Hibler, W. D. III , and K. Bryan, 1987: A diagnostic ice-ocean model. Journal of Physical Oceanography, 17(7), 987-1015.

Abstract: A coupled ice-ocean model suitable for simulating ice-ocean circulation over a seasonal cycle is developed by coupling the dynamic thermodynamic sea ice model of Hibler with a multilevel baroclinic ocean model (Bryan). This model is used to investigate the effect of ocean circulation on seasonal sea ice simulations by carrying out a simulation of the Arctic, Greenland and Norwegian seas. The ocean model contains a linear term that damps the ocean's temperature and salinity towards climatology. The damping term was chosen to have a three-year relaxation time, equivalent to the adjustment time of the pack ice. No damping, however, was applied to the uppermost layer of the ocean model, which is in direct contact with the moving pack ice. This damping procedure allows seasonal and shorter time-scale variability to be simulated in the ocean, but does not allow the model to drift away from ocean climatology on longer time scales.

For the standard experiment, an initial integration of five years was performed at one-day time steps and a 1.45° by 1.45° resolution in order to obtain a cycle equilibrium. For comparison, a five-year simulation with an ice-only model, and shorter one-year sensitivity simulations without surface salt fluxes and without ocean currents, were also carried out. Input fields consisted of climatological surface air temperatures and mixing ratios, together with daily geostrophic winds from 1979.

The surface-current structure at the end of the five-year simulation exhibits a stronger East Greenland Current and Beaufort Sea Gyre than the initial geostrophic estimates, and is in better agreement with observation. In the Greenland/Norwegian Sea the upper 0.5 km of the ocean becomes more isothermal, with a noticeable seasonal variation in temperature. This neutral density allows monthly averaged winter heat fluxes as large as 350 W m^-2 to be delivered to the upper ocean, thus yielding a much more realistic ice edge than is obtainable by the ice-only model. Spatial variations in ice thickness and ice drift prediction are also in better agreement in the full ice-ocean model as compared to the ice-only model. Except in very shallow regions, month-to-month fluctuations in ice motion are much larger than upper ocean current fluctuations, which also tend to be smaller than mean annual currents. In the central basin, the ice interaction is found ro reduce by about 40% the wind stress transferred into the ocean.

Analysis of the advance and retreat of the East Greenland ice edge shows that while there is some initial freezing in the fall, on a monthly-averaged basis the ice tends to melt during the winter, thus partially off-setting the advection of ice into the region. The amount of melt tends to oscillate from month to month, with large melt ratios coinciding with large oceanic heat fluxes and vice versa. Examination of shorter sensitivity simulations shows this realistic ice edge to be especially dependent on the inclusion of the full three-dimensional circulation in the ocean, and to a lesser degree sensitive to the inclusion of ice melt fluxes. Analysis of the global budgets shows that an annual northward heat transport across the Denmark Strait and Iceland-Faeroe-Shetland passages of about 0.18 x 10¹⁵ W is required to balance the atmospheric heat gain.