| 11 Mar 2026
Sea ice thickness distribution and ice keel characteristics in the Bothnian Bay based on high resolution ADCP measurements
Abstract. The northern part of the Baltic Sea, specifically the Bothnian Bay, is covered by drifting pack ice each winter. This requires icebreaker assistance for commercial shipping and presents challenges for planned offshore structures, such as wind farms. During the 2023/2024 ice season, a high-resolution dataset of ice draft was collected in the Bothnian Bay using an Acoustic Doppler Current Profiler (ADCP) located at 20 m depth in the central region of the bay. The integrated ice motion resulted in that draft data was gathered along a 737 km track. The ice draft analysis revealed a significant spatial frequency of deformed ice in March and April, with 60% of the ice having a draft greater than 1 m, 4 % exceeding 4 m, and 0.1 % surpassing 11 m. Additionally, the volume of deformed ice with a draft greater than 1 m accounted for over 90 % during March and April, indicating that dynamic ice production largely outweighed thermodynamic growth. Among the 5500 individually identified ice keels, 20 % had a keel depth larger than 5 m and 2 % a depth larger than 10 m. There was also an indication that one keel reached all the way down to the instrument at 20 m depth. Comparison with satellite data showed a qualitative agreement between the spatial variability in reflectance, represented by the image gradient, and the measured ice draft gradient. It is difficult to verify if the 2023/2024 ice season was extreme or normal with respect to the frequency and thickness of ice keels but here are indications that the relatively early freezup in late December provided preconditions for above average deformation and ridge formation.
I am confused by the lines beginning at 569: "In state-of-the-art sea ice models the ice thickness distribution evolves due to horizontal convergence, thermodynamical growth and mechanical redistribution in thickness space (see, e.g., eqn. 1 in Massonnet et al., 2019). The mechanical redistribution term yields a mathematical unclosed problem and leads to a somewhat arbitrary solution (Toppaladoddi et al., 2023)."
It is unclear whether the papers cited here have been read by the authors?
Firstly, Eq 1 of Massonnet et al., 2019 is, as noted therein, from Thorndike et al., 1975. So, a scholarly treatment is “In state-of-the-art sea ice models the ice thickness distribution evolves according to the theory of Thorndike et al., (1975), which includes horizontal convergence, thermodynamical growth and mechanical redistribution in thickness space (see, e.g., eqn. 1 in Massonnet et al., 2019).”
Secondly, it appears that the authors are ascribing “a somewhat arbitrary solution” of the mechanical redistribution function problem to Toppaladoddi et al., 2023, which is erroneous. Therein we note that it was Thorndike et al., 1975 who stated that "The present theory suffers from a burdensome and arbitrary redistribution function ψ" and in 2015 (Physical Review Letters, 115 (14), 148501) we showed how ψ can be written in terms of the PDF for the ice thickness distribution g(h,t), thereby solving the mathematical closure problem for ψ and writing the theory in terms of a Fokker-Planck equation for g(h,t). We solved this analytically to determine the wintertime invariant measure (see Fig. 1 in Toppaladoddi et al., 2023). This was generalized to the full seasonal cycle in Toppaladoddi et al., 2023, where we note further that the closure is not arbitrary: the Pawula theorem guarantees that the associated Fokker-Planck equation is well-posed in the sense of Hadamard. Therefore, this is the only form of the redistribution function that is NOT arbitrary.