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 We present an optimized 1992–2008 coupled ice-ocean simulation of the Arctic Ocean. A Green's function approach adjusts a set of parameters for best model-data agreement. Overall, model-data differences are reduced by 45%. The optimized simulation reproduces the negative trends in ice extent in the satellite records. Volume and thickness distributions are comparable to those from the Ice, Cloud, and land Elevation Satellite (2003–2008). The upper cold halocline is consistent with observations in the western Arctic. The freshwater budget of the Arctic Ocean and volume/heat transports of Pacific and Atlantic waters across major passages are comparable with observation-based estimates. We note that the optimized parameters depend on the selected atmospheric forcing. The use of the 25 year Japanese reanalysis results in sea ice albedos that are consistent with field observations. Simulated Pacific Water enters the Bering Strait and flows off the Chukchi Shelf along four distinct channels. This water takes ∼5–10 years to exit the Arctic Ocean at the Canadian Arctic Archipelago, Nares, or Fram straits. Atlantic Water entering the Fram Strait flows eastward, merges with the St Ana Trough inflow, and splits into two branches at the southwest corner of the Makarov Basin. One branch flows along Lomonosov Ridge back to Fram Strait. The other enters the western Arctic, circulates cyclonically below the halocline, and exits mainly through the Nares and Fram straits. This work utilizes the record of available observations to obtain an Arctic Ocean simulation that is in agreement with observations both within and beyond the optimization period and that can be used for tracer and process studies.
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 Global coupled ocean and sea ice models are widely used to study the responses of the ocean and sea ice to climate change. Existing model-data comparisons show large systematic differences in the character of the principal water masses in the Arctic Ocean. Some of the most common model shortcomings include the lack of a cold halocline in the Amerasian Basin, misrepresentations and systematic drifts in the core temperature of the Atlantic Water, and discrepancies in hydrographic and sea ice transports by factors of two or higher across Fram Strait [Holloway et al., 2007; Martin and Gerdes, 2007; Holland et al., 2006; W. Maslowski, personal communication, 2009]. These shortcomings are in part the result of the models' inability to resolve eddies and eddy-driven dynamics due to their limited horizontal resolution (50 to 100 km) and in part the result of unmodeled physics such as shelf water formation and tides [Holloway et al., 2007]. The prevalent model-data discrepancies can be identified using assessment metrics and sensitivity studies to models parameters.
 Previous attempts to incorporate data into model simulations in the polar region have focused primarily on adjusting either the sea ice or ocean system without considering their coupled behavior, [e.g., Zhang et al., 2003; Lindsay and Zhang, 2006; Harder and Fischer, 1999; Miller et al., 2006]. For sea ice, Kalman filters and optimal interpolation techniques are typically used to minimize differences between model and buoy/satellite ice drifts and concentration [e.g., Zhang et al., 2003; Lindsay and Zhang, 2006; Stark et al., 2008; Rollenhagen et al., 2009]. There are also studies that aimed to adjust model parameters such as ice albedos, drag coefficients, and strengths in stand-alone ice models using Monte Carlo approaches [e.g., Harder and Fischer, 1999; Miller et al., 2006]. These studies utilized hundreds of sensitivity experiments to narrow down the optimal sets of parameters. Often, nonuniqueness can result in multiple sets of parameters depending on initial and boundary conditions. In the ocean, 3D-Var and 4D-Var methods have been used to assimilate observed oceanic temperature and salinity to reconstruct regional or basin-wide circulation patterns [e.g., Nechaev et al., 2004; Panteleev et al., 2010]. In all the above efforts, the ocean and sea ice data assimilations are not coupled.
 In contrast to above studies, we use a Green's function approach to obtain an optimal set of ocean and sea ice model parameters for a coupled ocean and sea ice Arctic Ocean. In this paper, we provide an assessment of the “baseline” and of the “optimized” Arctic Ocean simulations. The baseline simulation exhibits many common issues identified by Holloway et al.  and Holland et al. . The optimized simulation reduces model-data difference by 45%. Additionally, this simulation does not contain discontinuities when and where data are ingested, as would be the case, for example, if a Kalman filter or an optimal interpolation approach had been used. Therefore the optimized simulation is suitable for budget analyses and for tracer studies [e.g., Manizza et al., 2009].
 The paper is organized as follows. Section 2 describes the data sets used in the optimization and in the assessment of the simulations. Section 3 discusses the Green's function approach, the MITgcm model configuration, and the optimized parameters. In section 4, we present the assessment of the models' sea ice and ocean water properties and, when available, compare our solution with those from the Arctic Ocean Models Intercomparison Project (AOMIP). Our model's strengths and weaknesses are assessed and future directions are discussed in section 5.
 Data used in this assessment are sea ice velocity, fluxes, area, thickness, oceanic vertical conductivity-temperature-depth (CTD) profiles, and oceanic heat and volume transports. Table 1 lists the data types, their spatial and temporal coverage, and expected quality. Data uncertainties are briefly discussed here and are used when considering the least squares weights in section 3.2.
Table 1. Data Used in the Optimization Procedure
Uncertainties are reported per winter (October–May).
Here 0.75 m for U.S. former classified data and 0.25 m for the rest of the ULS data.
 The U.S. Navy and Royal submarine upward looking sonar (ULS) ice draft from 1975 to 2000 is the only data set with long temporal coverage and it covers over half of the central Arctic [Rothrock and Wensnahan, 2007]. Individual 10–50 km section of the averaged ice draft has an expected bias of 0.29 m with an expected uncertainty of 0.25 m [Rothrock and Wensnahan, 2007]. In addition to the submarine data, In addition to the submarine data, the Alfred Wegener Institute (AWI) Moored ULS data set, which covers the Fram Strait and Greenland/Norwegian seas (Gr/No), for the 1992–2002 period is used [Witte and Fahrbach, 2005]. Individual AWI ice draft measurement has an accuracy of ±0.20 m [Witte and Fahrbach, 2005]. We average the data into ∼20 km sections using a typical sea ice speed of 0.1 m/s prior to comparing with model output. Drafts are converted to thickness by multiplying with a factor of 1.1, which is approximately the ratio of mean seawater density of 1024 kg/m3 and sea ice density of 910 kg/m3. The mean and standard deviation of ice drafts within each 20 km section are shown in Figures 4a and 4b. The ice draft standard deviations are ∼1 m in the Gr/No seas and 1–2 m in the Arctic Ocean.
2.2. Sea Ice Velocity
 Optimally interpolated ice motions at horizontal resolution 12.5 × 12.5 km2 from 1992–2003 can be downloaded at http://www-radar.jpl.nasa.gov/rgps/ice_motion_3.html [Kwok et al., 1998]. The optimally interpolated data set combines ice motion buoys and passive microwave from both 37 GHz and 85 GHz channels. Overall, the error in sea ice velocity is 4.4–6.7 km/d [Kwok, 2009]. Additionally, we use monthly averaged velocity fields to assess the model large-scale velocity patterns. In this case, we expect the standard errors to be σt/ ≈ 0.80 km/d or 0.01 m/s where N = 30 is the number of days per month.
2.3. Sea Ice Fluxes
 Winter sea ice fluxes across Fram Strait and the Canadian Arctic Archipelago (CAA) provide constraints to the Arctic ice exports and hence influence the sea ice and freshwater mass budgets. Fluxes are derived from passive microwave and RADARSAT Synthetic Aperture Radar images for the 1992–2002 period and are calculated across gates as defined by Kwok et al.  and Kwok . Across Fram Strait, uncertainties per winter (October–May) are 17,000–25,000 km2 for area flux and 100–240 km3 for volume flux [Kwok and Rothrock, 1999]. Across the CAA, uncertainties in area flux are ∼110 km2 per winter [Kwok, 2006].
2.4. Sea Ice Concentration
 Satellite sea ice concentration from the bootstrap technique [Comiso et al., 1997] is available on a 25 km horizontal grid at http://nsidc.org. Uncertainties in sea ice concentration are between 4 to 7% during the winter and are higher during the summer months [Kwok, 2009; Spreen et al., 2008]. We use concentration primarily to evaluate gross model biases in seasonal ice zones.
 Atmospheric boundary conditions considered in this study include the European Center for Medium-Range Weather Forecasts (ECMWF) 40 year reanalysis (ERA-40) and the Japanese 25 year Reanalysis Project (JRA25). JRA25 covers 1979–2004 and is described by Onogi et al. . The Japan Meteorological Agency (JMA) Climate Data Assimilation System (JCDAS) provides a near real-time analysis that is consistent with the JRA25 reanalysis starting in January 2005. Therefore using the JRA25/JCDAS atmospheric fields allows near real-time ocean-ice simulations. Section 3.5 discusses in more detail the effect of atmospheric boundary conditions on the simulation results.
3.1. Green's Function Approach
 Green's functions provide a simple yet effective method to adjust general circulation model (GCM) parameters [Menemenlis et al., 2005a]. The Green's function approach involves the computation of GCM forward sensitivity experiments for each parameter that is to be adjusted followed by a recipe for constructing a solution that is the best linear combination of these sensitivity experiments. Technically, Green's functions are used to linearize the GCM and discrete inverse theory [Menke, 1989] is used to estimate the GCM parameters. A short description of the Green's function approach follows using the notation of Wunsch .
 An ocean general circulation model can be thought of as a set of rules for time stepping an ocean state vector x(t) one time step Δt into the future
State vector x(t) includes ocean temperature, salinity, and velocity and sea ice thickness, concentration, and velocity on the model grid at time step t. Function M represents the numerical model and vector η contains model parameters, for example, initial and surface boundary conditions, subgrid-scale mixing, albedos, and drag coefficients. Parameters in η are not known exactly. We assume that they can be represented by a white noise process with mean ηo and covariance matrix Q.
 The observation equation relates state vector x to observations y through operator H
where vector x now represents the complete time history of the state vector, i.e.,
Vector ε is the observation noise process, which is assumed Gaussian with zero mean and covariance R. Equation (2) can also be written in terms of parameter vector η
where G represents the convolution of ocean model M and measurement model H. To solve the highly nonlinear equation (4) for η, we linearize it around a baseline ocean model integration, i.e., we integrate equation (1) with our best prior estimate ηo of the model parameters, and we rewrite the observation equation as
where Δη = η − ηo and Δy = y − G(ηo). Matrix G is the Jacobian matrix ∂y/∂η. Each column of matrix G can be computed using a model perturbation experiment, i.e., a model Green's function for the corresponding parameter in vector η.
 A cost function J that measures the length of the control parameter perturbation and of the model-data misfit is defined
where Wη and Wy are weight matrices for the control parameter perturbation Δη and the model-data misfit Δy − GΔη, respectively. If the model and observation error covariance matrices are known, minimizing J with Wη = Q−1 and Wy = R−1 provides the maximum likelihood estimate [Menke, 1989; Wunsch, 2006]. The minimization of cost function J with respect to Δη yields the solution
 An estimate of ocean circulation is then obtained by integrating the model equation (1) using parameters = ηo + . For global ocean models, the length of the parameter vector η can exceeds 109. Therefore the computation of the full Jacobian matrix G using a Green's function approach and the inversion of G, as required in equation (7), would be prohibitive. Nevertheless, as demonstrated herein and by Menemenlis et al. [2005a], the optimization of a small number of carefully chosen parameters η can lead to a substantial reduction of cost function J.
3.2. Error Covariances and Weights
 We consider three different alternatives for weight matrix Wy in the cost function, equation (6), because a prior data error covariances are not known and are difficult to estimate. In the first option each data set is assigned weights that are inversely proportional to the number of data points within that set, i.e., we divide each data set by the number of data points in that particular set. In the second option, weights are assigned such that each data set has approximately equal contribution to the overall cost function. In the third option, we scale each term of the cost function by the variance of the model-data difference. Admittedly, all three weight matrices are arbitrary and all three ignore the spatial and temporal covariances in the errors, i.e., the off-diagonal elements in Wy are set to zero. Of interest to the present discussion is that the three cases are different and that they allow us to explore a wide range of plausible solutions. The results presented in Table 2 are based on the second option, that is, Wy is a diagonal matrix with scaling factors chosen so that the respective contributions of each data set to the cost function are approximately equal. Given that the number of observations is much larger than the number of model parameters being estimated, we set Wη to zero. That is, we assume that there is no a priori knowledge about the control parameters.
Table 2. Model Parameters Used in Baseline A0, Optimized A1, and AOMIP Experiments
 The grid covering the Arctic domain is locally orthogonal with horizontal grid spacing of ∼18 km. There are 50 vertical levels ranging in thickness from 10 m near the surface to ∼450 m at a maximum model depth of 6150 m. The model employs the rescaled vertical coordinate “z*” of Adcroft and Campin  and the partial cell formulation of Adcroft et al. , which permits accurate representation of the bathymetry. Bathymetry is from the S2004 (W. Smith, unpublished data, 2004) blend of the Smith and Sandwell  and the General Bathymetric Charts of the Oceans (GEBCO) one arc minute bathymetric grid. The nonlinear equation of state of Jackett and McDougall  is used. Vertical mixing follows the K profile parameterization (KPP) of Large et al. . A seventh-order monotonicity-preserving advection scheme [Daru and Tenaud, 2004] is employed and there is no explicit horizontal diffusivity. Horizontal viscosity follows Leith  but is modified to sense the divergent flow [Fox-Kemper and Menemenlis, 2008].
 The ocean model is coupled to the MITgcm sea ice model described by Losch et al. . Ice mechanics follow a viscous plastic rheology and the ice momentum equations are solved numerically using the line successive over relaxation (LSOR) solver of Zhang and Hibler . Ice thermodynamics use a zero heat capacity formulation and seven thickness categories, equally distributed between zeros to twice the mean ice thickness in each grid cell. Ice dynamics use only two thickness categories: open water and sea ice. The model includes prognostic variables for snow thickness and for sea ice salinity.
 The baseline (or A0) Arctic Ocean integration is derived from a globally optimized simulation, which was generated by the Estimating the Circulation and Climate of the Ocean, Phase II project (ECCO2) [Menemenlis et al., 2008]. This ECCO2 simulation provides initial and lateral boundary conditions, surface atmospheric forcing fields, and various model parameter values for the A0 integration. In particular, surface boundary conditions are derived from the ERA-40 [Uppala et al., 2005] but have been adjusted during the 1992–2002 period using a global Green's function optimization. Because the ERA-40 reanalysis ends in August 2002, the ECMWF atmospheric analysis is used after August 2002. Six hourly surface winds, temperature, humidity, downward short- and long-wave radiation, and precipitation are converted to heat, freshwater, and wind stress fluxes using the Large and Yeager  bulk formulae. Short-wave radiation decays exponentially with depth as per Paulson and Simpson . Low-frequency precipitation has been adjusted using the pentad (5 day) data from the Global Precipitation Climatology Project (GPCP) [Huffman et al., 2001]. Monthly mean river runoff is based on the Arctic Runoff Database (ARDB) as prepared by P. Winsor (personal communication, 2007). Other baseline model parameters, which were used for the A0 integration, are listed in Table 2.
 Despite the global ECCO2 optimization on which it is based, A0 exhibits many common issues identified by Holloway et al.  and Holland et al. . A second Arctic Ocean simulation (called A1) based on a regional Green's function optimization is discussed next.
3.4. Optimized Simulation A1
 The Green's function approach requires one complete 1992–2004 model integration for each control parameter that is to be adjusted. As a result, only 16 model parameters that are expected to have a large impact on the solution are selected. They include initial conditions, surface boundary conditions, and several ocean and sea ice model parameters. Table 2 provides values for A0 and A1, and for the range of values used in AOMIP. For each parameter we carried out a sensitivity experiment relative to A0 in order to construct the Jacobian matrix, G in equation (5). Data used in the cost function, J in equation (6), include sea ice drift, concentration, thickness, and ocean T/S profiles (see section 2). In addition to adjusted parameters, the A1 simulation differs from A0 by the inclusion of the Nguyen et al.  salt plume parameterization. This parameterization distributes salt rejected during sea ice formation to the neutral buoyancy depth at the base of the mixed layer and improves the representation of water masses in A1.
3.5. Sensitivity Experiments
 Initial conditions in Table 2 pertains to initial conditions: a more realistic initial ocean and sea ice state minimizes model drift. The Arctic Ocean model was integrated with initial conditions from the Polar Science Center Hydrographic Climatology (PHC) [Steele et al., 2001], the World Ocean Atlas 2001 (WOA01) [Conkright et al., 1989], the World Ocean Atlas 2005 (WOA05) [Locarnini et al., 2006; Antonov et al., 2006], and the World Ocean Circulation Experiment Global Hydrographic Climatology (WGHC) [Gouretski and Koltermann, 2004]. WOA05 yielded the lowest cost and is used for optimized simulation A1.
 Atmospheric forcing in Table 2 pertains to atmospheric surface boundary conditions. We carried out four sensitivity experiments using atmospheric boundary conditions from the National Centers for Environmental Prediction (NCEP), the Common Ocean Reference Experiments (CORE) [Large and Yeager, 2004], the ECCO2/ERA40/ECMWF blend, and the JRA25 [Onogi et al., 2007]. JRA25 yielded the lowest cost and is used for optimized simulation A1.
 Optimized sea ice and snow albedos are comparable with those used in the AOMIP experiments and with observations (Table 2). The model is insensitive to dry ice albedo as winter ice is mostly snow covered. As a result, we use the AOMIP dry ice albedo of 0.7 in our optimized experiment. The decrease from the high albedos in A0 to more realistic albedos in A1 results from using atmospheric boundary conditions from JRA25 instead of the ECCO2/ERA40/ECMWF blend. Specifically, ERA40 overestimates downward short-wave radiation at the surface in high-latitude regions due to inaccuracies in the radiative properties of clouds [Allan et al., 2004]. As a consequence, albedos in experiments with ERA40 atmospheric boundary conditions have to be artificially increased to compensate for the excess downward short-wave radiation.
 In addition to albedos, several sea ice parameters including drag coefficients, strength, and lead closing parameters are optimized. Drag coefficients control sea ice drifts and are adjusted to yield reasonable velocity and sea ice/ocean transports [Harder and Fischer, 1999; Miller et al., 2006]. The sea ice pressure parameter P* (also known as “strength”) affects ice internal strength and dynamics, and is typically adjusted to bring ice motions and thickness to better agreement with observations [Steele et al., 1997]. Lastly, the ice demarcation thickness Ho controls the ice opening/closing rate in leads and polynyas [Hibler, 1979] and is adjusted to bring ice thickness and concentration to closer agreement with data. Values of the drag coefficients and of the sea ice strength parameter are consistent with those used in the AOMIP models (Table 2) [Martin and Gerdes, 2007].
 We also adjusted the KPP background vertical diffusivity and two salt plume parameters. Zhang and Steele  and Nguyen et al.  discussed the importance of adjusting the vertical diffusivity in order to reduce numerical diffusion and to improve properties of the Atlantic and Pacific waters. In addition, Nguyen et al.  showed that by including a subgrid-scale salt plume parameterization, a cold halocline could be realistically simulated in the Western Arctic Ocean.
 Lastly, we adjusted river runoff in order to bring the model freshwater budget closer to observations.
 Optimized parameter uncertainties can be estimated using equation (9) of Menemenlis et al. [2005a]. These uncertainties, however, depend on prior statistical assumptions, in particular on the implied data errors associated with the weights discussed in section 3.2. Option 2 of Wy yields the largest uncertainties (A1 in Table 2) and is used here as a representative upper bound.
 The optimization period covers 1992–2004. Simulation A1 is integrated past the optimization period, i.e., to May 2009, in order to assess the model's ability to reproduce the sea ice and ocean conditions in recent years. Here we discuss the cost function reduction of A1 relative to A0 (section 4.1) and we provide a detailed assessment of simulation A1, including comparisons with observations outside the period of optimization (section 4.2).
4.1. Cost Function Reduction
 Cost functions are computed using three different weights, as discussed in section 3.2, and are referred to as J1, J2, and J3. We optimize A1 using J2. In the following analyses, we also show costs J1 and J3 when they contribute additional insights. Figure 2 shows the total costs normalized by the cost of A0. The overall (ocean and sea ice) cost reduction in A1 is 44% relative to A0. Four data sets for sea ice and two sets for the ocean are used to calculate the net cost. To assess sea ice mass balances, we use observations of extent, thickness, velocity, and fluxes. For the ocean, T/S profiles are used, which are metrics for water mass formation and evolution. Current meter measurements across the Fram Strait are used to evaluate the improvement in transports across this gateway.
4.1.1. Sea Ice Extent
 Sea ice extent costs J1–3 reduce by 3–17% in A1 compared to A0 (Figure 3b). A geographic breakdown shows the largest reductions of 68% and 44% in the Amerasian and Eurasian basins. Costs increase in the marginal and seasonal ice zones such as in the Gr/No, Barents, and Bering seas (Figures 3b and 3c). In the Amerasian Basin and the CAA, a large fraction of the model-data difference is due to the model's mistiming of the onset of melting and freezing as compared to data (blue and red sharp extrema in Figure 3c). In the Gr/No and Barents Sea, the model produces more sea ice in both simulations compared to Special Sensor Microwave Imager (SSMI) data.
4.1.2. Sea Ice Thickness
 Sea ice thickness cost J1–3 reduce by 25–61% in A1 compared to A0 (Figure 4c). Regional reductions are ∼62% in the Arctic Ocean and 41% in the Gr/No seas. A0 has lower mean thickness than either A1 or observations, even though the albedos are unrealistically high to compensate for deficiencies in the ERA40/ECMWF surface short-wave radiation (Figures 4a and 4b and Table 2). In A1, more realistic ice and snow albedos are obtained and sea ice thickness is closer to observations (Figure 4a). Improvements in thickness are also, in part, due to improved sea ice drifts [e.g., Zhang and Rothrock, 2003].
4.1.3. Sea Ice Velocity
 Sea ice velocity costs J1–3 reduce by 14–50% in A1 relative to A0 (Figure 5). There is no apparent temporal variation in the residuals. When costs in A0 are partitioned into contributions from individual basins and seas and from the CAA, the Gr/No seas account for 68% of J1 and 28% of J2 (A0, Figure 5c). The spatial distribution of costs in A1 is similar to A0, with model-data differences in the Gr/No seas accounting for 71% of J1 and 43% of J2 (Figure 5d).
 Systematic spatial biases exist for sea ice velocity (Figure 5d). Within the Arctic Ocean, excluding the CAA and the Gr/No seas, model-data differences are higher along the coast. In A0, 55% of J2 occurs within 150 km from the coast, and 94% of J2 is within 300 km. A closer look at the velocity directions shows that, in addition to large speed differences, both simulations A0 and A1 have velocity directions approaching parallel to the coasts. In contrast, microwave data show sea ice flowing at angles 25–45° to the coast (not shown here). The large differences along the coast also reflect the model's inability to produce observed sea ice convergence/ridging. Overall, the reduction in sea ice velocity costs in A1 is largely a result of optimizing the air/sea ice drag coefficients (Table 2).
4.1.4. Sea Ice Transports
 Monthly and annual sea ice transports across Fram Strait (FS) are significantly closer to observations in A1 compared to A0 (Figures 6a and 6b). Overall, both J1 and J2 reduce by ∼58% (Figure 6c). Individual reductions of cost are 79% and 45% for FSa and FSb, respectively (see Kwok et al.  for locations of FSa and FSb). Similar to sea ice velocity, improvements in transports mostly come from optimizing the ice-air drag coefficient.
 The overall hydrographic cost reductions are 60% for J1 (not shown) and 54% for J2 (Figure 7). A breakdown of costs shows a reduction in J2 of 83% when compared to BGEP data (2003–2004) and a reduction of 54% when compared to SCICEX data (1992–2000, Figure 7). The largest decrease in J2 comes from improvements in the cold halocline representation in the Western Arctic at depth 50–250 m and, to a lesser extent, improvements in Atlantic Water properties below 250 m (Figure 8). Improvements in water mass productions are a result of using the salt plume parameterization in combination a low KPP background diffusivity [Nguyen et al., 2009]. Curvatures associated with the summer and winter Pacific Water at S ∼ 28–34 and at T < 0°C in the T/S diagram are also more realistically reproduced in A1 (Figure 8a). Vertical T/S profiles in MB, AB, and NB (see Figure 1 for locations) are similar and therefore we show vertical profiles for MB and T/S diagrams from AB and NB to aide visualizations in both depth space and T/S space (Figures 8b and 8c). In the Gr/No seas, both simulations produce thicker Atlantic Water than observed (Figure 8d) and as a result improvements in this region is negligible (Arctic/Subarctic Ocean Fluxes (ASOF) data, Figures 7 and 8d). The misrepresentation of the Atlantic Water is a common problem in the AOMIP models [Holloway et al., 2007].
 A possible mechanism contributing to a thicker Atlantic Water (AW) layer is the inability of our model to adequately represent restratification processes. Boccaletti et al.  show that within a few days after a deep mixing event, instabilities develop that cause the convection region to restratify. In our model, this restratification process is not resolved.
4.2. Assessment of Simulation A1
4.2.1. Sea Ice
 In this section we assess A1 relative to the mean, trend, and variability of sea ice conditions, with emphasis on recent years that are beyond the optimization period. With more realistic spatial sea ice thickness distribution, simulation A1 can reproduce the extent minima in the summers of 2007 and 2008 (Figures 9a and 9b). For the 1992–2004 optimization period and for the 2005–2008 period, the mean model-data differences in September sea ice minimum are 4% and 10%, respectively (Figure 9c). Parkinson and Cavalieri  report a negative trend of −450 ± 50 × 103 km2/decade in observed sea ice extent from 1979–2006. For the period considered in this study, 1992–2008, the trend is more negative, approximately −680 × 103 km2/yr for SSMI and −590 × 103 km2/yr for A1 (Figure 9d).
 For sea ice transport, A1 overestimates the area flux across Fram Strait by ∼20% in the annual mean and ∼65% during the summer months when compared to estimates from Kwok  (Figure 6b). This overestimation is in part because A1 produces a wider sea ice extent across Fram Strait during the summer compared to observations and in part because we use only winter velocity to construct the cost function. Over the period 1992–2008, the mean annual, winter, and summer transports in A1 are 109 ± 24 × 104, 90 ± 18 × 104, and 18 ± 8 × 104 km2, respectively. During the summer (June–September), A1 yields maximum sea ice exports in years 2005 and 2007, consistent with Kwok  but with a positive bias. In terms of interannual variability, annual transport peaks match the results of Kwok , with maxima in 1995, 1997, 2000, 2002, 2005, and 2007 (Figure 6b). The A1 simulation, however, has maximum area export in 2005, whereas observations show maximum export in 1995. Kwok  concluded that even though there is an increase in velocity across FSa, there is no increase in outflow because of negative trends of sea ice concentration across this gate since 1979. In A1 the reduction in ice concentration across Fram Strait for the 1992–2008 period is smaller than observed. As a result, due to increased velocity, the simulation has increased annual sea ice exports across this gate (Figure 6b).
 For sea ice thickness, the 2003–2008 A1 estimates are consistent with Ice, Cloud, and land Elevation Satellite (ICESat)-derived estimates both for the basin-averaged thickness as well as for the thickness distribution (e.g., the mean and long tail of thick ice in Figure 10b). Spatial distributions of thickness are also consistent with ICESat data, e.g., the very thick ice (>5 m) North of Greenland and the CAA and thin ice near the Siberian Coast (Figure 10a). A1 also reproduces the negative trend in mean November ice volume for the 2003–2007 period in the Arctic Ocean and Barents Sea; however the simulation underestimates the net volume loss, i.e., −3 × 103 km3 for A1 compared to −5 × 103 km3 for ICESat (Figure 10c).
4.2.2. Atlantic Water
 The AW in A1 is identified as the layer within 27.8 < σ < 33.0 kg/m3 (density anomaly relative to 1000 kg/m3), which roughly corresponds to the layer of temperature T > 0°C. In addition, outside the Arctic Ocean, AW is also defined as having salinity S > 34.5. To determine the sense and strength of Atlantic Water circulation, we use the scalar field “topostrophy” τ as defined by Holloway et al. 
where u and ∇D are velocity and gradient of bathymetry D, respectively. In the Northern Hemisphere, τ is positive when the flow is cyclonic with shallow topography to the right (Figure 11).
 In the Gr/No and Barents seas, AW is close to the surface and can be traced in the top 270 m of the water column (Figure 11, left). In the Nansen and Amundsen basins, AW is present at depths below 50–70 m and flows in a cyclonic sense. In the Canada Basin, AW is at greater depth and its circulation is strongly cyclonic along the rim of the Arctic Ocean with τ ∼ 0.4–0.8 (Figure 11, right). Figure 12 shows the 16 year mean AW flow in the Arctic Ocean with strongest imports across FS and the St Ana Trough (SA) into the Nansen Basin. Table 3 lists volume, heat, freshwater (relative to a salinity of 34.8), and salt transports across the major gates along the AW path. Transports here are calculated from the top of the AW to full depth of the water column. Salt transport in g/s is computed as volume flux (m3/s) × salinity (g of salt/kg of salt water) × salt water density (kg/m3), assuming a mean Atlantic salt water density of 1028 kg/m3.
Table 3. Transports in Simulation A1 Along the Atlantic Water Pathways in the Arctic Ocean and Barents and Kara Seasa
Gate locations are shown in Figures 1 and 12. Gates BA through VS are used for Barents and Kara seas budgets, and gates SA through CAA are used for Arctic Ocean budgets. Gate CAA is defined by Kwok  and its location is between gates MS and NS in Figure 1.
 The combined Kara and Barents seas are bounded by gates BA, SA, SF, and VS (Figure 13). The net inflows of volume, heat, and salt across these gates are 1.3 ± 0.4 Sv, 27 ± 11 TW, and 48.6 ± 16 Mg/s, respectively. The corresponding net outflows are 1.9 ± 0.3 Sv, 66 ± 9 Mg/s, and 4.6 ± 4.7 TW, respectively. The imbalance in heat transport is due to heat loss to the atmosphere and to sea ice melt. For freshwater, the annual mean runoff of 40.1 mSv from the Ob and Yenisey rivers contribute to a net flow of 20 ± 3 mSv of freshwater from the Barents and Kara seas into the Arctic Ocean.
 For the Arctic Ocean budget, AW volume and salt fluxes of 2.5 ± 0.3 Sv and 89 ± 11 Mg/s, respectively, through FS and 1.8 ± 0.3 Sv and 66 ± 9 Mg/s, respectively, through SA account for ∼90% of the inflows (Figure 13). For heat fluxes, ∼80% of the net input of 35 ± 5 TW is through FS and ∼20% is through SA. As expected, the Arctic Ocean acts as a heat sink with ∼30 TW of the input heat lost to sea ice melting and to the atmosphere and 3.5 ± 2 TW flowing out through FS. The addition of sea ice melt, river runoff (annual mean 39.5 mSv), and mixing with fresher Pacific Water likely accounts for the large freshwater pool with net outflow of 100 ± 20 mSv across the CAA, Nares Strait (NS), and FS.
 In term of circulation, AW enters the Arctic Ocean across FS and splits into two branches just inside this gate. The smaller branch of the two either recirculates and exits on the western side of FS or flows north across the Gakkel Ridge and reaches the Makarov Basin across gate A3 (Figure 12 and Table 3). The second branch flows east along the southern rim of Nansen Basin, merges with the inflow through SA, and continues eastward along the 500–2000 m isobaths in the Nansen and Amundsen basins (gate A1 in Table 3). At the southern end of the Lomonosov Ridge, the flow splits with ∼50% flowing along the Lomonosov Ridge back out to Fram Strait and ∼50% continuing along bathymetric contours near the Siberian Coast into the Canada Basin. Along the Canada Basin rim, AW flows beneath the lighter Pacific Water. Volume fluxes reduce from ∼1.5 Sv at gates C1–CK to 0.5–1.0 Sv across gates C2–C5 (Figure 12).
 The net volume flux across FS of 1.4 ± 0.6 Sv is comparable with observations of 2–4 Sv [Schauer and Fahrbach, 2004]. The individual northward and southward flows, however, are lower than the observed values of 9 ± 2 Sv (inflow) and 13 ± 2 Sv (outflow). Consequently, the heat flux into the Arctic Ocean across FS (28 ± 4 TW) is lower than the observed value of 28–46 TW. A closer look at T/S diagrams shows that the Atlantic Water in the Gr/No seas is thicker and extends deeper compared to climatology (Figure 8d). This misrepresentation of AW is also present in the AOMIP simulations and is identified as one of the major deficiencies in current generation coupled ocean and sea ice models [Holloway et al., 2007].
 Despite weaker than observed flows across Fram Strait, the strength of the cyclonic flow inside the Eurasian Basin, as measured by positive topostrophy (Figure 11), is stronger than flows in all AOMIP simulations that do not include a subgrid-scale parameterization to force flow along local topographic contours [Holloway and Wang, 2009]. The 15 year mean normalized τ for the upper 1500 m are 0.68 ± 0.19, 0.12 ± 0.32, 0.52 ± 0.08, and 0.58 ± 0.13 for the Eurasian, Amerasian, Barents and Kara seas, and Gr/No seas, respectively. The low τ in the Amerasian Basin is due to the inclusion of the upper ocean where the Beaufort Gyre dominates. For depth 150–1500 m in the Amerasian Basin, τ = 0.53 ± 0.41. These highly positive τ values in the entire Arctic Ocean indicate that cyclonic flow is prominent and that anticyclonic atmospheric circulation over the Beaufort Sea acts to weaken the AW flow below 300 m but does not reverse it.
4.2.3. Pacific Water
 Pacific Water (PW) in A1 enters the Canada Basin through Bering Strait (BS) and can be traced in the upper 270 m by the strongly negative topostrophy (anticyclonic flows, Figure 11, left). After crossing Chukchi Sea where nearly 50% of the heat input is lost, passive tracers show that PW follows roughly the bathymetric contours into the Arctic Ocean along the Barrow (BC1), Central (CC), Herald Canyons (HC), and Long Strait (LS) (Figure 14). Transports across the gates shown in Figure 14 and comparisons with previously published results are summarized in Table 4. At BS, the net imports of volume, heat, and freshwater are 0.86 ± 0.03 Sv, 9.34 ± 0.34 TW, and 70 ± 2.6 mSv, respectively. These transports are consistent with observed values of ∼0.8 Sv, 4.12–9.19 TW, and 41–67 mSv, respectively [Woodgate et al., 2005]. The fractional transports across BC1, CC, HC, and LS are 30%, 40%, 20%, and 10%, respectively (Table 4). For comparison, estimates from a Chukchi Sea high-resolution numerical model [Spall, 2007] and from mooring observations [Woodgate et al., 2006] across BC1, CC, and HC are ∼25%, ∼25%, and ∼50%, respectively, of the net ∼0.8 Sv inflow through BS. Residence time of PW in the Chukchi Sea is ∼1 year.
Table 4. Transports of Pacific Water in the Arctic Ocean for Simulation A1a
 At the northern end of the Chukchi Sea, flow across gate BC1 continues downstream to gate BC2. At BC2 80–90% of this flow merges with the flow through CC and becomes part of the anticyclonic Beaufort Gyre circulation. A small fraction of the flow (0.05 ± 0.02 Sv) at gate BC2 continues eastward as the rim current along the coast of Alaska. Transit time between gates CC1 and McClure Strait (MS) along the Beaufort Gyre circulation is 5–6 years. Downstream of HC, the flow splits into two branches. One branch merges with water from CC and becomes part of the anticyclonic Beaufort Gyre circulation. The second branch flows westward along the 500 m isobath near the East Siberian Sea, then flows into the Makarov Basin, crosses the Lomonosov Ridge, and reaches NS and FS. The transit time from BS to NS or from BS to FS is ∼10 years. The largest export of PW at the CAA comes from water along path A–B and exits through McClure Strait (0.34 ± 0.09 Sv, Table 4). Export at Amundsen Gulf (AG) comes from path A–B and from the rim current but is much weaker (0.05 ± 0.02 Sv). The net exports are 0.55 ± 0.12, 0.32 ± 0.08, and 0.41 ± 0.17 Sv across the entire Canadian Arctic Archipelago (gates CAA, AG, and MS), the Nares Strait, and the Fram Strait, respectively.
 Overall, net imports of volume, freshwater, and salt transports of 0.98 ± 0.03 Sv, 80 ± 2.2 mSv, and 31 ± 0.8 Mg/s across the four Chukchi Sea gates (BC, CC, HC, and LS) are balanced by net exports of 1.28 ± 0.22 Sv, 85 ± 11 mSv, and 40 ± 7 Mg/s through the CAA, Nares Strait, and Fram Strait. Here, a salt water density of 1025 kg/m3 is used to calculate salt transport.
4.2.4. Freshwater and Heat Budgets
 The heat content in simulation A1 in the Amerasian and Eurasian basins are close to the Environmental Working Group climatological range of −0.7 to −0.9 × 1022 J for the 1990s (Figure 15) [see Holloway et al., 2007, Figure 3]. A drift of ∼4.3 × 1020 J/decade in the Amerasian Basin is similar to that in AOMIP models [Holloway et al., 2007]. The largest increase in heat storage occurred after year 2000 and can be partially explained for by the increase of 1.6 × 1020 J/decade in heat flux across Bering Strait (gate BS in Figure 15b). This simulated heat flux trend is lower than the observed rate of ∼6 × 1020 J/decade between 2001 and 2004 [Woodgate et al., 2006].
 In the Eurasian Basin, a drift of ∼7.7 × 1020 J/decade is on the high end of the range of drifts seen in AOMIP models [Holloway et al., 2007]. A similar positive trend exists in the Gr/No seas region (Figure 15a). Dmitrenko et al.  and Schauer and Fahrbach  have reported an increase in the core AW temperature since the late 1990s in the Gr/No seas and in the Eurasian Basin. Specifically, Dmitrenko et al.  observed in mooring data a large jump in AW core temperature of ∼0.8°C. When the observed volume flux of ∼6 Sv across FS is used, the heat increase is ∼20 TW, which is consistent with the observed increase of 23 TW for the 1997–1999 period [Schauer and Fahrbach, 2004]. In simulation A1, however, two pulses of heat flux increase are seen at gate BA into the Barents Sea and there is no apparent increase across Fram Strait (Figure 15b). Overall, a heat flux rate of ∼9 × 1020 J/decade from the Barents and Kara seas into the Eurasian Basin across gates SF and SA explains for the heat storage trend in the Eurasian Basin.
 In the Amerasian basin, average incoming heat from the Bering Sea (∼5 TW in Figure 15b) is comparable with values of 4.1–9.2 estimated by Woodgate et al.  for the years 1998–2004. Overall, the net heat flux into the Arctic Ocean (sum of fluxes across gates CAA, FS, BS, SF, and SA) is dominated by values across FS and remains approximately constant (Figure 15b).
Figure 16 shows freshwater fluxes and storage in the Arctic Ocean. To be consistent with Serreze et al.  freshwater estimates, Arctic Ocean in this section includes the Barents and Kara seas. Freshwater content (FWC) in the Amerasian Basin is 55 ± 1 × 103 km3 and is higher than climatological values of 34 ± 2 × 103 km3 [Holloway et al., 2007, Figure 16c]. Inputs into the Amerasian Basin include inflows through BS (80 mSv, 2525 km3/yr, Tables 4 and 5), runoffs from the MacKenzie and Kolyma Rivers (∼9 mSv), and transports of freshwater along the AW path. Monthly mean river runoff is based on the ARDB and was prepared by P. Winsor (personal communication, 2007). In the Eurasian Basin, FWC of 13 ± 1 × 103 km3 is higher than the climatological value of 0 ± 3 × 103 km3 [Holloway et al., 2007, Figure 16c]. For comparison, AOMIP results yield wide ranges of −10 × 103 to 30 × 103 km3 for the Amerasian Basin and 10 × 103 to 100 × 103 km3 for the Eurasian Basin.
Freshwater content is calculated as FWC = (S − Sref)/Sref * Vol, where Sref = 34.8 is the reference salinity and Vol is the volume of water in the Arctic. Negative contributions are included in flux and excluded in storage calculations.
 A freshwater budget and comparison with Serreze et al.  (hereafter SR06) are shown in Table 5. For atmospheric input, the largest difference is in the mean evaporation, 780 km3/yr in our model versus 1300 km3/yr in SR06. This difference originates from the model not taking into account sublimation over sea ice. As a consequence of having less evaporation, simulation A1 requires less river runoff inputs than the observed values (Table 5). For sea ice fluxes, SR06 used the higher estimates of sea ice exports from Vinje et al.  instead of those from Kwok et al. . As a result, because we used Kwok et al.  sea ice export to optimize for the air/sea ice drag coefficients, our sea ice FW contributions are consistently smaller than corresponding values from SR06. For oceanic freshwater fluxes, the low export across Fram Strait is due to lower than observed volume transports (see section 4.2.2). Across gate BA (see Figure 1 for location), our estimates of freshwater fluxes from Barents Sea into Norwegian Sea are higher than the net outflow of −90 km3/yr in SR06 (positive Norwegian Coastal Current (+250 km3/yr) being balanced out by negative inflow of deep AW (−340 km3/yr)). In term of storage, the contribution from sea ice of 15100 ± 2600 km3 is slightly higher than the approximate number used in SR06. Overall, the net inflow of our optimized simulation is ∼85% of that in SR06. The simulation's outflow balances the input and closes the FW budget to within 2% (total percentage in Table 5).
5. Concluding Remarks
 An optimized ocean and sea ice solution is obtained for the Arctic Ocean using a Green's function approach for the 1992–2004 period. The solution, based on the adjustments of 16 ocean and sea ice parameters (Table 2), shows significant improvements compared to the baseline with an overall cost reduction of 45%.
 For surface boundary conditions, the change from ERA40 to JRA25 had a significant positive effect on the model solution. Specifically, the JRA25 fields with more realistic downward radiation [Onogi et al., 2007] result in improved sea ice thickness and extent, and in river runoffs that are closer to the Serreze et al.  estimates (Figures 4–9 and Table 5). Of note is that the optimized albedos are closer to the observed values when JRA25 forcing is used (Table 2).
 In the ocean, changing the KPP background diffusivity from 10−5 m2/s to 5.4 × 10−7 m2/s in combination with the salt plume parameterization of Nguyen et al.  maintains a vertical T/S stratification that is much closer to observations (Figure 8).
 For 2005–2008, the quality of the simulation remains comparable to that during the 1992–2004 optimization period. The simulation continues to reproduce the observed September monthly mean sea ice extent minima to within ∼10% (Figure 9). In addition, the observed 2003–2007 ICESat ice volume loss is reproduced in the simulation (Figure 10c). For the entire 1992–2008 period (i.e., including both the optimization period and the 2005–2008 extension), the loss of 590 × 103 km2/decade in sea ice extent is consistent with SSMI analysis (Figure 9d).
 Decadal circulation and transport of Atlantic and Pacific waters are consistent with other model estimates and with observations (Figures 11–14 and Table 4). The circulation of the Atlantic Water in the 16 year simulation is cyclonic with mean topostrophy 0.4–0.8. Net northward and southward fluxes across Fram Strait are 2.1 Sv and 0.8 Sv for volume and 36 TW and 9 TW for heat. These simulated fluxes across Fram Strait are lower than observations. Approximately 80% of the heat input from the Atlantic Water is lost to sea ice melt and to the atmosphere. The volume, heat, and freshwater transports of Pacific Water across Bering Strait are 0.86 ± 0.03 Sv, 9.34 ± 0.34 TW, and 70 ± 2.6 mSv, consistent with observations (Figure 14, Table 4). Pacific Water crosses the Chukchi Sea where it loses ∼50% of its heat before reaching the interior of the Arctic Ocean through the Barrow, Central, and Herald Canyons. The largest export of Pacific Water is through the Canadian Arctic Archipelago and the Nares Strait. The transit time from the Bering Strait to the Canadian Arctic Archipelago is ∼5 years and the transit times from the Bering Strait to the Nares and Fram straits are ∼10 years.
 Residual model-data differences after optimization persist and highlight deficiencies in the model equations and subgrid-scale parameterizations. Here, these residual differences include misrepresentation of Atlantic Water (Figure 8d), low transports across Fram Strait (Figure 12), and lack of sea ice deformation mechanisms (Figure 5). Understanding the causes for these residuals is a way toward improved representation of ice-ocean processes in climate models. For example, the misrepresentation of Atlantic Water might be improved either by increased resolution or by improved representation of subgrid-scale restratification processes [e.g., Fox-Kemper et al., 2008]. Although adjoint method studies, such as those of Kauker et al. , Fenty , and Heimbach et al.  provide a more complete description of model parameter sensitivities, this paper demonstrates that Green's functions are a simple but powerful tool for analyzing and optimizing a coupled ocean and sea ice simulation.
 Sea ice draft data were downloaded from the National Snow and Ice Data Center (NSIDC). This work is funded by the ECCO2 project, a contribution to the NASA Modeling Analysis and Prediction (MAP) program. We gratefully acknowledge computational resources and support from the NASA Advanced Supercomputing (NAS) Division and from the JPL Supercomputing and Visualization Facility (SVF).