During the melt season, surface melting, bottom melting, and lateral melting co-occur in natural ice floes. The bottom melting rate is larger than the lateral melting rate, followed by the surface melting rate, and the smaller the size of an ice floe, the higher the lateral melting rate. To add the scale index of small-scale ice to the melting parametrization scheme, experiments on the melting process of sea ice and artificial fresh-water ice samples in the shape of a disc were carried out in a low-temperature laboratory, under conditions of no radiation, current, or wind, with controlled air and water temperatures. The variations of diameter, thickness, and mass of the ice discs were measured through the experiments. According to the experimental data, a new indicator was created using the ratio of the diameter to the thickness of an ice sample. Based on physical and statistical analyses, the relationships between the surface/bottom melting rates and temperature gradient were formulated. Additionally, the relationships among the lateral melting rate, temperature difference, and the ratio of the diameter to the thickness were also quantified. The equations can be applied to the melting parametrization scheme of ice for a range of diameters up to 100 m, which covers simulations of the energy and mass balance values of the Arctic sea ice and coastal freshwater ice during the summer melt season.
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