Influence of incorporating geometric anisotropy on the construction of thematic maps of simulated data and chemical attributes of soi

Abstract

The study on spatial variability of soil properties performed through geostatistical techniques allow us to identify the spatial distribution of phenomena by means of a spatial model that considers degree of dependence among observed data, depending on distance and also the direction that separate them, if there is geometric anisotropy, in other words, a directional trend in spatial continuity. However, the main difficulty in decision making regarding the use of anisotropic spatial model focuses on its relevance to the parameters that express the geometric anisotropy in a spatial model exercise in relation to the estimation space. This study aims at identifying the degree of influence of geometric anisotropy on the accuracy of spatial estimation using simulated data sets with different sample sizes and soil chemical properties such as: Fe, potential acidity (H + Al), organic matter and Mn. Comparing the isotropic and anisotropic models, especially for smaller sample sizes (100 and 169) showed an increased sum of squares of differences between predictions anisotropy factor (Fa) equals 2. Furthermore, from Fa equals 2.5, over 50% of the simulations showed values of overall accuracy (OA) of less than 0.80 and values for the concordance index Kappa (K) and Tau (T) from 0.67 to 0.80, indicating differences between thematic maps. Similar conclusions were obtained for chemical properties of the soil, from Fa equals 2, showing that there are relevant differences regarding the inclusion or not of geometric anisotropy.

Relationship Between Sample Design and Geometric Anisotropy in the Preparation of Thematic Maps of Chemical Soil Attributes

“…These outliers occurred in simulat ions that produced an overestimat ion of the anisotropic ratio, in agreement with results obtained for the systematic sampling by Guedes et al (2013). However, these authors emphasize that this overestimat ion of the anisotropic ratio occurred only for small sample sizes.…”

“…This type of anisotropy occurs when a transitive model of semivariance function presents constant values of nugget and sill in all directions but different ranges. When geometric anisotropy is identified, it must be incorporated as an intrinsic feature of the process that describes the spatial dependence structure to improve the accuracy of the spatial estimat ion of the values of a georeferenced variable in unsampled locations, which results in the generation of maps that more accurately describe the s patial variability of the variable throughout the area under study (Guedes et al, 2008;2013).…”

“…Mucha & Blaszczyk (2012) used s imu lated data to determine that the influence of geometric anisotropy on spatial estimation depends on several factors associated with the spatial dependence structure, such as the distance over which the samples exh ibit spatial autocorrelat ion (range), the degree of intensity of spatial dependence (relative nugget effect) and the distance between the sampling units. According to the studies conducted by Guedes et al (2013), for simulated datasets, it follows that fro m the anisotropic ratio of 2, the spatial estimates in unsampled locations differ depending on the incorporation or o mission of geometric an isotropy.…”

“…However, Mucha & Blaszczyk (2012) and Guedes et al (2013) only considered systematic design (lattices) in their studies of spatial dependence. There are no studies that show the influence that the interaction between different samplings and the presence of anisotropy have on the estimat ion of the spatial dependence structure and on the estimat ion of values of the georeferenced variable in non-sampled locations.…”

Spatial Variability of the Water Depth Applied by Fixed Sprinkler Irrigation Systems

“…Being that R(φ 3 )=[(r iu )] is a symmetric matrix with its elements equal to: The parametric fo rm of the covariance matrix Σ given in [eq. 2], occurs for several stationary and isotropic processes (Guedes et al, 2013), in wh ich the covariance C(s i , s u ) = C(h iu ) can be expressed by the Matern functions' family, given by [eq. 3]: 3] corresponds to the exponential and Gaussian covariance functions, respectively.…”