An information metrics of soil texture -the Shannon Information Entropy-is proposed to analyze the contribution of the particle size distribution (PSD) in soil bulk density values.A database including 6239 soil samples from Florida is used. For each soil the Information Entropy is computed using mass proportions of the seven texture fractions that the database provides. The range interval of Information Entropy values is divided into an increasing number of subintervals of equal length, to study how differences in the soil texture metrics corresponded with differences in soil bulk density values. Grouping soil samples according to their information entropy, the average information entropy value in any of the resulting subintervals is plotted versus the corresponding average soil bulk density values. It was found that variations of less than 0.04 g/cm 3 in the mean bulk density values are explained with variations of mean information entropy values with an coefficient of determination equal to 0.99, being lower variations explained with no significant decrease in the fitting goodness. Predictions based in that linear regression give a mean predicted error (MPE) equal to 0.0015 g/cm 3 over the total number of soils, and a normal distribution of errors with standard deviation (SDPE) equal to 0.16 g/cm 3 . These results strongly support that Information Entropy serves as an indicator of the typical bulk density for a soil with a given PSD and average structure features.Information Entropy (IE) was also computed for all samples (6239) using clay, silt and sand content. Simple linear regression, now implemented using values of each soil sample, was used to predict bulk density values using the corresponding Information Entropy value as input. Additionally, different published bulk density pedotransfer functions (PTFs), including organic carbon (OC) content and texture inputs, are applied to the same data bank. Results show similar mean square predicting error (RSMPE) and standard deviation of predicted error (SDPE) when Information Entropy is used as unique input respect to those obtained using PTFs. The results become worse for soils in horizon A and better in horizon E, respectively, possibly due to the influence of the different OC content in those horizons. Notably, the MPE is, by average, about 3 3 orders of magnitude lower when IE is used respect to the MPE obtained by the PTFs, reflecting the potential of Information Entropy of texture in capturing mean soil bulk density values.Results show that Information Entropy metrics of soil texture provide a useful input for estimating bulk density, which also might be used together with other inputs as depth or OC content.

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A modelling of particle-size distribution in soil (PSD) by means of the fractal mass distribution is presented. The model is based on a new interpretation of the invariance of PSD with respect to the scale.It is shown that the modelized PSD can be mathematically determined from soil textural data. Combining some well-founded theoretical results from fractal geometry, the model allows us to simulate the PSD of a given soil and its characterization by means of the entropy dimension. The scaling behaviour of mass-size (or particlenumber) distribution empirically shown by different authors, is obtained from the model as a theoretical result.The model allows the testing of the degree of self-similarity of soil PSDs and can be used for predicting soil properties related to the PSD, as well as the characterization of soil textures.

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