Estimating soil bulk density with information metrics of soil texture

- An information theory-based metric of the soil texture is proposed.
- Bulk density mean values have linear dependence on Information Entropy mean values.
- Information Entropy serves as an indicator of the typical bulk density.

Using the Shannon Information Entropy (IE) as a soil structure metric is proposed to analyze the effect of the particle size distribution (PSD) heterogeneity on soil bulk density values. A data base including 6239 soil samples from Florida is used. For each soil the IE is computed using mass proportions of the seven texture fractions that the data base provides. The range of IE values is divided into subintervals of equal length to study how differences in the soil texture metric are reflected in differences in soil bulk density values. The total range of IE values divided into equal subintervals, each subinterval corresponds to the group of soils with IE in this subinterval, average bulk density for soils in each subinterval is found, and the average information entropy value in any of the subintervals is plotted versus the average soil bulk density values. Coefficients of determination of the linear regressions 'average IE vs. average bulk density' were 0.99 and 0.98 for 10 and 15 subintervals respectively. Predictions based in that linear relationship give the mean predicted error (MPE) equal to 0.0015 g/cm3 over the total number of soils, and the normal distribution of prediction errors with the standard deviation of to 0.16 g/cm3. These results strongly support the hypothesis that Information Entropy can serve as an indicator of the typical bulk density for a soil with a given PSD. Values of IE were also computed for all samples in the database using only three texture fractions: clay, silt and sand content. Simple linear regression using the IE value as the input variable was implemented to predict bulk density value. Additionally, several published bulk density pedotransfer functions (PTFs), including organic carbon (OC) content and texture inputs, were applied to the same data base. Results show the root-mean-squared error of predictions close to 0.16 g/cm3 when the IE is used as the sole input. Estimation of bulk density using Information Entropy as predictor became worse for soils in horizon A than in the horizon E, respectively, possibly due to the influence of the different organic carbon content in those horizons.Overall, the Information Entropy metric of soil texture provides a useful input for estimating bulk density, which also might be used together with other inputs as depth or OC content.