Scaling of semivariograms and the kriging estimation of field-measured properties

Two methods were evaluated for scaling a set of semivariograms into a unified function for kriging estimation of field-measured properties. Scaling is performed using sample variances and sills of individual semivariograms as scale factors. Theoretical developments show that kriging weights are independent of the scaling factor which appears simply as a constant multiplying both sides of the kriging equations. The scaling techniques were applied to four sets of semivariograms representing spatial scales of 30 x 30 m to 600 x 900 km. Experimental semivariograms in each set successfully coalesced into a single curve by variances and sills of individual semivariograms. To evaluate the scaling techniques, kriged estimates derived from scaled semivariogram models were compared with those derived from unscaled models. Differences in kriged estimates of the order of 5% were found for the cases in which the scaling technique was not successful in coalescing the individual semivariograms, which also means that the spatial variability of these properties is different. The proposed scaling techniques enhance interpretation of semivariograms when a variety of measurements are made at the same location. They also reduce computational times for kriging estimations because kriging weights only need to be calculated for one variable. Weights remain unchanged for all other variables in the data set whose semivariograms are scaled.

Variability of apparently homogeneous soilscapes in São Paulo state, Brazil: I. spatial analysis

The spatial variability of strongly weathered soils under sugarcane and soybean/wheat rotation was quantitatively assessed on 33 fields in two regions in São Paulo State, Brazil: Araras (15 fields with sugarcane) and Assis (11 fields with sugarcane and seven fields with soybean/wheat rotation). Statistical methods used were: nested analysis of variance (for 11 fields), semivariance analysis and analysis of variance within and between fields. Spatial levels from 50 m to several km were analyzed. Results are discussed with reference to a previously published study carried out in the surroundings of Passo Fundo (RS). Similar variability patterns were found for clay content, organic C content and cation exchange capacity. The fields studied are quite homogeneous with respect to these relatively stable soil characteristics. Spatial variability of other characteristics (resin extractable P, pH, base- and Al-saturation and also soil colour), varies with region and, or land use management. Soil management for sugarcane seems to have induced modifications to greater depths than for soybean/wheat rotation. Surface layers of soils under soybean/wheat present relatively little variation, apparently as a result of very intensive soil management. The major part of within-field variation occurs at short distances (< 50 m) in all study areas. Hence, little extra information would be gained by increasing sampling density from, say, 1/km² to 1/50 m². For many purposes, the soils in the study regions can be mapped with the same observation density, but residual variance will not be the same in all areas. Bulk sampling may help to reveal spatial patterns between 50 and 1.000 m.

State-space approach to evaluate the relation between soil physical and chemical properties

The state-space approach is used to evaluate the relation between soil physical and chemical properties in an area cultivated with sugarcane. The experiment was carried out on a Rhodic Kandiudalf in Piracicaba, State of São Paulo, Brazil. Sugarcane was planted on an area of 0.21 ha i.e., in 15 rows 100 m long, spaced 1.4 m. Soil water content, soil organic matter, clay content and aggregate stability were sampled along a transect of 84 points, meter by meter. The state-space approach is used to evaluate how the soil water content is affected by itself and by soil organic matter, clay content, and aggregate stability of neighboring locations, in different combinations, aiming to contribute to a better understanding of the relation among these variables in the soil. Results show that soil water contents were successfully estimated by this approach. Best performances were found when the estimate of soil water content at locations i was related to soil water content, clay content and aggregate stability at locations i-1. Results also indicate that this state-space model using all series describes the soil water content better than any equivalent multiple regression equation.

Spatial variability of aggregate stability in latosols under sugarcane

The spatial variability of soils under a same management system is differentiated, as expressed in the properties. The spatial variability of aggregate stability of a eutrophic Red Latosol (ERL) and a dystrophic Red Latosol (DRL) under sugarcane was characterized. Samples were collected in a regular 10 m grid, in the layers 0.0-0.2 and 0.2-0.4 m, with 100 points per area, and the following properties were determined: geometric mean diameter (GMD) of aggregates, mean weight diameter (MWD) of aggregates, percent of aggregates in the > 2.0 mm class and organic matter (OM) content. The eutrophic Red Latosol (ERL) had a higher aggregate stability thn the dystrophic Red Latosol (DRL), which may be attributed to the higher clay and OM content and the gibbsitic mineralogy of this soil class. The differentiated evolution of the studied Oxisols explains the wider range and lower variation coefficient and variability, for all properties studied in the eutrophic Red Latosol.

Spatial variability of the chemical, physical and biological properties in lowland cultivated with irrigated rice

In the areas where irrigated rice is grown in the south of Brazil, few studies have been carried out to investigate the spatial variability structure of soil properties and to establish new forms of soil management as well as determine soil corrective and fertilizer applications. In this sense, this study had the objective of evaluating the spatial variability of chemical, physical and biological soil properties in a lowland area under irrigated rice cultivation in the conventional till system. For this purpose, a 10 x 10 m grid of 100 points was established, in an experimental field of the Embrapa Clima Temperado, in the County of Capão do Leão, State of Rio Grande do Sul. The spatial variability structure was evaluated by geostatistical tools and the number of subsamples required to represent each soil property in future studies was calculated using classical statistics. Results showed that the spatial variability structure of sand, silt, SMP index, cation exchange capacity (pH 7.0), Al3+ and total N properties could be detected by geostatistical analysis. A pure nugget effect was observed for the nutrients K, S and B, as well as macroporosity, mean weighted diameter of aggregates, and soil water storage. The cross validation procedure, based on linear regression and the determination coefficient, was more efficient to evaluate the quality of the adjusted mathematical model than the degree of spatial dependence. It was also concluded that the combination of classical with geostatistics can in many cases simplify the soil sampling process without losing information quality.

Spatial and temporal variability of crop yield and some Rhodic Hapludox properties under no-tillage

Soil properties are closely related with crop production and spite of the measures implemented, spatial variation has been repeatedly observed and described. Identifying and describing spatial variations of soil properties and their effects on crop yield can be a powerful decision-making tool in specific land management systems. The objective of this research was to characterize the spatial and temporal variations in crop yield and chemical and physical properties of a Rhodic Hapludox soil under no-tillage. The studied area of 3.42 ha had been cultivated since 1985 under no-tillage crop rotation in summer and winter. Yield and soil property were sampled in a regular 10 x 10 m grid, with 302 sample points. Yields of several crops were analyzed (soybean, maize, triticale, hyacinth bean and castor bean) as well as soil chemical (pH, Soil Organic Matter (SOM), P, Ca2+, Mg2+, H + Al, B, Fe, Mn, Zn, CEC, sum of bases (SB), and base saturation (V %)) and soil physical properties (saturated hydraulic conductivity, texture, density, total porosity, and mechanical penetration resistance). Data were analyzed using geostatistical analysis procedures and maps based on interpolation by kriging. Great variation in crop yields was observed in the years evaluated. The yield values in the Northern region of the study area were high in some years. Crop yields and some physical and soil chemical properties were spatially correlated.

Spatial variability of physical attributes of an alfisol under different hillslope curvatures

The influence of relief forms has been studied by several authors and explains the variability in the soil attributes of a landscape. Soil physical attributes depend on relief forms, and their assessment is important in mechanized agricultural systems, such as of sugarcane. This study aimed to characterize the spatial variability in the physical soil attributes and their relationship to the hillslope curvatures in an Alfisol developed from sandstone and growing sugarcane. Grids of 100 x 100 m were delimited in a convex and a concave area. The grids had a regular spacing of 10 x 10 m, and the crossing points of this spacing determined a total of 121 georeferenced sampling points. Samples were collected to determine the physical attributes related to soil aggregates, porosity, bulk density, resistance to penetration and moisture within the 0-0.2 and 0.2-0.4 m depth. Statistical analyses, geostatistics and Student's t-tests were performed with the means of the areas. All attributes, except aggregates > 2 mm in the 0-0.2 m depth and macroporosity at both depths, showed significant differences between the hillslope curvatures. The convex area showed the highest values of the mean weighted diameter, mean geometric diameter, aggregates > 2 mm, 1-2 mm aggregates, total porosity and moisture and lower values of bulk density and resistance to penetration in both depth compared to the concave area. The number of soil attributes with greater spatial variability was higher in the concave area.

Selecting statistical models to study the relationship between soybean yield and soil physical properties

Statistical models allow the representation of data sets and the estimation and/or prediction of the behavior of a given variable through its interaction with the other variables involved in a phenomenon. Among other different statistical models, are the autoregressive state-space models (ARSS) and the linear regression models (LR), which allow the quantification of the relationships among soil-plant-atmosphere system variables. To compare the quality of the ARSS and LR models for the modeling of the relationships between soybean yield and soil physical properties, Akaike's Information Criterion, which provides a coefficient for the selection of the best model, was used in this study. The data sets were sampled in a Rhodic Acrudox soil, along a spatial transect with 84 points spaced 3 m apart. At each sampling point, soybean samples were collected for yield quantification. At the same site, soil penetration resistance was also measured and soil samples were collected to measure soil bulk density in the 0-0.10 m and 0.10-0.20 m layers. Results showed autocorrelation and a cross correlation structure of soybean yield and soil penetration resistance data. Soil bulk density data, however, were only autocorrelated in the 0-0.10 m layer and not cross correlated with soybean yield. The results showed the higher efficiency of the autoregressive space-state models in relation to the equivalent simple and multiple linear regression models using Akaike's Information Criterion. The resulting values were comparatively lower than the values obtained by the regression models, for all combinations of explanatory variables.

Local influence for spatial analysis of soil physical properties and soybean yield using student's t-distribution

The modeling and estimation of the parameters that define the spatial dependence structure of a regionalized variable by geostatistical methods are fundamental, since these parameters, underlying the kriging of unsampled points, allow the construction of thematic maps. One or more atypical observations in the sample data can affect the estimation of these parameters. Thus, the assessment of the combined influence of these observations by the analysis of Local Influence is essential. The purpose of this paper was to propose local influence analysis methods for the regionalized variable, given that it has n-variate Student's t-distribution, and compare it with the analysis of local influence when the same regionalized variable has n-variate normal distribution. These local influence analysis methods were applied to soil physical properties and soybean yield data of an experiment carried out in a 56.68 ha commercial field in western Paraná, Brazil. Results showed that influential values are efficiently determined with n-variate Student's t-distribution.

Spatial relationships between soil attributes and corn yield in no-tillage system

Soil properties play an important role in spatial variability of crop yield. However, a low spatial correlation has generally been observed between maps of crop yield and of soil properties. The objectives of the present investigation were to assess the spatial pattern variability of soil properties and of corn yield at the same sampling intensity, and evaluate its cause-and-effect relationships. The experimental site was structured in a grid of 100 referenced points, spaced at 10 m intervals along four parallel 250 m long rows spaced 4.5 m apart. Thus, points formed a rectangle containing four columns and 25 rows. Therefore, each sampling cell encompassed an area of 45 m² and consisted of five 10 m long crop rows, in which the referenced points represented the center. Samples were taken from the layers 0-0.1 m and 0.1-0.2 m. Soil physical and chemical properties were evaluated. Statistical analyses consisted of data description and geostatistics. The spatial dependence of corn yield and soil properties was confirmed. The hypothesis of this study was confirmed, i.e., when sampling the soil to determine the values of soil characteristics at similar to sampling intensity as for crop yield assessments, correlations between the spatial distribution of soil characteristics and crop yield were observed. The spatial distribution pattern of soil properties explained 65 % of the spatial distribution pattern of corn yield. The spatial distribution pattern of clay content and percentage of soil base saturation explained most of the spatial distribution pattern of corn yield.

Spatial and linear correlations between soil and corn

The Technologies setting at Agricultural production system have the main characteristics the vertical productivity, reduced costs, soil physical, chemical and biological improvement to promote production sustainable growth. Thus, the study aimed to determine the variability and the linear and special correlations between the plant and soil attributes in order to select and indicate good representation of soil physical quality for forage productivity. In the growing season of 2006, on the Fazenda Bonança in Pereira Barreto (SP), the productivity of autumn corn forage (FDM) in an irrigated no-tillage system and the soil physical properties were analyzed. The purpose was to study the variability and the linear and spatial correlations between the plant and soil properties, to select an indicator of soil physical quality related to corn forage yield. A geostatistical grid was installed to collect soil and plant data, with 125 sampling points in an area of 2,500 m². The results show that the studied properties did not vary randomly and that data variability was low to very high, with well-defined spatial patterns, ranging from 7.8 to 38.0 m. On the other hand, the linear correlation between the plant and the soil properties was low and highly significant. The pairs forage dry matter versus microporosity and stem diameter versus bulk density were best correlated in the 0-0.10 m layer, while the other pairs - forage dry matter versus macro - and total porosity - were inversely correlated in the same layer. However, from the spatial point of view, there was a high inverse correlation between forage dry matter with microporosity, so that microporosity in the 0-0.10 m layer can be considered a good indicator of soil physical quality, with a view to corn forage yield.

Characterization of soil chemical properties of strawberry fields using principal component analysis

One of the largest strawberry-producing municipalities of Rio Grande do Sul (RS) is Turuçu, in the South of the State. The strawberry production system adopted by farmers is similar to that used in other regions in Brazil and in the world. The main difference is related to the soil management, which can change the soil chemical properties during the strawberry cycle. This study had the objective of assessing the spatial and temporal distribution of soil fertility parameters using principal component analysis (PCA). Soil sampling was based on topography, dividing the field in three thirds: upper, middle and lower. From each of these thirds, five soil samples were randomly collected in the 0-0.20 m layer, to form a composite sample for each third. Four samples were taken during the strawberry cycle and the following properties were determined: soil organic matter (OM), soil total nitrogen (N), available phosphorus (P) and potassium (K), exchangeable calcium (Ca) and magnesium (Mg), soil pH (pH), cation exchange capacity (CEC) at pH 7.0, soil base (V%) and soil aluminum saturation(m%). No spatial variation was observed for any of the studied soil fertility parameters in the strawberry fields and temporal variation was only detected for available K. Phosphorus and K contents were always high or very high from the beginning of the strawberry cycle, while pH values ranged from very low to very high. Principal component analysis allowed the clustering of all strawberry fields based on variables related to soil acidity and organic matter content.

Mineralogy of the clay fraction of Alfisols in two slope curvatures: III - spatial variability

A good knowledge of the spatial distribution of clay minerals in the landscape facilitates the understanding of the influence of relief on the content and crystallographic attributes of soil minerals such as goethite, hematite, kaolinite and gibbsite. This study aimed at describing the relationships between the mineral properties of the clay fraction and landscape shapes by determining the mineral properties of goethite, hematite, kaolinite and gibbsite, and assessing their dependence and spatial variability, in two slope curvatures. To this end, two 100 × 100 m grids were used to establish a total of 121 regularly spaced georeferenced sampling nodes 10 m apart. Samples were collected from the layer 0.0-0.2 m and analysed for iron oxides, and kaolinite and gibbsite in the clay fraction. Minerals in the clay fraction were characterized from their X-ray diffraction (XRD) patterns, which were interpreted and used to calculate the width at half height (WHH) and mean crystallite dimension (MCD) of iron oxides, kaolinite, and gibbsite, as well as aluminium substitution and specific surface area (SSA) in hematite and goethite. Additional calculations included the goethite and hematite contents, and the goethite/(goethite+hematite) [Gt/(Gt+Hm)] and kaolinite/(kaolinite+gibbsite) [Kt/(Kt+Gb)] ratios. Mineral properties were established by statistical analysis of the XRD data, and spatial dependence was assessed geostatistically. Mineralogical properties differed significantly between the convex area and concave area. The geostatistical analysis showed a greater number of mineralogical properties with spatial dependence and a higher range in the convex than in the concave area.

Mineralogy of the clay fraction of alfisols in two slope curvatures: IV - spatial correlation with physical properties

Although the influence of clay mineralogy on soil physical properties has been widely studied, spatial relationships between these features in Alfisols have rarely been examined. The purpose of this work was to relate the clay minerals and physical properties of an Alfisol of sandstone origin in two slope curvatures. The crystallographic properties such as mean crystallite size (MCS) and width at half height (WHH) of hematite, goethite, kaolinite and gibbsite; contents of hematite and goethite; aluminium substitution (AS) and specific surface area (SSA) of hematite and goethite; the goethite/(goethite+hematite) and kaolinite/(kaolinite+gibbsite) ratios; and the citrate/bicarbonate/dithionite extractable Fe (Fe d) were correlated with the soil physical properties through Pearson correlation coefficients and cross-semivariograms. The correlations found between aluminium substitution in goethite and the soil physical properties suggest that the degree of crystallinity of this mineral influences soil properties used as soil quality indicators. Thus, goethite with a high aluminium substitution resulted in large aggregate sizes and a high porosity, and also in a low bulk density and soil penetration resistance. The presence of highly crystalline gibbsite resulted in a high density and micropore content, as well as in smaller aggregates. Interpretation of the cross-semivariogram and classification of landscape compartments in terms of the spatial dependence pattern for the relief-dependent physical and mineralogical properties of the soil proved an effective supplementary method for assessing Pearson correlations between the soil physical and mineralogical properties.

Comparison between artificial neural networks and maximum likelihood classification in digital soil mapping

Soil surveys are the main source of spatial information on soils and have a range of different applications, mainly in agriculture. The continuity of this activity has however been severely compromised, mainly due to a lack of governmental funding. The purpose of this study was to evaluate the feasibility of two different classifiers (artificial neural networks and a maximum likelihood algorithm) in the prediction of soil classes in the northwest of the state of Rio de Janeiro. Terrain attributes such as elevation, slope, aspect, plan curvature and compound topographic index (CTI) and indices of clay minerals, iron oxide and Normalized Difference Vegetation Index (NDVI), derived from Landsat 7 ETM+ sensor imagery, were used as discriminating variables. The two classifiers were trained and validated for each soil class using 300 and 150 samples respectively, representing the characteristics of these classes in terms of the discriminating variables. According to the statistical tests, the accuracy of the classifier based on artificial neural networks (ANNs) was greater than of the classic Maximum Likelihood Classifier (MLC). Comparing the results with 126 points of reference showed that the resulting ANN map (73.81 %) was superior to the MLC map (57.94 %). The main errors when using the two classifiers were caused by: a) the geological heterogeneity of the area coupled with problems related to the geological map; b) the depth of lithic contact and/or rock exposure, and c) problems with the environmental correlation model used due to the polygenetic nature of the soils. This study confirms that the use of terrain attributes together with remote sensing data by an ANN approach can be a tool to facilitate soil mapping in Brazil, primarily due to the availability of low-cost remote sensing data and the ease by which terrain attributes can be obtained.