ALBERT

Description: The objective of this work was to characterize the scaling properties of depth-dependent penetration resistance (PR) profiles using multifractal analyses and to explore the effects of increasing soil water deficit on the scaling heterogeneity of the studied data series. Soil PR was recorded at 11 successive dates with decreasing soil water content on a Mollisol (Argiudoll) from Entre Ríos Province, Argentina. For each date, 10 replicated PR vertical profiles were measured every centimeter from 0 to 80 cm. Both singularity and Rènyi spectra showed that all PR datasets exhibited a well-defined multifractal structure, so that the multifractal approach provided considerable detailed information on their depth-dependent structure. The entropy dimension, D 1 , significantly ( P 〈 0.05) increased with decreasing soil water content, and its mean values ranged from 0.976 to 0.981. Therefore, the drier the soil, the more the homogeneity and evenness of the PR depth-dependent profiles. Moreover, the amplitude of the branches of the Rényi and singularity spectra accounting for the most positive statistical moments, [0, 5], significantly ( P 〈 0.05) decreased with increased soil water deficit. However, for the most negative counterparts, [0, –5], these amplitudes tended to increase, although not significantly. Subsequently, increasing soil dryness increased the homogeneity of the highest PR values, but had no significant effect on the homogeneity of the lowest PR values. The multifractal approach was useful to characterize changes in inner structure, heterogeneity, and evenness of PR vertical profiles over a period with increasing soil water deficit.

Description: The physical processes taking place in the ground are influenced by solar radiation. This climatic variable presents a strong local behavior; therefore local models to estimate irradiation are usually more adequate than others which are more global. The aim of this study was to develop models for global, diffuse and direct radiation in A Coruña (Northwest of Spain), and to apply Multifractal Detrending Fluctuation Analysis (MFDFA) as tool for the assessment of model quality, complementing traditional validation parameters. Autoregressive Integrated Moving Average (ARIMA) methodology was used to obtain daily radiation models. The global irradiation series model explained over 55% of the variance. The model for diffuse radiation showed the lowest prediction errors, and the direct radiation model offered the worst outcomes with the highest errors and the lowest R 2 . MFDFA allowed us to check that the model for global irradiation reproduced the main statistical characteristics of the data series: scale exponent values and points of slope change, and, in general, the multifractal behavior. The diffuse model presented a similar behavior of the series for short-term large fluctuations, whereas the model for direct irradiation was not capable to reflect the multifractality of the data series. MFDFA can be used as a complement for model assessment, since it offers an analysis of model behavior at different timescales.

Description: The spatial variability of soil properties can be best characterized through concepts of scale invariance, fractals, and multifractals. The objectives of this study were to analyze and to compare the scaling patterns and structural heterogeneity of soil properties across two transects in Campinas, SP, Brazil, using the multifractal formalism. Two transects were marked parallel and perpendicular to land slope, with a length of 2.28 and 1.98 km, respectively. Soil samples were collected at the 0 to 20 cm depth every 30 m. The soil properties analyzed were: texture (sand, silt, clay), pH (H 2 O and KCl), organic carbon (OC) content, exchangeable Ca, H, and Al, exchangeable bases (SB), cation exchange capacity (CEC), and percent base saturation (V). Spatial variability of soil properties was controlled by natural causes, including parent material and topography, and by soil use and management. The variability of pH across the two transects was characterized by either quasi-monofractal behavior or by a relatively low degree of multifractality. The other soil properties studied showed stronger degrees of multifractality. Hence, the multifractality for OC and silt content was much higher at the transect perpendicular to land slope. Variables from the soil exchange complex, particularly exchangeable Al, Ca, and SB, were characterized by higher multifractal indices in the two transects. Patterns of spatial distribution assessed by multifractal analysis were linked to soil forming factors and processes. Our results suggest that scale heterogeneity in the spatial distribution of soil properties was enhanced by the interaction of various natural or anthropogenic sources of variability.