A sea ice concentration and motion assimilation scheme has been developed using the Met Office Forecasting Ocean Assimilation Model (FOAM). FOAM has been upgraded to include a more realistic sea ice rheology and a sea ice thickness distribution. The sea ice data assimilation scheme uses Special Sensor Microwave Imager (SSMI) and QuikSCAT satellite observations to provide ice concentration and motion. A number of 1-year test integrations have been undertaken, and the resulting sea ice analysis has been examined in detail. The assimilation is able to significantly reduce the model sea ice concentration error and is able to address the model biases. Owing to the faster response times of the elastic-viscous-plastic (EVP) sea ice rheology in the model compared to the viscous-plastic used in previous studies, a novel approach to sea ice motion assimilation using increments to the ice stress has been developed. The sea ice motion assimilation scheme is able to reduce the model sea ice velocity errors by approximately 50% when compared to independent data. Ice velocity assimilation was found to have little impact on the ice concentration, and ice concentration assimilation is found to have little impact on ice velocities. This implies that ice concentrations are primarily thermodynamically controlled and ice velocities are primarily dynamically driven. During the summer, model biases and poor-quality observations impair the performance of the assimilation.
 Sea ice is an important feature of the polar oceans resulting in both hazards and opportunities for those living and working there. The radiative feedbacks associated with sea ice also make it a sensitive indicator of climate changes and monitoring its variability and trends provide a useful indicator of the state of the global climate. Sea ice modeling has the potential to improve the welfare of people who encounter sea ice by providing forecasts and analyses of the sea ice state. Reanalysis activities also allow the assessment of the optimum combination of observations which provide the most accurate representation of the sea ice.
 Data assimilation is a method to produce a four-dimensional representation of the state of a physical system. Assimilation allows the observed data to be used in a systematic way in combination with the model, allowing the model physics to interpolate between a heterogeneous array of in situ and remote sensing measurements which sample imperfectly and irregularly in space and time [Bengtsson et al., 1981; Weaver et al., 2000]. This should result in an analysis combining the best features of all data sources. The assimilation procedure can also help to identify biases between the model and data. Previous sea ice concentration assimilation studies have employed either direct insertion or initialization from a prescribed sea ice concentration field [e.g., Van Woert et al., 2004] or a simple nudging scheme in which the model is nudged toward a gridded field of ice concentration derived from satellite measurements. Previous studies of ice motion assimilation [Meier and Maslanik, 2003; Zhang et al., 2003] have used an optimal interpolation procedure to assimilate the velocity which is then directly nudged into the model. The requirements for data assimilation include models (forward simulation models, interpolation operators and operators to extrapolate prior information) and error statistics for the observations (biases, variances and covariances).
 The assimilation of temperature and salinity measurements into ocean models is now routinely performed by many centers. One such system is the Met Office FOAM operational ocean model [Bell et al., 2000], which we extend within this paper to include sea ice concentration and motion assimilation.
 A selection of two dimensional physically based sea ice models are available. These models are used in stand alone mode or as components of climate system models. The trend in model development is toward more complexity and higher resolution, for example incorporating the ice thickness distribution instead of a one or two level approximation [e.g., Flato and Hibler, 1995]. All models of physical processes are only approximations to the “truth” and even the best models have built-in errors and uncertainties. The measurements available to the scientific community for sea ice monitoring are for ice area, ice motion/deformation and, to a limited extent, ice thickness. Some studies have been completed which link data and models [Kwok et al., 1995; Thomas et al., 1996; Meier and Maslanik, 2003; Zhang et al., 2003], but so far the community is only beginning direct data assimilation into dynamic models.
 In this paper we describe the direct data assimilation of ice concentration and ice motion into the Met Office operational ocean forecasting model, FOAM [Bell et al., 2000; Martin et al., 2007]. The FOAM model is forced at the surface by fields from the Met Office numerical weather prediction (NWP) model analysis. This work is among early efforts to assimilate ice concentration and ice motion data into a state-of-the-art sea ice model (including EVP and ice thickness distribution) coupled to an ocean model. The assimilation procedure adopted here incorporates a novel approach to ice motion assimilation in which the velocity analysis is introduced to the model using an additional stress on the ice. The objective of this paper is to describe this work and its impact on the simulated sea ice. The sea ice data selected for assimilation are first discussed in section 2. The scheme for assimilating sea ice concentration and motion data is discussed in section 3, with the results of test integrations shown in section 4. A summary and discussion is presented in section 6.
2. Description of the Observation Sources
2.1. Ice Concentration
 The shortage of in situ observations is a recurring theme in oceanography and one which is particularly acute for polar regions. The harsh polar environment and sparse human activities make in situ monitoring a challenge. The Nimbus-5 satellite, launched in 1972, carried the first satellite borne imaging passive microwave sensor, the Electrically Scanning Microwave Radiometer (ESMR). This and subsequent Earth monitoring platforms provide a wealth of remotely sensed observations of sea ice.
 Passive microwave satellite instruments are the current workhorses of sea ice remote sensing because of the large contrast in emissivity between open water and ice cover [Eppler et al., 1992] and the transparency of clouds at these wavelengths. Microwave emission from the Earth's surface is detected in a number of atmospheric ‘window’ frequency bands, typically in the range 6–90GHz. The higher the emission frequency the more opaque the atmosphere, resulting in the contamination of the surface signal by atmospheric emission and scattering (particularly from clouds). At microwave frequencies and at temperatures encountered on the Earth, the strength of the emission from a surface varies proportionally to the surface temperature (the Rayleigh-Jeans approximation). Using variations in the emissivity, which depends on the dielectric properties of the surface, its roughness, snow depth and microstructure, the sea-ice cover may be inferred [Gloersen, 1973]. The number of free parameters is generally less than the number of independent observations (frequency bands observed) and the consequent ambiguity necessitates an empirical approach to the interpretation of microwave observations. Consequently, a number of empirical algorithms have been developed in order to reduce sensitivity to time varying surface conditions and derive useful physical quantities, such as sea ice concentration. These include the NASA Team [Cavalieri et al., 1984], Bootstrap [Comiso, 1986] and Cal/Val [Hollinger et al., 1987] algorithms.
 Recent developments of SSM/I ice concentration algorithms have focused on the use of the 85GHz channels [e.g., Markus and Cavalieri, 2000; Kaleschke et al., 2001] to improve the accuracy of the retrieval. The higher resolution of the 85 GHz channels compared to the 19GHz and 37GHz can improve the representation of the state of the ice edge (diffuse or compact) and may improve the detection of coastal zone polynyas. The increased sensitivity of the 85GHz channels to atmospheric and snow cover effects requires careful treatment, and they are typically used in combination with the lower frequency channels. In situ (ship based) validation of the Artist Sea Ice (ASI) algorithm [Kaleschke, 2003] showed better temporal correlation (0.66) with the observed ice concentration than competing algorithms. Validation of ASI has been performed using a number of methods, including ship, aircraft and satellite based sensors [Kaleschke et al., 2001]. The technique could provide erroneous results during adverse weather and unusual snow conditions, which are not well represented in the validation data. The good performance of ASI in tracking changes in ice concentration indicates that this algorithm is more likely to be consistent with forcing fields.
 The raw SSM/I radiance swath data are used as the source in this study. Although gridded radiance data are available, the ice concentration algorithms are nonlinear and consequently ice concentrations from gridded radiance data will not necessarily be consistent with the individual swath measurements. The swath data also allow each measurement to be individually quality controlled and better reflects the data that would be available operationally in near real time. The 85GHz channels of SSM/I are sampled at twice the along track and across track resolution compared to the lower frequency channels. The data are subsampled to include only those with radiance measurements in all channels (1 in 4 of the 85GHz points). A mask is then applied to discard points within 100km of land and those further away than 200km from a climatological maximum ice extent. The extended land mask was required since the radiances can be contaminated by emission from land entering through the sidelobes of the sensor, leading to spurious ice detection along coastlines. The maximum extent mask was used to prevent spurious ice “observations” outside the likely domain, and to reduce the overall data volume, by removing the numerous “0% ice” observations that would otherwise result. The mask was generated using the monthly mean HadISST1 climatology [Rayner et al., 2003] for the years 1979 to 2001. Examples of the mask are shown in Figure 1.
 The NASA Team [Cavalieri et al., 1991] sea ice algorithm (NTA) is then applied, together with a weather filter [Cavalieri et al., 1995] to enhance the ice mask. The weather filter cannot distinguish between very low ice concentrations (less than 10%) and weather contaminated (cloud, rain, large waves and foam) retrievals, leading to most ice free observations being flagged. For this reason, the sea ice concentration is set to zero for weather flagged observations. Observations with NTA ice concentrations less than 30%, that were not flagged by the weather filter, were treated as ‘unknown’ and were not assimilated, allowing the model to evolve freely in these areas. This is the result of a trade-off between contamination by weather leading to erroneous detection of low ice concentrations and accurate representation of the ice edge. Where sea ice with a concentration of at least 30% are detected by the lower resolution NTA, the higher-resolution ASI algorithm is used to compute the final sea ice concentration observation, which is then assimilated. Hence, the assimilated ice concentrations are based on the ASI data as the output from a 2 stage process, with the NTA concentration used as a filter in the first stage.
 At the start of the assimilation test period, 1999–2000, two DMSP satellites carrying SSM/I instruments were flying. These were joined by a third, launched in December 1999. Data from this satellite are available to us from March 2000. Each satellite provides around 300,000 processed sea ice observations per day. These are assimilated once a day.
 The assimilation scheme assumes that the observations have Gaussian error characteristics. Owing to the bounded range of ice concentration measurements, from 0% to 100%, the errors are non-Gaussian, which results in a suboptimal analysis. The errors also vary with ice concentration, wet snow, and the presence of summer melt ponds [Carsey, 1985]. In the simulations described here the observation error was set to 8% where the surface air temperature (from the NWP forcing fields) is less than 0°C, and 30% where the air temperature is greater than 0°C [Kaleschke, 2003].
 At scales of order 1 m sea ice has a very complex structure which varies significantly from location to location. Remotely sensed observations from passive microwave satellites cannot resolve these scales, resulting in observations which represent the sea ice within the measurement footprint. Here we treat sea ice concentration measurement from the satellite sensor as the fractional area covered by sea ice within the area measured. Young ice, such as grease ice is poorly detected by passive microwave sensors, resulting in concentrations of approximately 30% of the actual value [Kern et al., 2003]. These systematic under estimates may be detectable using information from the model, but no adjustment to the measurements is made in this study, where we take the passive microwave ice concentration to indicate the ice area fraction with a thickness of at least 1cm.
2.2. Ice Motion
 Two sources of ice motion data are used; SSM/I observations from Fowler  and QuikSCAT from Ezraty and Piollé . Hereafter, we refer to these data as Fowler and Ezraty and Piollé respectively. Both data sources are generated in a similar manner, using maximum cross correlation between two composite images of the sea ice separated in time. The Fowler data use the passive microwave SSM/I satellite data, whereas the Ezraty and Piollé data employed here use the active microwave QuikSCAT satellite data. Since they use different observing platforms, the two data sets may be regarded as independent. As discussed in detail by Kwok et al.  and Agnew et al.  the errors in these data sources are dominated by the tracking error, which is determined by the sensor resolution and time between images. A finer resolution and longer time between images allows a more accurate determination of the average motion in the period between images. Both SSM/I and QuikSCAT have similar spatial resolution, but the Fowler data use images one day apart and the Ezraty and Piollé data use images 3 d apart. Although the image resolution is 12.5km, velocity data are typically not available at every point, which reduces the spatial density of observations. High-frequency motion, such as tides and inertial motions, may be aliased by the image pairs, leading to biases, especially in daily data. The availability of both SSM/I and QuikSCAT data is reduced during the summer months as the presence of melt ponds makes the tracking of ice motion difficult. The Ezraty and Piollé data are supplied with a quality indicator flag, which was used to filter the data. Only data with a quality flag equal to 1 are used. This passes data with good (≥0.6) correlation only. For the Fowler data, no quality information is supplied and all data were used. The ice velocity observation errors are set to 0.06ms−1 for the Fowler data [Emery et al., 1997] and 0.035 ms−1 for the Ezraty and Piollé data. The error for the Ezraty and Piollé data was estimated on the basis of the pixel size (12.5km) and time window (3 d).
2.3. Validation Data
 In order to assess model performance, an independent (not assimilated), well validated source of observations is important. For ice concentration this presents a problem, since there are few sources of observations that have the necessary coverage, that do not make use of passive microwave satellites. Although SAR data are available, the coverage is limited and would not give representative results for the whole model area or time period. Monthly mean sea ice concentration fields are compared with the monthly HadISST1 reanalysis data set [Rayner et al., 2003]. Since this data set makes use of SSM/I data in addition to ice chart data, it cannot be considered to be completely independent of the data used in the sea ice assimilation performed here. Thus, owing to the lack of independent data, the performance of the ice concentration assimilation was difficult to judge quantitatively. The solution used here is to assume the assimilated data are ‘truth’ and hence verify the model performance against the original data.
 For ice motion, buoy data offer the best ground truth for verification of the model since the positions are accurately tracked. They are independent of the model, but the representativity of the point measurements compared to model grid cells of order 100km is a source of error. The buoys will also be subject to small-scale motions due to tides which are not represented in the model. Ice motion can be inferred from the movement of buoys placed within the ice pack. In the Arctic, the International Arctic Buoy Program (IABP) [Rigor, 2002] produces suitable data used for comparison. Approximately 30 drifting buoys were available in the Arctic during the period used for the model simulations. Simulated Lagrangian buoy drifts were derived from the model fields, using 24-h mean simulated ice velocities.
 The RADARSAT Geophysical Processing System (RGPS) [Lindsay and Stern, 2003] provides sea ice motion data derived from the synthetic aperture radar (SAR) sensor on board the RADARSAT satellite. The RGPS data set currently provides the only source of wide coverage sea ice data derived from SAR. Data from the RGPS is useful for validation, since it is entirely independent of the assimilation. The data set provides between ten and fifteen thousand observations per day, but the spatial coverage is limited by proximity to the Alaska SAR receiving station. Some preprocessing was required to make comparisons between the RGPS data and the model. The RGPS data [Kwok and Cunningham, 2000] consists of many Lagrangian tracks in SSMI grid space (polar stereographic), consisting of many displacement vectors per track. Ideally, Lagrangian particle tracks would be created from the model data and compared directly with the RGPS data. Owing to the vast number of observations, creating a Lagrangian track from the model for each was impractical, so the observation was compared with a 4-d model average centered on the observation. Four days was chosen because the vast majority of the RGPS displacement vectors cover 3 to 4 d. Each RGPS displacement vector was treated as an observation, linearly interpolated to halfway between the end points in both time and space.
3. Sea Ice-Ocean Model
 The ocean model used was based on the operational FOAM system, described by Storkey . The model is a primitive equation z-level model, based on the Bryan-Cox formulation [Bryan, 1969; Cox1984]. Within this study, the global 1° model configuration has been used. The model is driven by fluxes supplied by the Met Office numerical weather prediction (NWP) model, interpolated from 6 hourly mean fields. The ocean model assimilates surface temperature from satellites, ships and buoys as well as temperature and salinity profile data. The data source is the Met Office observation database (MetDB) which ingests and archives data from the Global Telecommunications System (GTS). Although this data is available globally, very few observations are available in polar regions and the ocean model is effectively free running here. The global average root-mean square errors for FOAM in surface temperature and salinity are approximately 1K and 0.3PSU respectively [Martin et al., 2007].
 The sea ice component of FOAM in this study is identical to that in the Hadley Centre climate model (HadGEM1) as described by McLaren et al. . The HadGEM1 sea ice model shares much of its code with the CICE sea ice model [Hunke and Lipscomb, 2004]. The ocean and sea ice models are fully coupled, exchanging fluxes of momentum, heat and mass each time step. The sea ice is represented through prognostic variables which define the average sea ice conditions within a grid cell. The thermodynamic representation of the sea ice includes a five-category sea ice thickness distribution (ITD) scheme with ice category thicknesses shown in Table 1. Each sea ice thickness category has an associated ice concentration (fractional area) and thickness. The model does not distinguish between sea ice types, such as grease ice, nilas and so on, except through the thickness distribution. The minimum sea ice thickness modeled is 1cm. The dynamic representation of the sea ice uses the elastic-viscous-plastic (EVP) dynamical model of Hunke and Dukowicz .
 Since we are not using a fully coupled ocean-ice-atmosphere model we cannot guarantee that the surface fluxes provided by the atmosphere are consistent with the modeled sea ice conditions. To partially compensate for this the atmospheric fluxes are split into an ‘ice’ and ‘lead’ portion (according to the sea ice boundary condition seen by the atmosphere) which is repartitioned according to the sea ice model open water and ice-covered area.
3.1. Assimilation of Sea Ice Concentration
 The assimilation of ice concentration was performed using the standard FOAM analysis – correction framework [Martin et al., 2007]. The cost function takes the form
where yo are the observation values, x is the desired analysis, xb is the background model state, (O + F) is the sum of the observation and representivity error covariance matrices, B is the background error covariance matrix, and h is an operator to perform the mapping from model to observation space.
 The analysis increments are given by
where HT is the adjoint of h.
 The optimal interpolation scheme used in FOAM approximates the inverse above, to allow the increments to be computed in the following form:
with weights, W given by
and normalization factor
 The iterative formulation of equation (2) used by the FOAM system applies increments to both the model space (x) and observation space (y) values to obtain the uth estimate, according to
 The initial values, x and y, are the model background and observation values respectively, i.e., x = xb, and y = yo.
 The background error covariance between a model grid point m and observation point i is approximated as the product of the variance at the observation point, and a correlation μmi.
 The function μ is approximated as a second-order autoregressive (SOAR) function,
where hmi is the distance between observation i and grid point m and s is the correlation scale. The observation error matrix, (O + F) is taken to be diagonal; that is, the observation errors are assumed to be uncorrelated. An analysis field for the sea ice concentration is produced using an optimal interpolation approach similar to that used for sea surface temperature (SST). The analysis increments are nudged in equally over the period of a day, so that the total increment is applied after 24 h.
 The distribution of the ice concentration increments onto the ice thickness categories could be done in a number ways. The optimal solution would depend on an accurate knowledge of the model thickness error covariance, which we do not know a priori. Two main sources of model error exist, errors due to ice motion and errors due to thermal forcing. Whereas atmospheric thermal forcing has a greater impact on thinner ice categories, errors in the advected flow affect all categories. Errors in the divergence of the flow will tend to impact the thinner ice first as it is easier to deform. The solution we have adopted is to minimize the impact of the assimilation on the ice volume. This means that a fraction of the thinnest ice in each grid box is removed when the analysis increment is negative. Where the analysis increment is positive, new ice is added by adjusting the ice thickness distribution to represent the addition of 10cm thick ice. Analysis increments smaller than 1% per day on ice free grid points are likely due to numerical artifacts and these are removed. The analysis increments to the ice concentration were nudged in at each model time step (every hour), so that the total increment is applied over a day. A sensitivity test was performed in which the ice concentration analysis increments were applied as a uniform scaling to all ice categories, rather than just to the thinnest, but this approach was rejected as it led to a significant degradation in the representation of the ice thickness. Changes to the ice concentration were balanced by associated changes to the ocean surface salinity to conserve total salt. No direct changes were made to the ocean temperature by the ice concentration assimilation since we are unable to determine a priori whether the heat fluxes should be exchanged with ocean or atmosphere. We assume here that, because of the one way coupling, the atmospheric fluxes are the primary cause of the model to observation differences diagnosed by the assimilation.
3.2. Assimilation of Sea Ice Motion
 Using the model velocity components as control variables we assimilate the ice motion observations using a multivariate method described by Daley . This scheme allows the divergence introduced by the assimilation to be controlled. In practice the method has a major deficiency for sea ice assimilation; the method has no knowledge of the limited domain, such as coastlines and ice extent. This can lead to unrealistic circulation near the ice edge, coastlines and islands. We therefore implemented the method without any constraint on the additional divergence added by the assimilation. This is in contrast to previous studies, such as that by Zhang et al.  who introduce constraints on the divergence to prevent unrealistic flow. Here we rely on the model physics to control the flow, described in section 3.3.
 For QuikSCAT observations, in which the sea ice drift is determined using pairs of images 3 d apart, the model background sea ice motion field is the average of 4 consecutive daily mean motion fields. The start and end days are given 50% of the weight of the central days, since the observations are created from daily composites. The four day model background drift includes a 2-d forecast and the previous 2 d analysis. For the Fowler SSMI observations, a 2-d average model drift was used as the background.
 Sea ice inertia is small, compared to the external forces (wind stress, ocean stress and Coriolis) acting on it, on timescales greater than an hour or so. This means that the sea ice model is able to reject any direct increments to the ice velocity field unless balancing increments are made to the forces acting upon the ice. Previous authors [Zhang et al., 2003] who have performed sea ice velocity assimilation have typically exploited the slow response times of viscous-plastic sea ice model formulations or created a velocity field that is not dynamically active. This allows their direct assimilation increments to be used successfully. Hunke and Dukowicz  show that the EVP sea ice models respond much faster to changes in the velocity than viscous-plastic models which means they are not suitable for direct nudging of the sea ice velocities.
3.3. Assimilation of Ice Motion Using Ice Stress Increments
 In order to allow the analysis increments to take effect in the model, an additional stress term, τi is introduced into the sea ice momentum equation. The resulting momentum equation integrated by the EVP process is given by
where m is the combined mass of ice and snow per unit grid box area, τa and τw are the grid box mean (GBM) wind and ocean stresses, u is the ice velocity, a is the ice fractional area, f is the Coriolis parameter, and ∇ · σ represents the internal forces exerted by the ice. We do not attempt to attribute the additional stress to any specific physical process (such as wind stress, ice-ocean stress or internal ice stress), but to an unknown combination of stresses that the model has not accurately represented.
 The stress increment, τi, represents the stress required to change the equilibrium velocity by the analysis increment, ui. We assume the inertia term, m is much less than the other terms in equation (10), and that the internal ice stress, ∇ · σ is unchanged by the change in the ice velocity diagnosed by the analysis. The low inertia approximation is reasonable since the model appears to come close to equilibrium within an hour or so, as shown earlier. The ice stress increment required to obtain a new equilibrium state, at velocity u + ui is given by
where τw(u)gives the ice-ocean stress at ice velocity u. Here, the wind stress and internal ice stresses are assumed to be independent of ice velocity. While this is a good approximation for the wind stress, the internal ice stresses are likely to be dependent on the ice velocity, owing to changes in the strain rate, especially in the central ice pack, but we assume their magnitude is small enough to neglect.
 The sea ice-ocean stress is computed in the model using a quadratic drag formulation,
where cw is the drag coefficient, ρw is the density of seawater, and uw is the ocean surface velocity. The ice stress bias, τb is computed using a linear approximation to the ice-ocean stress, by treating ∣uw − u∣ as a constant. This results in an ice stress increment given by
 At the start of the EVP time step, the model evolves rapidly and can be far from equilibrium. To reduce the noise this introduces and to improve stability a running mean ice stress increment is used in the momentum equation,
where β is a constant, with 0 ≤ β ≤ 1, τki is the instantaneous ice stress increment, and k+1i is the smoothed ice stress increment, passed to the EVP scheme. The EVP scheme iterates toward a solution, using 120 time steps, each 30 s long, for each model time step. This approach is analogous to the nudging of assimilation increments in slowly during 24 h, rather than shocking the model by applying the full increment at the start. A 4-h smoothing timescale was used (β = 0.002).
 In order to improve the model forecast (and hence the background velocity) the bias correction method of Bell et al.  has been applied to ice motion assimilation.
 This makes use of the assumption that the sea ice velocity increments are primarily governed by persistent biases in the model or forcing fields. Bias fields have been introduced for the u and v components of the ice velocity and are updated according to
where uk is the ice velocity field at time tk, the superscript b indicates a bias field, superscript a indicates an analysis, superscript f indicates a forecast, superscript o denotes observations, Hk interpolates from the model grid to motion observation positions.
 A simple form for the gain matrix is chosen,
where Kkx is the gain matrix used when assimilating the model state. The forecast model for the bias is assumed to be a decay,
where γ is a constant, with 0 ≤ γ ≤ 1. This is because we expect the ice velocity field to change on the timescales of synoptic weather systems, around 5 d or so. Combining 15, 16 and 17, the bias evolves as
 The increment used when calculating the ice stress increments is given by the sum of the ice velocity bias and the analysis increment for the current analysis period,
where ukia is the analysis increment at time index k, given by
 The bias is added to the current analysis increment when the ice stress increment is calculated.
 The initial tests of this approach showed that the bias field is larger than the increments, shown in Figure 2. This indicates that the ice velocity errors are mainly due to persistent biases in the stress acting upon the ice. The persistence of the bias field improves the forecast out to 5 d, as shown in Figure 3. At short forecast ranges (2–3 d) the bias field significantly improves the forecast quality. At 5–8 d, persisting the bias degrades the forecast (gray dashed line), and decaying the bias by 20% per day offers some improvement (black solid line).
3.4. Overview of the Model Integrations
 The integration period chosen is October 1999 to December 2000. The period is slightly longer than 1-year so that a complete annual cycle is captured. The selected period is chosen for the availability of both QuikSCAT and RGPS ice motion. Four model hindcasts are undertaken: (1) The control simulation (Control) includes the assimilation of three-dimensional ocean temperature and salinity, but the model sea ice is allowed to evolve freely. (2) Ice concentration assimilation simulation (IceConc) is similar to Control with the addition of sea ice concentration assimilation using the scheme described in 3.1, but ice motion is not assimilated. (3) Ice motion assimilation simulation (IceVel) is similar to Control with the addition of sea ice motion assimilation as described in 3.4, but ice concentration is not assimilated. (4) Full assimilation simulation (ConcVel) is similar to Control with the addition of both sea ice concentration and sea ice motion assimilation.
Table 2 describes the data assimilated during all the model simulations. These are temperature and salinity data, which are assimilated in the same manner as the operational FOAM system. Table 3 summarizes the sea ice data sources used in the simulations.
Table 2. Data Assimilated by All 1-Year Model Integrations
Data Source Short Name
Autonomous drifting buoys from the Argo program
In situ temperature and salinity
Sparse, global, to 2000 m depth.
Very few available during 1999–2000
Data from Expendable Bathythermographs (XBTs)
In situ temperature
Global, mainly on shipping routes
All data supplied via the Global Telecommunication System (GTS)
Data from Conductivity-Temperature-Depth (CTD) probes
In situ temperature and salinity
All data supplied via the Global Telecommunication System (GTS)
In situ SST
Data from moored and drifting surface buoys and ships
Global; regular supply from moored buoys; dense along shipping routes
All data supplied via the Global Telecommunication System (GTS)
Sea surface temperature derived from AVHRR
All ice-free ocean
Coarse resolution gridded product used
Table 3. Sea Ice Data Assimilated During Year-Long Model Integrations
Data Source Short Name
SSMI ice conc.
Sea ice concentration from SSMI using he ASI algorithm
Sea ice concentration
Global, All year
Using method developed in this study; used in IceConc and ConcVel
Fowler sea ice velocity
Sea ice velocity measured using SSM/I images on consecutive days
Sea ice velocity.
Global ice covered ocean; sparse near ice edge and in summer
From NSIDC; assimilated using method developed in this study; used in IceVel and ConcVel
CERSAT sea ice velocity.
Sea ice velocity measured using QuikSCAT images from composites 3 d apart
Sea ice velocity
Northern hemisphere, winter only; no data from May to September inclusive
Assimilated using method developed in this study; used in IceVel and ConcVel
4. Assimilation Results
4.1. Impact of Assimilation on Ice Concentration
 The modeled ice concentration with assimilation is a much closer match to the observations than the Control simulation without assimilation. Representative snapshots of the modeled sea ice and observations are shown in Figure 4 and Figure 5 respectively for the 1 March 2000. This demonstrates that the assimilation is successfully matching the model to the observations. The ice motion assimilation had little impact on the ice concentration, which is why Figure 4a and Figure 4c appear almost identical. This indicates that either the motion assimilation had no impact on the ice velocities (which we will show later is not the case) or that the modeled sea ice concentration is primarily thermodynamically controlled. This in turn suggests that inaccurate oceanic and atmospheric surface heat fluxes are the most likely cause of model error in sea ice concentration. This type of error has been noted in reanalysis products [Liu et al., 2005[DE5]] and is associated with the failure of NWP models to fully capture large-scale synoptic events.
 A persistent bias between the observations and modeled sea ice is found in the central Arctic (Figure 4), to the north of Svalbard, in which the observations show anomalously low ice concentrations. In this area the model thermodynamics attempts to increase the ice concentration to more than 95%, reflecting the large surface heat fluxes that arise in winter when even small areas of open water appear. The observations consistently gave ice concentrations of around 80%. We believe this is due to surface properties of the sea ice (fresh snow), which give rise to erroneous ice concentration estimates in the observations. It is found that the model response to this bias can be controlled by altering the thickness of new ice grown thermodynamically. By making the new ice thicker (up to 0.2m from a default of 0.1m) its area growth rate is reduced, allowing the low ice concentrations introduced by the assimilation to remain, whereas thinner ice allows the model to rapidly reject the assimilation increments. Further increasing the thickness of new ice to 0.5m allows the model to better match the observations in this area, but had a detrimental impact on the ice thickness distribution. This coarse tuning led to the choice of 0.2m for the thickness of new ice, providing the best model fit to observations without a severe impact on the ice thickness distribution. Without independent, accurate alternative information, the true nature of the ice in the Svalbard region cannot be determined. Models with a resolution comparable to this version of FOAM have been shown to have biases caused by inaccurate oceanic heat fluxes through the Fram Strait and Barents Sea [e.g., Oka and Hasumi, 2006] which may be the cause of the anomaly. Here we utilize a global tuning parameter, which allows the assimilation to alter the model behavior in the Svalbard region without degrading the performance elsewhere. Future work should improve on this, for instance through better diagnosis of the origin of the discrepancy between model and observations or by adding balancing changes to heat fluxes which allow the model to accept the assimilated ice concentration. Comparisons of ASI concentrations with NT2 and Bootstrap Algorithm ice concentrations should help to determine the accuracy of the ASI algorithm in a range of conditions. Current developments in sea ice retrieval algorithms and algorithm intercomparison should also improve the situation [Comiso and Parkinson, 2008; Comiso and Nishio, 2008]. Through the use of more spectral information, by combining the 85GHz channels with lower frequencies as in the NT2 algorithm, the sensitivity to surface changes may be mitigated.
Figure 6 shows the RMS differences in ice concentration between HadISST1 and the simulations performed for this study. Since the ice motion assimilation had very little impact on the ice concentrations, only the Control and ConcVel simulations are compared. Over the summer melt period the model shows very large errors without assimilation, which are corrected well by the assimilation, giving RMS errors of less than 10% throughout most of the year, and less than 20% in summer. The large summer errors are due to the simulation melting too much ice (Figure 7a). This is mostly corrected by the assimilation (Figure 7b), but still differs from the HadISST ice (Figure 7c).
 The assimilation gives an improvement in the ice concentration of at least 5% in the Northern Hemisphere, and between 5% and 10% in the Southern Hemisphere. The largest deviations from HadISST1 are during the summer months in both hemispheres. This may be due to the model tendency to create unrealistically large areas of low ice concentration during these periods. This is also the period in which the assimilation offers the greatest improvement. Large areas of relatively thin, low concentration ice around the ice edge are present in HadGEM1 [McLaren et al., 2006]. For the purposes of comparison with observations, these areas are usually treated as ice free [Parkinson et al., 2006] owing to the poor detections of thin ice by passive microwave sensors. We looked in detail at the causes of the low summer ice concentration. Two mechanisms contribute: (1) Poor representation of mixed layers in the ocean model lead to inaccurate ocean heat fluxes, which in turn allow ice to form. The relatively thick 10m top ocean level contributes to this owing to poor representation of the mixed layer. This mechanism appears dominant around the ice edges. (2) The specification of the atmospheric heat fluxes to the ocean maintain a constant flux in the ‘lead’ and ‘ice’ regions represented in a grid cell. As the lead fraction increases so too does the fraction of heat into the ocean, but the one way coupling does not permit an increase in outgoing long-wave radiation. This leads to a positive feedback in the summer melt, as the “trapped” ocean heat must melt more sea ice. We found that summer ocean to ice heat flux was 80 Wm2, more than double the observations seen in the SHEBA experiments. This highlights one of the problems in driving an ice-ocean model with fixed atmospheric fluxes.
4.2. Impact of Assimilation on Ice Motion
 The results from the ice motion assimilation were compared to the Ezraty and Piollé QuikSCAT data product. The RMS motion differences between the model simulations and the observations are shown in Figure 8. The RMS velocity difference was computed as
where e is the spatially averaged RMS error, vi is the sea ice velocity observation for observation i, Hi ( ) is an interpolation function mapping the model velocity, u to the observation location. The observation location was interpreted as the midpoint between the start and end of the ice motion observation. These data are not independent, since they were assimilated. These results show the extent to which the assimilation is able to match the data it is presented with. Figure 8 shows that the motion assimilation is able to alter the model sea ice velocities to match the observations throughout the period these observations are available. The ice concentration assimilation has very little impact on the ice velocities, indicating that the ice dynamics is primarily constrained by external stresses.
4.2.1. Comparison Against RGPS Data
 The motion assimilation improved the sea ice velocities against the RGPS observations motion by approximately 2 cm s−1 RMS, shown in Figure 9, with greater improvements during some periods such as March 2000. This is a significant improvement given the large number of observations used for verification, of order 10,000 per day.
4.2.2. Comparison With Buoy Motion
 Lagrangian drift maps from simulation and buoys are shown in Figure 10. Shown are 28 d of buoy drift computed from the model fields, using 24-h mean ice velocities. The results show that the variability is captured fairly well by the model, but the magnitude and direction of the actual drift is only partially captured. In the case of buoys 1222 and 2388, both ice concentration and ice motion assimilation improve the modeled drift, but the motion assimilation has the larger impact. In the case of buoy 8066, during June 2000, the modeled drift is smaller than observed and shows no significant improvement with assimilation. This may be because surface melt in June reduces the availability of data for assimilation. Although a useful test, these buoys only give an indication of the model performance. In order to measure the performance of the model over the whole Arctic, the displacement error for all buoys accumulated over 10 d was converted into a mean motion error for all available buoys (approximately 25) and is shown in Figure 11. The ice motion assimilation gave most improvement (2 cm s−1 or 50%) during the winter, when Ezraty and Piollé observations are available. Even during the summer, when only Fowler observations are available, there is some improvement, but not as significant.
4.3. Statistical Comparison of Buoy and Model Motion
 Buoy motion data were computed from the raw IABP tracks, using only buoys with locations given at midnight on consecutive days. An interpolated motion measurement is derived at the midpoint, and compared with the 24-h mean model motion spatially interpolated to that point. Approximately 9000 suitable buoy motion data are available for the period between October 1999 and November 2000. For each model simulation, the bias, standard deviation (SD), error SD and correlation are computed. The results are given in Tables 4 and 5 for the winter and summer periods.
Table 4. Winter Comparisons of Model to Buoy Arctic Sea Ice Velocitiesa
Mean Model Ice Speed
SD of Model Motion
Winter is October through March. Velocities are given in m/s.
Table 5. Summer Comparisons of Model to Buoy Arctic Sea Ice Velocitiesa
Mean Model Ice Speed
SD of Model Motion
Summer is April through September. Velocities are given in m/s.
 In winter, the motion assimilation improves both the error SD and correlation, with correlations in excess of 0.9 for both the u and v components. The biases are also reduced by the assimilation. Ice concentration assimilation has virtually no impact on the motion. In summer, the assimilation does not improve the ice motion. This suggests that the errors in the Fowler SSMI observations are too large during summer to improve the motion on short timescales.
4.4. Impact of Sea Ice Data Assimilation on the Ocean
 The ocean state is impacted by the changes to the sea ice forced by the assimilation. Although the ocean model assimilated temperature and salinity data during the simulations, there are very few of these in the polar regions and the model is essentially free running here. During the polar winter the SST is strongly constrained by the large heat fluxes, resulting in temperatures close to the freezing point of sea ice. Changes to the ocean surface conditions were largest during the summer, when exposed areas of ocean are heated by the sun. After one year of assimilation, the area–weighted root mean square difference in Arctic SSTs was 0.7°C and the difference in sea surface salinities was 0.1PSU R.M.S. The spatial distribution is shown in Figure 12. The largest changes in SSTs were in summer, in areas of ocean that the assimilation reduced the ice area., such as Baffin Bay and the Bering Sea. Here the increased solar input allows more significant warming, of over 4K compared to the Control run. Under ice the SST is constrained to be close to freezing, and little difference is apparent between the runs. For salinity the picture is more complex. A reduction in surface salinity, associated with thicker ice (see following section), is apparent in the region around Svalbard, extending through the FRAM strait. Also, not evident within these short simulations, the ocean can store biases that would only become apparent after several years owing to large-scale circulation changes.
4.5. Impact of Sea Ice Assimilation on Ice Thickness
 The sea ice assimilation is expected to have an impact on the sea ice thickness, both directly, as a result of changes to the ice thickness distribution, or indirectly by ridging, convergence and divergence induced by the velocity increments. A comparison of the monthly mean ice thickness between the four simulations is shown in Figure 13. This shows that in the case of ice concentration assimilation only, the Arctic ice is generally thinned. During the freezeup (October to January) the thickest ice areas north of Greenland are thickened further. This indicates that the ice model is able to transfer the 10cm ice added during assimilation into the thicker ice categories. In contrast, the ice velocity assimilation tends to increase the ice thickness over most of the domain, suggesting that the ice velocity assimilation induces extra ridging. The net result of both concentration and velocity assimilation is to thin the ice in the Bering and Chukchi seas, but increase the ice thickness north of Greenland.
4.6. Comparison With Submarine Ice Thickness Data
 Submarine data from a cruise in October 2000 [National Snow and Ice Data Center, 1998] bas been compared with the model output. The submarine track positions are shown in Figure 14. The data is supplied as integrated statistics covering 10 d intervals during October 2000. The locations are specified to the nearest 0.1 degree, this is adequate for comparison with the 1° model used here. The submarine ice draft profile was remapped to the 5 ice thickness categories used in the model. In order to convert draft to ice thickness, the following formula was used:
where hi is the ice thickness, ρi, ρw and ρs are the densities of sea ice (915.1 kgm−3), snow (330 kgm−3) and seawater (1023.9 kgm−3) respectively, hd is the ice draft, and hs is the model snow thickness. For thin ice (<0.5 m) the snow cover was assumed to be zero.
 Submarine measurements of ice draft have been estimated to have a bias of 0.29 m due to the poor estimate of the open water reference surface, and a standard deviation of 0.25 m [Rothrock and Wensnahan, 2007], A comparison of the submarine and simulated ice thickness are shown in Figure 15, in which we have subtracted the observation bias of 0.29 m given by Rothrock and Wensnahan . October is the month following regional minimum ice cover and so we expect to see new ice and some multiyear ice. The assimilation has greatest impact on the thinnest ice, leaving the thicker ice virtually unchanged. The ice thickness for the thinner ice compares more favorably with the observations following ice drift and concentration assimilation. The thicker ice appears to be too thin, suggesting that there is not sufficient ice ridging in the model, but assimilation does not alter this.
5. Moored ULS Data
 Data is available from two moored submerged buoys carrying upward looking sonar (ULS) devices that were deployed by Alfred Wegener Institute (AWI) in 1999 [Witte and Fahrbach, 2005]. These were moored in the Fram Strait at (74.4°N, 10.3°W) and (79.0°N, 2.1°W). The locations of the buoys are shown in Figure 16. Like the submarine data, a probability density function (PDF) of ice drafts is available. As for the submarine data, the PDF of drafts were mapped to the model equivalent ITD, converting drafts to ice concentration using equation (22). The buoys are in the marginal ice zone during March 2000 with strong gradients in ice concentration, consequently comparisons are sensitive to errors in the modeled ice edge.
Figure 17 shows that the ice concentration for the buoy further north (buoy 25) is fairly well matched to the observations in both assimilation and control runs. The other buoy (buoy 32) is closer to the ice edge, and the indication is that the assimilation erodes the ice edge too far, leading to more open water than is present in the ULS observations.
6. Summary and Discussion
 An ice concentration and motion assimilation scheme has been developed using the Met Office Forecasting Ocean Assimilation Model (FOAM). FOAM has been modified to include a realistic ice rheology (elastic-viscous-plastic) and an ice thickness distribution. The ice concentration assimilation scheme uses SSMI satellite swath data, and the ice motion assimilation scheme uses data from both SSMI and QuikSCAT. A number of 1-year test integrations have been undertaken from 1999 to 2000 using a 1° global sea ice–ocean model. The model performance assimilating sea ice data has been analyzed in detail. The assimilation is able to constrain the model RMS error to below 10%. During the summer the assimilation is impaired by poor quality observations and model biases arising from the absence of a rigorous energy conservation due to the one-way atmospheric coupling scheme. A novel ice motion assimilation scheme has been developed in order to cope with the faster response times of the EVP sea ice rheology in the model compared to the viscous-plastic used in previous studies. In this scheme an additional ice stress is diagnosed and applied to the ice in order to achieve the changes diagnosed by the analysis. This scheme is able to reduce the RMS velocity error by approximately 50%. The results showed little coupling between the ice concentration and ice motion, indicating that the sea ice dynamics is controlled mainly by external stresses and that the sea ice concentration is thermodynamically controlled. Verification of the ice velocities against independent data (RGPS and buoys) clearly demonstrate a quantitative improvement using assimilation. A validation of the model ice thickness against submarine and moored ULS observations indicate that the assimilation does not degrade the representation of ice thickness. Indeed, assimilation provides a marginal improvement in the representation of thin ice. A small drift in ice volume throughout the one year simulation is not inconsistent with interannual variability. The assimilation scheme has been shown to be useful in providing information on other limitations of the model, including surface stresses.
 The ice concentration scheme described in this study is well suited for operational use, with only minor modifications for near real time processing. The ice motion assimilation would be less suitable for operational implementation, since the time-average nature of the observations would require several model days to be rerun every day. This would significantly increase the required processing time. Improving the ice motion did not have a significant impact on the ice concentration, which is the primary sea ice product for users of the FOAM system. Further work could look at more efficient ways of utilizing the ice motion observations, and further examine the trade-off between short timescale motion observations with lower accuracy and longer observations with improved accuracy.
 This work was funded by the European Space Agency (ESA) under ESA/ESTEC contract 17334/03/NL/FF. We thank Lars Kaleschke for the provision of the Artist sea ice algorithm, and we thank the anonymous reviewers for their constructive comments.