A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

Influence of mass diffusion in sea ice dynamical models

The mixing of floes of different thickness caused by repeated deformation of the ice cover is modeled as diffusion, and the mass balance equation for sea ice accounting for mass diffusion is developed. The effect of deformational diffusion on the ice thickness balance is shown to reach 1% of the divergence effect, which describes ridging and lead formation. This means that with the same accuracy the mass balance equation can be written in terms of mean velocity rather than mean mass-weighted velocity, which one should correctly use for a multicomponent fluid such as sea ice with components identified by floe thickness. Mixing (diffusion) of sea ice also occurs because of turbulent variations in wind and ocean drags that are unresolved in models. Estimates of the importance of turbulent mass diffusion on the dynamic redistribution of ice thickness are determined using empirical data for the turbulent diffusivity. For long-time-scale prediction (≫5 days), where unresolved atmospheric motion may have a length scale on the order of the Arctic basin and the time scale is larger than the synoptic time scale of atmospheric events, turbulent mass diffusion can exceed 10% of the divergence effect. However, for short-time-scale prediction, for example, 5 days, the unresolved scales are on the order of 100 km, and turbulent diffusion is about 0.1% of the divergence effect. Because inertial effects are small in the dynamics of the sea ice pack, diffusive momentum transfer can be disregarded.

The influence of ocean flow on newly forming sea ice

The heat and mass balance of the Arctic Ocean is very sensitive to the growth and decay of sea ice and the interaction between the heat and salt fields in the oceanic boundary layer. The hydraulic roughness of sea ice controls the detailed nature of turbulent fluxes in the boundary layer and hence is an important ingredient in model parameterizations. We describe a novel mechanism for the generation of corrugations of the sea ice–ocean interface, present a mathematical analysis elucidating the mechanism, and present numerical calculations for geophysically relevant conditions. The mechanism relies on brine flows developing in the sea ice due to Bernoulli suction by flow of ocean past the interface. For oceanic shears at the ice interface of 0.2 s−1, we expect the corrugations to form with a wavelength dependent upon the permeability structure of the sea ice which is described herein. The mechanism should be particularly important during sea ice formation in wind-maintained coastal polynyas and in leads. This paper applies our earlier analyses of the fundamental instability to field conditions and extends it to take account of the anisotropic and heterogeneous permeability of sea ice.

Method of determining a geophysical-scale sea ice rheology from laboratory measurements

We present a methodology that allows a sea ice rheology, suitable for use in a General Circulation Model (GCM), to be determined from laboratory and tank experiments on sea ice when combined with a kinematic model of deformation. The laboratory experiments determine a material rheology for sea ice, and would investigate a nonlinear friction law of the form τ ∝ σ n⅔, instead of the more familiar Amonton's law, τ = μσn (τ is the shear stress, μ is the coefficient of friction and σ n is the normal stress). The modelling approach considers a representative region R containing ice floes (or floe aggregates), separated by flaws. The deformation of R is imposed and the motion of the floes determined using a kinematic model, which will be motivated from SAR observations. Deformation of the flaws is inferred from the floe motion and stress determined from the material rheology. The stress over R is then determined from the area-weighted contribution from flaws and floes

Examining reliability of seasonal to decadal sea surface temperature forecasts: the role of ensemble dispersion

Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.

Objective determination of feature resolution in two sea surface temperature analyses

Considerable effort is presently being devoted to producing high-resolution sea surface temperature (SST) analyses with a goal of spatial grid resolutions as low as 1 km. Because grid resolution is not the same as feature resolution, a method is needed to objectively determine the resolution capability and accuracy of SST analysis products. Ocean model SST fields are used in this study as simulated “true” SST data and subsampled based on actual infrared and microwave satellite data coverage. The subsampled data are used to simulate sampling errors due to missing data. Two different SST analyses are considered and run using both the full and the subsampled model SST fields, with and without additional noise. The results are compared as a function of spatial scales of variability using wavenumber auto- and cross-spectral analysis. The spectral variance at high wavenumbers (smallest wavelengths) is shown to be attenuated relative to the true SST because of smoothing that is inherent to both analysis procedures. Comparisons of the two analyses (both having grid sizes of roughly ) show important differences. One analysis tends to reproduce small-scale features more accurately when the high-resolution data coverage is good but produces more spurious small-scale noise when the high-resolution data coverage is poor. Analysis procedures can thus generate small-scale features with and without data, but the small-scale features in an SST analysis may be just noise when high-resolution data are sparse. Users must therefore be skeptical of high-resolution SST products, especially in regions where high-resolution (~5 km) infrared satellite data are limited because of cloud cover.

Recovery mechanisms of Arctic summer sea ice

We examine the recovery of Arctic sea ice from prescribed ice-free summer conditions in simulations of 21st century climate in an atmosphere–ocean general circulation model. We find that ice extent recovers typically within two years. The excess oceanic heat that had built up during the ice-free summer is rapidly returned to the atmosphere during the following autumn and winter, and then leaves the Arctic partly through increased longwave emission at the top of the atmosphere and partly through reduced atmospheric heat advection from lower latitudes. Oceanic heat transport does not contribute significantly to the loss of the excess heat. Our results suggest that anomalous loss of Arctic sea ice during a single summer is reversible, as the ice–albedo feedback is alleviated by large-scale recovery mechanisms. Hence, hysteretic threshold behavior (or a “tipping point”) is unlikely to occur during the decline of Arctic summer sea-ice cover in the 21st century.

Assimilation of sea-ice concentration in a global climate model — physical and statistical aspects

We investigate the initialization of Northern-hemisphere sea ice in the global climate model ECHAM5/MPI-OM by assimilating sea-ice concentration data. The analysis updates for concentration are given by Newtonian relaxation, and we discuss different ways of specifying the analysis updates for mean thickness. Because the conservation of mean ice thickness or actual ice thickness in the analysis updates leads to poor assimilation performance, we introduce a proportional dependence between concentration and mean thickness analysis updates. Assimilation with these proportional mean-thickness analysis updates significantly reduces assimilation error both in identical-twin experiments and when assimilating sea-ice observations, reducing the concentration error by a factor of four to six, and the thickness error by a factor of two. To understand the physical aspects of assimilation errors, we construct a simple prognostic model of the sea-ice thermodynamics, and analyse its response to the assimilation. We find that the strong dependence of thermodynamic ice growth on ice concentration necessitates an adjustment of mean ice thickness in the analysis update. To understand the statistical aspects of assimilation errors, we study the model background error covariance between ice concentration and ice thickness. We find that the spatial structure of covariances is best represented by the proportional mean-thickness analysis updates. Both physical and statistical evidence supports the experimental finding that proportional mean-thickness updates are superior to the other two methods considered and enable us to assimilate sea ice in a global climate model using simple Newtonian relaxation.

Assimilation of sea-ice concentration in a global climate model — physical and statistical aspects

We investigate the initialisation of Northern Hemisphere sea ice in the global climate model ECHAM5/MPI-OM by assimilating sea-ice concentration data. The analysis updates for concentration are given by Newtonian relaxation, and we discuss different ways of specifying the analysis updates for mean thickness. Because the conservation of mean ice thickness or actual ice thickness in the analysis updates leads to poor assimilation performance, we introduce a proportional dependence between concentration and mean thickness analysis updates. Assimilation with these proportional mean-thickness analysis updates leads to good assimilation performance for sea-ice concentration and thickness, both in identical-twin experiments and when assimilating sea-ice observations. The simulation of other Arctic surface fields in the coupled model is, however, not significantly improved by the assimilation. To understand the physical aspects of assimilation errors, we construct a simple prognostic model of the sea-ice thermodynamics, and analyse its response to the assimilation. We find that an adjustment of mean ice thickness in the analysis update is essential to arrive at plausible state estimates. To understand the statistical aspects of assimilation errors, we study the model background error covariance between ice concentration and ice thickness. We find that the spatial structure of covariances is best represented by the proportional mean-thickness analysis updates. Both physical and statistical evidence supports the experimental finding that assimilation with proportional mean-thickness updates outperforms the other two methods considered. The method described here is very simple to implement, and gives results that are sufficiently good to be used for initialising sea ice in a global climate model for seasonal to decadal predictions.

The transient versus the equilibrium response of sea ice to global warming

To examine the long-term stability of Arctic and Antarctic sea ice, idealized simulations are carried out with the climate model ECHAM5/MPIOM. Atmospheric CO2 concentration is increased over 2000 years from pre-industrial levels to quadrupling, is then kept constant for 5940 years, is afterwards decreased over 2000 years to pre-industrial levels, and finally kept constant for 3940 years.Despite these very slow changes, the sea-ice response significantly lags behind the CO2 concentration change. This lag, which is caused by the ocean’s thermal inertia, implies that the sea-ice equilibrium response to increasing CO2 concentration is substantially underestimated by transient simulations. The sea-ice response to CO2 concentration change is not truly hysteretic and in principle reversible.We find no lag in the evolution of Arctic sea ice relative to changes in annual-mean northern-hemisphere surface temperature. The summer sea-ice cover changes linearly with respect to both CO2 concentration and temper...

Predictability of large interannual Arctic sea-ice anomalies

In projections of twenty-first century climate, Arctic sea ice declines and at the same time exhibits strong interannual anomalies. Here, we investigate the potential to predict these strong sea-ice anomalies under a perfect-model assumption, using the Max-Planck-Institute Earth System Model in the same setup as in the Coupled Model Intercomparison Project Phase 5 (CMIP5). We study two cases of strong negative sea-ice anomalies: a 5-year-long anomaly for present-day conditions, and a 10-year-long anomaly for conditions projected for the middle of the twenty-first century. We treat these anomalies in the CMIP5 projections as the truth, and use exactly the same model configuration for predictions of this synthetic truth. We start ensemble predictions at different times during the anomalies, considering lagged-perfect and sea-ice-assimilated initial conditions. We find that the onset and amplitude of the interannual anomalies are not predictable. However, the further deepening of the anomaly can be predicted for typically 1 year lead time if predictions start after the onset but before the maximal amplitude of the anomaly. The magnitude of an extremely low summer sea-ice minimum is hard to predict: the skill of the prediction ensemble is not better than a damped-persistence forecast for lead times of more than a few months, and is not better than a climatology forecast for lead times of two or more years. Predictions of the present-day anomaly are more skillful than predictions of the mid-century anomaly. Predictions using sea-ice-assimilated initial conditions are competitive with those using lagged-perfect initial conditions for lead times of a year or less, but yield degraded skill for longer lead times. The results presented here suggest that there is limited prospect of predicting the large interannual sea-ice anomalies expected to occur throughout the twenty-first century.

Seasonal to interannual Arctic sea-ice predictability in current GCMs

We establish the first inter-model comparison of seasonal to interannual predictability of present-day Arctic climate by performing coordinated sets of idealized ensemble predictions with four state-of-the-art global climate models. For Arctic sea-ice extent and volume, there is potential predictive skill for lead times of up to three years, and potential prediction errors have similar growth rates and magnitudes across the models. Spatial patterns of potential prediction errors differ substantially between the models, but some features are robust. Sea-ice concentration errors are largest in the marginal ice zone, and in winter they are almost zero away from the ice edge. Sea-ice thickness errors are amplified along the coasts of the Arctic Ocean, an effect that is dominated by sea-ice advection. These results give an upper bound on the ability of current global climate models to predict important aspects of Arctic climate.