Parameterisation of sea and lake ice in numerical weather prediction models of the German Weather Service

A bulk thermodynamic (no rheology) sea-ice parameterisation scheme for use in numerical weather prediction (NWP) is presented. The scheme is based on a self-similar parametric representation (assumed shape) of the evolving temperature profile within the ice and on the integral heat budget of the ice slab. The scheme carries ordinary differential equations (in time) for the ice surface temperature and the ice thickness. The proposed sea-ice scheme is implemented into the NWP models GME (global) and COSMO (limited-area) of the German Weather Service. In the present operational configuration, the horizontal distribution of the sea ice is governed by the data assimilation scheme, no fractional ice cover within the GME/COSMO grid box is considered, and the effect of snow above the ice is accounted for through an empirical temperature dependence of the ice surface albedo with respect to solar radiation. The lake ice is treated similarly to the sea ice, except that freeze-up and break-up of lakes occurs freely, independent of the data assimilation. The sea and lake ice schemes (the latter is a part of the fresh-water lake parameterisation scheme FLake) show a satisfactory performance in GME and COSMO. The ice characteristics are not overly sensitive to the details of the treatment of heat transfer through the ice layer. This justifies the use of a simplified but computationally efficient bulk approach to model the ice thermodynamics in NWP, where the ice surface temperature is a major concern whereas details of the temperature distribution within the ice are of secondary importance. In contrast to the details of the heat transfer through the ice, the cloud cover is of decisive importance for the ice temperature as it controls the radiation energy budget at the ice surface. This is particularly true for winter, when the long-wave radiation dominates the surface energy budget. During summer, the surface energy budget is also sensitive to the grid-box mean ice surface albedo with respect to solar radiation. Considering the crucial importance of the surface radiation budget, future efforts should go into the development of a refined formulation of the grid-box mean surface albedo, including the albedo of ice itself and the fractional ice cover. NWP models may also benefit from an explicit treatment of snow above the ice. As the results from single-column experiments suggest, a bulk snow parameterisation holds promise but improved formulations of the snow density and the snow temperature conductivity are required.