Dethloff, Klaus

The Arctic sea ice cover is constantly in motion driven by the wind and ocean currents. The transport of freshwater and latent heat is associated with the ice drift. Furthermore, the drift causes deformation of the sea ice cover under compressive and shear forces and pressure ridges form. Ridges in turn affect the momentum and---to a minor degree---the heat exchange between sea ice and atmosphere and ocean because they strongly increase the local surface roughness and thickness of the ice. Therefore, the sea ice drift and deformation interact with the climate system and its changes, and it is a key issue to both the remote-sensing and modelling community to provide products of good quality. The present thesis splits into three parts: a study of modelled and observed drift estimates, an analysis of sea ice ridge quantities derived from laser altimeter and airborne electromagnetic measurements and an investigation of different numerical algorithms for the representation of ridges in a large-scale sea ice model.The study of sea ice drift focuses on the comparison of different sea ice-ocean coupled models and the validation with buoy and remote-sensing data of the period 1979--2001 on the basis of monthly averages. According to drift speed distributions the group of models, which matches best the observations, has a mode at drift speeds around 0.03 m/s and a short tail towards higher speeds. However, there are also models with much larger drift speeds. In general, all models are capable of producing realistic drift pattern variability although differences are found between models and observations. Reasons for these differences are manifold and lie in discrepancies of wind stress forcing as well as sea ice model characteristics and sea ice-ocean coupling.The investigation of sea ice ridges is based on Arctic-wide in situ measurements of the period 1995--2005 which include different sea ice roughness regimes. While sail density is found to emphasise local deformation events sail height features a large-scale, positive gradient from the Siberian shelf seas towards the Lincoln Sea, where sails of up to 10 m height were found. However, regionally averaged sail heights are found to vary little between 1.1 m and 1.6 m. Rather large ratios of 10 sails per keel and 1:6.3 m for sail height to keel depth are derived. Linear relationships are determined for sail to keel density and sail height to keel depth. Furthermore, functional relationships of sail height and level ice thickness are found.Three different approaches to the simulation of pressure ridge formation are introduced and tested in idealised experiments and for realistic Arctic conditions. Simulations are evaluated with airborne laser profiles of the sea ice surface roughness. The main characteristics of the respective ridging algorithms are: (1) a prognostic derivation of deformation energy from which ridge parameters are deduced, (2) a redistribution function, transforming level ice to a second, ridged ice category, combined with a stochastic simulation of ridge quantities, and (3) prognostic equations for ridge density and height resulting in the formation of ridged ice volume. The model results show that the ridge density is mainly related to the sea ice drift whereas the mean sail height relates to the parent ice thickness. Most deformation occurs at coastlines. In general, all of the three algorithms produce realistic distributions of ridges. Finally, the second ridging scheme is regarded to be most appropriate for climate modelling while the third scheme is found to be advantageous for short-term sea ice forecasting.

This thesis describes the adaptive shallow water model PLASMA-FEMmE. It solves on the sphere the shallow water equations, the prototype for partial differential equations in atmospheric modeling, using a semi-implicit semi-Lagrangian time step and linear finite elements. Both statically and dynamically adapted grids created by the grid generator amatos are investigated. The results are compared with those of the predecessor model FEMmE that uses a static uniform grid.The outcome demonstrates the capability of the chosen approach as well as its limits. Grid adaptation can easily be achieved with amatos. No reflexions at the grid interfaces are observed. Though in one test case instabilities are released at the grid interfaces. The numerical errors are reduced without a considerable enhancement of the computational effort in another test case with a well-known analytical solution. In respect to the conservation properties the results are more complicated. Mass conservation can be achieved in one test case with an appropriate static grid. In case of complex flow regimes all conservation properties are weakened duringthe simulation using dynamic grid adaptation.Nevertheless it can be concluded that the investigated scheme works out fine within the expectations. There is additional research effort to get a deeper understanding of the interactions between the involved physical processes and the numerical schemes. Together with that understanding and conservative advection schemes as well as more sophisticated adaption criteria there is hope that the aforementioned problems can be overcome.

Dethloff, Klaus

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