Spatial variability of soil physical properties

According to the French mathematician J.B. Fourier (1768–1830), any continuous single-valued function can be represented by an infinite number of sinusoidal waves of different length, amplitude, and phase. If the variance of soil state variables taken across a spatial or temporal domain is not random, it follows some pattern at various scales, manifested as local trends. Managed soils often exhibit a spatially cyclic variation in properties caused by the repetitious pattern of management, e.g., row spacing, wheel traffic, tillage, irrigation, and fertilization. Landscape topography, pedogenesis, hydropedologic conditions, and vegetation cause trends and curvature in the spatial series of data observed over larger scales. The variance in regularly repeating observation patterns and their causal factors can be decomposed in spectral analysis. Typical contributions to the variance are illustrated in the power spectrum, which depicts the main frequencies, periods, wavelengths, or scales over which variance occurs. In a study of intensive soil tillage for tobacco, spatial soil penetration resistance data series, measured perpendicular to the main tillage direction and at different soil depths, exhibited typical variation patterns at different scales. Spectral and cross-spectral analysis quantified cyclic variation components. Their typical wavelengths varied with depth and could be linked to different wheel traffic and soil management patterns. In a landscape-scale study on soil water storage, soil texture and crop yield, spectral analysis was helpful in detecting different spatial patterns in soil water storage throughout the year. Coherency spectra identified the main common scales of variation. Typical variation scales for corn yield, after a relatively dry growing season, were related mainly to those for soil water storage measured when that storage was relatively high. In order to predict significant spatial patterns for important variates and their spatial processes such as crop yield, optimum times for measuring the distribution pattern of underlying soil state variables can be identified using cross-spectral and coherency analysis.