Spatial variability and sampling density of chemical attributes in archaeological black earths under pasture in southern Amazonas, Brazil

. Spatial mapping of soil chemical attributes is essential for sampling efficiency and agricultural planning management, ensuring a regional development and sustainability of the unique characteristics of archaeological black earths (ABEs). Thus, this study was developed aiming at assessing the spatial variability and sampling density of chemical attributes in soils of ABEs under pasture in southern Amazonas, Brazil. A sampling grid of 56 × 80 m with regular spacings of 8 m was 20 installed in the experimental area and samples were taken from the crossing points at depths of 0.0–0.05, 0.05–0.10, and 0.10– 0.20 m, totaling 264 georeferenced points. The chemical attributes pH in water, organic carbon, Ca, Mg, K, P, Al, and potential acidity were determined in these samples, while CEC, SB, V, t, T, and m were calculated. The attributes present a spatial dependence varying from strong to moderate, being Al3+ the only chemical attribute that does not present a spatial dependence structure in the assessed depths. Scaled semivariograms satisfactorily reproduce the spatial behavior of attributes in the same 25 pattern of individual semivariograms, allowing their use to estimate the variability of soil attributes. required sampling density is higher at a depth of 0.0–0.05 m, requiring 2 and 1 point ha−1 at depths of 0.05–0.10 and 0.10–0.20 m, respectively, to represent the spatial pattern of chemical attributes.

essential to know the spatial variability of its attributes (Oliveira et al., 2014) since it is a complex interaction of factors and processes of formation, having as additional sources the management of soil, crop, and landscape variations (Campos et al., 2012;Roger et al., 2014;Oliveira et al., 2017;Brito et al., 2018). Thus, agricultural success or an adequate and efficient soil management can only be possible when the spatial pattern of its attributes is defined (Gomes et al., 2017).
The variability of soil attributes is often inferred by descriptive statistics (mean, standard deviation, coefficient of variation, 50 etc.). Although these measures of dispersion provide an idea of variation, they do not consider the space, which can often provide misleading information and, consequently, lead to failure of agricultural planning management (Gomes et al., 2018).
In the Amazonas State, some studies such as those of Campos et al. (2012) have been a pioneer in characterizing the spatial variability of soil chemical and physical attributes, as well as have served as a reference for conducting other investigations on this subject. Many of these studies have revealed the potential of ABEs for agricultural purposes (Silva et al., 2016;Gomes et 55 al., 2017;2018;Brito et al., 2018). However, many of these researchers have warned that an adequate ABE management has altered their natural and desirable chemical properties.
In this scenario, geostatistics is a promising tool for identifying and characterizing soil attributes, considering man-made management in the most varied landscape forms (Gomes et al., 2017). Geostatistics can be used in interpreting and projecting results based on the structure of natural variability, indicating alternatives of use, in addition to allowing a better understanding 60 of attribute distribution and, consequently, its influence on yield (Guan et al. 2017). Moreover, the ideal minimum number of samples representative from the lithological, pedological, and geomorphological diversity of a given region can be determined from a scaled semivariogram (Teixeira et al., 2017). The combination of these tools maximizes sampling efficiency and reduces costs with manpower.
With the aid of geostatistics, it will be possible to characterize in detail the organic carbon and the chemical attributes of ABEs. https://doi.org/10.5194/soil-2019-26 This is just a preview and not the publishedpreprint.
Soil attributes were analyzed by descriptive statistics, being calculated the mean, median, maximum, minimum, standard deviation, coefficient of variation, and the coefficients of skewness and kurtosis. The hypothesis of normality of the data was tested by the Kolmogorov-Smirnov (KS) test (p≤0.05) by using the software Minitab 14 (Minitab, 2000).
Geostatistics was used to assess the spatial variability of the studied attributes, as in Vieira et al. (1983). For this, the spatial 05 dependence was verified by means of the semivariogram graph using the software GS+ version 7. Based on the assumption of stationarity of the intrinsic hypothesis, the semivariogram was estimated by equation 1: (1) where γ(h) is the semivariance value for a distance h, N(h) is the number of pairs involved in the semivariance calculation, Z(xi) is the value of the attribute Z in the position xi, Z(xi+h) is the value of the attribute Z separated by a distance h from 10 the position xi.
The experimental semivariograms were chosen based on the number of pairs involved in the semivariance calculation, presence of a clearly defined sill (Burrough & McDonnel, 2000), better coefficient of the cross-validation test, and higher coefficient of determination (R 2 ), in which the values vary from 0 to 1, where those close to 1 characterize the model as more efficient to express the studied phenomenon.

15
From the adjustment of a mathematical model to the calculated values of γ(h), theoretical model coefficients are defined for the semivariogram: nugget effect (C0) is the semivariance value for a distance zero, which represents the component of random variation; structural variance (C1); sill (C0+C1) is the semivariance value at which the curve stabilizes over a constant value; and range (a) is the distance from the origin to where the sill reaches stable values, expressing the distance beyond which the samples are not correlated (Vieira et al., 1983;Trangmar et al., 1985).

20
The degree of spatial dependence was analyzed according to the Cambardella et al. (1994) classification, in which semivariograms that have a nugget effect to sill ratio [C0/(C0+C1)] lower than or equal to 25% have a strong spatial dependence, between 25 and 75% have a moderate spatial dependence, and higher than 75% have a weak spatial dependence. After adjustment of the permissible mathematical models, data interpolations were performed by means of kriging in the software Surfer version 13.00.

25
Scaled semivariograms were also used in order to reduce them to the same scale, making the comparison between the results of different variables easy. The experimental semivariograms were scaled by dividing the semivariance by the sample variance of each studied variable (Vieira, 1983). With the dimensionless semivariance, the nugget effect expressed directly in sill percentage (total semivariance) the random component of the variance structure. According to Vieira (1983), a proportionality is verified when scaled semivariograms allow the adjustment of a single model for the variable under study.

30
The scaled experimental semivariograms were adjusted to the spherical model: org/10.5194/soil-2019-26 This is just a preview and not the publishedpreprint.
where C0 is the nugget effect, C0+C1 is the sill, h is the separation distance between two observations, and a is the range of 35 the spatial dependence.
Subsequently, the scaled semivariograms served as a basis of information to calculate the minimum number of soil samples and determine the variability of all attributes at different depths.
where N is the minimum number of samples required for determining a sampling grid, A is the total area (ha), and a is the 40 semivariogram range (m).

Results and discussion
The attributes active acidity (pH), calcium (Ca 2+ ), magnesium (Mg 2+ ), potassium (K + ), phosphorus (P), aluminum (Al 3+ ), The average values of chemical attributes (Table 1) indicated a soil with an active acidity of medium toxicity, high potential acidity, low exchangeable aluminum, and very low aluminum saturation, as defined by Embrapa (2013). High pH values from 4.8 -6.4, according to Falcão et al. (2009), reflect the reduced acidic condition common in ABE. This is associated with processes that change soil acidity, such as organism respiration and decomposition of organic matter, which are very active in 55 ABEs soils. Low concentrations of Al 3+ show a potential acidity that consists mainly of H + ions, which is not harmful to plants (Hernández-Soriano, 2012). This behavior is of great importance from an agronomic point of view since high concentrations of Al 3+ promote a reduction in P and Ca contents in leaves and roots, thus delaying the availability and absorption of nutrients (Meriño-Gergichevich et al., 2010). A high Al content is not detrimental to plants in soils that have high organic carbon content, as some of the components of organic matter form complexes with Al within soil solution, making it unavailable to plants 60 (Hernández-Soriano, 2012).
Thus, soluble Al is not considered to be a problem for such soils, even if they have a low pH. High values of pH, OC, P, Ca 2+ , and Mg 2+ at depths of 0.0-0.05 m, 0.05-0.10 m, and 0.10-0.20 m are related to the anthropic horizon at the soil surface (Aquino et al., 2016). According to these authors, the high contents of Ca 2+ and P in ABEs are due to the presence of human and animal bones, fish bones, and chelonian shells. For Alquino et al. (2016), the higher P content in ABE is due to the mineralogical composition of the ceramics found in the areas that have high levels of this element. Another hypothesis is that https://doi.org/10.5194/soil-2019-26 This is just a preview and not the publishedpreprint. § c Author(s) 2019. CC-BY 4.0 License.
6 the formation of complexes of cationic ions with high stability OM contributes to ABE chemical richness (Lima et al., 2002;Novotny et al., 2007). According to Oguntunde et al. (2004), the increase in soil pH after the partial burning of pyrogenic coal is attributed to an increase in Ca 2+ and Mg 2+ made available in soil by this material. The increase of these cations may have masked the Al 3+ activity, which is a desirable behavior.

70
The classification of soil in good and very good classes for P, Ca 2+ , and Mg 2+ allows considering it with a high fertility level (Embrapa, 2013) although K + has presented very low contents. Falcão & Borges (2006) attributed a low productivity of banana and coconut to K + deficiency when no potassium fertilization was applied in ABEs. Such fact indicates that ABEs do not necessarily have a high availability of all essential nutrients for plants (Lehmann et al., 2003). The excess of Ca 2+ , Pand Mg 2+ from ABE soil can establish a nutritional imbalance by competing with K + for the same cation exchange site. In addition, the 75 retention energy of the Ca 2+ , Mg 2+ and K + exchangeable cations to the soil colloids follows a lyotropic series (Tan, 2011), occupying the fifth element of this series, K becomes less adsorbed to soil colloids. Therefore, in well drained soils, for example, in the Amazon region, the leaching is higher, decreasing the concentration of K in the soil solution.
The abundance in OC content, with an average ranging from 135 to 133 g dm −1 , is in accordance with the results obtained by  (Zech et al., 1990;Lehmann et al., 2003;Glaser, 2007). This is a remarkable feature of EBEs, where OC content has been reported about 1.5 times higher when compared to adjacent soils, not EBEs (Aquino et al., 2016).
Regarding, it is not only the amount of OC that is responsible for the high CEC, the quality of the OC really has a greater 95 effect. Studies have shown that OM in ABE contains larger amounts of carboxylic groups and phenolic groups compared to surrounding soils, and therefore OC in ABE has a higher CEC than OC in natural soils (Zech et al., 1990;Liang et al., 2006).
The results showed that the chemical quality of ABE is strongly dependent on soil organic carbon. Thus, it is important to map the spatial pattern of the OC and the chemical properties of the ABEs to establish specific zones of management and agricultural planning, since the knowledge of the spatial variability of soil attributes allows the more efficient and economic 00 recommendation of fertilizers and correctives (Roger et al., 2014;Brito et al, 2018;Oliveira et al., 2018).
The coefficient of variation (CV), parameterized in the Warrick & Nielsen (1980) proposal, was low (CV ≤ 12%), medium (60% < CV < 12%), or high (CV ≥ 60%) depending on the attribute and depth (Table 1) Semivariogram parameter assessment indicated a spatial structure dependence (  Figure 2). According to Gomes et al. (2018), this indicates that Al 3+ is spatially independent, that is, it has little correlation. In general, PNE is extremely important since it indicates the unexplained variability, which may be due to measurement errors or undetected microvariations considering the sampling distance used (Cambardella et al., 1994). This 20 behavior indicates the need to increase, in future studies, the grid spacing between sampling points in order to detect the spatial dependence of Al 3+ .
https://doi.org/10.5194/soil-2019-26 This is just a preview and not the publishedpreprint. The attributes pH at a depth of 0.0-0.05 m, K + , Ca 2+ , SB, t, T, and OC at a depth of 0.05-0.10 m, and Ca 2+ , SB, and T at a depth of 0.10-0.20 m presented a strong degree of spatial dependence (DSD), which is expressed by the ratio between the nugget effect (C0) and range (C0+C1) (Cambardella et al., 1994). However, the attributes H+Al, Al 3+ , K + , Ca 2+ , Mg 2+ , SB, t, 10 T, V, m, P, and OC at a depth of 0.0-0.05 m, pH, H+Al, Al 3+ , Mg 2+ , V, m, and P at a depth 0.05-0.10 m, and pH, H+Al, Al 3+ , K + , Mg 2+ , V, m, P, and OC presented a moderate DSD (Table 2). These results are similar to those found by Oliveira et al. (2014), who observed a moderate DSD for most of the studied attributes. According to Cambardella et al. (1994), the strong spatial dependence is an intrinsic soil property, a natural characteristic dependent on factors and processes of soil formation, while moderate and weak spatial dependences are more related to soil management, which can homogenize some 15 soil attributes.
The range values (Table 2 and Figure 2), which defines the maximum radius whose variable has spatial dependence (Trangmar et al., 1985), revealed a large amplitude of spatial variability, ranging from 20.

5
These results highlight the importance of mapping soil attributes in order to establish a regional management of soil and pasture in ABE areas. In addition to the knowledge of the spatial variability of these attributes, sampling density allows the feasibility of extending the study in large areas, for example to the Amazonas State, whose great territorial extension and geomorphological diversity would be a hindrance to the development of this study by traditional methods. The use of these techniques maximizes sampling efficiency, time, cost reduction, and manpower, enabling the development of detailed maps 10 of the southern Amazon.