Rev. Bras. Ciênc. Solo.2025;49:e0250042.

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Proposal and validation of geostatistical-based metrics to quantify within-field variability

Enio Júnior Seidel , Marcelo Silva de Oliveira

28/Oct/2025

DOI: 10.36783/18069657rbcs20250042

Graphical Abstract

ABSTRACT

Metrics are fundamental to quantify and classify the spatial dependence of soil and agricultural attributes. This study aimed to propose and validate metrics based on two distinct approaches, one additive, which considers the arithmetic mean of the vertical and horizontal components, and the other multiplicative, which considers the geometric mean of the vertical and horizontal components of the semivariogram. Furthermore, we intend to propose the classification of spatial dependence based on the categorization of these metrics. Finally, a function in R language is presented to calculate the metrics and classify spatial dependence. The spatial dependence arithmetic index 1 (SDAI1) and spatial dependence arithmetic index 2 (SDAI2) are constructed in a dimensionless way, in the range between 0 and 100 %, considering the sum (arithmetic mean) between the vertical and horizontal components of the semivariogram. The spatial dependence geometric index 1 (SDGI1) and the spatial dependence geometric index 2 (SDGI2) are constructed in a dimensionless way, in the range between 0 and 100 %, considering the multiplication (geometric mean) between the vertical and horizontal components of the semivariogram. The SDAI1, SDAI2, SDGI1, and SDGI2 metrics are compared with other metrics existing in the literature, such as the spatial dependence degree (SPD), the integral scales J1 and J2, the mean correlation distance (MCD), the spatial dependence index (SDI), and the spatial dependence measure (SDM). For different spatial dependence scenarios, correlations are calculated between the geostatistical-based metrics and the performance measures Moran’s I, mean squared error (MSE), and kriging variance (KV). The metrics perform well in describing spatial dependence, with the exception of J1 (or MCD) and J2. However, the SDAI1, SDAI2, and SDGI1 metrics have slightly better correlations with the Moran’s I, MSE, and KV measures, when compared to the SDI, SDM, SDGI2, and SPD metrics. Furthermore, the SDAI1 and SDAI2 metrics show superior performance in capturing the vertical and horizontal effects of the semivariogram. Finally, a function in R language was developed to calculate the metrics and classify spatial dependence.