Multiresolution analysis of data on electrical conductivity of soil using wavelets

The variation of soil properties at the field scale can be complex. Particular challenges for the analysis of data on soil variables arise when components of variation operate at a range of scales, show intermittent effects, and are not spatially stationary in the variance, fluctuating more in some regions than in others. Wavelet analysis addresses these problems. Any data set of finite variance (appropriately sampled) may be analysed with the dilations and translations of a basic wavelet function. Wavelet functions oscillate locally and damp rapidly to zero either side of their centre, so that they only respond to variation within a local neighbourhood. To provide a complete analysis of a data set the wavelet must be translated across the data, generating a set of local coefficients. The basic wavelet can also be dilated to analyse the data at a specified spatial scale. A single wavelet coefficient therefore describes the variation of a variable in some locality at a particular spatial scale. Data were collected at a variable, 32.4 ha salt affected site in the Tulare Lake Bed region of California using electrical conductivity sensors (mobile fixed-array, electrical resistivity equipment). We show how wavelets can be used to analyse the variation within these data, how the analysis partitions the variance of the data by scale and location, and how it can be used to extract components from the data which appear to be more useful for predicting soil properties than are the raw data. q 2002 Elsevier Science B.V. All rights reserved.

[1]  William H. Press,et al.  Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing , 1992 .

[2]  P. Abry,et al.  Wavelets, spectrum analysis and 1/ f processes , 1995 .

[3]  Donald P. Percival,et al.  On estimation of the wavelet variance , 1995 .

[4]  J. D. Rhoades,et al.  Electrical Conductivity Methods for Measuring and Mapping Soil Salinity , 1993 .

[5]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[6]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Alex B. McBratney,et al.  Using AVHRR images for spatial prediction of clay content in the lower Namoi Valley of eastern Australia. , 2000 .

[8]  R. Webster,et al.  Optimal interpolation and isarithmic mapping of soil properties: I The semi‐variogram and punctual kriging , 1980, European Journal of Soil Science.

[9]  Pierre Goovaerts,et al.  Scale-dependent correlation between topsoil copper and cobalt concentrations in Scotland , 1994 .

[10]  Marc Voltz,et al.  A comparison of kriging, cubic splines and classification for predicting soil properties from sample information , 1990 .

[11]  Praveen Kumar,et al.  Wavelets in Geophysics , 1994 .

[12]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[13]  I. Daubechies,et al.  Wavelets on irregular point sets , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[15]  R. M. Lark,et al.  Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transform , 2001 .

[16]  Dennis L. Corwin,et al.  Assessment and field-scale mapping of soil quality properties of a saline-sodic soil , 2003 .

[17]  William H. Press,et al.  Numerical recipes , 1990 .

[18]  R. M. Lark,et al.  Analysis and elucidation of soil variation using wavelets , 1999 .

[19]  Praveen Kumar,et al.  Wavelet Analysis in Geophysics: An Introduction , 1994 .

[20]  R. Webster,et al.  Filtering SPOT imagery by kriging analysis , 2000 .

[21]  Budiman Minasny,et al.  Spatial prediction of topsoil salinity in the Chelif Valley, Algeria, using local ordinary kriging with local variograms versus whole-area variogram , 2001 .

[22]  I. Daubechies,et al.  Wavelets on the Interval and Fast Wavelet Transforms , 1993 .

[23]  R. Reese.  Geostatistics for Environmental Scientists , 2001 .

[24]  Joseph H. Chesson,et al.  MECHANIZATION OF SOIL SALINITY ASSESSMENT FOR MAPPING , 1993 .

[25]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[26]  R. M. Lark,et al.  Regression analysis with spatially autocorrelated error: simulation studies and application to mapping of soil organic matter , 2000, Int. J. Geogr. Inf. Sci..

[27]  Peter Guttorp,et al.  Wavelet analysis of covariance with application to atmospheric time series , 2000 .

[28]  D. Cook,et al.  Multiple regression in geographical mortality studies, with allowance for spatially correlated errors. , 1983, Biometrics.

[29]  Timothy C. Coburn,et al.  Geostatistics for Natural Resources Evaluation , 2000, Technometrics.

[30]  David J. Strauss,et al.  Spatial Prediction of Soil Salinity Using Electromagnetic Induction Techniques: 2. An Efficient Spatial Sampling Algorithm Suitable for Multiple Linear Regression Model Identification and Estimation , 1995 .

[31]  R. Webster,et al.  Optimal interpolation and isarithmic mapping of soil properties. II. Block kriging. , 1980 .

[32]  Peter Guttorp,et al.  Long-Memory Processes, the Allan Variance and Wavelets , 1994 .

[33]  D. Corwin,et al.  Application of Soil Electrical Conductivity to Precision Agriculture , 2003 .