Quantifying multifrequency acoustic characterization accuracy for ice model development applications

Abstract. Multi-frequency acoustic profiling is critically examined to estimate accuracies currently attainable in characterizing frazil suspensions: with primary interests focused on measuring fractional ice volume, a key factor in river ice growth models. The central issue is the adequacy of representations of backscatter cross sections of disk shaped frazil particles in a well-established theory of elastic spherical targets. An initial investigation established criteria for the existence of three-frequency solutions capable of providing lognormal statistical descriptions in terms of effective radii. These criteria restricted analyses of available field data with such models to inputs at two-frequencies limiting outputs to: a common effective radius, particle number density and frazil volume. Additional frazil cross section information is shown to be required to more fully exploit the full capability of multi-frequency profiling. An approximate relationship between cross sections and the product of acoustic wavenumbers and particle effective radii (k1ae) is developed from laboratory polystyrene disk and sphere data and transformed into the natural ice environment. Field data within the transformed range is transposed to higher frequencies in order to allow testing at still larger field values of k1ae. Two-frequency analyses utilizing the resulting “pseudo-frazil” relationship confirmed a close match with the field data and increased compatibility with existence criteria for three-frequency solutions. The results showed that, within transducer calibration limits, the originally tested spherical backscattering extractions consistently under-estimate frazil ice volume concentrations by 25 % confirming its continued use for accurate estimates in conjunction with a constant scaling factor of about 1.25.