Dependence between standard deviation and measurement length for C-band backscattering signatures of the Baltic Sea ice

This paper studies whether the standard deviation (std) of the Baltic Sea ice backscattering coefficient (sigma(o)) depends the length of measurement (l). For many kinds of surfaces, especially for a fractal one, this is the case. The study was conducted using one-dimensional C-band helicopter-borne scatterometer data and ENVISAT synthetic aperture radar (SAR) images. The results with both data sets indicate mostly a strong linear dependence between ln(l) and ln(std(sigma(o))) up to a distance of at least a few kilometers. Based on the analysis of empirical and simulated data (fractal and nonfractal profiles), it seems that sea ice sigma(o) as a function of l is not completely described either by fractional Brownian motion or by a process with a single-scale autocorrelation function. Neither can the values of sigma(o) be regarded as samples from only one probability distribution. The regression coefficients describing the dependency of ln(l) versus ln(std(sigma(o))) do not discriminate various ice types better than just mean and std of sigma(o). However, the use of regression coefficients instead of mean and std is preferred due to their scale-invariant comparability with the results of other studies. The dependence of std(sigma(o)) on l should also be taken generally into account in the data analysis, e.g., when constructing classifiers for sea ice SAR data.