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Sea ice models have become essential components of weather, climate, and ocean models. A realistic representation of sea ice affects the reliability of process representation, environmental forecast, and climate projections. Realistic simulations of sea ice kinematics require the consideration of both large-scale and finescale geomorphological structures such as linear kinematic features (LKF). We propose a multiscale directional analysis (MDA) that diagnoses the spatial characteristics of LKFs. The MDA is different from previous analyses in that it (i) does not detect LKFs as objects, (ii) takes into account the width of LKFs, and (iii) estimates scale-dependent orientation and intersection angles. The MDA is applied to pairs of deformation fields derived from satellite remote sensing data and from a numerical model simulation with a horizontal grid spacing of ~4.5 km. The orientation and intersection angles of LKFs agree with the observations and confirm the visual impression that the intersection angles tend to be smaller in the satellite data compared to the model data. The MDA distributions can be used to compare satellite data and numerical model fields using conventional metrics such as a Euclidean distance, the Bhattacharyya coefficient, or the Earth mover’s distance. The latter is found to be the most meaningful metric to compare distributions of LKF orientations and intersection angles. The MDA proposed here provides a tool to diagnose if modified sea ice rheologies lead to more realistic simulations of LKFs.

Sea ice models have become essential components of weather, climate and ocean models. The reliability of process studies, environmental forecasts and climate projections alike depend on a realistic representation of sea ice. Developing and evaluating sea ice models requires methods for both large scales and fine-scale geomorphological structures such as linear kinematic features (LKF). We introduce a Multiscale Directional Analysis (MDA) method that diagnoses distributions of LKF orientation and intersection angles. The MDA method is different from previous methods in that it (a) takes into account the width of LKFs instead of estimating the orientation of centerlines; (b) separates curve-like features from point-like features providing the opportunity to reach a unified definition of LKF in both numerical and observational fields; (c) estimates scale-dependent intersection angles.

The field of Arctic sea ice prediction on “weather time scales” is still in its infancy with little existing understanding of the limits of predictability. This is especially true for sea ice deformation along so-called Linear Kinematic Features (LKFs) including leads that are relevant for marine operations. Here the potential predictability of the sea ice pack in the wintertime Arctic up to ten days ahead is determined, exploiting the fact that sea ice-ocean models start to show skill at representing sea ice deformation at high spatial resolutions. Results are based on ensemble simulations with a high-resolution sea ice-ocean model driven by atmospheric ensemble forecasts. The predictability of LKFs as measured by different metrics drops quickly, with predictability being almost completely lost after 4–8 days. In contrast, quantities such as sea ice concentration or the location of the ice edge retain high levels of predictability throughout the full 10-day forecast period. It is argued that the rapid error growth for LKFs is mainly due to the chaotic behaviour of the atmosphere associated with the low predictability of near surface wind divergence and vorticity; initial condition uncertainty for ice thickness is found to be of minor importance as long as LKFs are initialized at the right locations.

A host of studies has recognized that truncation errors of the discretized advection terms lead to spurious mixing and dissipation (Fig. 1) and may interact nonlinearly with turbulent mixing and transport. To investigate the impacts of spurious mixing and dissipation, we implemented some of the most novel advection schemes into the coastal ocean model GETM. We quantified spurious dissipation [Klingbeil, 2014] and mixing of the advection schemes (Fig. 3) in idealized experiments of baroclinic instabilities (Fig. 2) ranging from mesoscales (small Rossby number) to sub-mesoscales (order-one Rossby number). The processes at submesosales are distinct from mesoscale by their contribution to restratification of the mixed layer. Such analyses (Fig. 4) help to choose between highly accurate but complex schemes and lower-order less complex schemes balancing accuracy and computational costs. The major outcome of the present study is that both, numerically induced dissipation (leading to a decrease of kinetic energy) and numerically induced mixing (leading to an increase of background potential energy), artificially delay the restratification process [Mohammadi-Aragh, 2015], an effect that needs to be taken into account if parameterizations for eddy-induced mixing and dissipation are compared with numerical model simulations.

The discretisation of the advection terms in transport equations introduces truncation errors in numerical models. These errors are usually associated with spurious diffusion, i.e. numerically-induced mixing of the advected quantities or dissipation of kinetic energy associated with the advection of momentum. Especially the numerically-induced diapycnal mixing part is very problematic for realistic model simulations. Since any diapycnal mixing of temperature and salinity increases the reference potential energy (RPE), numerically-induced mixing is often quantified in terms of RPE. However, this global bulk measure does not provide any information about the local amount of numerically-induced mixing of a single advected quantity. In this talk we will present a recently developed analysis method that quantifies the numerically-induced mixing of a single advected quantity locally (Klingbeil et al., 2014***). The method is based on the local tracer variance decay in terms of variance fluxes associated with the corresponding advective tracer fluxes. Because of its physically sound definition, this analysis method provides a reliable diagnostic tool, e.g., to assess the performance of advection schemes and to identify hotspots of numerically-induced mixing. At these identified positions the model could be adapted in terms of resolution or the applied numerical schemes. In this context we will demonstrate how numerically-induced mixing of temperature and salinity can be substantially reduced by vertical meshes adapting towards stratification. *** Klingbeil, K., M. Mohammadi-Aragh, U. Gräwe, H. Burchard (2014) . Quantification of spurious dissipation and mixing – Discrete Variance Decay in a Finite-Volume framework. Ocean Modelling. doi:10.1016/j.ocemod.2014.06.001.

This paper quantifies spurious dissipation and mixing of various advection schemes in idealised experiments of lateral shear and baroclinic instabilities in numerical simulations of a re-entrant Eady channel for configurations with large and small Rossby numbers. In addition, a two-dimensional barotropic shear instability test case is used to examine numerical dissipation of momentum advection in isolation, without any baroclinic effects. Effects of advection schemes on the evolution of background potential energy and the dynamics of the restratification process are analysed. The advection schemes for momentum and tracers are considered using several different methods including a recently developed local dissipation analysis. As highly accurate but computationally demanding schemes we apply WENO and MP5, and as more efficient lower-order total variation diminishing (TVD) schemes we use among others the SPL-max-View the MathML source13 and a third-order-upwind scheme. The analysis shows that the MP5 and SPL-max-View the MathML source13 schemes provide the most accurate results. Following our comprehensive analysis of computational costs, the MP5 scheme is approximately 2.3 times more expensive in our implementation. In contrast to the configuration with a small Rossby number, in which significant differences between schemes are apparent, the different advection schemes behave similarly for a larger Rossby number. Regions of high numerical dissipation are shown to be associated with low grid Reynolds numbers. The major outcome of the present study is that generally positive global numerical dissipation and positive background potential energy evolution delay the restratification process.