In ice-covered regions it is challenging to determine constituent budgets –
for heat and momentum, but also for biologically and climatically active
gases like carbon dioxide and methane. The harsh environment and relative
data scarcity make it difficult to characterize even the physical properties
of the ocean surface. Here, we sought to evaluate if numerical model output
helps us to better estimate the physical forcing that drives the air–sea gas
exchange rate (
The ocean surface is a dynamic region where momentum, heat and salt, as well
as biogeochemical compounds, are exchanged with the atmosphere and with the
deep ocean. At the sea–air interface, gases of biogenic origin and
geochemical significance are exchanged with the atmosphere. Theory indicates
that the aqueous viscous sublayer, which has a length scale of 20 to
200
When the ocean surface is not restricted by fetch, TKE is mostly dominated by wind speed and waves (Wanninkhof, 1992; Zemmelink et al., 2006; Wanninkhof and McGillis, 1999; Nightingale et al., 2000; Sweeney et al., 2007; Takahashi et al., 2009). In the polar oceans, wind energy and atmospheric forcing are transferred in a more complex manner as a result of sea ice cover (Loose et al., 2009, 2014; Legge et al., 2015). Sea ice drift due to Ekman flow (McPhee and Martinson, 1992), freezing and melting of ice leads on the surface ocean (Morison et al., 1992) and short period waves (Wadhams et al., 1986; Kohout and Meylan, 2008) all constitute important sources of momentum transfer. Considering the scarcity of data on marginally covered sea ice zones (Johnson et al., 2007; Gerdes and Köberle, 2007), especially during Arctic winter time, the environment is too poorly sampled to constrain these processes through direct measurement or empirical relationships.
Lacking sufficient data to constrain these processes, we wonder whether it
is possible for a numerical model to adequately capture forcing of air–sea
gas exchange in the sea ice zone and consequently improve predictions of
air–sea flux. The parameters of interest are sea ice concentration (or
fraction of open water), sea ice velocity, mixed-layer depth (MLD), and water
current speed and direction in the ice–ocean boundary layer (IOBL)
(Loose et al., 2014). Here we use the budget of
The radon deficit method involves sampling
Since the
This memory integrates the physical oceanography properties of the IOBL,
including sea ice cover, MLD and water current speed. These
processes are likely to vary significantly during this period and it is
important to consider them as a source of uncertainty in Eq. (1). To
illustrate this uncertainty, consider a mixed layer that rapidly changes by a
factor of 2 just prior to sampling for radon. If the mixed-layer becomes
shallower by stratification,
Conversely, if the mixed layer deepens due to mixing,
The “memory” of gas exchange forcing that radon experiences is further
complicated by the presence of sea ice. Consider two alternate water parcel
drift paths that lead to the
A graphic illustration of two possible back trajectories for a single sampling station.
This observation about drift paths in the sea ice zone strongly implies that we must consider both time and space in estimating the forcing conditions that are recorded in the radon deficit. In other words, we require a Lagrangian back trajectory of water parcels to track the evolution of the mixed layer and its relative velocity 4 weeks prior to sampling.
Although satellite data, ice-tethered drifters (Krishfield et al., 2008) and moorings (Krishfield et al., 2014; Proshutinsky et al., 2009) have provided valuable seasonal and spatial information about the sea ice zone, they do not track individual water parcels and tend to convolve space and time variations. The spatial limitation of these data poses a challenge to producing a back trajectory of the water parcel.
To address the above mentioned challenges, we use a suite of the Estimation of the Circulation and Climate of the Ocean (ECCO) project's Arctic regional configurations to test the if a numerical model can be used to follow the back trajectory of a radon-labeled water parcel and the gas exchange forcing acting upon it and yield the missing information required for the Radon deficit method.
The variables and derived quantities of interest from the numerical model include MLD, sea ice concentration and speed (Loose et al., 2014), and the water velocity in the MLD. We note that as part of the Arctic Ocean Model Intercomparison Project (AOMIP), a number of Arctic ocean-ice models' capability to represent the main ice–ocean dynamics have been assessed (Proshutinsky et al., 2001; Lindsay and Rothrock, 1995, p. 995; Proshutinsky et al., 2008). Our reasons for choosing ECCO over other Arctic models stem from the higher correlation between the ECCO's regional Arctic simulated outputs to satellite-derived sea ice data (Johnson et al., 2012) and the feasibility in the Massachusetts Institute of Technology general circulation model (MITgcm) to adapt a high near-surface vertical resolution to existing configurations.
The remainder of the article is organized as follows: in Sect. 2 we provide the details of the ECCO ice–ocean models. Section 3.1 and 3.2 focus on model outputs of sea ice concentration and velocity and comparison with observations from satellite and ice-tethered profilers. Section 3.3 investigates the modeled output salinity and temperature structure and the resulting upper ocean density structure and mixed layer. Section 3.4 evaluates the correlation in near-surface water velocity. In Sect. 4 we discuss the results and sources of error and their impact on estimated gas exchange and lastly, Sect. 5 provides the summary of our results.
Three ECCO configurations are used, at horizontal grid spacings of 36, 9 and 2 km,
respectively. The models are based on the MITgcm code and employ
the
We introduced a set of new vertical grid spacings to allow us to capture near-surface small details which cannot be represented with the coarser grid system. In the 36 km (hereafter referred to as A1) and 9 km (called A2) models, the spacing is 2 m in the upper 50 m of the water column and gradually increases to a maximum of 650 m. In contrast, the 2 km model (called A3) has 25 layers in the top 100 m of water column, starting from 1 m and increasing to 15 m step. All the boundary conditions from ECCO2 have been interpolated to match the new vertical grid system.
Satellite-derived estimation of sea ice cover at 25 km horizontal resolution (Comiso, 2000) is interpolated to a horizontal grid system to facilitate model–data comparison. In addition, sea ice drift gathered by 28 ice-tethered profilers (ITPs) (Krishfield et al., 2008) which have more than 2 months of data in the Beaufort Sea between 2006 and 2013 have been used to do the ice velocity comparison.
We compared near-surface water velocity data from an ice-tethered profiler with velocity instruments (ITP-V) (Williams et al., 2010) to A1 and A2 and an upward-looking acoustic doppler current profiler installed on a McLane moored profiler (MMP) (McPhee et al., 2009; Cole et al., 2014) to A1, A2 and A3 in order to compute the accuracy and feasibility of calculating back trajectory of parcels located in the mixed layer. We limit our comparison of ITP-V, which runs from October 2009 to March 2010, to A1 and A2 since those models run from 2006 to 2013 and A3 runs from 2011 to 2013.
Using salinity and temperature profiles from ITPs (Krishfield et al., 2008) we calculated MLD and compared it to 2 m vertical resolution model output (A1, A2). Most of the observed data exist in the Beaufort Gyre, hence we mostly focus our comparison to that geographic perimeter. Figure 2 depicts the bathymetry and location of most important observations we used to make the comparisons with the model.
Bathymetry and location of ITP-V and mooring for data comparison.
For sea ice concentration analysis we introduced a grid system covering the
Beaufort Gyre and interpolated the data from satellite (Comiso, 2000) and A1
onto the grid. The analysis grid extends from 70 to 80
The ice cover at P1, P2 and P3 (Fig. 3) can be divided into 3 ice phases: (a) fully covered in ice, (b) open water and (c) a transition between (a) and (b). P3, which is the furthest south, has all three phases. In contrast P1 ice cover only dips below 60 % for two brief periods during the 7-year time series depicted in Fig. 3 – once in 2008 and again in 2012. These three points illustrate where and when the model has the greatest challenge reproducing the actual sea ice cover. At the extremities of the ice pack, where the water is predominantly covered by 100 or 0 % ice (P1 and P3), the model captures the seasonal advance and retreat and the percentage of ice cover itself is accurate. However, in the transition regions that are characterized by marginal ice for much of the year (P2), the model has more difficulty reproducing the observed sea ice cover as well as the timing of the advance and retreat. This behavior is consistent with the description that has been explained by Johnson et al. (2007), that models have a higher accuracy predicting sea ice concentration in central Arctic and less accuracy near its periphery and the lower latitudes.
The spatial sensitivity of the model can be observed using root mean square
(RMS) error (Hyndman and Koehler, 2006) Eq. (2), calculated over the
1992–2013 period (Fig. 3). The area with the highest misfits coincides
with area between the 80 and 60 % contour lines (Fig. 3) and is
concentrated primarily in the Western Beaufort. The RMSE error of 0.2 is the
maximum value away from land, this same level of error can also be found
near land which is caused by fast-ice generation. Fast ice in the model is
replaced with packs of drifting sea ice; this error is common among numerical
models and has been brought to attention during AOMIP (Johnson et al., 2012).
An important source of errors in the model ice concentration comes from the reanalysis surface forcing. Fenty and Heimbach (2012) showed that adjustments in the air temperature that are within the uncertainties of this reanalysis field can help bring the model ice edge into agreement with the observations. Of note also is that the uncertainty in satellite-derived ice cover can be the highest in the marginal ice zone due to tracking algorithms that are sensitive to cloud liquid water or cannot distinguish thin ice from open water (Ivanova et al., 2015); this error also manifests itself in quantification of model–data misfits.
Ekman turning causes ice and water to move at divergent angles with respect
to each other. Ice moves the fastest, with mean values of 0.09 m s
To generate a more quantitative comparison between the results, we utilized the same method introduced by Timmermans et al. (2011), to compare ice velocity components (eastward–northward) of A1 to ITP velocity and compute the correlation coefficient of each experiment with the daily-averaged actual drift velocity from the ITPs (Fig. 4).
Time series of sea ice velocity components and speed of ITP 53 vs. 36 km horizontal resolution of MITgcm (A1). The correlations between eastward, northward and magnitude of velocity between ITP 53 data and A1 are 78, 75 and 80 %, respectively.
Salinity and temperature of the top 70 m based on ITPs and A1.
When averaged over all the ITPs operating in Beaufort Gyre during 2006 to
2013, A1 had correlations of 0.8 with actual velocity components and 0.82
correlation with speed magnitude. RMSE calculated for A1 based on Eq. (2)
shows an error of 0.043 ms
We chose four hydrographic profiles in the Beaufort Sea to assess the simulated vertical salinity and temperature. The first two sets of profiles are from ITP-1 winter and summer 2006; the third set is from ITP-43 during winter 2010 and the fourth is from ITP-13 during summer 2008 (Fig. 5). For visualization we linearly extrapolated the profiles from the first layer of the model up to the surface, which occurs over the top 1 m of the water column.
During winter time, the model temperature and salinity profiles show a well
mixed layer that extends below 15 m, followed by a very large gradient.
The mixed-layer temperature is close to the local freezing point in a
condition called “ice bath” (Shaw et al., 2009). The ITP profiles are
similar; however the ITP MLD is deeper by nearly 10 m,
indicating more ice formation and convective heat loss over this water
column, as compared to the model water column. In summer the model mixed-layer shoals to approximately 5 m depth following two local temperature
extrema; the bigger maximum is at
Data and model profiles in Fig. 5b show better agreement in the shape and the
absolute value of the
In addition, we note that recent studies show that eddies with diameters of 30 km or less (Nguyen et al., 2012; Spall et al., 2008; Zhao et al., 2014; Zhao and Timmermans, 2015; Zhao et al., 2016) play an important role in transporting Pacific water from the shelf break into the Canada Basin. Adequate representation of ocean eddies and investigation into their roles in setting the water column stratification require a model with finer horizontal resolution. Hence, moving forward, in addition to A1, we utilize the 9 km model (A2) to investigate the density profiles as well as study the MLD.
We compared the 36 and 9 km model outputs of density to the time series of density profiles from ITP-35 (Fig. 6) from October 2009 to March 2010. A black mask indicates locations where there is no data from ITP-35 – particularly in the upper 7 m of the water column. As ITP-35 transited through the Canada Basin, density profiles contain both temporal and spatial changes.
We are able to discern some broad similarities between the model and ITP density profiles. From November through January, both ITP and model density profiles remain relatively constant. Between February and March, ITP-35 appears to drift through a zone of convection, likely caused by ice formation, with a sudden increase of density near the surface. The same feature can be observed in both A1 and A2 density. However, on a smaller scale, there is significantly more variation in the ITP data than what the model represents.
For exploring the reason behind the density signals, we used the simulated fraction of sea ice cover and ice thickness (Fig. 6). The dominating effect appears to result from a sea ice fraction when there is an almost continuously covered area. The changes from sea ice thickness can be observed in the volume of fresh water in the water column, as seen by outcropping of the 1022.5 isopycnal coinciding with the increase of sea ice thickness. An increase in near-surface density can be seen in late January and early February accompanied by an increase in ice thickness and insertion of brine in the water column. The second peak, which is not as pronounced, happens in late February when ice fraction decreases from 100 to 95 % and exposes the surface water to cold atmosphere, leading to the production of newly formed sea ice. We further examine these signals in the MLD section below.
There are many different methods in the literature for calculating MLD (Brainerd and Gregg, 1995;
Wijesekera and Gregg, 1996; Thomson and
Fine, 2003; de Boyer Montégut et al., 2004; Lorbacher et al., 2006; Shaw et
al., 2009). The methods can be divided into two main types (Dong et al.,
2008): the first type of algorithm looks for the depth (
We compare these two methods by applying them to the profiles from Fig. 5, and the results are shown in Fig. 7. In case (a) and (b) M1 produces a MLD that is 8 to 12 m deeper, compared to the other method. A visual examination of profiles indicates that the M1 criteria may be too flexible of a criteria. The results from M1 appear to be intermittently “realistic”, whereas M2 can be difficult to implement for data sampled at high vertical resolution as a result of greater small-scale variability. In practice, we find M1 is the most straightforward to implement.
Methods M1 and M2 applied to selected ITP profiles,
It should be mentioned that it is difficult to consistently compare
performance of the M1(
To compare the methods over a longer time period, we calculated the MLD from model data and ITP-35 data along the ITP-35 drift track. We used M1 to determine the MLD for A1, A2 and for ITP-35 data (Fig. 8). Both model results show a shallower ML compared to the ITP data; the most prominent feature in late January corresponds to a sudden change in density found in Fig. 6. Beside the above-mentioned peak, A1 fails to capture any variability in MLD whereas A2 shows that the ML deepens by about 10 m in mid February corresponding to ice opening occurring during the same time span (Fig. 6). The difference between A1 and A2, and their ability to capture MLD change, can be explained by the capability of a higher-resolution model to capture small-scale fractures in the ice cover (Fig. 8), and conversely, the inability of the coarser resolution to do so is due to averaging over a larger grid. The wind appears to be the primary driving mechanism for the divergence in ice cover, which in turn exposes the ocean to the cold atmosphere and leads to a loss of buoyancy and an increase in MLD. With higher resolution these openings can be captured, leading to a better agreement with data in marginal ice zones. The changes in MLD are of first-order importance to the calculation of gas budgets such as the radon deficit. In this regard a fine-scale grid resolution has real advantages through its ability to capture both the ice advection and openings in ice cover that lead to MLD change. Coarser resolution would be justified when the point of interest is sufficiently far away from leads and marginal ice zones where the effect of sea ice dynamics on MLD is important, so the effects of area averaging would be small enough to omit.
Sea ice cover higher than 0.9 with gray circle marking the area of
ITP operation for
One last important note is the effect of the SPP on MLD. Nguyen et al. (2009) demonstrated the need to remove the artificial excessive vertical mixing in coarse horizontal resolution models. To rule out the dependency of this parameterization to vertical resolution as a source in MLD bias, we performed a suite of 1-D tests, with and without the SPP, on a variety of vertical resolutions (not shown here) and sea ice melting/freezing scenarios and confirmed that SPP is not dependent on vertical grid spacing. We also investigated MLD in A3 (no SPP) run compared to A2, and confirmed that the average MLD is the same between these two runs.
We have very little information from direct observations that permit us to track a water parcel, especially beneath sea ice. This is one area where model output could be critical as there are not obvious alternatives. To assess the consistency of the model water current field, we compared 2-D model water velocity to data gathered from two sources: (1) from ADCPs mounted on moorings that were deployed starting in 2008 in Beaufort Gyre (Proshutinsky et al., 2009) and (2) the ITP-V sensor equipped with MAVSs (Modular Acoustic Velocity Sensors) (Williams et al., 2010), which was the only operating ITP before 2013 which had an acoustic sensor mounted on it.
We compared the velocity components averaged from 5 to 50 m to account for flow direction that is moving the water parcels in the mixed layer over the duration of ITP-V working days, which was from 9 October 2009 to 31 March 2010 (Fig. 9). The ITP data has been daily averaged to remove higher frequency information which we do not expect the model to capture due to the low frequency (6-hourly) wind forcing. Both A1 and A2 show less than 0.3 correlations with data with no improvement in respect to resolution.
We further add A3 to our comparison for moorings velocities (Fig. 9), and
compared velocities at 25 m, which is the level that is shared between all
our models and removes the necessity of any interpolation. The simulation
results show RMSE normalized by data of higher than 5 and correlations of
less than 0.3 over three moorings and almost 2 years of data. This result
indicates that ocean currents are not well captured in the model irrespective of
horizontal grid resolution. We must therefore look into the atmospheric
forcing as a likely source of error on high frequency water velocities near
the surface. As noted above, the wind inputs into the model from the reanalyses
are available at a 6-hourly frequency. Chaudhuri et al. (2014) and Lindsay
et al. (2014) have compared various available reanalysis products over the
Arctic which we used to force our model, along with multiple other reanalysis
products with available ship-based and weather station data, and found out
that wind products in all of those have low correlation, i.e., less than 0.2.
To investigate we compared JRA-55 (Onogi et al., 2007) and NCEP
(Kalnay et al., 1996) to shipboard data gathered during 2014 in a time span
of 2 months in the Arctic and found that JRA-55 had
Up to this point we have spent extensive effort assessing the skill of the
MITgcm to reproduce the key forcing parameters listed in our introduction.
This effort is motivated by the potential for using the MITgcm model output
as a tool to improve our ability to model gas budgets in the IOBL and to
improve our estimates of
Utilizing the results from Sect. 3.1, 3.2 and 3.3, we calculated gas exchange
velocities at P1, P2 and P3 (Fig. 10), over the course of the model
simulation (i.e.,
The result yields a point cloud of values that varies depending primarily on
the range of ice velocity, wind speed and sea ice cover. The values of
The results in Sect. 3.4 showed that the difference between model and data water trajectories accumulated too much error to be useful, and indicate that for a regional GCM to be useful for reconstructing the back trajectories of radon-labeled water parcels, we will need improved wind-forcing fields. With current reanalysis products, finding the back trajectory of radon-labeled water parcels is not feasible. When improved wind fields are available, the Green's functions approach (Menemenlis et al., 2005; Nguyen et al., 2011) or adjoint method (Forget et al., 2015, p. 4; Wunsch and Heimbach, 2013) can be used to reduce misfits between modeled and observed MLD velocity and likely make the model a valuable tool for tracking back trajectories, either in a smaller domain or full Arctic regional configuration. A possible source of wind data can be from shipboard measurements, assuming the measurements persist over 10 days in the given sampling station.
However, it may be possible to improve on the existing approach. When the
drift trajectory is not known, one solution is to resort to averaging IOBL
properties within a radius that is equal to the 30-day drift track (e.g., as
done by Rutgers Van Der Loeff et al., 2014). The averages within this circle
are treated as the representative IOBL properties. The radius of spatial
averaging should be restricted by the average magnitude of the water parcel's
velocity multiplied by the time span of interest. When applying a spatial
averaging, if the timescale of changes in forcings is smaller than time span
of interest, the time dependency of forcings should be accounted for.
Typically sea ice velocity is
We have used 36, 9 and 2 km versions of the ECCO ocean–sea ice coupled models based on the MITgcm to investigate whether numerical model outputs can be used to compensate for lack of data in constraining air–sea gas exchange rate in the Arctic. The goal is to understand if model outputs can improve estimation of gas exchange velocity calculation and to evaluate the capability of the model to fill in the missing information in the radon deficiency method. This systematic comparison of upper-ocean processes has revealed the following.
The coarse-resolution model showed a good fidelity in regard to reproducing sea ice concentration. Depending on the location and/or season, the error of simulated ice concentration varied between 0.02 and 0.2. Away from ice fronts or active melting/freezing zones the model tended to have higher accuracy. Even in the marginal ice zone, due to the potentially high error in the satellite-derived ice concentration, the model can still be used to quantify the air–sea gas exchange rate, though with an expected higher uncertainty due to the combination of model and data errors. In addition to sea ice concentration, we also found good correlation (82 %) between model ice speed and ITP drift.
Gas exchange estimated model outputs of wind and sea ice speed at
locations P1: 77.4
The estimation of MLD is challenging due to its dependence on unconstrained density anomaly or density gradient thresholds. No MLD algorithm performs well in all situations. In addition, CTD profiles from drifting buoys often do not include the top 7–10 m of the surface ocean where stratification can be important. Adding to the challenge is the dependence of the ocean density structure on vertical fluxes. In these model–data comparisons we found model MLD to be consistently biased on the shallower side in all model resolutions. We note however that this result can partly be due to the missing upper 7 m in moored drifters such as ITPs, thus resulting in a one-sided bias in the observed MLD. The evolution of the mixing events showed that MLD correlates to sea ice fraction: in areas of nearly-full ice cover, small openings may result in exposure of water to the cold atmosphere and the resulting freezing events would deepen the mixed layer via brine rejection. The higher the resolution, the higher the capability of the model to capture these openings and the resulting deepening effects. The usage of the SPP does not play an important role in determining the MLD.
The A1, A2 and A3 experiments consistently could not capture the water velocity observed in ITPs or mooring. We speculate that this discrepancy may be the result of the quality of the reanalysis wind products that are forcing these models. The wind products have been shown to have poor correlation with observed data at high frequencies. Considering that the response of near-surface water is occurs almost simultaneously to the wind forcing, low correlation in wind velocity would have direct impact on the modeled near-surface water velocities and likely yield low correlations between modeled and observed ocean currents. Conversely, the same wind fields at lower frequencies and on broader spatial scale have higher accuracy, as evidenced by the high correlation between the modeled and observed sea ice velocity.
Taking into accounts all the misfits through detailed model–data comparisons, we were able to quantify the usefulness of a numerical model to improve gas exchange rate and parameterization methods. We showed an example of how the sea ice concentration, velocity and MLD can affect the gas exchange rate by up to 200 % in marginal sea ice zones and that the model outputs can help constrain this rate. By finding the low correlation in near-surface ocean velocities, irrespective of model horizontal resolution, we concluded that finding the back trajectory of radon-labeled water parcels is currently not feasible. Furthermore, we speculate as to the source for the common errors in our models, namely the high frequency and under-constrained atmospheric forcing fields, and identify alternative approaches to enable the use of a model to achieve the back trajectory calculation task. The alternative approach includes using the MITgcm Green's functions and adjoint capability to help constrain the model ocean velocity to observations, and performing the simulations in a smaller dedicated domain based on the specific spatial distribution of data for both atmospheric winds and ocean currents in the mixed layer.
Due to sheer volume of A0, A1 and A2 model outputs (89 GB per 3-D field),
the simulation results are archived at NASA Supercomputing Center and NCAR
GLADE storage system and can be extracted upon request by contacting the
primary author. The observational data can be accessed through
We gratefully acknowledge computational resources and support from the NASA
Advanced Supercomputing (NAS) Division and from the JPL Supercomputing and
Visualization Facility (SVF) and high-performance computing support from
Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR's Computational and
Information Systems Laboratory, sponsored by the National Science Foundation.
The ice-tethered profiler data were collected and made available by the
Ice-Tethered Profiler Program (Toole et al., 2011; Krishfield et al., 2008)
based at the Woods Hole Oceanographic Institution
(