Describing soil surface microrelief by crossover length and fractal dimension

International audienceAccurate description of soil surface topography is essential because different tillage tools produce different soil surface roughness conditions, which in turn affects many processes across the soil surface boundary. Advantages of fractal analysis in soil microrelief assessment have been recognised but the use of fractal indices in practice remains challenging. There is also little information on how soil surface roughness decays under natural rainfall conditions. The objectives of this work were to investigate the decay of initial surface roughness induced by natural rainfall under different soil tillage systems and to compare the performances of a classical statistical index and fractal microrelief indices. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plow, chisel plow, disc harrow + disc level, disc plow + disc level and chisel plow + disc level were tested. Measurements were made four times, firstly just after tillage and subsequently with increasing amounts of natural rainfall. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental surfaces. The sampling scheme was a square grid with 25×25 mm point spacing and the plot size was 1350×1350 mm, so that each data set consisted of 3025 individual elevation points. Statistical and fractal indices were calculated both for oriented and random roughness conditions, i.e. after height reading have been corrected for slope and for slope and tillage tool marks. The main drawback of the standard statistical index random roughness, RR, lies in its no spatial nature. The fractal approach requires two indices, fractal dimension, D, which describes how roughness changes with scale, and crossover length, l, specifying the variance of surface microrelief at a reference scale. Fractal parameters D and l, were estimated by two independent self-affine models, semivariogram (SMV) and local root mean square (RMS). Both algorithms, SMV and RMS, gave equivalent results for D and l indices, irrespective of trend removal procedure, even if some bias was present which is in accordance with previous work. Treatments with two tillage operations had the greatest D values, irrespective of evolution stage under rainfall and trend removal procedure. Primary tillage had the greatest initial values of RR and l. Differences in D values between treatments with primary tillage and those with two successive tillage operations were significant for oriented but not for random conditions. The statistical index RR and the fractal indices l and D decreased with increasing cumulative rainfall following different patterns. The l and D decay from initial value was very sharp after the first 24.4 mm cumulative rainfall. For five out of six tillage treatments a significant relationship between D and l was found for the random microrelief conditions allowing a covariance analysis. It was concluded that using RR or l together with D best allow joint description of vertical and horizontal soil roughness variations

A multifractal approach to characterize cumulative rainfall and tillage effects on soil surface micro-topography and to predict depression storage

Most of the indices currently employed for assessing soil surface micro-topography, such as random roughness (RR), are merely descriptors of its vertical component. Recently, multifractal analysis provided a new insight for describing the spatial configuration of soil surface roughness. The main objective of this study was to test the ability of multifractal parameters to assess in field conditions the decay of initial surface roughness induced by natural rainfall under different soil tillage systems. In addition, we evaluated the potential of the joint use of multifractal indices plus RR to improve predictions of water storage in depressions of the soil surface (MDS). Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plough, chisel plough, disc harrow + disc level, disc plough + disc level and chisel plough + disc level were tested. In each treatment soil surface micro-topography was measured four times, with increasing amounts of natural rainfall, using a pin meter. The sampling scheme was a square grid with 25 × 25 mm point spacing and the plot size was 1350 × 1350 mm (≈1.8 m<sup>2</sup>), so that each data set consisted of 3025 individual elevation points. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental data sets. MDS was estimated from grid elevation data with a depression-filling algorithm. Multifractal analysis was performed for experimental data sets as well as for oriented and random surface conditions obtained from the former by removing slope and slope plus tillage marks, respectively. All the investigated microplots exhibited multifractal behaviour, irrespective of surface condition, but the degree of multifractality showed wide differences between them. Multifractal parameters provided valuable information for characterizing the spatial features of soil micro-topography as they were able to discriminate data sets with similar values for the vertical component of roughness. Conversely, both, rough and smooth soil surfaces, with high and low roughness values, respectively, can display similar levels of spectral complexity. Although in most of the studied cases trend removal produces increasing homogeneity in the spatial configuration of height readings, spectral complexity of individual data sets may increase or decrease, when slope or slope plus tillage tool marks are filtered. Increased cumulative rainfall had significant effects on various parameters from the generalized dimension, <i>D</i><sub>q</sub>, and singularity spectrum, <i>f</i>(α). Overall, micro-topography decay by rainfall was reflected on a shift of the singularity spectra, <i>f</i>(α) from the left side (<i>q</i>>>0) to the right side (<i>q</i><<0) and also on a shift of the generalized dimension spectra from the right side (<i>q</i>>>0) to the left side (<i>q</i><<0). The use of an exponential model of vertical roughness indices, RR, and multifractal parameters accounting for the spatial configuration such as <i>D</i><sub>1</sub> or <i>D</i><sub>5</sub> improved estimation of water stored in surface depressions

Componentes no cristalinos y cristalinos (gibbsita y caolinita) en los productos de neoformación de rocas graníticas de Galicia.

[Resumen] El estudio de los recubrimientos y costras existentes en las diaclasas y fracturas superficiales de rocas graníticas de Galicia permite la diferenciación de dos tipos de materiales: a) Materiales con predominio de componentes con bajo grado de orden. Se localizan en las fracturas subhorizontales por las que discurre el agua que atraviesa el suelo y la saprolita. b) Materiales cristalinos de naturaleza gibbsítica y/o caolinítica. Se localizan en las fracturas verticales.[Abstract] The study of 'coatings and crust on the diaclasas and cracks on the surface of granitic rocks in Galicia, let us differenciate two kinds of materials. a) Materials in wich low order degree components are predominant. These are lacated in subhorizontal cracks through wich water flows. b) Crystalline materials with a gibbsitic and/or kaolinitic minerals, located in the vertical crack

Assessment of the spatial variability of soil chemical properties along a transect using multifractal analysis

[Abstract]The spatial variability of soil properties can be assessed through concepts of scale invariance, fractals and multifractals. The aim of this study was to characterize the scaling patterns and structural heterogeneity properties of general soil chemical properties along a short (i.e. 52 m large) transect. Field measurements were carried out at the experimental farm of CIAM located in Mabegondo, A Coruña, Spain. The studied transect was marked following land slope, and 66 soil samples were collected at the 0-20 cm depth every 0.8 m. The soil properties analyzed were: pH (H2O ), organic carbon content, exchangeable Ca, Mg and K, exchangeable acidity (H + Al), exchangeable bases (SB), cation exchange capacity (CEC), percent base saturation (V) and extractable P. The soil properties studied showed various degrees of multifractality. The spatial distribution of pH was characterized by quasi-monofractal behaviour; CEC, (H+Al) and OM, presented a relatively low degree of multifractality, and the other soil properties studied showed stronger degrees of multifractality, being the highest one for Olsen extractable P. In general, the scaling features of the properties studied implied a multifractal nature, where the low and high density regions scaled differently

Support vector machines framework for linear signal processing

This paper presents a support vector machines (SVM) framework to deal with linear signal processing (LSP) problems. The approach relies on three basic steps for model building: (1) identifying the suitable base of the Hilbert signal space in the model, (2) using a robust cost function, and (3) minimizing a constrained, regularized functional by means of the method of Lagrange multipliers. Recently, autoregressive moving average (ARMA) system identification and non-parametric spectral analysis have been formulated under this framework. The generalized, yet simple, formulation of SVM LSP problems is particularized here for three different issues: parametric spectral estimation, stability of Infinite Impulse Response filters using the gamma structure, and complex ARMA models for communication applications. The good performance shown on these different domains suggests that other signal processing problems can be stated from this SVM framework.Publicad

Análise granulométrica de Argissolo Vermelho-Amarelo da região dos Tabuleiros Costeiros por difração de raios laser.

A granulometria influencia diretamente processos químicos e físico-hídricos. Assim, a análise granulométrica do solo deve ser procedida da maneira mais detalhada possível a fim de melhor entender sua composição e as variações que ocorrem horizontalmente no perfil e lateralmente, quando se considera uma área. O objetivo deste trabalho foi comparar a análise granulométrica de um perfil de Argissolo Amarelo característico da região dos Tabuleiros Costeiros, pela técnica de difração de raios com a determinação pelo método da pipeta, discutindo a importância do melhor fracionamento permitido pela utilização de raios laser. De uma maneira geral, se observou maiores porcentagens de argila e silte fino pelo método de difração de raios laser, enquanto os maiores valores relativos de silte grosso foram determinados pelo método da pipeta. As maiores disparidades foram observadas no horizonte transicional EB entre 20 e 40cm, onde se encontra a maior expressão do caráter coeso no perfil. Foi possível observar que, em todos os horizontes, a exceção do EB (20-40cm), as partículas entre 0,6um e 1,0um representam aproximadamente a metade da fração argila e que predomina no silte fino os diâmetros entre 2,0um e 6,0um. Entre as frações de silte, os diâmetros entre 20um e 50um predominaram no horizonte eluvial (5-20cm) e nos horizontes Bt (40-200cm). Comparando todos os diâmetros de partículas analisados a partir da técnica de difração de raios laser, se observou que o horizonte transicional EB se diferenciou dos demais, sendo observadas nele as maiores concentrações dos maiores diâmetros das frações argila e silte

Multiscale Soil Investigations: Physical Concepts And Mathematical Techniques

Soil variability has often been considered to be composed of “functional” (explained) variations plus random fl uctuations or noise. However, the distinction between these two components is scale dependent because increasing the scale of observation almost always reveals structure in the noise (Burrough, 1983). Soils can be seen as the result of spatial variation operating over several scales, indicating that factors infl uencing spatial variability differ with scale. Th is observation points to variability as a key soil attribute that should be studied

Interspecific Introgression in Cetaceans: DNA Markers Reveal Post-F1 Status of a Pilot Whale

Visual species identification of cetacean strandings is difficult, especially when dead specimens are degraded and/or species are morphologically similar. The two recognised pilot whale species (Globicephala melas and Globicephala macrorhynchus) are sympatric in the North Atlantic Ocean. These species are very similar in external appearance and their morphometric characteristics partially overlap; thus visual identification is not always reliable. Genetic species identification ensures correct identification of specimens. Here we have employed one mitochondrial (D-Loop region) and eight nuclear loci (microsatellites) as genetic markers to identify six stranded pilot whales found in Galicia (Northwest Spain), one of them of ambiguous phenotype. DNA analyses yielded positive amplification of all loci and enabled species identification. Nuclear microsatellite DNA genotypes revealed mixed ancestry for one individual, identified as a post-F1 interspecific hybrid employing two different Bayesian methods. From the mitochondrial sequence the maternal species was Globicephala melas. This is the first hybrid documented between Globicephala melas and G. macrorhynchus, and the first post-F1 hybrid genetically identified between cetaceans, revealing interspecific genetic introgression in marine mammals. We propose to add nuclear loci to genetic databases for cetacean species identification in order to detect hybrid individuals.