Arctic sea ice temperature profile estimation via backstepping observer design

Recent rapid loss of the Arctic sea ice motivates the study of the Arctic sea ice thickness. Global climate model that describe the ice's thickness evolution, require an accurate temperature profile of the Arctic sea ice. However, measuring the complete temperature profile is not feasible due to a limited number of thermal sensors. Instead, measuring the ice's thickness is doable based on the acquisition of data from submarine and satellite devices. In this paper, we develop a backstepping observer algorithm to estimate temperature profile for the Arctic sea ice model via available measurements of sea ice thickness, sea ice surface temperature, and temperature gradient at the ice-ocean interface. The observer is designed in a rigorous manner to drive the temperature profile estimation error to zero, for salinity-free sea ice model. Moreover, the proposed observer is used to estimate the temperature profile of the original sea ice model with salinity via numerical simulation. In comparison with the straightforward open-loop algorithm, the simulation results illustrate that our observer design achieves faster convergence of the estimated temperature.