More adequate probability distributions to represent the saturated soil hydraulic conductivity

Abstract

The saturated soil hydraulic conductivity (Ksat) is one of the most relevant variables in studies of water and solute movement in the soil. Its determination in the laboratory and in the field yields high dispersion results, which could be an indication that this variable has a no symmetrical distribution. Adjustment of the normal, lognormal, gamma and beta distributions were examined in order to search for a probability were density function that would more adequately describe the distribution of this variable. The experiment consisted in determining the saturated hydraulic conductivity, through the constant head permeameter method, in undisturbed samples of three soils of different textures from the central western region of the São Paulo State, Brazil, and submitting the results to the statistical tests for identification of the most adequate asymmetrical distribution to represent them. Ksat presented high variability, non normal distribution and lognormal, gamma and beta distributions fit. The lognormal probability density function was the most indicated to describe the variable, due to the verified greater agreement.

Improvement of a testing apparatus for dynamometry: procedures for penetrometry and influence of strain rate to quantify the tensile strength of soil aggregates

“…Additionally, robust statistical techniques were used for the quantification of experimental errors (Zacharias et al, 1996;Mesquita et al, 2002), i.e. techniques that do not require normal data distribution, except for equations (13) and (14) ( Table 2).…”

“…This indicates that not all experimental observations were symmetrically distributed around these statistical indexes, which probably requires prior data transformation so that results can be analyzed and interpreted correctly (Mesquita et al, 2002). The Kolmogorov-Smirnov test was applied to verify normal residual distribution of variance analysis, where the need for logarithmic data transformation to stabilize the treatment variances and tailor them to parametric statistical tests was confirmed (McIntyre & Tanner, 1959;Logsdon & Jaynes, 1996;Mesquita et al, 2002).…”

An analysis of polynomial chaos approximations for modeling single-fluid-phase flow in porous medium systems

“…Whether conductivities can reasonably be assumed lognormal is a regular topic of investigation: the distribution in a sandstone formation, for example, varied with the part sampled [18], while a soil investigation concluded the lognormal distribution fit the data better than a gamma distribution [59]. Although the validity of using Gaussian fields to describe log-conductivities remains open to question [27], we adopt the hypothesis here because it is convenient for calculation and has commonly been assumed [82].…”

“…For the standard simplex with vertices defined by the origin and standard basis vectors, one considers vectors ζ ≡ (z ω 1 , z ω 2 , ⋯ , z ω e ) of non-negative integers satisfying |ζ| ≤ d and takes as knots the points with spatial coordinates n ζ ≡ ζ/d. The corresponding interpolatory polynomials are defined by (59) If instead, one dilates the standard simplex by the factor d, the knots coincide with the vectors ζ and the polynomials become p ζ (ω/d). Carnicer et al [12] have obtained error estimates for such interpolations.…”

Alternativa para caracterização da condutividade hidráulica saturada do solo utilizando probabilidade de ocorrência

“…Há referências na literatura mostrando que os valores de condutividade hidráulica saturada em uma área específica podem ser muito distintos, assumindo grande amplitude total e elevados coeficientes de variação (BREJDA et al, 2000;COOKE et al, 1995;COOLEY, 1999;HANN & ZHANG, 1996;KUTILEK & NIELSEN, 1994;MESQUITA, 2001;MESQUITA et al, 2002;MOURA et al, 1999;PAZ et al, 1996;SMESRUD & SELKER, 2001;WARRICK & NIELSEN, 1980). Isto pode ser um indicativo de que a propriedade não é representada por uma distribuição de probabilidade simétrica e, portanto nem sempre a média e/ou mediana podem ser assumidas como valores representativos de toda a área.…”