Uncertainty analysis of single- and multiple-size-class frazil ice models

Abstract

The formation of frazil ice in supercooled waters has been extensively studied, both experimentally and numerically, in recent years. Numerical models, with varying degrees of complexity, have been proposed; these are often based on many parameters, the values of which are uncertain and difficult to estimate. In this paper, an uncertainty analysis of two mathematical models that simulate supercooling and frazil ice formation is carried out within a probabilistic framework. The two main goals are (i) to provide quantitative insight into the relative importance of contributing uncertain parameters, to help identify parameters for optimal calibration, and (ii) to compare the output scatter of frazil ice models with single and multiple crystal size classes. The derivation of single- and multi-class models is presented in light of recent work, their numerical resolution is discussed, and a list of the main uncertain parameters is proposed. An uncertainty analysis is then carried out in three steps. Parameter uncertainty is first quantified, based on recent field, laboratory and numerical studies. Uncertainties are then propagated through the models using Monte Carlo simulations. Finally, the relative influence of uncertain parameters on the output time series - i.e., the total frazil volume fraction and water temperature - is assessed by means of Sobol indices. The influence of input parameters on the long-term asymptote as well as short-term transient evolution of the systems is discussed, depending on whether gravitational removal is included or not in the models.