Statistical Optimization and Analysis on the Spatial Distributions of Ice Ridge Keel in the Northwestern Weddell Sea, Antarctica

Statistical optimization methods serve as fundamental tools for studying sea-ice-related phenomena in the polar regions. To comprehensively analyze the spatial distributions of ice ridge keels, including the draft and spacing distributions, a statistical optimization model was developed with the aim of determining the optimal keel cutoff draft, which differentiates ice ridge keels from sea ice bottom roughness. By treating the keel cutoff draft as the identified variable and minimizing the relative errors between the theoretical and measured keel spatial distributions, the developed model aimed to seek the optimal keel cutoff draft and provide a precise method for this differentiation and to explore the impact of the ridging intensity, defined as the ratio of the mean ridge sail height to spacing, on the spatial distributions of the ice ridge keels. The utilized data were obtained from observations of sea ice bottom undulations in the Northwestern Weddell Sea during the winter of 2006; these observations were conducted using helicopter-borne electromagnetic induction (EM-bird). Through rigorous analysis, the optimal keel cutoff draft was determined to be 3.8 m, and this value was subsequently employed to effectively differentiate ridge keels from other roughness features on the sea ice bottom. Then, building upon our previous research that clustered measured profiles into three distinct regimes (Region 1, Region 2, and Region 3, respectively), a detailed statistical analysis was carried out to evaluate the influence of the ridging intensity on the spatial distributions of the ice ridge keels for all three regimes. Notably, the results closely matched the predictions of the statistical optimization model: Wadhams’80 function (a negative exponential function) exhibited an excellent fit with the measured distributions of the keel draft, and a lognormal function proved to effectively describe the keel spacing distributions in all three regimes. Furthermore, it was discovered that the relationship between the mean ridge keel draft and frequency (number of keels per kilometer) could be accurately modeled by a logarithmic function with a correlation coefficient of 0.698, despite considerable data scatter. This study yields several significant results with far-reaching implications. The determination of the optimal keel cutoff draft and the successful modeling of the relationship between the keel draft and frequency represent key achievements. These findings provide a solid theoretical foundation for analyzing the correlations between the morphologies of the sea ice surface and bottom. Such theoretical insights are crucial for improving remote sensing algorithms for ice thickness inversion from satellite elevation data, enhancing the accuracy of sea ice thickness estimations.