Properties Of Sea Ice Research Articles

Optical properties of sea ice doped with black carbon – an experimental and radiative-transfer modelling comparison

Abstract. Radiative-transfer calculations of the light reflectivity and extinction coefficient in laboratory-generated sea ice doped with and without black carbon demonstrate that the radiative-transfer model TUV-snow can be used to predict the light reflectance and extinction coefficient as a function of wavelength. The sea ice is representative of first-year sea ice containing typical amounts of black carbon and other light-absorbing impurities. The experiments give confidence in the application of the model to predict albedo of other sea ice fabrics. Sea ices, ∼ 30 cm thick, were generated in the Royal Holloway Sea Ice Simulator ( ∼ 2000 L tanks) with scattering cross sections measured between 0.012 and 0.032 m2 kg−1 for four ices. Sea ices were generated with and without ∼ 5 cm upper layers containing particulate black carbon. Nadir reflectances between 0.60 and 0.78 were measured along with extinction coefficients of 0.1 to 0.03 cm−1 (e-folding depths of 10–30 cm) at a wavelength of 500 nm. Values were measured between light wavelengths of 350 and 650 nm. The sea ices generated in the Royal Holloway Sea Ice Simulator were found to be representative of natural sea ices. Particulate black carbon at mass ratios of ∼ 75, ∼ 150 and ∼ 300 ng g−1 in a 5 cm ice layer lowers the albedo to 97, 90 and 79 % of the reflectivity of an undoped clean sea ice (at a wavelength of 500 nm).

Wave-induced stress and breaking of sea ice in a coupled hydrodynamic discrete-element wave–ice model

Abstract. In this paper, a coupled sea ice–wave model is developed and used to analyze wave-induced stress and breaking in sea ice for a range of wave and ice conditions. The sea ice module is a discrete-element bonded-particle model, in which ice is represented as cuboid grains floating on the water surface that can be connected to their neighbors by elastic joints. The joints may break if instantaneous stresses acting on them exceed their strength. The wave module is based on an open-source version of the Non-Hydrostatic WAVE model (NHWAVE). The two modules are coupled with proper boundary conditions for pressure and velocity, exchanged at every wave model time step. In the present version, the model operates in two dimensions (one vertical and one horizontal) and is suitable for simulating compact ice in which heave and pitch motion dominates over surge. In a series of simulations with varying sea ice properties and incoming wavelength it is shown that wave-induced stress reaches maximum values at a certain distance from the ice edge. The value of maximum stress depends on both ice properties and characteristics of incoming waves, but, crucially for ice breaking, the location at which the maximum occurs does not change with the incoming wavelength. Consequently, both regular and random (Jonswap spectrum) waves break the ice into floes with almost identical sizes. The width of the zone of broken ice depends on ice strength and wave attenuation rates in the ice.

New methodology to estimate Arctic sea ice concentration from SMOS combining brightness temperature differences in a maximum-likelihood estimator

Abstract. Monitoring sea ice concentration is required for operational and climate studies in the Arctic Sea. Technologies used so far for estimating sea ice concentration have some limitations, for instance the impact of the atmosphere, the physical temperature of ice, and the presence of snow and melting. In the last years, L-band radiometry has been successfully used to study some properties of sea ice, remarkably sea ice thickness. However, the potential of satellite L-band observations for obtaining sea ice concentration had not yet been explored. In this paper, we present preliminary evidence showing that data from the Soil Moisture Ocean Salinity (SMOS) mission can be used to estimate sea ice concentration. Our method, based on a maximum-likelihood estimator (MLE), exploits the marked difference in the radiative properties of sea ice and seawater. In addition, the brightness temperatures of 100 % sea ice and 100 % seawater, as well as their combined values (polarization and angular difference), have been shown to be very stable during winter and spring, so they are robust to variations in physical temperature and other geophysical parameters. Therefore, we can use just two sets of tie points, one for summer and another for winter, for calculating sea ice concentration, leading to a more robust estimate. After analysing the full year 2014 in the entire Arctic, we have found that the sea ice concentration obtained with our method is well determined as compared to the Ocean and Sea Ice Satellite Application Facility (OSI SAF) dataset. However, when thin sea ice is present (ice thickness ≲ 0.6 m), the method underestimates the actual sea ice concentration.

On the Definition of Marginal Ice Zone Width

AbstractSea ice features a dense inner pack ice zone surrounded by a marginal ice zone (MIZ) in which the sea ice properties are modified by interaction with the ice-free open ocean. The width of the MIZ is a fundamental length scale for polar physical and biological dynamics. Several different criteria for establishing MIZ boundaries have emerged in the literature—wave penetration, floe size, sea ice concentration, etc.—and a variety of definitions for the width between the MIZ boundaries have been published. Here, three desirable mathematical properties for defining MIZ width are proposed: invariance with respect to translation and rotation on the sphere; uniqueness at every point in the MIZ; and generality, including nonconvex shapes. The previously published streamline definition is shown to satisfy all three properties, where width is defined as the arc length of a streamline through the solution to Laplaces’s equation within the MIZ boundaries, while other published definitions each satisfy only one of the desired properties. When defining MIZ spatial average width from streamline results, the rationale for averaging with respect to distance along both MIZ boundaries was left implicit in prior studies. Here it is made rigorous by developing and applying the mathematics of an analytically tractable idealization of MIZ geometry—the eccentric annulus. Finally, satellite-retrieved Arctic sea ice concentrations are used to investigate how well streamline-based MIZ spatial average width is approximated by alternative definitions that lack desirable mathematical properties or local width values but offer computational efficiency.

Arctic Radiation-IceBridge Sea and Ice Experiment: The Arctic Radiant Energy System during the Critical Seasonal Ice Transition

Abstract The National Aeronautics and Space Administration (NASA)’s Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) acquired unique aircraft data on atmospheric radiation and sea ice properties during the critical late summer to autumn sea ice minimum and commencement of refreezing. The C-130 aircraft flew 15 missions over the Beaufort Sea between 4 and 24 September 2014. ARISE deployed a shortwave and longwave broadband radiometer (BBR) system from the Naval Research Laboratory; a Solar Spectral Flux Radiometer (SSFR) from the University of Colorado Boulder; the Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research (4STAR) from the NASA Ames Research Center; cloud microprobes from the NASA Langley Research Center; and the Land, Vegetation and Ice Sensor (LVIS) laser altimeter system from the NASA Goddard Space Flight Center. These instruments sampled the radiant energy exchange between clouds and a variety of sea ice scenarios, including prior to and after refreezing began. The most critical and unique aspect of ARISE mission planning was to coordinate the flight tracks with NASA Cloud and the Earth’s Radiant Energy System (CERES) satellite sensor observations in such a way that satellite sensor angular dependence models and derived top-of-atmosphere fluxes could be validated against the aircraft data over large gridbox domains of order 100–200 km. This was accomplished over open ocean, over the marginal ice zone (MIZ), and over a region of heavy sea ice concentration, in cloudy and clear skies. ARISE data will be valuable to the community for providing better interpretation of satellite energy budget measurements in the Arctic and for process studies involving ice–cloud–atmosphere energy exchange during the sea ice transition period.

Sea ice thermohaline dynamics and biogeochemistry in the Arctic Ocean: Empirical and model results

Large changes in the sea ice regime of the Arctic Ocean have occurred over the last decades justifying the development of models to forecast sea ice physics and biogeochemistry. The main goal of this study is to evaluate the performance of the Los Alamos Sea Ice Model (CICE) to simulate physical and biogeochemical properties at time scales of a few weeks and to use the model to analyze ice algal bloom dynamics in different types of ice. Ocean and atmospheric forcing data and observations of the evolution of the sea ice properties collected from 18 April to 4 June 2015, during the Norwegian young sea ICE expedition, were used to test the CICE model. Our results show the following: (i) model performance is reasonable for sea ice thickness and bulk salinity; good for vertically resolved temperature, vertically averaged Chl a concentrations, and standing stocks; and poor for vertically resolved Chl a concentrations. (ii) Improving current knowledge about nutrient exchanges, ice algal recruitment, and motion is critical to improve sea ice biogeochemical modeling. (iii) Ice algae may bloom despite some degree of basal melting. (iv) Ice algal motility driven by gradients in limiting factors is a plausible mechanism to explain their vertical distribution. (v) Different ice algal bloom and net primary production (NPP) patterns were identified in the ice types studied, suggesting that ice algal maximal growth rates will increase, while sea ice vertically integrated NPP and biomass will decrease as a result of the predictable increase in the area covered by refrozen leads in the Arctic Ocean.

Calculating exceedance probabilities using a distributionally robust method

Calculation of exceedance probabilities or the inverse problem of finding the level corresponding to a given exceedance probability occurs in many practical applications. For instance, it is often of interest in offshore engineering to evaluate the wind, wave, current, and sea ice properties with annual exceedance probabilities of, e.g., 10−1, 10−2, and 10−3, or so-called 10-year, 100-year, and 1000-year values. A methodology is provided in this article to calculate a tight upper bound of the exceedance probability, given any probability distribution from a wide range of commonly used distributions. The approach is based on a generalization of the Chebyshev inequality for the class of distributions with a logarithmically concave cumulative distribution function, and has the potential to relieve the often-debated exercise of determining an appropriate probability distribution function based on limited data, particularly in terms of tail behavior. Two numerical examples are provided for illustration.

Sea ice draft observations in Nares Strait from 2003 to 2012

AbstractTime series observation of sea ice draft and velocity from Nares Strait between 2003 and 2012 provides new insights on the statistical properties of sea ice leaving the Arctic for the Atlantic Oceans. Median ice draft is 0.8 m, but it varies annually from 1.5 m in 2007–2008 to 0.5 m in 2008–2009. Probability density distributions of sea ice draft depend on location across the channel with thicker ice near Canada and thinner ice near Greenland. Nevertheless, sea ice motion stops seasonally due to arching land‐fast ice that spans the 30–40 km wide channel for up to 190 days per year such as during the 2011–2012 winter. In contrast, the 2006–2010 period exhibits a single ice arch lasting 47 days in April/May 2008. Hence sea ice statistics are weighted by space not by time, using sea ice velocities estimated from colocated velocity observations. Multiyear sea ice with drafts exceeding 5 m constitute between 9% (2003–2004) and 16% (2007–2008) of the observed sea ice. The probability g(D) of this thick, ridged, multiyear ice decays exponentially with draft D at an e‐folding scale D0 of 3.0 ± 0.2 m. The trend of D0 with time is statistically indistinguishable from zero. This observation suggests a steady export of multiyear sea ice at decadal time scales. We speculate that our observations document the draining of the last reservoir of thick ice from the Arctic Ocean found to the north of Ellesmere Island and Greenland.

Influence of snow depth and surface flooding on light transmission through Antarctic pack ice

AbstractSnow on sea ice alters the properties of the underlying ice cover as well as associated physical and biological processes at the interfaces between atmosphere, sea ice, and ocean. The Antarctic snow cover persists during most of the year and contributes significantly to the sea‐ice mass due to the widespread surface flooding and related snow‐ice formation. Snow also enhances the sea‐ice surface reflectivity of incoming shortwave radiation and determines therefore the amount of light being reflected, absorbed, and transmitted to the upper ocean. Here, we present results of a case study of spectral solar radiation measurements under Antarctic pack ice with an instrumented Remotely Operated Vehicle in the Weddell Sea in 2013. In order to identify the key variables controlling the spatial distribution of the under‐ice light regime, we exploit under‐ice optical measurements in combination with simultaneous characterization of surface properties, such as sea‐ice thickness and snow depth. Our results reveal that the distribution of flooded and nonflooded sea‐ice areas dominates the spatial scales of under‐ice light variability for areas smaller than 100 m‐by‐100 m. However, the heterogeneous and highly metamorphous snow on Antarctic pack ice obscures a direct correlation between the under‐ice light field and snow depth. Compared to the Arctic, light levels under Antarctic pack ice are extremely low during spring (<0.1%). This is mostly a result of the distinctly different dominant sea ice and snow properties with seasonal snow cover (including strong surface melt and summer melt ponds) in the Arctic and a year‐round snow cover and widespread surface flooding in the Southern Ocean.

Modeling Sea Ice Surface Emissivity at Microwave Frequencies: Impact of the Surface Assumptions and Potential Use for Sea Ice Extent and Type Classification

In this paper, the surface emissivity is retrieved over the Arctic sea ice/open seas using observations from the advanced microwave sounding unit window channels during the year 2009. The emissivity computation is performed using two contrasted surface assumptions: specular and Lambertian assumptions. The obtained sea ice surface emissivities are studied in this paper with a focus on the effect of the surface assumption. Some factors of variability of the obtained emissivities are analyzed: variability in space, in time, with the zenith angle, and with respect to the frequency. We show that the near-nadir surface emissivity and emissivity difference (obtained using two contrasted surface assumptions) could be used as an excellent proxy to detect ice/no ice regions. We also show that near-nadir sea ice emissivity at some selected frequencies and the combination of both high and low window frequencies could also be very useful to better characterize sea ice surface physical properties and provide additional information for existing sea ice classifications, as they bring relevant information about first year and multiyear sea ice properties and their seasonal evolution.

Towards a semi-empirical model of the sea ice thickness based on hyperspectral remote sensing in the Bohai Sea

Sea ice thickness is one of the most important input parameters for the prevention and mitigation of sea ice disasters and the prediction of local sea environments and climates. Estimating the sea ice thickness is currently the most important issue in the study of sea ice remote sensing. With the Bohai Sea as the study area, a semiempirical model of the sea ice thickness (SEMSIT) that can be used to estimate the thickness of first-year ice based on existing water depth estimation models and hyperspectral remote sensing data according to an optical radiative transfer process in sea ice is proposed. In the model, the absorption and scattering properties of sea ice in different bands (spectral dimension information) are utilized. An integrated attenuation coefficient at the pixel level is estimated using the height of the reflectance peak at 1 088 nm. In addition, the surface reflectance of sea ice at the pixel level is estimated using the 1 550–1 750 nm band reflectance. The model is used to estimate the sea ice thickness with Hyperion images. The first validation results suggest that the proposed model and parameterization scheme can effectively reduce the estimation error associated with the sea ice thickness that is caused by temporal and spatial heterogeneities in the integrated attenuation coefficient and sea ice surface. A practical semi-empirical model and parameterization scheme that may be feasible for the sea ice thickness estimation using hyperspectral remote sensing data are potentially provided.

Improved Sea Ice Fraction Characterization for L-Band Observations by the Aquarius Radiometers.

Radiometers operating at L-band (1.4 GHz) are used to retrieve sea surface salinity over ice-free oceans and have been used recently to study the cryosphere. One hindrance of their use in the high latitudes is the preponderance of mixed scenes, where seawater and sea ice are both present in the sensor's field of view (FOV). Accurately characterizing the scene is crucial for oceanographic and cryospheric applications. To that end, a sea ice fraction model, composed of passive microwave sea ice concentration retrievals and an instrument simulator that integrates radiative power coming from all around the antenna, is used. We investigate the model currently used operationally to derive the ice fraction affecting the Aquarius observations and show that it can be significantly improved. On the one hand, the current model tends to overestimate sea ice fraction in the marginal ice zone where observations are used for salinity retrievals. On the other hand, the current model underestimates ice fraction within the ice pack where observations are used to derive sea ice properties. For the northern hemisphere, we also find evidence of the sea ice type impact on L-band radiometric observations. We present a model to derive sea ice fractions that are in better agreement with Aquarius radiometric observations using the Advanced Microwave Scanning Radiometer 2 Bootstrap algorithm for sea ice concentration and using high-resolution integration over the sensor's FOV.

In situ field measurements of the temporal evolution of low-frequency sea-ice dielectric properties in relation to temperature, salinity, and microstructure

Abstract. The seasonal evolution of sea-ice microstructure controls key ice properties, including those governing ocean–atmosphere heat and gas exchange, remote-sensing signatures, and the role of the ice cover as a habitat. Non-destructive in situ monitoring of sea-ice microstructure is of value for sea-ice research and operations but remains elusive to date. We examine the potential for the electric properties of sea ice, which is highly sensitive to the brine distribution within the ice, to serve as a proxy for microstructure and, hence, other ice transport properties. Throughout spring of 2013 and 2014, we measured complex dielectric permittivity in the range of 10 to 95 kHz in landfast ice off the coast of Barrow (Utqiaġvik), Alaska. Temperature and salinity measurements and ice samples provide data to characterize ice microstructure in relation to these permittivity measurements. The results reveal a significant correlation between complex dielectric permittivity, brine volume fraction, and microstructural characteristics including pore volume and connectivity, derived from X-ray microtomography of core samples. The influence of temperature and salinity variations as well as the relationships between ice properties, microstructural characteristics, and dielectric behavior emerge from multivariate analysis of the combined data set. Our findings suggest some promise for low-frequency permittivity measurements to track seasonal evolution of a combination of mean pore volume, fractional connectivity, and pore surface area-to-volume ratio, which in turn may serve as proxies for key sea-ice transport properties.

Reflective properties of white sea ice and snow

Abstract. White ice (ice with a highly scattering granular layer on top of its surface) and snow-covered ice occupy a large part of the sea ice area in the Arctic, the former in summer, the latter in the cold period. The inherent optical properties (IOPs) and the reflectance of these types of ice are considered from the point of view of the light scattering and radiative transfer theories. The IOPs – the extinction and absorption coefficients and the scattering phase function – are derived with the assumption that both the snow cover and the scattering layer of white ice are random mixtures of air and ice with the characteristic grain size significantly larger than the wavelength of incident light. Simple analytical formulas are put forward to calculate the bidirectional reflectance factor (BRF), albedo at direct incidence (the directional–hemispherical reflectance), and albedo at diffuse incidence (the bihemispherical reflectance). The optical model developed is verified with the data of the in situ measurements made during the R/V Polarstern expedition ARK-XXVII/3 in 2012.

Community review of Southern Ocean satellite data needs

AbstractThis review represents the Southern Ocean community’s satellite data needs for the coming decade. Developed through widespread engagement and incorporating perspectives from a range of stakeholders (both research and operational), it is designed as an important community-driven strategy paper that provides the rationale and information required for future planning and investment. The Southern Ocean is vast but globally connected, and the communities that require satellite-derived data in the region are diverse. This review includes many observable variables, including sea ice properties, sea surface temperature, sea surface height, atmospheric parameters, marine biology (both micro and macro) and related activities, terrestrial cryospheric connections, sea surface salinity, and a discussion of coincident andin situdata collection. Recommendations include commitment to data continuity, increases in particular capabilities (sensor types, spatial, temporal), improvements in dissemination of data/products/uncertainties, and innovation in calibration/validation capabilities. Full recommendations are detailed by variable as well as summarized. This review provides a starting point for scientists to understand more about Southern Ocean processes and their global roles, for funders to understand the desires of the community, for commercial operators to safely conduct their activities in the Southern Ocean, and for space agencies to gain greater impact from Southern Ocean-related acquisitions and missions.

Physical And Mechanical Properties Of Sea Ice In Bending

<p>The work presents the study of changes in the physical and mechanical properties of sea ice in bending. Strength limit σ<sub>в</sub> and deformation module Е<sub>в</sub> of ice under bending are conditional mechanical characteristics of sea ice. These characteristics do not reflect the actual stress state of ice destruction at the time. The ratio of the module to the strength limit Е<sub>в</sub>/σ<sub>в</sub> determines the relative radius of curvature of neutral layer in the place of ice destruction. It is shown that this ratio increases with the increase of ice temperature. Dependencies for determining of Е<sub>в</sub> and σ<sub>в</sub> of sea ice that generalize the experimental data are obtained.</p>

Fine-Scale Sea Ice Structure Characterized Using Underwater Acoustic Methods

Antarctic sea ice is known to provide unique ecosystem habitat at the ice–ocean interface. Mapping sea ice characteristics—such as thickness and roughness—at high resolution from beneath the ice is difficult due to access. A Geoswath Plus phase-measuring bathymetric sonar mounted on an autonomous underwater vehicle (AUV) was employed in this study to collect data underneath the sea ice at Cape Evans in Antarctica in November 2014. This study demonstrates how acoustic data can be collected and processed to resolutions of 1 m for acoustic bathymetry and 5 cm for acoustic backscatter in this challenging environment. Different ice textures such as platelet ice, smooth ice, and sea ice morphologies, ranging in size from 1 to 50 m were characterized. The acoustic techniques developed in this work could provide a key to understanding the distribution of sea ice communities, as they are nondisruptive to the fragile ice environments and provide geolocated data over large spatial extents. These results improve our understanding of sea ice properties and the complex, highly variable ecosystem that exists at this boundary.

The Role of Springtime Arctic Clouds in Determining Autumn Sea Ice Extent

AbstractRecent studies suggest that the atmosphere conditions arctic sea ice properties in spring in a way that may be an important factor in predetermining autumn sea ice concentrations. Here, the role of clouds in this system is analyzed using surface-based observations from Barrow, Alaska. Barrow is a coastal location situated adjacent to the region where interannual sea ice variability is largest. Barrow is also along a main transport pathway through which springtime advection of atmospheric energy from lower latitudes to the Arctic Ocean occurs. The cloud contribution is quantified using the observed surface radiative fluxes and cloud radiative forcing (CRF) derived therefrom, which can be positive or negative. In low sea ice years enhanced positive CRF (increased cloud cover enhancing longwave radiative forcing) in April is followed by decreased negative CRF (decreased cloud cover allowing a relative increase in shortwave radiative forcing) in May and June. The opposite is true in high sea ice years. In either case, the combination and timing of these early and late spring cloud radiative processes can serve to enhance the atmospheric preconditioning of sea ice. The net CRF (April and May) measured at Barrow from 1993 through 2014 is negatively correlated with sea ice extent in the following autumn (r2 = 0.33; p < 0.01). Reanalysis data appear to capture the general timing and sign of the observed CRF anomalies at Barrow and suggest that the anomalies occur over a large region of the central Arctic Ocean, which supports the link between radiative processes observed at Barrow and the broader arctic sea ice extent.

A 1/16° eddying simulation of the global NEMO sea-ice–ocean system

Abstract. Analysis of a global eddy-resolving simulation using the NEMO general circulation model is presented. The model has 1/16° horizontal spacing at the Equator, employs two displaced poles in the Northern Hemisphere, and uses 98 vertical levels. The simulation was spun up from rest and integrated for 11 model years, using ERA-Interim reanalysis as surface forcing. Primary intent of this hindcast is to test how the model represents upper ocean characteristics and sea ice properties. Analysis of the zonal averaged temperature and salinity, and the mixed layer depth indicate that the model average state is in good agreement with observed fields and that the model successfully represents the variability in the upper ocean and at intermediate depths. Comparisons against observational estimates of mass transports through key straits indicate that most aspects of the model circulation are realistic. As expected, the simulation exhibits turbulent behaviour and the spatial distribution of the sea surface height (SSH) variability from the model is close to the observed pattern. The distribution and volume of the sea ice are, to a large extent, comparable to observed values. Compared with a corresponding eddy-permitting configuration, the performance of the model is significantly improved: reduced temperature and salinity biases, in particular at intermediate depths, improved mass and heat transports, better representation of fluxes through narrow and shallow straits, and increased global-mean eddy kinetic energy (by ∼ 40 %). However, relatively minor weaknesses still exist such as a lower than observed magnitude of the SSH variability. We conclude that the model output is suitable for broader analysis to better understand upper ocean dynamics and ocean variability at global scales. This simulation represents a major step forward in the global ocean modelling at the Euro-Mediterranean Centre on Climate Change and constitutes the groundwork for future applications to short-range ocean forecasting.

Open-Ended Coaxial Probe Technique for Dielectric Spectroscopy of Artificially Grown Sea Ice

The dielectric properties of sea ice are important for both passive and active microwave remote sensing of sea ice. In this paper, we present a new technique for dielectric measurements of artificially grown sea ice in the frequency range between 0.3 and 12 GHz using an open-ended coaxial probe. To provide a solid contact between the probe and ice, we slightly submerge and then freeze the probe's flange in sea water in a cold laboratory with a preset temperature. Once the ice is formed, we conduct a measurement of the complex reflection coefficient in the cold room using a vector network analyzer. To calibrate the system, we propose a set of measurements from air, shorting block (short), and pure methanol to be conducted immediately after. Both the real and imaginary parts of the complex dielectric constant as functions of frequency are then derived using a coaxial probe inverse model fed by these data. X-ray microtomography analysis of our samples revealed that the ice formed under the described conditions has completely isotropic microstructure typical for the frazil layer of natural first-year sea ice. To evaluate the experimental system's accuracy, we conducted extensive test measurements of standard materials (saline water, methanol, butanol, and pure ice). We also demonstrate that our sea ice dielectric measurements are close to corresponding values previously reported in the literature. The proposed measurement technique is valuable for developing a sea ice dielectric mixture model at microwave frequencies for different temperatures and salinities.