Freshwater Sources and Sinks for Arctic Sea Ice in Summer

On Arctic sea ice, the melt of snow and sea ice generate a summertime flux of fresh water to the upper ocean. The partitioning of this freshwater to storage in melt ponds and deposition in the ocean has consequences for the surface heat 10 budget, the sea ice mass balance, and primary productivity. Synthesizing results from the SHEBA field experiment, we calculate the sources and sinks of freshwater produced during summer melt. The total freshwater input to the system from snow melt, ice melt, and precipitation from 1 June to 9 August was equivalent to a layer of water 80 cm thick over the icecovered and open ocean. 85% of this freshwater was deposited in the ocean and only 15% of this freshwater was stored in ponds. The cumulative contributions of freshwater input to the ocean from drainage from the ice surface and bottom melting 15 were roughly equal.

upper ocean, bottom topography to trap the freshwater, and calm conditions with little ocean mixing. Under these conditions, false bottoms can form under the sea ice (Untersteiner, 1961;Eicken, 1994;Eicken et al., 1995;Notz et al., 2003). These false bottoms are below the true ice bottom and are a source of ice production during the melt season. Freshwater accumulation in leads between floes can also develop into well-defined stable layers (Richter-Menge et al., 2001).
The freshwater input impacts the thermohaline structure of the upper ocean, ecosystems, and biogeochemistry. The freshwater 35 layer is a barrier for heat transfer from the ocean to the ice bottom, thus slowing bottom ablation. The upper ocean stratification affects the distribution of microbial and faunal communities and the overall productivity (Melnikov et al., 2002;Li et al., 2009). The freshwater layer can impact gas exchange between the ocean and the atmosphere and may inhibit aerosol particle production.
The importance of the amount and disposition of freshwater in the summer sea ice cover leads directly to several questions. 40 How much freshwater is produced? What are the relative contributions from different sources? What fraction of surfaceproduced freshwater is stored in ponds? Here we address these questions by computing a freshwater budget, from a sea ice perspective, over the summer melt season by synthesizing results from the SHEBA experiment (Uttal et al., 2002). Both sources and sinks of freshwater are determined. We examine the time series of freshwater produced through surface snow and ice melt, bottom melt, lateral melt, and rain, and explore the sinks of drainage to the ocean and storage in melt ponds. 45

Approach
We calculate the amount and distribution of freshwater sources and sinks during the summer melt cycle of Arctic sea ice by synthesizing results from the SHEBA program. SHEBA was a yearlong (October 1997-October 1998 drift experiment in the Beaufort Sea. The overarching goals of SHEBA were to increase understanding of the ice albedo and cloud radiation feedbacks through interdisciplinary studies of the atmosphere, ice, and ocean and use that understanding to improve models 50 (Uttal et al., 2002). Here, data from the SHEBA field experiment are used to determine contributions from snow melt, surface melt, bottom melt, lateral melt, and rain, as well as the volume storage in melt ponds.
This work is a synthesis of existing mass balance results from the SHEBA drift experiment. The data sources for the variables needed for the study are summarized in Table 1. The underlying assumption in this study is that, by design, the SHEBA ensemble of mass balance point measurements provides a statistically representative picture of the SHEBA floe (Perovich et 55 al., 2003). The region of interest for this paper is the SHEBA measurement area of roughly 100 km 2 . The focus is on the period from 1 June 1998 to 9 August 1998. This period was selected since it includes the beginning of the melt season and was the time of maximum surface melt, pond evolution, lateral melting, upper ocean stratification, and data availability.

Variable
Units Definition Source s = 0.3 g cm -3 Snow density from SHEBA snow observations Sturm et al., 2002 i =0.9 g cm -3 Ice density measured from cores Perovich et al. 1999 ( ) cm d -1 Average snow melt rate from 135 manual thickness gauges, 77 of which operated over an entire annual cycle. Perovich et al. 2003 ( )   Condensation is small compared to the other terms and is not considered in this study. There are four sinks for freshwater on the sea ice surface: storage in ponds (Pv), drainage vertically through the ice to the ocean (Dv), drainage horizontally from the 75 ice to leads (Dh), and evaporation. As was the case for condensation, evaporation is small and neglected in this study. For continuity, surface sources equal surface sinks giving These terms are expressed as a time series of an equivalent layer thickness of freshwater. The freshwater produced by snow melt is 80 where s is the density of snow and ( ) is the time series of average snow melt rate on the floe. The freshwater produced by surface ice melt is i is the density of ice and ( ) is the time series of average surface ice melt rate on the floe. R(t) is the time series of rain 85 during the summer. The freshwater stored in ponds is

Input to the upper ocean
Freshwater drainage is important when considering freshwater input to the ocean. The total freshwater input to the ocean, , is a sum of the sources: horizontal and vertical drainage, bottom melting, lateral melting Ml(t), and rain falling on leads.
Here, terms are scaled by the ice concentration time series, C(t), to account for freshwater contributions spread over an area that includes both the ice and the leads. Bottom melting is ( ) is the time series of average surface ice melt rate on the floe. Lateral melting is expressed as 100 ml(t) is the lateral melt rate and Hi(t) is the ice thickness at the floe edge. PA(t) is the floe perimeter per unit area of the floe (units of km km -2 ).

Ice surface freshwater balance
The daily freshwater input to the ice surface from snow melt, surface ice melt, and rain is plotted in Figure 2. In early June, 105 the largest contribution comes from snow melt reaching a maximum of about 0.6 cm d -1 . As the snow cover melts away, the snow contribution decreases and the ice contribution begins to increase. The surface ice melt contribution increases through The time series of melt pond fraction and average pond depth is shown in Figure 3. Pond measurements along the survey line started about 10 days after the initial melt pond formation. The pond survey on 20 June coincides with the first pond area 115 maximum as observed from aerial photography . The pond fraction decreased from 20 June to 25 June, due to drainage. This was primarily due to vertical drainage associated with high ice permeability (Eicken et al., 2002).
Afterwards, there was a steady increase in pond fraction and depth through early August, reaching maximum values of 0.37 for fraction and 39 cm for average depth. The time series of cumulative freshwater input to the sea ice surface and the amount stored in ponds is plotted in Figure 4. As before, the cumulative water input is presented as the equivalent depth of a layer of freshwater placed on top of the floe.
Initially, the fraction of the surface freshwater stored in ponds was 0.25. It rapidly decreased to 0.07 in only 5 days as a result of vertical drainage and a reduction in pond coverage. After that, the fraction stored in ponds steadily increased to a final value 125 of 0.23 on 8 August. Throughout the melt season, the majority of the surface freshwater is drained into the upper ocean rather than being stored in ponds. The time series of the cumulative freshwater drained both horizontally and vertically is the difference between the total cumulative input and the amount stored in ponds. By 8 August, the drained amount was equal to a 50 cm layer of freshwater on the ice surface. There was a steady increase in the amount drained from 20 June to 27 July followed by a gradual tapering to 8 August. During summer, the surface melt rates, pond depths, and pond areas were 130 continually changing. However, even with all those changes, there was a consistency in drainage. From 20 June to 23 July, with an average increase of 1.02 cm d -1 and a standard deviation of 0.09 cm d -1 . This provided a steady influx of freshwater from the ice surface into the ocean.  storage in ponds (Pv), and drained to ocean.

Input to the upper ocean
The time series of freshwater input to the upper ocean (Ofw (t)) is calculated using Equation 5. Here the freshwater input represents a layer over the area covered by both the ice and leads. Freshwater inputs from the ice are scaled by the ice concentration to account for the total area of ice plus leads. Helicopter-based aerial photography was used to determine the 140 time series of ice concentration at SHEBA as shown in Figure 5  . In mid-June, the ice concentration dropped to 0.8 and stayed between 0.8 and 0.85 for the remainder of the period of interest.
Rain falling on leads was a very minor component of the freshwater input to the upper ocean. After adjusting for ice concentration, the cumulative input was only 0.13 cm. The contribution from surface drainage is simply the residual from Eq. 1, as shown in Figure 4, scaled by the ice concentration.
The average bottom melt rate ( ) is computed using the same array of thickness gauges used to determine surface melt rates (Perovich et al., 2003). Initially the average bottom melt rate was only about 0.2 cm d -1 (Figure 6). There was a gradual increase 150 over the summer, reaching a peak of 1.1 cm d -1 in late July.
Determining the contribution from lateral melting is somewhat complicated. During SHEBA, there was only one site where a complete time series of lateral melting was measured. We assume that this one site is representative of the entire floe. Lateral melting can result in wall profiles with overhanging lips, shelves, and scallops (Perovich et al., 2003). Lateral melt rates were determined by measuring the change in wall area and applying it to a hypothetical vertical wall generating a lateral melt rate. 155 The ice thickness at the floe edge was measured using a thickness gauge. The ratio of floe perimeter to floe area was used to compare lateral melting to surface and bottom melting. This ratio was determined from the analysis of aerial photography where both the floe perimeter and floe area were computed. For most of the summer, the largest contribution was from drainage through the ice. By 9 August, though, the contributions from surface drainage and bottom melt were equal. The lateral melt contribution was the smallest. The cumulative total freshwater input increase was well represented (R 2 = 0.999) by a second order polynomial of the form 170 = 0.0105 ′ + 0.432 + 0.658 , where t' is the number of days since 8 June.

Discussion and Conclusions
From 1 June to 9 August, the total freshwater produced was equal to a layer 80 cm thick and the input to the ocean was equivalent to a layer 68 cm thick. This suggests that most of the freshwater produced over the Arctic summer was deposited in the ocean; on 9 August, only 15% of the freshwater produced was stored in ponds. This does not mean that on 9 August there was a 68 cm thick freshwater layer under the ice. The freshwater could be stored under the ice, in leads, and mixed deeper 180 in the ocean. The fate of this freshwater depends on multiple factors including ice bottom topography, the dynamics of the ice cover, and the horizontal and vertical partitioning of drainage. This paper determined the amount of drainage from the ice surface to the ocean, but was unable to delineate between horizontal and vertical drainage. This misses an important distinction since freshwater input to leads or to the underside of the ice will have different behaviours and impacts. Horizontal transport will fill leads with freshwater, creating a stable surface layer that 190 can be warmed by solar heating (Richter-Menge et al., 2001). Lateral melting also contributes directly to freshening of leads.
This results in a stable surface layer in leads affecting ocean-ice heat transfer and ocean-atmosphere gas exchange. Opening and closing of leads will mix this freshwater layer, transport heat to the ice edge, and force it under the ice. In contrast, vertical drainage can form a freshwater layer under the ice leading to the formation of false bottoms, isolate the ice from the ocean, and impact nutrient fluxes. Ice motion can mix and dissipate this layer. 195 While we cannot quantitatively define the distribution of vertical to horizontal drainage, we can make some qualitative observations about the timing of when vertical vs. horizontal drainage occurred. Ponds above freeboard provide hydrostatic head to promote vertical drainage. In early June, most ponds were above freeboard. In mid-June, there was rapid drainage and a decrease in pond coverage. This occurred when the ice warmed, its brine volume increased, and it became permeable enough for vertical drainage to occur (Eicken et al., 2002). Also at this time, ponds were amorphous with no established horizontal 200 drainage system to link ponds to the floe edge (see Figure 9). By early August, the situation had changed. Many of the ponds were at sea level, with no hydrostatic head. There was an elaborate melt channel network connecting melt ponds to each other and to the ice edge (Hohenegger et al., 2012) (see Figure   9). The lead fraction had increased from 0.03 to 0.18. Floes had broken, increasing the floe perimeter from 7.4 km km -2 (22 June) to 45.0 km km -2 (7 August). At this stage, horizontal drainage increased. 205 It is possible to generate a rough estimate of the horizontal to vertical drainage for a brief period. During SHEBA, vertical profiles of temperature and salinity were made at a lead site. This showed the gradual buildup of freshwater and heat in the lead and how a dynamic ice event mixed this upper layer and greatly enhanced lateral melting (Richter-Menge et al., 2001).
From 10 July to 20 July there was a steady deepening of the freshwater layer from 70 cm to 120 cm. This occurred during a quiescent period with little winds and little ice motion. Making a few assumptions, we use the 10-day, 50-cm increase in the 210 freshwater layer to estimate the fraction of surface freshwater that is horizontally drained.
We assume that i) the freshwater in leads only comes from lateral melting and horizontal drainage, ii) all lateral melting contributes to freshening of the lead, iii) no freshwater in the lead is lost under the ice or deeper in the ocean, and iv) measurements at the lead site are representative of the broader area. Using these assumptions, the increased depth of the freshwater layer in the lead from 10 July to 20 July is equal to the contribution from lateral melting and horizontal drainage. These results are from a multiyear floe in the Beaufort Sea during the summer of 1998. Future work should explore the spatial variability of the freshwater seasonal cycle and changes over time. Some information can be obtained from autonomous buoys.
For example, autonomous sea ice mass balance measurements in the Beaufort Sea indicate large increases in bottom melting in recent years . This has resulted in a larger freshwater contribution from bottom melt 230 and a larger fraction of the freshwater production deposited in the ocean. While the contributions from surface and bottom melt are straightforward to measure autonomously, the contributions from lateral melting and the amount stored in melt ponds are more challenging. This gap could be partially filled by sensors measuring temperature and salinity profiles in the upper