**Arctic Ice and Ocean Heat and Freshwater Fluxes: A FAMOS Model Intercomparison Project**

Sheldon Bacon and Yevgeny Aksenov

National Oceanography Centre, Southampton, UK; November 2013.

**1. Introduction**

It is important to understand how models perform in comparison with each other, and in comparison with the real world. One way to do this is to define a metric that can be objectively quantified in all circumstances (in principle). Over the last few years, we have achieved this in the real world by the combination of a set of Arctic Ocean measurements into a near-complete boundary monitoring array. Together with land, this array completely encircles the Arctic Ocean, such that the principle of mass conservation can be applied, and therefore that real fluxes of heat and freshwater can be calculated, independent of any assumptions about reference values. The procedure is described in Tsubouchi et al. (JGR, 2012).

Reduced to the very simplest representation, warm waters enter the Arctic; these waters leave the Arctic cooler, and the export includes some sea ice. These waters are also fresher when they leave than when they arrive. The cooling and freshening is caused by surface fluxes. Therefore on some timescale, the net surface fluxes should equal the ice and ocean boundary fluxes. The question of timescales, however, is a difficult one due to the great range of residence times within the Arctic for water masses. In the Fram Strait recirculation, some Atlantic water may only cross the boundary for months, or maybe just weeks, before heading back south. At the opposite extreme, the deep waters of the Canada Basin may not be refreshed for centuries. With model runs of typical duration of order decades, it will be interesting to see how the ocean circulation filters the surface fluxes to produce the boundary fluxes, and to compare the amplitudes and phases of the modelled annual cycles of surface and boundary fluxes.

We note here three important assumptions that enable the analysis to proceed. First, that an appropriate timescale long enough to allow mass conservation but short enough to be useful is one month; so the outputs will be time series of monthly-mean fluxes (Tsubouchi et al., 2012). Second, that Fury and Hecla Strait is closed; if a model does indeed open this strait, then it should be included; but see Tsubouchi et al. (2012) for the rationale behind its exclusion. Third, while a timescale of one month allows mass conservation, it says nothing about heat or freshwater (or salinity) storage. While there have been publications describing storage changes on decadal timescales, we have as yet no information on the nature of storage on monthly timescales. Therefore we can treat storage as an uncertainty (again, as in Tsubouchi et al., 2012). However, if time and resources permit, we ask that participants in this experiment calculate month-to-month changes in mass, heat and salinity storage.

Finally, before describing the method, we note that with this approach to model analysis, we very much welcome the inclusion of results both from forced and from coupled models, and also from both global and regional models – as long as the latter span the defined region. We also welcome results for multiple runs of the same model, where used (eg) to study the impact of parameter changes.

2. Method

*2.1 Geography*

The actual measurement locations are shown in Tsubouchi et al. (2012), which is reproduced here as figure 1. We slightly simplify the definition of the boundary, in order that it conforms to meridians of longitude and parallels of latitude. The Arctic Ocean is enclosed by sections across the four main gateways – Fram, Davis and Bering Straits, and the Barents Sea Opening (BSO). We define the locations of these gateways as follows.

Fram Strait: coast-to-coast, Greenland to Svalbard, across 79˚N

Davis Strait: coast-to-coast, Baffin Island to Greenland, across 67˚N

Bering Strait: coast-to-coast, Siberia to Alaska, across 65.75˚N

BSO: coast-to-coast, Norway to Svalbard, up 19˚E.

To calculate the balance for the fresh water and heat in the Arctic, the models are required to produce model masks for the surface flux calculations to enclose the vertical model transects. Note that the end points of the sections should be chosen according the individual model coastlines to cover the straits from land to land. Models which need to use “staircase” transects should check that their positions do not deviate significantly from the observational transects. If tolerance becomes a problem, we would be happy to discuss this further. Included in the transect model cells should be tracer (ie, temperature and salinity) points. For staggered grids, the velocity used in the transport calculations should be interpolated in a consistent manner with the calculations used in the model runs under analysis. For regional models with open boundaries in Bering Strait, the model transect in the strait should be away from the model boundary and at least one model row inside the domain. We cannot accommodate models which have open boundaries north of Davis Strait.

Specify the surface flux mask for the area enclosed by the transects (as above). For “staircase” transects, the border points of the mask should follow the “staircases”. Care should be taken to match the transects (as the boundaries) and border points of the mask.

2.2 Surface Fluxes

The aim is to produce time series of monthly means of surface heat and freshwater fluxes (using the same time base as for boundary fluxes, §2.3 below). First, specify whether forced or coupled model is used. If forced, then specify the forcing set, any modifications to it, and procedures involved in converting input data to surface fluxes (if applicable). Most models will store surface heat and freshwater fluxes in some form, either as integrals or possibly as components (eg latent, sensible, long-wave, short-wave for heat; or precipitation, evaporation, runoff for freshwater).

If the model uses a surface salinity restoring (relaxation) term, it should be included in the freshwater balances. The currently commonly-used approach for the salinity restoring is to correct surface (top model level/layer, k=1 below) salinity towards observational (climatological) values by adding a virtual freshwater flux “FWcor” to the surface freshwater forcing of the ocean, ie:

FWcor=gamma*dz*[Sal(k=1) – Sal_obs]/Sal(k=1)

Here, Sal(k=1) is the simulated top level salinity, Sal_obs is the observed top level salinity, dz is the thickness of the top model box and gamma is the restoring timescale. Following this technique, FWcor is added to the freshwater balance as an additional surface freshwater forcing without changing the volume of the ocean. For other restoring techniques, a different approach may need to be discussed. If other freshwater balancing components are applied (this for example concerns regional models which may have “drying effects” of the ocean due to imbalance in atmospheric fluxes), then they need to be included in the total surface fresh water fluxes.

*2.3 Ice and Ocean Fluxes*

The aim is to produce time series of monthly means of boundary heat and freshwater fluxes (using the same time base as for surface fluxes, §2.2 above). While the main outputs must be vertical-area integrals around the whole circuit, integrals for each of the four straits should also be stored, as diagnostics. We next describe the calculations required for heat flux (first) and freshwater (second). Terms are standard: velocity (v, m/s), density (rho, kg/m3), specific heat capacity (cp, J/kg/˚C), latent heat capacity (L, J/kg), temperature (temp, ˚C), potential temperature (theta, ˚C), salinity (S, no units); note that vertical area integrals are dxdz, where z is depth (m) and x the along-section coordinate (m), from the sea bed up to the surface, with due allowance made for sea ice, as described in context below.

Note that for linear free surface models, sea surface heights are not included in the volume transport calculations, but only in the freshwater and heat transport calculations. For non-linear free surface models, the sea surface heights are included in the volume transport calculations as well.

2.3.1 Heat fluxes

(i) For the liquid (seawater, sensible heat) component, calculate the area integral of:

cp[seawater] x rho x v x theta

(ii) For the solid (sea ice, latent heat) component, calculate the area integral of:

v[sea-ice] x rho[sea-ice] x L

(iii) For the solid (sea ice, sensible heat) component, this calculation will depend on sea ice model implementation, ie, whether the sea ice is (a) embedded, or (b) “levitating”. If embedded, then include the ice temperature in the liquid integral, so add the area integral of:

cp[sea-ice] x rho[sea-ice] v[sea-ice] x temp[sea-ice]

If the sea ice is levitating, we need the difference between the ocean temperature where the ice “should be” and modelled ice temperature, so, for the cross-sectional area of the sea ice, add the area integral of:

cp[sea-ice] x rho[sea-ice] x v[sea-ice] x temp[sea-ice] minus cp[seawater] x rho x v x theta

(iv) Add all three components (one liquid plus two solid) together. Note the possibility of variable cp both for seawater and sea ice.

2.3.2 Freshwater fluxes

(i) For each month, calculate total vertical boundary area mean salinity Sbar, including both ice and seawater, and also including snow.

(ii) The subsequent calculation again differs depending on whether sea ice is embedded or levitating. The embedded case is straightforward. For the liquid component, compute:

the area integral of (v x S) plus area integral of (v[sea-ice] x S[sea-ice]), all divided by Sbar

For the levitating case, for the solid component, for the cross-sectional area of sea ice, calculate the area integral of (v[sea-ice] x S[sea-ice] minus [v x S]). Add the result to the area integral of (v x S) for the liquid component.

*2.4 Time Period*

We hope participants will analyse the whole of their model runs, assuming these to be generally multi-decadal. If this is not possible, we wish to focus first on the modern period (after 1950), and second on 2000-2010, as this period is best for observations. We are happy to discuss this.

*2.5 Storage*

Seawater mass storage, heat storage and salinity storage should be calculated as the net changes of ocean mass, temperature and salinity for both liquid and solid components (therefore including sea ice), from month to month. It may be that we need to correspond about these issues.

**3. Outcomes**

When ready, please send your time series products to Bacon & Aksenov. We aim for collation of results in the hope that initial results, at least, might be ready for presentation to the Royal Society Sea Ice meeting being organised by Daniel Feltham and to be held in London in September 2014. We expect a subsequent multi-author publication to appear in Proc. Roy. Soc. A.

If all goes well, we would like to discuss next steps at the FAMOS 2014 meeting.

Figure 1: Bathymetric configuration in Davis, Fram, and Bering Straits, and the Barents Sea Opening (BSO), showing CTD stations (red cross), model grid points (green cross), mooring locations (blue diamond), and station numbers (including model grid points). Bathymetric contour intervals (CI) are shown for each strait; the CI for the Arctic panel is 1000 m. From Tsubouchi et al. (2012).

**Reference**

Tsubouchi, T., S. Bacon, A. C. Naveira Garabato, Y. Aksenov, S. W. Laxon, E. Fahrbach, A. Beszczynska-Möller, E. Hansen, C. M. Lee and R. B. Ingvaldsen, 2012: The Arctic Ocean in summer: a quasi-synoptic inverse estimate of boundary fluxes and water mass transformation. *J. Geophys. Res.*, **117**, C01024*, *doi:10.1029/2011JC007174.