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RESEARCH ARTICLE

Multifractal analysis of soil hydraulic properties in arid areas

N. Pahlevan A , M. R. Yazdani A C , A. A. Zolfaghari A and M. Ghodrati B
+ Author Affiliations
- Author Affiliations

A Faculty of Desert Studies, Semnan University, Semnan 35196-45399, Iran.

B Semnan Agriculture and Natural Resources Research Center, Semnan 35147-54374, Iran.

C Corresponding author. Email: m_yazdani@semnan.ac.ir

Soil Research 54(8) 914-925 https://doi.org/10.1071/SR15284
Submitted: 6 October 2015  Accepted: 22 June 2016   Published: 26 September 2016

Abstract

Physical and hydraulic properties of soil are variable at different spatial scales. This indicates the necessity of understanding spatial patterns of soil properties. Scaling analysis, such as multifractal analysis, has been used to determine the spatial variability of soil properties. There are however limited numbers of studies concerning the applications of multifractal techniques applied to characterise spatial variability of soil properties in arid lands. The objective of this study was to quantify the scaling patterns of soil properties measured across a transect and to apply multifractal analysis in arid land areas. A transect with a length of 4.80 km was selected, and soil properties were measured at 0–20 cm depth every 145 m along the transect. The soil properties analysed were: texture (sand, silt, clay), pH, electrical conductivity (EC), bulk density (BD), soil hydraulic properties (saturated hydraulic conductivity Ks and the van Genuchten soil water-retention equation’s parameters nv and αv), saturated water content (θs), and the slope of the soil water-retention curve at its inflection point (S). Results showed that the variability of pH and BD was characterised by quasi-monofractal behaviour. Results showed that soil hydraulic properties such as Ks, αn, nv, S, and θs were characterised by higher multifractal indices in the transects. EC showed the highest tendency to a multifractal type of scaling or the higher degree of multifractality.

Additional keywords: asymmetry index, box-counting method, hydraulic properties, tension infiltrometer.


References

Abd Rashid NS, Askari M, Tanaka T, Simunek J, van Genuchten M (2015) Inverse estimation of soil hydraulic properties under oil palm trees. Geoderma 241–242, 306–312.
Inverse estimation of soil hydraulic properties under oil palm trees.Crossref | GoogleScholarGoogle Scholar |

Ankeny MD, Ahmed M, Kaspar TC, Horton R (1991) Simple field method for determining unsaturated hydraulic conductivity. Soil Science Society of America Journal 55, 467–470.
Simple field method for determining unsaturated hydraulic conductivity.Crossref | GoogleScholarGoogle Scholar |

Biswas A, Zeleke TB, Si BC (2012) Multifractal extended fluctuation analysis in examining scaling properties of the spatial pattern of soil water storage. Nonlinear Processes in Geophysics 19, 227–238.
Multifractal extended fluctuation analysis in examining scaling properties of the spatial pattern of soil water storage.Crossref | GoogleScholarGoogle Scholar |

Bosch HE, Oliver MA, Webster R (2004) Wavelets and the generalization of the variogram. Mathematical Geosciences 36, 147–186.

Caniego FJ, Espejo R, Martín MA, San José F (2005) Multifractal scaling of soil spatial variability. Ecological Modelling 182, 291–303.
Multifractal scaling of soil spatial variability.Crossref | GoogleScholarGoogle Scholar |

Caridad-Cancela R, Vidal Vázquez E, Vieira SR, Abreu CA, Paz González A (2005) Assessing the spatial uncertainty of mapping trace elements in cultivated fields. Communications in Soil Science and Plant Analysis 36, 253–274.
Assessing the spatial uncertainty of mapping trace elements in cultivated fields.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2MXjslGrtrY%3D&md5=1db2ba20cf050eb2909fb823cc7d6649CAS |

Chhabra A, Jensen RV (1989) Direct determination of the f(α) singularity spectrum. Physical Review Letters 62, 1327–1330.
Direct determination of the f(α) singularity spectrum.Crossref | GoogleScholarGoogle Scholar | 10039645PubMed |

Evertsz CJG, Mandelbrot BB (1992) Multifractal measures. In ‘Chaos and fractals’. (Eds H Peitgen, H Jürgens, D Saupe) pp. 921–953. (Springer: Berlin)

Falconer K (1997) ‘Techniques of fractal geometry.’ (John Wiley & Sons: Chichester)

Folorunso OA, Puente CE, Rolston DE, Pinzón JE (1994) Statistical and fractal evaluation of the spatial characteristic of soil surface strength. Soil Science Society of America Journal 58, 284–294.
Statistical and fractal evaluation of the spatial characteristic of soil surface strength.Crossref | GoogleScholarGoogle Scholar |

Gardner W (1958) Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Science 85, 228–232.
Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table.Crossref | GoogleScholarGoogle Scholar |

Gee GW, Bauder JW (1986) Particle size analysis. In ‘Methods of soil analysis. Part 1. Physical and mineralogical methods. Agronomy Handbook No. 9’. (Ed. A Klute) pp. 383–411. (Soil Science Society of America: Madison, WI)

Goovaerts P, Gérard G, Frankart R (1989) Etude de la variabilité spatiale de quelques propriétés chimiques du sol en Fagne de Chimay, Belgique. Pédologie 39, 191–207.

Grassberger P (1983) Generalized dimensions of strange attractors. Physics Letters 97, 227–230.
Generalized dimensions of strange attractors.Crossref | GoogleScholarGoogle Scholar |

Grundmann GL, Debouzie D (2000) Geostatistical analysis of the distribution of NH4+ and NO2 oxidizing bacteria and serotypes at the millimeter scale along a soil transect. FEMS Microbiology Ecology 34, 57–62.

Halsey TC, Jensen MH, Kadanoff LP, Procaccia I, Shraiman BJ (1986) Fractal measures and their singularities: the characterization of strange sets. Physical Review A. 33, 1141–1151.
Fractal measures and their singularities: the characterization of strange sets.Crossref | GoogleScholarGoogle Scholar |

Hentschel HE, Procaccia I (1983) The infinite number of generalized dimensions of fractals and strange attractors. Physica D. Nonlinear Phenomena 8, 435–444.
The infinite number of generalized dimensions of fractals and strange attractors.Crossref | GoogleScholarGoogle Scholar |

Hussen AA, Warrick AW (1995). Tension infiltrometer for the measurement of vadose zone hydraulic properties. In ‘Handbook of Vadose zone characterization & monitoring’. (Eds LG Wilson, LG Everett, SJ Cullen) pp. 189–201. (Lewis Publishers: Boca Raton)

Kelishadi H, Mosaddeghi MR, Hajabbasi MA, Ayoubi S (2014) Near-saturated soil hydraulic properties as influenced by land use management systems in Koohrang region of central Zagros, Iran. Geoderma 213, 426–434.
Near-saturated soil hydraulic properties as influenced by land use management systems in Koohrang region of central Zagros, Iran.Crossref | GoogleScholarGoogle Scholar |

Kirkham MB (2005) ‘Principles of soil and plant water relations.’ (Elsevier Academic Press: Cambridge, MA)

Kravchenko AN (2008) Stochastic simulations of spatial variability based on multifractal characteristics. Vadose Zone Journal 7, 521–524.
Stochastic simulations of spatial variability based on multifractal characteristics.Crossref | GoogleScholarGoogle Scholar |

Kravchenko AN, Boast CW, Bullock DG (1999) Multifractal analysis of soil spatial variability. Agronomy Journal 91, 1033–1041.
Multifractal analysis of soil spatial variability.Crossref | GoogleScholarGoogle Scholar |

Mach J, Mas F, Sagués F (1995) Two representations in multifractal analysis. Journal of Physics. A, Mathematical and General 28, 5607–5622.
Two representations in multifractal analysis.Crossref | GoogleScholarGoogle Scholar |

Mc Bratney AB, Webster R (1981) Spatial dependence and classification of the soil along a transect in northeast Scotland. Geoderma 26, 63–82.
Spatial dependence and classification of the soil along a transect in northeast Scotland.Crossref | GoogleScholarGoogle Scholar |

McBratney AB, Minasny B, Cattle SR, Vervoort RW (2002) From pedotransfer functions to soil inference systems. Geoderma 109, 41–73.
From pedotransfer functions to soil inference systems.Crossref | GoogleScholarGoogle Scholar |

Morales LA, Vidal Vázquez E, Paz Ferreiro J (2011) Influence of liming on the spatial and temporal variability of Mehlich-1 extractable Fe in a rice field. Journal of Geochemical Exploration 109, 78–85.
Influence of liming on the spatial and temporal variability of Mehlich-1 extractable Fe in a rice field.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3MXltl2qurc%3D&md5=4a73273bef3b0cc72a603e8cb2de2b10CAS |

Pachepsky YA, Timlin D, Varallyay G (1996) Artificial neural networks to estimate soil water retention from easily measurable data. Soil Science Society of America Journal 60, 727–733.
Artificial neural networks to estimate soil water retention from easily measurable data.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK28XjtFanurc%3D&md5=948c633fb8be2520e2c50e8fbc84bdf7CAS |

Paz A, Taboada MT, Gómez MJ (1996) Spatial variability in topsoil micronutrient contents in a one-hectare cropland plot. Communications in Soil Science and Plant Analysis 27, 479–503.
Spatial variability in topsoil micronutrient contents in a one-hectare cropland plot.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK28XhsFWqt7w%3D&md5=445987806af7be62a1ba64c5930e64a6CAS |

Simůnek J, van Genuchten MT (1997) Estimating unsaturated soil hydraulic properties from multiple tension disc infiltrometer data. Soil Science 162, 383–398.
Estimating unsaturated soil hydraulic properties from multiple tension disc infiltrometer data.Crossref | GoogleScholarGoogle Scholar |

Simunek J, van Genuchten MT, Sejna M (2000) The DISC computer software for analyzing tension disc infiltrometer data by parameter estimation. Ver. 1.0., U.S. Salinity Laboratory, Riverside, CA.

van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, 892–898.
A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.Crossref | GoogleScholarGoogle Scholar |

Vidal-Vázquez E, Camargo OA, Viera SR, Miranda JGV, Menk JRF, Siqueira GM, Miras-Avolas JM, Pas Gonzeles A (2013) Multifractal analysis of soil properties along two perpendicular transects. Vadose Zone Journal 12, 3.
Multifractal analysis of soil properties along two perpendicular transects.Crossref | GoogleScholarGoogle Scholar |

Vieira SR, Hatfield JL, Nielsen DR, Biggar JW (1983) Geostatistical theory and application to variability of some agronomical properties. Hilgardia 51, 1–75.
Geostatistical theory and application to variability of some agronomical properties.Crossref | GoogleScholarGoogle Scholar |

Warrick AW (1992) Models for disk infiltrometers. Water Resources Research 28, 1319–1327.
Models for disk infiltrometers.Crossref | GoogleScholarGoogle Scholar |

Webster R (1977) Spectral analysis of gilgai soil. Soil Research 15, 191–204.
Spectral analysis of gilgai soil.Crossref | GoogleScholarGoogle Scholar |

Webster R, Cuanalo de la C HE (1975) Soil-transect correlograms of north Oxfordshire and their interpretation. European Journal of Soil Science 26, 176–194.
Soil-transect correlograms of north Oxfordshire and their interpretation.Crossref | GoogleScholarGoogle Scholar |

Webster R, Oliver MA (2000) ‘Geostatistics for environmental scientists.’ (John Wiley & Sons: Chichester)

Wooding R (1968) Steady infiltration from a shallow circular pond. Water Resources Research 4, 1259–1273.
Steady infiltration from a shallow circular pond.Crossref | GoogleScholarGoogle Scholar |

Xie S, Cheng Q, Xing X, Bao Z, Chen Z (2010) Geochemical multifractal distribution patterns in sediments from ordered streams. Geoderma 160, 36–46.
Geochemical multifractal distribution patterns in sediments from ordered streams.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3cXhsFSmtrjI&md5=d44ae38a3999d9090926f6ba604309c6CAS |

Zeleke TB, Si BC (2006) Characterizing scale-dependent spatial relationships between soil properties using multifractal techniques. Geoderma 134, 440–452.
Characterizing scale-dependent spatial relationships between soil properties using multifractal techniques.Crossref | GoogleScholarGoogle Scholar |