного тренда в увеличении содержания меди в центральной части землепользования для зоны 1; в снижении содержания меди в направлении север-юг для зоны 2 и увеличении его содержания на севере-юге и западе-востоке для зоны 3. Полученная информация может использоваться для разработки карт-заданий по дифференцированному внесению микроудобрений при внедрении элементов точного земледелия.
Ключевые слова: кислоторастворимая медь, геопространственная статистика, менеджмент-зоны, почва, кластеризация, индекс Морана, Getis-OrdGi. тренд.
Introduction
Copper is one of the most important trace elements involved in oxidation processes, it enhances respiration rate, promotes protein synthesis and is a part of 19 enzymes that belong to copper-containing proteins (ascorbin oxidase, urease, diphenyl oxidase, ceruloplasmin) [1]. Its content in the soil primarily depends on the mineralogical and granulometric composition of the parent rocks, the type of soil-formed processes, the chemistry and level of groundwater, the quantity and quality of the organic matter of the soil, as well as the intensity of anthropogenic activity [2]. The main parent rocks of Belarus are traditionally poor in copper, especially fluvioglacial and ancient alluvial sand deposits, as well as weathering products of crystalline rocks. In this regard, soils formed on such rocks have low reserves of gross and mobile copper.
Over the past 15 years, the weighted average content of acid-soluble copper in the soils of Belarus has decreased from 1.89 mg / kg to 1.83 mg / kg, and the proportion of the area of the first and second groups with a Cu content of less than 3.0 mg / kg ranges from 66.5 -97.5 % depending on the region. The soils of improved hayfields and pastures are also poor in mobile copper and they need dressing with copper-containing micronutrient fertilizers in 80.8% of the area. Arable soils in the Mogilev region are characterized by a predominantly low (56.1% of the area) content of mobile forms of copper, and soils highly provided with cop-
per have a small distribution (5.1 %). In the Goretsky district, 58.9 % of arable land has a copper content in the range of 1.51-3.0 mg/kg and only 2.8 % contains more than 5 mg/kg of this element [3].
The application of the capabilities of GIS analysis is the most optimal for the search for spatial patterns in the distribution of certain soil indicators and the relationships between them. However, in modern practice of agrochemical monitoring carried out both in the Republic of Belarus and in neighboring countries, soil surveys are provided without precise positioning, therefore, it is difficult to say with certainty that the samples were taken at the same place during repeated observation. This practice makes it impossible to reflect the real dynamics of soil indicators within land use, which subsequently leads to incorrect results when calculating the doses of fertilizers and chemical reclamants, and directly affects both the economic activity of the agricultural enterprise and the environmental situation within the agricultural landscape [4].
Main part
The purpose of the study is to analyze the possibility of using geospatial statistics methods to assess the spatial distribution of acid-soluble copper in the soil of arable land of the Republican Unitary Enterprise "Educational Experimental Farm of BSAA" for the formation of management zones when introducing elements of the precision farming system.
The objectives of the study include the following:
1) to perform data grouping analysis using the k-means algorithm;
2) to determine the minimum and maximum distances of the neighborhood of the search for the nearest neighborhood, making it possible to choose the optimal value of the neighborhood of the searchwhen modeling the spatial distribution of acid-soluble copper;
3) to calculate the global Moran index, which allows to determine whether there is a clustering phenomenon in relation to attributive data on the content of acid-soluble copper in the soil;
4) to determine the overall Getis-OrdG index for assessing the overall structure and trend of geodata, as well as the degree of clustering of high and/or low sample values of acid-soluble copper;
5) to calculate the Getis-OrdG * index, which allows to establish the presence of data clustering with high and low values;
6) to form management zones for the content of acid-soluble copper in the soil.
The studies were carried out on the territory of Gorky district of Mogilev region within the land use of RUE "Educational Experimental Farm of BSAA" on an area of 8206.41 thousand hectares. The data about the content of acid-soluble copper obtained from the agrochemical survey of the territory of RUE "Educational Experimental Farm of BSAA", executed in 2018 by the Mogilev Regional Design and Exploration Station of Agrochemicalization, were used for the analysis. The soil cover of the study area is represented by Sod-podzolic, Umbric Retisols (WRB, 2016); Eutric Podzoluvisol (FAO, 1988) [5].
The spatial distribution analysis was performed using the functionality of the Spatial Statistics Tools of ArcGIS version 10.5. Statistical characteristics of a sample of data on the content of acid-soluble copper used to perform geostatistical analysis were as follows: minimum value - 0.76 mg/kg; maximum value - 4.15; mean - 2.14; median value - 2.09; standard deviation - 0.62 mg/kg; coefficient of variation - 28.9%; kurto-sis - 3.26; skewness - 0.49.
The global Moran (I) index was calculated by the formula (1) [6]:
where n denotes the number of units in the sample; Wj denotes the weight of the spatial relationship between the i-th and j-th sampling units; yi denotes the attribute value for the i-th sample unit; y denotes the sample mean value of the attribute.
The Getis-OrdGi * index value was counted using the formula (2) [6]:
where Xj denotes the attributive value of the object of observation; Wij denotes spatial weight between objects i and j; n denotes the total number of objects.
Grouping analysis is an effective tool for studying geospatial data that performs the classification procedure, the purpose of which is to search for natural clusters in the data. With its help, data on soil parameters are distributed on a given number of groups in which all indicators are most similar to each other, while the
groups themselves are as different as possible from each other. Using the analysis of grouping it is possible to establish the presence within the land use of homogeneous zones with a specific set of parameters. In our case, a "set of parameters" means the intervals of the content of copper in the soil according to the gradation given in the guidelines for conducting large-scale agrochemical and radiological surveys of the soils of agricultural lands of the Republic of Belarus [7]. Since the minimum copper content in the soil was 0.76 and the maximum was 4.15 mg/kg, three groups of clusters were identified in the analysis of grouping. The localization of the selected clusters is shown in Figure 1, and their main characteristics are described in Table 1. The maximum area of the selected clusters has group 2 - 3928.25 ha, while group 1 has a cluster area of 2792.79, and group 3 - 1485.37 ha.
Table 1. Statistical characteristics of identified cluster groups according to the content of acid-soluble copper in the soil
Group of clusters Mean Sd Minimum value Maximum value R2
1 1.51 0.26 0.76 1.86 0.32
2 2.22 0.23 1.87 2.67 0.24
3 3.12 0.36 2.68 4.15 0.43
It is necessary to add that the value of R2 reflects the extent to which the variation in the source data was saved during the grouping process, respectively, the more R2 is for a certain variable, the better this variable distinguishes between values.
Average content of Cu:
| group 1 - 1.51 mg/kg IB group 2 - 2.22 mg/kg B group 3-3.12 mg/kg
Scale 1 : 100 000
Fig. 1. Spatial localization of identified groups of acid-soluble copper content clusters within the land use of the RUE «Educational Experimental Farm of BSAA» (a - copper content according to the generally accepted classification; b - identified cluster groups)
In general, we can state the following: 1) the analysis of grouping allows to establish the presence of homogeneous zones with a certain content of acid-soluble copper within the land use; 2) the selected groups of clusters give a certain idea of the nature of the spatial distribution of copper within the study area, but are unsuitable for establishing the boundaries of management zones.
Performing cluster analysis, in contrast to grouping analysis, allows not only to establish the presence of clusters and to assess the reliability of clustering, but also to analyze clusters, identify outliers of high and low values and establish the boundaries of management zones with different content of copper in soil. To
determine the value of a fixed distance or the minimum distance of a neighborhood searching for a neighborhood between the values of the content of acid-soluble copper in the soil, the tool "Incremental Spatial Autocorrelation" was used. The value of the initial (distance at which it is necessary to start the analysis of spatial autocorrelation) and incremental (distance by which it is necessary to increase the initial distance at each subsequent iteration) distances were set in the dialog box of this tool. As a result of the calculations, the distance at which it is necessary to begin the analysis of spatial autocorrelation was 550 m, while the magnitude of the increment (lag) established empirically is 250 m. Ten distance intervals evenly distributed throughout the extent were highlighted by performing incremental spatial autocorrelation. The global Moran index was calculated for each interval and the interval for which this index would be the largest was recommended as the optimal distance for the search neighborhood. As a result, we got a graph on which the minimum and maximum distances of the neighborhood of the search for the nearest neighborhood are marked (Figure 2).
Distance, meters
Fig. 2. Graphical interpretation of the minimum distance of the neighborhood search neighborhood between the values of the content of acid-soluble copper in the soil
The value of the global Moran index was calculated in order to determine whether there is a clustering phenomenon in relation to attribute data. This index is a measure of spatial autocorrelation and characterizes the presence or absence of spatial autocorrelation of geodata. The results of determining the magnitude of the global Moran index, calculated for the sample by the attribute values, as well as the z-score value, which allow judging the nature of the data distribution, are presented in the Table 2.
Table 2. The results of determining the magnitude of the global Moran index and the general Getis-OrdG index
Indicator name and sample size Actual value Expected value p-value z-score
Global Moran index
Cu, mg/kg, n=1611 0.218027 -0.000621 0.000013 59.681461
General Getis-OrdGi index
Cu, mg/kg, n=1611 0.054925 0.053854 0.000001 4.855469
The actual value of the global Moran index is 0.218027; therefore, data on the content of acid-soluble copper in the soil within the study area are not randomly distributed and clustered. Since the value of the z-score exceeds 2.58, it can be argued with a probability of 99 % that the clustered type of data distribution is not random.
The degree of clustering of values (searching for unexpected bursts of high or low values in space) was determined by calculating the overall Getis-OrdG index, which was used to evaluate the overall structure and trend of geodata. Since the actual value of the overall Getis-OrdG index is larger than expected, there is a clustering of data with high attribute values (see Table 2).
As a result of the analysis of hot spots, the purpose of which is to determine the presence of statistically significant differences in the studied attribute from the entire range of values in the vicinity of the object, statistically significant spatial clusters of high values (hot spots) and low values (cold spots) for the content of acid-soluble copper in the soil were determined as well as visualization of the obtained data is performed. The analysis of clusters and outliers allows to identify the concentrations of high and low values and helps to
establish where the clearest boundaries between the contours with high and low copper content in the soil are located (Figure 3).
Fig. 3. «Hot Spot Analysis» results within the land use of the RUE «Educational Experimental Farm of BSAA» (a - identified reliable localization of high and low values; b) dedicated management zones)
Based on the results of the analysis of the hot spots, three management zones with different contents of acid-soluble copper were identified: zone 1 - average content of acid-soluble copper 1.75 mg/kg, area -2395.13 hectares; zone 2 - the average content of acid-soluble copper is 2.14 mg/kg, the area is 3270.97 hectares; zone 3 - the average content of acid-soluble copper is 2.52 mg/kg, the area is 2540.31 hectares. The statistical characteristics of the content of acid-soluble copper within the identified zones are shown in Table 3.
Table 3. Statistical characteristics of a sample of data on the content of acid-soluble copper (mg/kg) within the limits of identified zones
Identified zones and sample size Indicator value Sd Cv, % Med Kurtosis Skewness
min max mid
Zone 1, n=471 0.76 3.22 1.75 0.48 27.4 1.73 2.81 0.24
Zone 2, n=641 0.82 3.72 2.14 0.49 22.8 2.11 3.18 0.44
Zone 3, n=499 0.82 4.15 2.52 0.64 25.4 2.45 2.78 0.30
Note: Sd is the standard deviation; Cv is the coefficient of variation; Med is the median.
It was also found that there is a steady trend in increasing the copper content in the central part of land use for zone 1; in reducing the copper content in the north-south direction for zone 2 and increasing its content in the north-south and west-east for zone 3.
It should also be noted that the selected management zones through the use of GIS functionality can be divided into work parcels formed according to the working width of the used high-precision agricultural
equipment used for the differential application of mineral fertilizers when introducing precision farming system, and the resulting cartographic images can be used as task maps to ensure the effective operation of the equipment.
Conclusion
Using a geostatistical analysis of data on the content of acid-soluble copper in the soil allows you to:
1) to identify and mathematically evaluate the spatial distribution of this trace element;
2) to study spatial autocorrelation of data and determine the lag value that should be taken into account when selecting a step in the process of creating a monitoring network for monitoring the copper content in soil for precision farming;
3) to evaluate the clustering of data on the copper content in the soil and determine the location of clusters in space;
4) to visualize clusters by constructing cartographic images;
5) to determine the boundaries and areas of management zones for precision farming, within which it is possible to apply the differential application of micronutrient fertilizers.
Further research should be concentrated in the direction of studying the mutual influence of the spatial distribution of humus and the pH of the soil solution on the spatial differentiation of acid-soluble copper in the soil.
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