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

ABSTRACT

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.

• numerical weather prediction
• sea and lake ice
• parameterisation
• bulk approach

6. Acknowledgements

Thanks are due to Ulrich Damrath, Jochen Förstner, Sergej Golosov, Thomas Hanisch, Erdmann Heise, Georgiy Kirillin, Ekaterina Kourzeneva, Aurelia Müller, Van-Tan Nguyen, Ulrich Schättler, Natalia Schneider, Christoph Schraff, Arkady Terzhevik and Miklós Vörös for numerous discussions and helpful suggestions. The authors are particularly grateful to Ulrich Damrath, Jochen Förstner, Thomas Hanisch and Ulrich Schättler for their invaluable help in implementing and testing the new ice parameterisation schemes in GME and COSMO. Comments of the anonymous reviewers helped to considerably improve the manuscript. Empirical data from Lake Pääjärvi are made available through the collaboration with the Division of Geophysics of the University of Helsinki that is supported by the Academy of Finland (project ‘Ice Cover in Lakes and Coastal Seas’) and by the Vilho, Yrjö and Kalle Väisälä Foundation of the Academy of Sciences and Letters, Finland (project ‘Modelling of Boreal Lakes’). The ECMWF forecast products used for comparison are taken from the ECMWF MARS archive. The work was partially supported by the EU Commissions through the projects INTAS-01-2132 and INTAS-05-1000007-431, and by the Nordic Research Board through the Nordic Networks on Fine-Scale Atmospheric Modelling (NetFAM) and Towards Multi-Scale Modelling of the Atmospheric Environment (MUSCATEN).

Notes

¹The terms ‘parameterisation scheme’ and ‘model’ can be used interchangeably. The term ‘parameterisation scheme’ is used in the NWP and climate modelling community to differentiate a component (module) of a modelling system from its host that is referred to as an NWP (climate) model.

²Notice a close analogy between the concept of self-similarity of the thermocline and the mixed-layer concept that has been successfully used in geophysical fluid dynamics over several decades. Indeed, using the mixed-layer temperature and its depth as appropriate scales, the mixed-layer concept states that the dimensionless temperature profile can be expressed through a universal function of dimensionless depth, where that universal function is simply a constant equal to one, that is , where . A function that describes the temperature profile in the thermocline is not merely a constant but a more sophisticated function of dimensionless depth.

³Equation (1) is merely Eq. (A.9) with . Equation (2) is obtained from Eq. (A.5) with H _s =0 and I(0)=0 by replacing ρ _s  c _s  θ _s on the left-hand side of Eq. (A.5) with ρ _i  c _i  θ _i and using Eq. (1). Equation (3) is obtained by setting θ _s =θ _i , ρ _s =ρ _i , H _s =0, dH _s /dt=0 and in Eq. (A.10) and adding the result to Eq. (A.11) with I(0)=0. The resulting system of equations, namely Eqs. (1)–(4), can be arrived at by performing derivations in Appendix A with H _s ≡0 from the outset.