Abstract
An adequate understanding of soil spatial variation as a function of space and scale is necessary in ecological modeling, environmental prediction, precision agriculture, soil quality assessment and natural resources management. Soil spatial variation can be partitioned into frequencies (scale) and positions (location) by the wavelet transform. This review focuses mainly on different applications of the continuous wavelet transform (CWT) for the identification of the scale and location dependence of soil attributes. We discussed both wavelet spectra and wavelet coherence in our analysis of soil spatial variation. Global wavelet spectra, being the sum of wavelet spectra over all spatial locations at a scale, can be used to examine the dominant scale of variation. Furthermore, some variations at a particular scale persist over all locations (termed global features), whereas others are present at only a few locations (localized features). Wavelet spectra can be used to identify both localized and global features. The combination of localized and global features provides a complete picture of the scale-location information of different processes in the field and may provide better guidance in designing efficient management practices. Wavelet coherency partitions the total correlation between two variables into correlations at different scales and locations, while also revealing the scale- and location-specific relationship between those two variables. This relationship may be helpful in developing predictive links between one property and another.
Similar content being viewed by others
References
Biswas A, Si BC, Walley FL (2008) Spatial relationship between δ 15N and elevation in agricultural landscapes. Nonlinear Process Geophys 15(3):397–407
Bosch EH, Oliver MA, Webster R (2004) Wavelets and generalization of variogram. Math Geol 36(2):147–186
Brillinger DR (2001) Time series: data analysis and theory. Soc Ind Appl Math, Philadelphia
Burrough PA (1983) Multiscale sources of spatial variation in soil. 1. The application of fractal concepts to nested levels of soil variation. J Soil Sci 34(3):577–597
Chui CK (1992) An introduction to wavelets. Academic Press, New York
Corwin DL, Hopmans J, Rooij GH (2006) From field- to landscape-scale vadose zone processes: Scale issues, modeling, and monitoring. Vadose Zone J 5(1):129–139
Farge M (1992) Wavelet transform and their applications to turbulence. Annu Rev Fluid Mech 24:395–457
Frantziskonis G (2002) Wavelet based analysis of multiscale phenomena: Application of material porosity and identification of dominant scales. Probab Eng Mech 17:349–357
Furon AC, Wagner-Riddle C, Smith CR, Warland JS (2008) Wavelet analysis of wintertime and spring thaw CO2 and N2O fluxes from agricultural fields. Agric For Meteorol 148(8–9):1305–1317
Gajem YM, Warrick AW, Myers DE (1981) Spatial dependence of physical properties of a Typic Torrifluvent soil. Soil Sci Soc Am J 45(4):709–715
Goderya FS (1998) Field scale variations in soil properties for spatially variable control: A review. J Soil Contam 7(2):243–264
Graps A (1995) An introduction to wavelets. IEEE Comput Sci Eng 2(2):1–18
Grinsted A, Moore JC, Jevrejeva S (2004) Application of cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process Geophys 11(5–6):561–566
Heuvelink GBM, Pebesma EJ (1999) Spatial aggregation and soil process modelling. Geoderma 89(1–2):47–65
Isaaks EH, Srivastava RM (1989) An introduction to applied geostatistics. Oxford Univ Press, Toronto
Jenny H (1941) Factors of soil formation. McGraw-Hill, New York
Kachanoski RG, Rolston DE, de Jong E (1985) Spatial and spectral relationships of soil properties and microtopography: I. Density and thickness of A horizon. Soil Sci Soc Am J 49(4):804–812
Keitt TH, Fischer J (2006) Detection of scale-specific community dynamics using wavelets. Ecology 87(11):2895–2904
Kumar P, Foufoula-Georgiou E (1993) A multicomponent decomposition of spatial rainfall fields: 1. Segregation of large- and small-scale features using wavelet transforms. Water Resour Res 29(8):2515–2532
Kumar P, Foufoula-Georgiou E (1997) Wavelet analysis of geophysical applications. Rev Geophys 35(4):385–412
Lark RM (2007) Inference about soil variation from the structure of the best wavelet packet basis. Eur J Soil Sci 58(3):822–831
Lark RM, Webster R (1999) Analysis and elucidation of soil variation using wavelets. Eur J Soil Sci 50(2):185–206
Lark RM, Webster R (2004) Analysing soil variation in two dimensions with the discrete wavelet transform. Eur J Soil Sci 55(4):777–797
Lark RM, Milne AE, Addiscott TM, Goulding KWT, Webster R, O’Flaherty S (2004) Scale- and location-dependent correlation of nitrous oxide emissions with soil properties: An analysis using wavelets. Eur J Soil Sci 55(3):611–627
Lau KM, Weng H (1995) Climate signal detection using wavelet transform: How to make a time series sing. Bull Am Meteorol Soc 76(12):2391–2402
Li BL, Loehle C (1995) Wavelet analysis of multiscale permeabilities in the subsurface. Geophys Res Lett 22(23):3123–3126
Lindsay RW, Perceval DB, Rothrock DA (1996) The discrete wavelet transform and the scale analysis of the surface properties of sea ice. IEEE Trans Geosci Remote Sens 34(3):771–787
Mallat J (1999) A wavelet tour of signal processing. Academic Press, New York
Maraun D, Kurth J, Holschneider M (2007) Nonstationary Gaussian processes in wavelet domain: Synthesis estimation, and significance testing. Phys Rev E 75. doi:10.1103/PhysRevE.75.016707
Matheron G (1963) Principles of geostatistics. Econ Geol 51(8):1246–1266
McBratney AB, Bishop TFA, Teliatnikov IS (2000) Two soil profile reconstruction techniques. Geoderma 97(3–4):209–221
Milne AE, Lark RM (2009) Wavelet transforms applied to irregularly sampled soil data. Math Geosci 41(6):661–678
Neupauer RM, Powell KL (2005) A fully anisotropic Morlet wavelet to identify dominant orientations in porous medium. Comput Geosci 31(4):465–471
Neupauer RM, Powell KL, Qi X, Lee DH, Villhauer DA (2006) Characterization of permeability anisotropy using wavelet analysis. Water Resour Res 42:W07419. doi:10.1029/2005WR004364
Nielsen DR, Biggar JW, Erh KT (1973) Spatial variation of field measured soil water properties. Hilgardia 42(7):214–259
Oliver MA (1987) Geostatistics and its application to soil science. Soil Use Manag 3(1):8–20
Oliver MA, Webster R (1991) How geostatistics can help you. Soil Use Manag 27(4):206–217
Parent AC, Anctil F, Parent LE (2006) Characterization of temporal variability in near surface soil moisture at scales from 1 h to 2 weeks. J Hydrol 325(1–4):56–66
Parkin TB (1987) Soil microsites as a source of denitrification variability. Soil Sci Soc Am J 51(5):1194–1199
Percival DB, Walden AT (2000) Wavelet methods for time series analysis. Cambridge University Press, Cambridge
Perfect E, Caron J (2002) Spectral analysis of tillage-induced differences in soil spatial variation. Soil Sci Soc Am J 66(5):1587–1595
Piňuela JA, Andian D, McInnes KJ, Tarquis AM (2007) Wavelet analysis in a structured clay soil using 2D images. Nonlinear Process Geophys 14(4):425–434
Qi X, Neupauer RM (2008) Wavelet analysis of dominant scales of heterogeneous porous media. Water Resour Res 44:W09406. doi:10.1029/2006WR005720
Shu Q, Liu Z, Si BC (2008) Characterizing scale and location dependent correlation of water retention parameters with soil physical properties using wavelet techniques. J Environ Qual 37(6):2284–2292
Shumway RH, Stoffer DS (2000) Time series analysis and its applications. Springer, New York
Si BC (2003) Spatial and scale dependent soil hydraulic properties: A wavelet approach. In: Pachepsky Y et al (eds) Scaling method in soil physics. CRC Press, New York, pp 163–178
Si BC (2008) Spatial scaling analysis of soil physical properties: A review of spectral and wavelet methods. Vadose Zone J 7(2):547–562
Si BC, Farrell RE (2004) Scale dependent relationships between wheat yield and topographic indices: A wavelet approach. Soil Sci Soc Am J 68(2):577–588
Si BC, Zeleke TB (2005) Wavelet coherency analysis to relate saturated hydraulic properties to soil physical properties. Water Resour Res 41:W11424. doi:10.1029/2005WR004118
Si BC, Kachanoski RG, Reynolds WD (2007) Analysis of soil variation. In: Gregorich EG (ed) Soil sampling and methods of analysis. CRC Press, New York, pp 1163–1191
Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78
Torrence C, Webster PJ (1999) Interdecadal changes in the ENSO-monsoon system. J Climate 12:2679–2690
Trangmar BB, Yost RS, Uehara G (1985) Application of geostatistics to spatial studies of soil properties. Adv Agron 38:45–94
Van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(5):892–898
Van Wambeke A, Dulal R (1978) In: Diversity of soils in the tropics. Am Soc Agron Spec Publ 34:13–28
Van Wesenbeeck IJ, Kachanoski RG, Rolston DE (1988) Temporal persistence of spatial patterns of soil-water content in the tilled layer under a corn crop. Soil Sci Soc Am J 52(4):934–941
Viera SR, Hatfield JL, Nielsen DR, Biggar JW (1982) Geostatistical theory and application to variation of some agronomical properties. Hilgardia 51:1–75
Watkins L, Neupauer RM, Compo GP (2009) Wavelet analysis and filtering to identify dominant orientations of permeability anisotropy. Math Geosci 41(6):643–659
Webster R (1977) Spectral analysis of gilgai soil. Aust J Soil Res 15(3):191–204
Western AW, Grayson RB, Blöschl G (2002) Scaling of soil moisture: A hydrologic perspective. Annu Rev Earth Planet Sci 30:149–180
Yates TT, Si BC, Farrell RE, Pennock DJ (2006a) Probability distribution and spatial dependence of nitrous oxide emission: Temporal change in hummocky terrain. Soil Sci Soc Am J 70(3):753–762
Yates TT, Si BC, Farrell RE, Pennock DJ (2006b) Wavelet spectra of nitrous oxide emission from hummocky terrain during spring snowmelt. Soil Sci Soc Am J 70(4):1110–1120
Yates TT, Si BC, Farrell RE, Pennock DJ (2007) Time, location, and scale dependence of soil nitrous oxide emission, water, and temperature using wavelet coherency analysis. J Geophys Res 112:D09104. doi:10.1029/2006JD007662
Zeleke TB, Si BC (2007) Wavelet based multifractal analysis of field scale variation in soil water retention. Water Resour Res 43(7):W07446. doi:10.1029/2006WR004957
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Biswas, A., Si, B.C. Application of Continuous Wavelet Transform in Examining Soil Spatial Variation: A Review. Math Geosci 43, 379–396 (2011). https://doi.org/10.1007/s11004-011-9318-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-011-9318-9