Scaled Semivariogram in the Sample Planning of Soils Cultivated With Sugarcane

Sugarcane cultivation has expanded in areas previously occupied by degraded pastures. In the first years of cultivation, besides the physical and chemical restrictions of the soils, other factors can make impossible the maximum productive expression of the crop, like the climatic and edaphic factors. The objective of this work was to evaluate the ideal sampling density and spatial variability of the physical and chemical attributes of soils cultivated with sugarcane. Georeferenced data provided by the Sugarcane Technology Center (STC) of an area of approximately 19,000 hectares located in the northwest region of São Paulo were evaluated. The granulometric fractions of the soils and organic matter contents and base saturation were determined at depths of 0.00-0.25 and 0.25-0.50 m. An index named edaphic environment (ENV) was calculated based on the records of rainfall of the areas and the productivity of the sugarcane, being represented with aptitude scores ranging from 0 (worst condition) to 10 (best condition). The results showed a strong correlation between clay and organic matter attributes with ENV index. Regions with aptitude ≥ 6.65 of ENV index corresponded to sites with clay (CL) and organic matter (OM) content above 335 g kg and 30 g kg, respectively. Only 10.86% of the area presented base saturation (V%) concentration ≥ 68%, correlating positively with CL and ENV. Through the scaled semivariogram it was possible to verify that a density of sampling of a sample to each 18 ha can be used for a mapping in macroscale of the evaluated attributes in the northwest region of the state of São Paulo.


Introduction
Brazil is among the countries designed to meet the growing demand for food and biofuels in the next four decades (Strassburg et al., 2014).Among the segments of its economy, the production of sugarcane has a relevant socioeconomic role, due to the production of ethanol, as a source of renewable energy, and in natura, for animal feed and sugar and alcohol manufacture.
It is estimated that ethanol production from sugarcane increases from 21 to 61.6 billion liters by 2021, consequently, 6.4 million hectares of planted area will be needed to meet this demand (Goldemberg et al., 2014).Currently, the state of São Paulo is the largest Brazilian producer, with 4558.6 thousand hectares of planted area and average productivity of 77,268 kg ha -1 (CONAB, 2017).
The expansion of this crop in recent years has occurred mainly in the northwest region of the state, where small rural properties are leased by sugar and alcohol mills in the region.Such a condition can be justified by the inefficiency in the income transformation of small farmers who practice extensive livestock farming.The poor management of livestock and the low natural fertility of soils do not favor the maximum productive expression of the pastures, which directly infers in the erosive process of the soil that culminates with the degradation (Garbiate et al., 2011).This situation reinforces the need to adopt specific management practices for the production of sugarcane in these areas (Crusciol et al., 2014).ion is also rela he availability tic conditions and do Prado of the propertie e mean, media mmetry were c between the m CV) was classi ix was perform ed by the geo tion 1: is the tance The exponential (Equation 2), spherical (Equation 3) and Gaussian (Equation 4) semivariogram models were tested, and the selection criteria were: a) the smallest sum of the squares of the deviations (SQD); b) the highest spatial dependence coefficient (R 2 ) and c) the highest spatial dependence degree.The final decision of the adjustment model to be considered was based on the cross-validation of the data observed and estimated by the model, as well as the definition of the neighborhood size of points that would provide the best interpolation for ordinary kriging.The analysis of the Spatial Dependence Evaluator (SDE) and its classification was performed according to Montanari et al. (2010).
where, γ (h) is the estimated semivariance; C 0 is the pure nugget effect; C is the contribution of semivariance; A 0 is the range (m) and h is the distance vector (m); d corresponds to the maximum distance analyzed.
The theoretical semivariograms were scaled by dividing the semivariance by statistical variance (Ceddia et al., 2009;Comegna & Basile, 1994;Ferreyra et al., 2002;Vieira et al., 1981).The choice of the scaled semivariogram model that best fit the data was based on the higher R 2 and the smaller sum of squares of the residues, generated from the observed and estimated data, besides the practical knowledge of the behavior of the assessed attributes.Subsequently the scaled semivariogram served as the basis for calculating the minimum number of soil samples (Oliveira et al., 2014(Oliveira et al., , 2015)), according to Equation 5: where, N is the minimum number of samples required for the determination of a sampling mesh in an area α (ha).

Results and Discussion
The results showed a high variability of the silt (ST) and clay (CL) in both layers evaluated, with coefficients of variation (CV) above 45% (Table 1).These CV values can be justified by the diversity of soil classes and their particle size distribution present in the northwest region of São Paulo (IPT, 1981).CL ranged from 30 to 730 g kg -1 and ST from 10 to 380 g kg -1 , considering the two evaluated layers (Table 1).Note.ENV, SD, ST, CL, OM and V% are respectively the production environment, sand, silt, clay, organic matter and base saturation values in the 0.00-0.25 m layer when followed by the number 1 and in the layer 0.25-0.50m when followed by the number 2; SD, Var. and Assm.are respectively the standatd deviation and coefficients of variation (%) and asymmetry.
Soil organic matter (OM) was classified as medium in the superficial layer 0-0.25 m (20 g kg -1 ), and low in the sub-superficial layer 0.25-0.50m (13 g kg -1 ) (Table 1).Although these values are unsatisfactory for sugarcane cultivation, the respective CVs of 41.7% and 37.2% indicated the existence of sites with values up to 81 g kg -1 , which are classified as very high.The mechanized harvesting of sugarcane provides great deposition of residues on the soil surface, however, Segnini et al. (2013) reported in their studies that the incorporation of straw in the conventional soil preparation does not improve the accumulation of OM, as well as the carbon stocks and its quality.Therefore, conventional management may not be feasible for the maintenance of OM in the superficial layers of the soil, causing high spatial variability.
The sand (SD) and base saturation (V%) contents presented low CV values in comparison to the other attributes, classified as medium < 35% (Table 1).The mean V% was 60% in the 0-0.25 layer and 56% in the 0.25-0.50m layer, indicating soil profiles with constructed fertility.
In the overall mean, the ENV index was 5.3 and its CV was classified as medium 34%.According to the STC classification methodology, the region would be classified as production environment "C" for sugarcane cultivation, however, it can be inferred the existence of sites with index 1 and 9 according to minimum and maximum values (Table 1).It is evident the existence of sites with production environments "A" and "E" and a local investigation is necessary in order to identify the limiting factors of production, thus defining specific management zones.
All attributes presented average values close to the median, however, only ENV index, V%1 and V%2 presented values of asymmetry and kurtosis close to zero, being considered the only attributes with symmetric frequency distributions (Table 1).
Significant linear correlations of the ENV index with all attributes were observed, being positive with the contents of ST, CL, OM, V%, and negative with SD (Table 2).Among the coefficients obtained, there was a moderate correlation between the CL content and the ENV index in both evaluated layers, being, therefore, the attribute that most influenced the edaphic environment.It is understood that the CL content is directly linked to the inputs of OM and V%, in which the agricultural suitability of the soils favors the use of high technological level in the cultivation of sugarcane.This can be proved by the positive correlations between CL × OM and V%, in which coefficients of 0.52** and 0.26** in the 0-0.25 m layer, and 0.41** and 0.30** in the layer of 0.25-0.50m, respectively, were found (Table 2).Note.ENV, SD, ST, CL, OM and V% are respectively the production environment, sand, silt, clay, organic matter and base saturation values in the 0.00-0.25 m layer when followed by the number 1 and in the layer 0.25-0.50m when followed by the number 2; ** significant at 1% probability.
As for the SD content, this was negatively correlated with all attributes.It is understood that SD is related to lower water retention (Zhao et al., 2010) and low soil fertility (Souza et al., 2010), consequently lower availability of nutrients to the plants, not favoring the supply of soil OM.The highest SD contents occurred near to the dam of the river that cuts the map, represented by classes above 729 g kg -1 in the 0.00-0.25 m layer and above 675 g kg -1 in the 0.25-0.50m layer, occupying 34.11% and 42.61% of the area, respectively (Figures 5E and 5F).This condition suggests the existence of soils with low agricultural ability.Therefore, the contents of CL at these sites do not exceed 180 g kg -1 .
High V% levels occurred in the same region, represented by classes above 68% for V%1 and 64% for V%2, corresponding to 10.86% and 19.24% of the total area, respectively (Figures 5I and 5J).These results support the linear correlations obtained between V% × CL and OM, which, although weak, between 0.26** and 0.44**, are justified by spatial distribution.The V%2 map presented spatial distribution similar to the map of CL2, being soils with the best agricultural aptitude (Figures 5B and 5J).
The spatial distribution of OM indicated levels above 30 g kg -1 for OM1 and 24 g kg -1 for OM2 near the river, which corresponded to 25.69% and 5.43% of the area, respectively.The best OM condition was observed at sites with CL and V% above 272 g kg -1 and 54% at 0-0.25 m layer, and above 255 g kg -1 and 64% at the 0.25-0.50m, respectively.Corroborating with the results of the linear correlation between OM × V% and CL, indicating that the contribution of organic matter is influenced by the clay content and base saturation in the layer of 0.25-0.50m.
The best environments for the sugarcane production were verified in the coastal regions (Figure 5K).It is observed by the spatial distribution of the ENV index by highest occurrence of environments "A", "B" and "C" representing 65.83% of the area.In addition, it was verified that 34.17% of the area presented soils with a score lower than 5, that is, soils with medium to low production potential classified as "D" to "E" environments.
In the comparison between ENV index maps and soil attributes, it can be seen that CL, OM and V% levels follow the distribution of "A" and "B" environments with grades above 6.65 (Figures 5K,5B,5G and 5J).The CL content also followed the distribution of the production environments, however in an inverse way, that is, the higher the sand content, the worse the production environment.Similar result to the behavior of the simple linear correlation matrix (Table 2).Souza et al. (2010) affirm that spatial variability of soil attributes should be taken into account in agricultural planning to optimize fertilizer applications and increase sugarcane productivity, thus reducing production costs and environmental problems.

Conclusion
Through the scaled semivariogram it was possible to verify that the sampling density of a sample for each 18 ha can be used for a mapping in macroscale in the northwest region of the state of São Paulo.
The semivariance structures of the soil attributes and index of production environments were better fitted to exponential models, with moderate to high spatial dependence classification and ranges up to 13920 m.
The index based on production environments for sugarcane was positively correlated with the contents of silt, clay, organic matter and saturation by bases, and negatively with the sand content.
The best environments for the production of sugarcane were verified in the coastal regions, due to the higher clay content, organic matter and better soil base saturation, considering the two layers evaluated.
Further sample planning studies should be carried out in other regions and soils with different characteristics from those observed in the present study, in order to verify the influence of the spatial variability of the soil attributes in the appropriate sample grid size.

Table 1 .
Descriptive analysis of the production environment for the sugarcane crop and the soil attributes analyzed in the 0 to 0.25 and 0.25 to 0.50 m

Table 2 .
Pearson correlation matrix and respective coefficients between production environment for sugarcane and soil attributes analyzed