Influence of Surface Roughness Sample Size for C-Band SAR Backscatter Applications on Agricultural Soils

Soil surface roughness determines the backscatter coefficient observed by radar sensors. The objective of this letter was to determine the surface roughness sample size required in synthetic aperture radar applications and to provide some guidelines on roughness characterization in agricultural soils for these applications. With this aim, a data set consisting of ten ENVISAT/ASAR observations acquired coinciding with soil moisture and surface roughness surveys has been processed. The analysis consisted of: 1) assessing the accuracies of roughness parameters <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${l}$ </tex-math></inline-formula> depending on the number of 1-m-long profiles measured per field; 2) computing the correlation of field average roughness parameters with backscatter observations; and 3) evaluating the goodness of fit of three widely used backscatter models, i.e., integral equation model (IEM), geometrical optics model (GOM), and Oh model. The results obtained illustrate a different behavior of the two roughness parameters. A minimum of 10–15 profiles can be considered sufficient for an accurate determination of <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula>, while 20 profiles might still be not enough for accurately estimating <inline-formula> <tex-math notation="LaTeX">${l}$ </tex-math></inline-formula>. The correlation analysis revealed a clear sensitivity of backscatter to surface roughness. For sample sizes >15 profiles, <inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> values were as high as 0.6 for <inline-formula> <tex-math notation="LaTeX">${s}$ </tex-math></inline-formula> and ~0.35 for <inline-formula> <tex-math notation="LaTeX">${l}$ </tex-math></inline-formula>, while for smaller sample sizes <inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> values dropped significantly. Similar results were obtained when applying the backscatter models, with enhanced model precision for larger sample sizes. However, IEM and GOM results were poorer than those obtained with the Oh model and more affected by lower sample sizes, probably due to larger uncertainly of <inline-formula> <tex-math notation="LaTeX">${l}$ </tex-math></inline-formula>.