SPATIAL DEPENDENCE INDEX FOR CUBIC, PENTASPHERICAL AND WAVE SEMIVARIOGRAM MODELS

This study aims to propose a spatial dependence index (and its classification), from the concept of spatial correlation areas, for the Cubic, Pentaspherical and Wave models. The index, called Spatial Dependence Index (SDI), covers the following parameters: the range (), the nugget effect (0) and the contribution (1), beyond considering the maximum distance (MD) between sampled points and the model factor (MF). The proposed index, unlike the most used in the literature, considers the influence of the range parameter to describe the spatial dependence, highlighting the importance of this formulation. The spatial dependence classification, based on the observed asymmetric behavior in the SDI, was performed considering categorizations from the median and the 3rd quartile of the index. We obtain the spatial dependence classification in terms of weak, moderate, and strong, just as it is usually described in literature

PROPOSAL OF THE SPATIAL DEPENDENCE EVALUATION FROM THE POWER SEMIVARIOGRAM MODEL

In Geostatistics, the use of measurement to describe the spatial dependence of the attribute is of great importance, but only some models (which have second-order stationarity) are considered with such measurement. Thus, this paper aims to propose measurements to assess the degree of spatial dependence in power model adjustment phenomena. From a premise that considers the equivalent sill as the estimated semivariance value that matches the point where the adjusted power model curves intersect, it is possible to build two indexes to evaluate such dependence. The first one, SPD*, is obtained from the relation between the equivalent contribution (α) and the equivalent sill (C* = C0 + α), and varies from 0 to 100% (based on the calculation of spatial dependence areas). The second one, SDI*, beyond the previous relation, considers the equivalent factor of model (FM*), which depends on the exponent β that describes the force of spatial dependence in the power model (based on spatial correlation areas). The SDI*, for β close to 2, assumes its larger scale, varying from 0 to 66.67%. Both indexes have symmetrical distribution, and allow the classification of spatial dependence in weak, moderate and strong

SPATIAL DEPENDENCE INDEX FOR CUBIC, PENTASPHERICAL AND WAVE SEMIVARIOGRAM MODELS

Abstract: This study aims to propose a spatial dependence index (and its classification), from the concept of spatial correlation areas, for the Cubic, Pentaspherical and Wave models. The index, called Spatial Dependence Index (SDI), covers the following parameters: the range (a), the nugget effect (C 0 ) and the contribution (C 1 ), beyond considering the maximum distance (MD) between sampled points and the model factor (MF). The proposed index, unlike the most used in the literature, considers the influence of the range parameter to describe the spatial dependence, highlighting the importance of this formulation. The spatial dependence classification, based on the observed asymmetric behavior in the SDI, was performed considering categorizations from the median and the 3rd quartile of the index. We obtain the spatial dependence classification in terms of weak, moderate, and strong, just as it is usually described in literature

PROPOSAL OF THE SPATIAL DEPENDENCE EVALUATION FROM THE POWER SEMIVARIOGRAM MODEL

Abstract: In Geostatistics, the use of measurement to describe the spatial dependence of the attribute is of great importance, but only some models (which have second-order stationarity) are considered with such measurement. Thus, this paper aims to propose measurements to assess the degree of spatial dependence in power model adjustment phenomena. From a premise that considers the equivalent sill as the estimated semivariance value that matches the point where the adjusted power model curves intersect, it is possible to build two indexes to evaluate such dependence. The first one, SPD * , is obtained from the relation between the equivalent contribution (α) and the equivalent sill (C * = C 0 + α), and varies from 0 to 100% (based on the calculation of spatial dependence areas). The second one, SDI * , beyond the previous relation, considers the equivalent factor of model (FM * ), which depends on the exponent β that describes the force of spatial dependence in the power model (based on spatial correlation areas). The SDI * ,for β close to 2, assumes its larger scale, varying from 0 to 66.67%. Both indexes have symmetrical distribution, and allow the classification of spatial dependence in weak, moderate and strong

Some aspects about the spatial dependence index for variability of soil attributes

ABSTRACT: The main purpose of this article was to evaluate the behavior and relationship of the range and components of SDI (Spatial Dependence Index) in general and in function of field factors such as soil types, type of attribute and soil layers. This evaluation was based on real data collected in national journals. It was noticed that the parameter range, in general and for different field factors, presented asymmetric positive behavior. The components of the SDI showed approximately symmetrical behavior. The SDI can capture the range behavior more intensely (the spatial variability behavior in the horizontal direction of the semivariogram), and, in a less intense way, the behavior of the contribution and sill parameters (the spatial dependence behavior in the vertical direction of the semivariogram). Thus, the SDI describes the behavior of spatial dependence of the total set of aspects of the semivariogram