A rate and state friction law for saline ice

Sea ice friction models are necessary to predict the nature of interactions between sea ice floes. These interactions are of interest on a range of scales, for example, to predict loads on engineering structures in icy waters or to understand the basin-scale motion of sea ice. Many models use Amonton's friction law due to its simplicity. More advanced models allow for hydrodynamic lubrication and refreezing of asperities; however, modeling these processes leads to greatly increased complexity. In this paper we propose, by analogy with rock physics, that a rate- and state-dependent friction law allows us to incorporate memory (and thus the effects of lubrication and bonding) into ice friction models without a great increase in complexity. We support this proposal with experimental data on both the laboratory (∼0.1 m) and ice tank (∼1 m) scale. These experiments show that the effects of static contact under normal load can be incorporated into a friction model. We find the parameters for a first-order rate and state model to be A = 0.310, B = 0.382, and μ0 = 0.872. Such a model then allows us to make predictions about the nature of memory effects in moving ice-ice contacts.

Advancements in the estimation of ice particle fall speeds using laboratory and field measurements

Accurate estimates for the fall speed of natural hydrometeors are vital if their evolution in clouds is to be understood quantitatively. In this study, laboratory measurements of the terminal velocity vt for a variety of ice particle models settling in viscous fluids, along with wind-tunnel and field measurements of ice particles settling in air, have been analyzed and compared to common methods of computing vt from the literature. It is observed that while these methods work well for a number of particle types, they fail for particles with open geometries, specifically those particles for which the area ratio Ar is small (Ar is defined as the area of the particle projected normal to the flow divided by the area of a circumscribing disc). In particular, the fall speeds of stellar and dendritic crystals, needles, open bullet rosettes, and low-density aggregates are all overestimated. These particle types are important in many cloud types: aggregates in particular often dominate snow precipitation at the ground and vertically pointing Doppler radar measurements. Based on the laboratory data, a simple modification to previous computational methods is proposed, based on the area ratio. This new method collapses the available drag data onto an approximately universal curve, and the resulting errors in the computed fall speeds relative to the tank data are less than 25% in all cases. Comparison with the (much more scattered) measurements of ice particles falling in air show strong support for this new method, with the area ratio bias apparently eliminated.

The consolidation and bond strength of rafted sea ice

The consolidation and bond strength of rafted sea ice were investigated through a series of experiments undertaken in the Ice Physics Laboratory at the UCL. To simulate a section of rafted sea ice, blocks of laboratory grown saline ice were stacked in an insulated tank with spacers between adjacent blocks to allow saline water to flood in. The rate of consolidation was then monitored using a combination of temperature readings recorded in the ice and liquid layer, salinity measurements of the liquid layer, and cores taken at specific times of interest. Two states of consolidation were observed: thermodynamic consolidation where the ice blocks were physically bonded but the bond strength was weak, and mechanical consolidation where the bond had reached full strength. Results showed that the rafted ice had physically bonded in less than a day, however it took many more days (6 to 30 depending on the environmental conditions) for the bond to reach maximum strength. Increasing the thickness of the ice, the salinity of the water and the inter-block gap size all increased the consolidation time. Once consolidated, ice cores were taken and sheared using the asymmetric four-point bending method to measure the strength of the bond between the ice blocks. These were then compared to the shear strength of solid ice blocks simulating level sea ice. Our results show that the shear strength of the bond between the rafted ice blocks is about 30% weaker than that of level 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

Ice supersaturation in the ECMWF integrated forecast system

A parametrization for ice supersaturation is introduced into the ECMWF Integrated Forecast System (IFS), compatible with the cloud scheme that allows partial cloud coverage. It is based on the simple, but often justifiable, diagnostic assumption that the ice nucleation and subsequent depositional growth time-scales are short compared to the model time step, thus supersaturation is only permitted in the clear-sky portion of the grid cell. Results from model integrations using the new scheme are presented, which is demonstrated to increase upper-tropospheric humidity, decrease high-level cloud cover and, to a much lesser extent, cloud ice amounts, all as expected from simple arguments. Evaluation of the relative distribution of supersaturated humidity amounts shows good agreement with the observed climatology derived from in situ aircraft observations. With the new scheme, the global distribution of frequency of occurrence of supersaturated regions compares well with remotely sensed microwave limb sounder (MLS) data, with the most marked errors of underprediction occurring in regions where the model is known to underpredict deep convection. Finally, it is also demonstrated that the new scheme leads to improved predictions of permanent contrail cloud over southern England, which indirectly implies upper-tropospheric humidity fields are better represented for this region.

Theory and observations of ice particle evolution in cirrus using Doppler radar: evidence for aggregation

Vertically pointing Doppler radar has been used to study the evolution of ice particles as they sediment through a cirrus cloud. The measured Doppler fall speeds, together with radar-derived estimates for the altitude of cloud top, are used to estimate a characteristic fall time tc for the `average' ice particle. The change in radar reflectivity Z is studied as a function of tc, and is found to increase exponentially with fall time. We use the idea of dynamically scaling particle size distributions to show that this behaviour implies exponential growth of the average particle size, and argue that this exponential growth is a signature of ice crystal aggregation.

The fall speeds of sub-100 mu m ice crystals

Estimates for the sedimentation rate of realistic ice crystals at sizes smaller than 100 µm are presented. These calculations, which exploit new results for the capacitance of ice crystals, are compared with laboratory studies and found to be in good agreement. The results highlight a weakness in contemporary ice particle fall speed parametrizations for very small crystals, which can lead to sedimentation rates being overestimated by a factor of two. The theoretical approach applied here may also be useful for calculating the sedimentation rate and mobility of non-spherical aerosol particles.

Testing the influence of small crystals on ice size spectra using Doppler lidar observations

Analysis of the vertical velocity of ice crystals observed with a 1.5micron Doppler lidar from a continuous sample of stratiform ice clouds over 17 months show that the distribution of Doppler velocity varies strongly with temperature, with mean velocities of 0.2m/s at -40C, increasing to 0.6m/s at -10C due to particle growth and broadening of the size spectrum. We examine the likely influence of crystals smaller than 60microns by forward modelling their effect on the area-weighted fall speed, and comparing the results to the lidar observations. The comparison strongly suggests that the concentration of small crystals in most clouds is much lower than measured in-situ by some cloud droplet probes. We argue that the discrepancy is likely due to shattering of large crystals on the probe inlet, and that numerous small particles should not be included in numerical weather and climate model parameterizations.