An ice‐ocean coupled model

An ice model, an ocean model, and a method of coupling the models are described. The ice model is a synthesis, with variations and extensions, of previous modeling ideas. Ice thickness, concentration, velocity, and internal energy are prognostic variables. The ice thermodynamics are represented by temperatures at the snow surface, ice surface, the interior, and the bottom surface. Melting and freezing rates are calculated at the ice‐atmosphere, ice‐ocean, and atmosphere‐ocean interfaces. A prescribed portion of summer meltwater can be stored on the surface and refrozen in the fall. The ocean model includes a second moment, turbulence closure submodel and enables one to solve for oceanic heat flux, the interfacial stress, and subsurface properties. In this paper the model is applied to one‐dimensional simulations, but the equations are cited in a form for implementation by two‐ and three‐dimensional models. In a companion paper (Kantha and Mellor, this issue) the model is used for two‐dimensional (vertical plane) simulations in the Bering Sea. Several one‐dimensional sensitivity studies are performed in the case where the ice model is decoupled from the ocean; here the oceanic heat flux and sea surface temperature are prescribed constants. The studies reveal the role and sensitivity of surface trapped meltwater, ice concentration, and ice divergence. With the coupled ice‐ocean model, the seasonally varying oceanic heat flux and mixed layer properties are determined by the model. Some comparisons with observations in the central Arctic ocean are possible. The role of the molecular sublayer immediately adjacent to the ice is examined; frazil ice production is related to the large disparity in the molecular diffusivities for temperature and salinity. The mixed layer model contains empirical constants which are known from turbulence data. The molecular sublayer parameterization requires one empirical parameter b , which is uncertain but, from this study, is assuredly greater than zero, the value implicit in previous models. The ice model requires the empirical parameters Φ F and Φ M to quantitatively account for freezing or melting processes in open leads; their values are also uncertain, but we present reasoning and sensitivity studies to suggest specific values. Finally, an empirical parameter G is introduced; it is the ratio of the value of the ice thickness used to represent average ice volume in the dynamic and thermodynamic equations to the value of the thickness needed in the heat conduction equation. Estimates of G are made from observed thickness distribution functions; sensitivity studies show it to be an important parameter.