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Multifractal Analysis of Vertical Profiles of Soil Penetration Resistance at The EGU Journal Logos (RGB) Open Access Open Access Open Access Nonlin. Processes Geophys., 20, 529–541, 2013 Advanceswww.nonlin-processes-geophys.net/20/529/2013/ in Annales Nonlinear Processes doi:10.5194/npg-20-529-2013 Geosciences© Author(s) 2013. CC AttributionGeophysicae 3.0 License. in Geophysics Open Access Open Access Natural Hazards Natural Hazards and Earth System and Earth System Sciences Sciences Multifractal analysis of verticalDiscussions profiles of soil penetration Open Access Open Access Atmosphericresistance at the field scaleAtmospheric Chemistry Chemistry and PhysicsG. M. Siqueira1, E. F. F. Silva1, A. A. A. Montenegroand Physics1, E. Vidal Vazquez´ 2, and J. Paz-Ferreiro2,3 1 Department of Rural Technology, Federal Rural UniversityDiscussions of Pernambuco, Dom Manoel de Medeiros s/n, Open Access 52171-900Open Access Recife-PE, Brazil Atmospheric2Faculty of Sciences, University of Coruna,˜ CampusAtmospheric A Zapateira, 15008 Coruna,˜ Spain 3 MeasurementDepartment of Edaphology, Polytechnic UniversityMeasurement of Madrid, Av. Complutense sn, 28040 Madrid, Spain TechniquesCorrespondence to: J. Paz-Ferreiro ([email protected])Techniques Discussions Received: 31 August 2012 – Revised: 6 May 2013 – Accepted: 9 June 2013 – Published: 23 July 2013 Open Access Open Access Biogeosciences BiogeosciencesAbstract. Soil penetration resistance (PR) is widely used as 1 Introduction Discussions an indirect indicator of soil strength. Soil PR is linked to ba- sic soil properties and correlated to root growth and plant production, and as such it is extensively used as a practi- Soil strength is defined as the resistance that has to be over- Open Access comeOpen Access to cause soil physical deformation. Soil strength is an cal tool for assessing soil compaction and to evaluateClimate the Climateeffects of soil management. This study investigates how re- important soil physical property as it affects basic aspects of agricultural soils, including root growth, seedling emer- of thesults Past from multifractal analysis can quantify keyof elements the ofPast depth-dependent soil PR profiles and how this informationDiscussionsgency, compaction, erodibility, trafficability and bearing ca- can be used at the field scale. We analysed multifractality of pacity (Guerif,´ 1990; Soane and Van Ouwerkerk, 1994). Di- rect measurement of soil strength properties are difficult to Open Access 50 PR vertical profiles, measured from 0 to 60 cm depth and Open Access randomly located on a 6.5 ha sugar cane fieldEarth in northeast- Systemperform, so they have remained until now rather scarce. In- Earth Systemern Brazil. The scaling property of each profile was typified stead, most frequently, soil resistance to deformation is indi- Dynamicsby singularity, and Renyi´ spectra estimated by theDynamics method of rectly and empirically assessed by measuring the resistance moments. The Hurst exponent was used to parameterizeDiscussions the to penetration of a metallic plunger with a particular shape, autocorrelation of the vertical PR data sets. The singularity usually a cone, which is referred to as a penetrometer (e.g. and Renyi` spectra showed that the vertical PR data sets ex- ASAE, 1986). Thus, penetrometers are simple and relatively Open Access Open Access Geoscientifichibited a well-defined multifractal structure. HurstGeoscientific exponent inexpensive devices, easily providing an indirect indication Instrumentationvalues were close to 1, ranging from 0.944Instrumentation to 0.988, indicat- of soil strength. Penetration resistance is an easily measurable parameter Methodsing and strong persistence in PR variation with soilMethods depth. Also, and the Hurst exponent was negatively and significantly corre- which has been found to depend on basic soil properties that Data Systemslated to coefficient of variation (CV), skewnessData and Systems maxi- are vital for plant growth, mainly soil composition, struc- mum values of the depth-dependent PR. Multifractal analysisDiscussionsture, bulk density and water content. In addition, PR corre- Open Access Open Access lates with several properties of agronomic importance, such added valuable information to describe the spatialGeoscientific arrange- Geoscientificment of depth-dependent penetrometer data sets, which was as crusting, compaction or vehicle trafficability. Thus, PR has not taken into account by classicalModel statistical Development indices. Multi- been often used as a surrogate measurement of key soil prop- Model Development fractal parameters were mapped over the experimentalDiscussions field erties (e.g. Dexter et al., 2007). Indeed, penetrometers have and compared with mean and maximum values of PR. Com- been utilized in a number of field experiments to assess soil compaction (e.g. O’Sullivan et al., 1987) or the effects of bination of spatial variability survey and multifractal analysis Open Access Open Access Hydrologyappear and to be useful to manage soil compaction.Hydrology andsoil management (e.g. Castrignano´ et al., 2002). Conversely, equations for predicting penetrometer resistance from soil Earth System Earth Systemproperties have been proposed (e.g. Dexter et al., 2007; Vaz Sciences Scienceset al., 2011). Moreover, soil PR above a given threshold has Discussions Open Access PublishedOpen Access by Copernicus Publications on behalf of the European Geosciences Union & the American Geophysical Union. Ocean Science Ocean Science Discussions Open Access Open Access Solid Earth Solid Earth Discussions Open Access Open Access The Cryosphere The Cryosphere Discussions 530 G. M. Siqueira et al.: Multifractal analysis of soil PR been shown to affect root penetration and hence crop produc- Ness (1968). The Bm model corresponds to a Gauss–Markov tion (Hakansson¨ et al., 1988). Consequently, field penetrom- process, i.e. a random process consisting of a sequence of eters also have been frequently employed for estimating re- discrete steps of fixed length, where correlation between suc- sistance to root growth in soil as soil PR is a rough indicator cessive values vanishes. For a f Bm model the Hurst parame- of the pressure encountered by roots for elongation. ter H, (0 < H < 1), is directly related to the long-term mem- Nowadays, micropenetrometers are increasingly used in ory of the studied variable. The range 1/2 < H < 1 is usu- laboratory conditions. This is because of the wide acceptance ally associated with persistence (positive autocorrelation) or of a quality index based on three main soil physical proper- long-range dependencies, whereas the range 0 < H < 1/2 ties: soil strength, matric potential and aeration. This index represents anti-persistent behaviour (negative autocorrela- was defined by Letey (1985) as “the range of moisture con- tion) and short-range dependencies (e.g. Feder, 1988). More tent at which plant water uptake is neither limited by soil re- recently, it has been also recognized that a large class of mul- sistance when dry, nor by poor aeration when too wet”, and is tifractal processes could be approximated by the multifractal now referred to as “least limiting water range” (LLWR), fol- Brownian motion (mBm) models, based on the fact that the lowing Da Silva et al. (1994). Soil strength data required for power law behaviour of second-order statistics allows esti- LLWR evaluation are readily provided by PR measurements. mation of a generalized Hurst scaling function (e.g. Leland Soils are highly variable and heterogeneous over several et al., 1994; San Jose´ Mart´ınez et al., 2010). It is worth noth- spatial scales. Over the past few decades scaling analysis, ing that, similar to the Hurst exponent, the generalized Hurst such as fractal and multifractal analysis have been applied scaling function can be categorized into three types, i.e. per- to characterize soil properties and processes, and many stud- sistent, entirely random distribution and anti-persistent. ies have revealed scale-dependent patterns of soil variability Several studies also have reported self-affine scale- from very short distances (e.g. Pachepsky et al., 1996; Paz- dependent patterns and singularity of the spatial variation of Ferreiro et al., 2010) to geomorphologic landscapes units soil PR itself in horizontal layers (e.g. Usowicz and Lipiec, (Biswas et al., 2012), or even continents and the whole plane- 2009; Perez´ et al., 2010). Furthermore, multifractal analysis tary scale (Caniego et al., 2006). Both fractal and multifractal has been used to assess patterns of spatial variation of pen- scaling assume a hierarchical distribution of mass in space etrometric data sets measured along transects (Folorunso et so that the whole results from the union of similar subsets. al., 1994) or on planes (Roisin, 2007), providing valuable in- While in the fractal approach subsets are considered similar formation to better understand the inner structure of PR for to the whole, multifractal distributions hypothesize that sub- horizontal soil layers. However, to the best of our knowledge, sets are related to the whole through varying scaling factors until now multifractal analysis has not been applied to char- (e.g. Tarquis et al., 2003). As a consequence, in monofrac- acterize the spatial heterogeneity of depth-dependent, verti- tal scaling, one single exponent is sufficient to characterize cal resistance profiles obtained by penetrometer. Therefore, the scaling behaviour, whereas multifractal scaling involves a the objectives of this work were (a) to characterize the in- continuous spectrum of scale exponents, which are related to
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