articles/IGS/IGS_ECCO2_Greenland_Final.tex

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\title{Spreading of warm ocean waters around Greenland as a possible cause for glacier acceleration.}

\author[Rignot and others]{E. Rignot$^{1,2}$, I. Fenty$^{2}$,  D. Menemenlis$^{2}$, Y. Xu$^{1}$ }

\affiliation{$^{1}$Department of Earth System Science, University of California, Irvine, California\\
$^{2}$Jet  Propulsion  Laboratory, Pasadena, California, USA}

\abstract{ We examine the pattern of spreading of warm subtropical-origin waters around Greenland for the years 1992--2009 using 
a high resolution (4-km horizontal grid) coupled ocean and sea ice simulation. The simulation, provided by the Estimating the Circulation 
and Climate of the Ocean, Phase II (ECCO2) project, qualitatively reproduces the observed warming of subsurface waters in the subpolar 
gyre associated with changes of the North Atlantic atmospheric state that occurred in the mid-1990s. The modeled subsurface ocean 
temperature warmed by +1.5${^\circ}$C in Southeast and Southwest Greenland during 1994--2005 and subsequently cooled by 
0.5${^\circ}$C; modeled subsurface ocean temperature increased by +2 to +2.5${^\circ}$C in Central and then Northwest Greenland during 1997--2005 and 
stabilized thereafter; while it increased after 2005 by less than 0.5${^\circ}$C in North Greenland. Comparisons with {\it in situ} measurements off the continental shelf in the 
Labrador and Irminger Seas indicate that the model initial conditions were 0.4${^\circ}$C too warm in the south but the simulated warming is correctly reproduced; while measurements from
the Eastern Baffin Bay reveal that the model initial conditions were 1.0${^\circ}$C too cold in the northwest but the simulated ocean warming brought 
modeled temperature closer to observations, i.e., the simulated warming is 1.0${^\circ}$C too large.  At several key locations, the modeled 
oceanic changes off the shelf and below the seasonal mixed layer were rapidly transmitted to the shelf within troughs towards (model-unresolved) fjords.  
Unless blocked in the fjords by shallow sills, these warm subsurface waters had potential to propagate down the fjords and melt the glacier fronts. Based on
model sensitivity simulations from an independent study (Xu and others, 2012), we show that the oceanic changes have very likely increased the subaqueous 
melt rates of the glacier fronts, and in turn impacted the rates of glacier flow.}

\maketitle
\section{1.0 Introduction}

Greenland glaciers have been experiencing a growing mass deficit in the last two decades, half of which is caused by an  increase in surface melt 
(Ettema and others, 2009; van den Broeke and others, 2009) and half by an acceleration in glacier flow (Rignot and Kanagaratnam, 2006; Rignot and others, 
2011). The acceleration was initiated in the glacier frontal regions and rapidly propagated upstream (Thomas and others, 2004; Joughin and others, 2004). 
Several studies have examined the role of subglacial water in triggering the acceleration. The results suggest that this forcing is not sufficient to destabilize 
the glaciers and does not yield an increase in speed comparable in magnitude to observations (e.g., Shepherd and others, 2009).  

Ocean warming has been hypothesized as an alternative cause of glacial destabilization  (e.g., Holland and others, 2008; Hanna and others, 2009; Christoffersen 
and others, 2011; Howat and others, 2008; Murray and others, 2010; Straneo and others, 2010; Rignot and others, 2010).  In Greenland, the vast majority of the ice 
discharged into the ocean is controlled by marine-terminating or tidewater glaciers, i.e., glaciers that terminate in the ocean, melt in contact with the ocean, and 
calve into icebergs. An increase in the temperature of the subsurface waters at the front of these glaciers would increase the subaqueous melt rates of their calving faces, cause 
retreat of the glacier fronts, and yield changes in force balance that could trigger speed up. Floating ice tongues only exist north of  76${^\circ}$N (Rignot and others, 2001). At low latitudes, 
Jakobshavn Isbrae (JKS) at 69$^\circ$N was the only glacier that maintained a floating ice tongue until it disintegrated in 2002 (Weidick and others, 2003). Holland and others (2008) attributed
its disintegration to the intrusion of warm Irminger waters into Disko Bay in the mid-1990s. A similar subtropical origin of oceanic heat was suggested by Howat and others (2008), 
Straneo and others (2010), and Christoffersen and others (2011) for glaciers that accelerated in the east. 

The Irminger Waters (IW) found around the margins of southern and western Greenland are named due to their advection through the Irminger Sea, the eastern 
lobe of the North Atlantic subpolar gyre (SPG). The variability of water mass properties of the IW is related to North Atlantic atmospheric forcing variability (Myers and others, 2007).  
Variability of the North Atlantic atmospheric state is described in terms of the phase of the North Atlantic Oscillation (NAO). The NAO describes the large-scale westerly wind intensity 
and air-sea heat and buoyancy fluxes in the North Atlantic. During periods of sustained positive NAO index, intense westerly winds and large air-sea heat and buoyancy fluxes 
cause the SPG to expand which, in turn, reduces the amount of subtropical-origin waters entering the SPG from the North Atlantic Drift. A shift in NAO phase from high to low 
causes more subtropical-origin waters to enter the SPG and Greenland's boundary current system. Moreover, since air-sea heat and buoyancy losses are positively correlated with 
the NAO, subtropical waters brought into the SPG are subject to less cooling during periods of negative NAO.  Therefore, a switch from positive to negative NAO conditions is followed 
by a warming of IW in the SPG due to an increase of lateral ocean heat flux convergence and a decrease of air-sea heat loss (Yashayaev and Loder, 2009).

From the late 1980s to the early 1990s, the NAO was mainly in a positive phase resulting in a cooler, fresher, and laterally expansive SPG with comparatively colder and fresher 
IW in the SPG and the East/West Greenland Current (EGC/WGC). Following this period of sustained positive values, the NAO exhibited a dramatic reduction in the mid-1990s and 
remained mixed through the mid-2000s.  The switch away from sustained positive NAO conditions led to a dramatic warming of the subtropical waters in the Irminger Sea. Soon thereafter, 
this warmer IW began to propagate around Greenland by EGC/WGC (Myers and others, 2007).  The warming of the subtropical-origin waters in the upper SPG and the IW 
component of the EGC/WGC has been observed with various {\it in situ} measurements (Yashayaev and Loder, 2009; Holland and others, 2008; Myers and others, 2007).  
The Baffin Bay has far fewer contemporary {\it in situ} measurements relative to the SPG, but existing data suggests ongoing ocean warming in that region as well (Laidre and others, 2010).  

Here, we examine the propagation of anomalously warm subsurface temperature around Greenland from the mid-1990s using a high-resolution coupled ocean and sea ice 
numerical simulation. The simulation is provided by the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) project and it spans the 1992--2009 time 
period. We report changes in ocean temperature at several key regions around Greenland, compare the results with {\it in situ} observations, and summarize subsurface 
ocean temperature changes around the entire periphery of Greenland. Using the results of model simulations described in a companion paper (Xu and others, 2012), we then 
discuss the impact of these temperature changes on the subaqueous melt rates and their likely impact on glacier flow. We conclude on the relevance of the subsurface ocean on 
glacier stability in Greenland. 

\section{2.0 Model configuration and Methodology.}

The results described herein are based on a regional configuration of the Massachusetts Institute of Technology general circulation model (MITgcm; Marshall and others, 1997). 
The domain of integration includes the entire Arctic Ocean and parts of the North Pacific and North Atlantic (see Fig.\ 1 in Nguyen and others, 2011).  Model grid spacing is 
4 km in the horizontal and ranges between 10 and 450 m over 50 levels in the vertical.  The model employs the rescaled vertical coordinate  z$^{*}$ of Adcroft and Campin (2004) and the partial-cell formulation of Adcroft and others (1997) . The ocean model is coupled to the dynamic and thermodynamic sea ice model described in Losch and others (2010) and employs the salt plume parameterization of 
Nguyen and others (2009). Ocean and sea ice model parameters are identical to the 18-km optimized solution called A1 in Nguyen and others (2011).   Ocean initial and lateral open boundary conditions of temperature and salinity are derived from the World Ocean Atlas 2005 (WOA05; Boyer and others, 2006) while velocities on the open boundaries are derived from the global, eddying ECCO2 state estimate of Menemenlis and others (2008).  Air-sea fluxes are calculated with the bulk formulae of Large and Yeager (2008) and the Japanese 25-year ReAnalysis and the Japan Meteorological Agency Climate Data Assimilation System (JRA-25/JCDAS; Onogi and others, 2007).  Bathymetry is derived from the International Bathymetric Chart of the Arctic Ocean (IBCAO) (Jakobsson and others, 2008).  A preliminary 
evaluation of the Arctic Ocean in the model is given in Nguyen and others (2012).

The realistic simulation of hydrographic variability and circulation dynamics in glacial fjords requires very high model horizontal resolution ($<$ 1 km), good bathymetric data, and, in some locations, representation of the effects of tidal forcing.  Given the model resolution, the lack of a tidal submodel, and limited bathymetry knowledge, the model is analyzed near the mouths of the glacial fjords.  Hydrographic changes at the fjord mouths may only be partially transmitted through the fjords to the glacier fronts. Most Greenland fjords are sill fjords (Buch, 2002; and Table 1), i.e., warm subsurface waters have to overcome topographic barriers to penetrate the glacial fjords and reach the glacier fronts. Once at the ice fronts, these ocean waters participate in a vigorous convective circulation driven by subglacial water discharge at the glacier front, the buoyancy of freshwater at the 
front, and the pressure dependence of the melting point of seawater (Motyka and others, 2003; Xu and others, 2012). When subglacial flow is low or absent, the forced convection is 
strongly reduced, and vigorous ice melting ceases as observed on Columbia Glacier, Alaska (Walters and others, 1988). 
 
\section{3.0 Results}
\subsection{3.1 General trends.}

Figure 1a shows the simulated ocean temperature at 250 m depth, time-averaged for the entire 1992--2009 period. The warmest, saltiest waters are found to the east of the Reykjanes 
Ridge. These are subtropical-origin waters transported northward by the North Atlantic Current, with temperatures $\geq 8^\circ$C at this depth. These waters are transported west by 
the Irminger Current (IC, Fig.\ 1b) towards Southeast Greenland and north towards Svalbard and Northeast Greenland by the Norwegian Atlantic and West Spitsburgen Currents.  At the shelf 
along Southeast Greenland they combine with the cold (1$^\circ$C), low salinity shelf waters of the EGC coming from the Arctic and Nordic Seas (Sutherland and Pickard, 2008) to 
form a two-component current with cold fresh waters above the shelf and warm salty waters along the slope.  The EGC rounds the southern tip of Greenland at Cape Farewell to become 
the northward-flowing WGC,  with subsurface ocean temperatures 2--3$^\circ$C lower than the IC, due to air-sea heat losses and lateral mixing. IW on the WGC is traceable in Fig.\ 1 as 
the warm and fast-moving water flowing northward along the slope at 250 m.  A portion of the WGC bifurcates west into the Labrador Sea and joins the Labrador Current (LC) to complete 
the western branch of the SPG (Fig.\ 1b).  The non-bifurcating northward-flowing branch of the WGC passes through eastern Davis Strait into Baffin Bay (Buch, 2002).   In northern Baffin Bay, 
the now significantly cooler IW on the WGC (1$^\circ$C) meets colder ($\leq 0^\circ$C), fresher southward-flowing Arctic currents from 
Nares Strait, and from Jones and Lancaster Sound.  Together, these waters flow southward along Baffin Island in the Baffin Island Current (BIC) through western Davis Strait to the LC.  In Northeast Greenland, the subtropical-origin waters joining the EGC are much cooler (3.5--5$^\circ$C) than those waters joining farther south, a result of cooling during its northward transit.
 
The 4-km ECCO2 solution reveals major changes in subsurface ocean temperature around Greenland during the 1992--2009 time period (Fig.\ 1c and d).  As the NAO ceased its sustained positive 
phase, IW in the SPG warmed and propagated along the EGC/WGC, yielding positive subsurface temperature anomalies in Southeast, Southwest, and Northwest Greenland.  The warming around North and Northeast Greenland took considerably longer, a result of the longer advective timescales associated with the propagation of subtropical-origin waters into the Greenland Sea and Arctic Ocean (Fig.\ 1c).  During 
the second half of the simulation period, the model indicates widespread warming in Baffin Bay and Greenland Sea and a cooling in the Eastern Irminger Sea and Southeast Greenland (Fig.\ 1d).  

\subsection{3.2 Comparison with {\it in situ} data}

We compare the 4-km ECCO2 solution with {\it in situ} observations in the central Labrador Sea (within 150 km of the AR7W line and in depths exceeding 3,250 m), the western Irminger Sea 
(within 150 km of the AR7E line, in depths exceeding 2,500 m, and west of 36$^\circ$W), and in Eastern Baffin Bay (between 71--74$^\circ$N, east of 60$^\circ$W, and in waters shallower 
than 550 m) (Fig.\ 2).  Temperature data are drawn from CTDs, autonomous profiling floats, and expendable bathy-thermographs (XBT) compiled from the Hydrobase 2 of Curry (2001), the
Global Temperature and Salinity Profile Program of the National Oceanographic Data Center Operational Ocenography Group (NODC 2006), and the ICES Oceanographic Database 
and Services (ICES 2012).

The 4-km ECCO2 simulation is initialized from the WOA05, a temperature and salinity atlas, which, by coincidence,  includes several important observed features of the SPG in 1992 including 
a relatively cool and weakly-stratified interior.  Compared to observations in the Labrador and Irminger Seas between 1992 and 1996, the WOA05 has approximately +0.4$^\circ$C 
bias.  This constant bias has been removed from the model results in Figs.\ 2 and 3 in order to focus the discussion on temporal trends. 

Waters within the SPG have significantly warmed since the mid-1990s owing to a shift to generally milder wintertime atmospheric conditions.  With reduced wintertime air-sea heat losses, 
net lateral advective heat flux convergence into the subpolar gyre has dominated over atmospheric heat loss.  The model closely reproduces the magnitude and timing of the observed interior warming of the Labrador and Irminger Seas: about +1.0$^\circ$C in the upper 500 m between 1992 and 2004 and 
+0.6$^\circ$C between 500 and 2,000 m.  In the Labrador Sea, temperatures in the upper 500 m cease their dramatic warming by 2004 and thereafter exhibit 
inter-annual variability consistent with known atmospheric variability (e.g., the cooling/deep convection event of 2008; Vage, 2011).

We expect the simulated SPG warming to be limited for several reasons.  Lohmann and others (2009) showed that the response of the SPG to a shift from NAO+ to NAO$-$ conditions is 
sensitive to the amount of preconditioning by the atmosphere.  The model initial conditions are identical to the WOA05 and are, therefore, not preconditioned by the NAO+ forcing, which 
began in the late 1980s.  In addition, because the lateral ocean open boundaries are taken from WOA05, the waters feeding the SPG do not exhibit realistic inter-annual 
hydrographic variability.  Finally, model-data differences include errors in the JRA-25/JCDAS surface boundary conditions and inaccuracies in the model subgrid-scale 
parameterizations. 

Comprehensive model-data comparison for the Eastern Baffin Bay region is considerably more difficult than the SPG owing to the paucity of {\it in situ} observations over the simulation period, 
especially during the first four years where no measurements are available.  Assuming that the ocean state in 1992 is similar to measurements taken in 1988 and 1990, the data indicate 
a warming of +1.0$^\circ$C between 100 and 300 m between 1992 and 1999.   At these depths, the model is initially about 1.0$^\circ$C cooler than observations --- possibly an artifact of the 
sparse data used to generate the WOA05.  However, the model warms to temperatures comparable to initial conditions by 1998 and then to contemporaneous observations by 1999-2000.  
A dip in 2005 temperatures is reproduced, as well as the subsequent +0.5$^\circ$C warming.  Simulated temperatures in this region for the 2000's are in broad agreement with 
Narwhal-based observations reported by Laidre and others (2010) who found maximum wintertime temperatures up to 3.4$^\circ$C  at 350 m in the same region. 

In terms of total temperature change, the model exhibits an extra degree of warming in the Eastern Baffin Bay region than observed.  Without additional experiments it is impossible to determine how much of the warming is due to a realistic model response to the specified atmospheric forcing as opposed to the model evolving away from imperfect initial conditions or to systematic model errors.  It also must be noted that the model analyses use all grid points and times whereas the 
observation analyses rely on temporally and spatially sparse measurements.  To illustrate, the impact of sample density on the observation 
analyses can be seen by comparing the temperature reconstructions before and after the widespread arrival of ARGO floats in 2002.

\subsection{3.3 Modeled regional changes}

We examine changes in subsurface temperature at 7 key locations, spanning different oceanic regimes  (Fig.\ 3). 
The survey starts at Kangerdlugssuaq Glacier on the East Coast, closest to the source of IW, and continues clockwise around Greenland.  We analyze 
both off-the-shelf  (triangles in Fig.\ 1a) and on-the-shelf (diamonds) simulated subsurface ocean temperature data, averaged over one-year periods and over the range of depths indicated 
in Table~\ref{table:locations}.  Anomalies in subsurface temperature are calculated in reference to the average temperature for the entire period. The comparison of off-the-shelf 
versus on-the-shelf temperature documents whether changes in ocean temperature are transmitted across the shelf break. Off-the-shelf locations are selected at the edge of the 
continental shelf, near major troughs in the seafloor; on-the-shelf locations are selected in front of major glacial fjords, within troughs.  Troughs are important because they provide 
a natural pathway for subsurface warm waters to intrude onto the continental shelf and reach the glacial fjords.

At off-the-shelf location K$_O$ (Fig.\ 1a), the initial ocean temperatures have the warmest (5.8$^\circ$C) IW of the seven selected locations.  K$_O$ is far offshore from K$_S$ due to a broad continental shelf in that area. 
In 1994--2004, the modeled subsurface ocean temperature increased by +1.3$^\circ$ at K$_O$; and did not significantly change thereafter.  On the shelf, the temperature at K$_S$ is initially 3.1$^\circ$C 
colder than off the shelf (2.7$^\circ$C at K$_S$ vs 5.8$^\circ$C at K$_O$); and the warming is +1.2$^\circ$C in 1994--2004, with little warming in later years.  At SE$_O$ in the southeast, ocean temperature 
changes are synchronous with K$_O$ with a warming of +1.2$^\circ$C in 1994--2004. In contrast with K$_O$ and K$_S$, both on- and off-the-shelf areas decline by 0.5$^\circ$C after 
2005, yielding an overall warming for the entire period of about +1$^\circ$C.

On the west coast at N$_O$, simulated subsurface temperature changes are +1.8$^\circ$C in 1994--2004 and $-0.6^\circ$C after 2006. At N$_S$, both the warming (+2$^\circ$C) and cooling 
($-1.0^\circ$C)  are larger than at N$_O$.  Larger temperature changes are modeled near the mouth of Disko Bay with +2.5$^\circ$C in 1993--2003 at J$_O$. After 2004, J$_S$ continues to warm by 
another +0.5$^\circ$C, but not J$_O$. Ocean waters at J$_O$ are initially 4$^\circ$C colder than at K$_O$.

Farther north, in Melville Bay, modeled ocean waters at M$_O$ are 2.6$^\circ$C colder than in Disko Bay at J$_O$ (0.4$^\circ$C versus 3$^\circ$C for the entire period) and warmed by +3$^\circ$C 
in 1994--2009 for both the off- and on-shelf locations. The most significant warming takes place after 1997 and after 2004. This delayed warming compared to the south is expected from the 
northward spreading of warm waters. In North and Northeast Greenland, where subsurface temperature anomalies are not directly linked to the SPG via the WGC pathway, warming is delayed until 
after 2004. The modeled change at 79N$_S$ (+1$^\circ$C) is less than at 79N$_O$ (+1.5$^\circ$C), suggesting that only a fraction of the available ocean heat is transmitted up to the shelf at this location.

\subsection{3.4 Modeled regional trends versus observations}

The +1.6$^\circ$C modeled warming at K$_S$ between 1995 and 1998 is consistent with the +1.8$^\circ$C warming reported by Christoffersen and others (2011).  On the southwest coast at N$_S$ and 
N$_O$, the +1.5 to +2$^\circ$C modeled warming for 1995--1999 is consistent with the observations reported by Myers and others (2007), followed by a cooling in 2007--2009. In Disko Bay, Holland  
and others (2008) reported an increase of +1.2$^\circ$C in 1991--1996 to almost +3$^\circ$C in 1997--1999 from fish trawl data, depth-averaged between 150 and 600~m in their Region 2 (Wieland 
and Kanneworff, 2002). Over the entire survey area, they report an increase from +1.7$^\circ$C to +3.5$^\circ$C until year 2002. Over that same period, the model indicates a +2$^\circ$C  warming, 
which agrees with the fish trawl data, and a continuous warming after 2002. In terms of timing, the modeled change in ocean temperature at J$_S$ is abrupt in 1995--1998 and 
moderate in 1998--2002, which is again consistent with fish trawl data. 

Few observations exist in Eastern Baffin Bay near M$_S$ and M$_O$ to evaluate the realism of the simulated trend.  As discussed in Section 3.2, existing data suggest that the model started 1$^\circ$C too cold and the modeled warming 
is also 1$^\circ$C too large. At P$_S$, Johnson and others (2010) report only +0.25$^\circ$C warming from 2003 to 2009 versus approximately +0.4$^\circ$C in the model over that time period. We conclude that 
the model results in the north tend to overestimate the warming compared to observations.

\subsection{3.5 Potential for ocean heat to intrude glacial fjords}

Our analysis suggests that over the sites considered, changes in ocean temperature off the shelf are transmitted rapidly on the shelf. Whether the on-the-shelf changes reach the 
glacier fronts depends on winds, air-ocean heat exchange within the fjords, and, most importantly, seafloor topography, i.e., the presence of sills that may block the migration of warm, 
subsurface waters. Most sill depths are not well known (Buch, 2002).  At Kangerdlugssuaq and Helheim (K$_S$ and SE$_S$), the main sill depth of 550 m should let warm subsurface waters penetrate the glacial fjord
(Table 1). Sill depths farther south are unknown (Buch, 2002). At N$_S$, the main sill depth of 80 m should block warm water inflow. At JKS, the 350-m deep sill is not sufficient to block warm waters from 
intruding the fjord (Holland and others, 2008), but at Torssukataq the sill depth is only 285 m. In northwest Greenland, there is no bathymetry data within 100 km of the coastline in 
the IBCAO data base. At P$_S$, the  380-m depth sill should not not block warm waters, but a shallower sill exists inside the fjord. At 79N$_S$, the sill depth is 
20 to 200 m, so warm waters are blocked off.

\subsection{3.6 Comparison of enhanced melt rates with glacier-front retreat and acceleration}

Model simulations suggest that the subaqueous melt rate of a glacier calving face increases linearly with thermal forcing, defined as the difference between the water temperature and 
the {\em in situ} freezing point of seawater (Xu et al., 2012). We use this linear relationship herein to calculate the percentage increase in subaqueous melt rate resulting from an increase in
ocean temperature (Table 1). We use a constant freezing point of seawater of $-2.08^\circ$C for a depth of 250 m and a salinity of 34.5 psu. 

At K$_S$, Kangerdlugssuaq Gletscher doubled its speed in 2004--2005, retreated 6 km, and then re-advanced by 2 km in 2007--2009 with a 50\% reduction in speed (Howat and others, 2007). In the model,
warm waters intruded at K$_S$ from 1996 to 2004, followed by a slight cooling. The modeled temperatures translate into a 24\% increase in melt rate over the entire time period and 36\%
between 1992 and 2004 (Table 1). 
At Helheim,  the glacier accelerated in 2002--2003 and doubled its speed by 2005; the ice front retreated by 7 km before re-advancing by 3 km in  2005--2006 and slowing down by 25\%  
(Howat and others, 2007). The modeled changes in temperature at SE$_S$ suggests a 14\% increase in subaqueous melt  for 1993--2009 and 21\% for 1993--2004.  The 1993--2004 increase in melt 
rate may have been sufficient to retreat the glacier front behind a shallow bathymetric feature (Joughin and others, 2008) and trigger speed up. The timing of the retreat and advance coincides 
with the warming and subsequent cooling of ocean waters at SE$_S$ after 2004. A similar time evolution is found in Southeast Greenland (Murray and others, 2010).

Near Nuuk, glacier changes at Kangiata Nunata have been few despite the presence of warm waters on the continental shelf, probably because shallow sills block the entrance 
of warm subsurface waters. In Disko Bay, the ocean warming translates into a 68\% increase in melt rate, the largest in Greenland. Farther north, in Torssukataq fjord, glacier changes 
have been less significant, which may be due to the presence of a shallower sill.

In Northwest Greenland, glacier acceleration along the coast has been sporadic (e.g., Moon and Joughin, 2007), but the glaciers have consistently lost mass since the 1990s and the mass
loss accelerated after 2006 (Kahn and others, 2010). In fjords where subsurface warm waters intruded the fjords, our results suggest a potential increase in subaqueous melting 
of +65\%, which is comparable to the record increase in Disko Bay.

At Petermann Fjord, no significant glaciological changes occurred until a major calving event took place in 2010 (Johnson and others, 2011). Further observations and model 
evaluation are  needed to determine whether ocean warming had an impact on the stability of the floating ice tongue. In the northeast, the 79north glacier has been stable since the 1990's, which
is consistent with the presence of shallow sills at the mouth of the fjord. 

\section{4.0 Discussion.}

The dramatic change of atmospheric conditions in the North Atlantic in the mid-1990's is widely understood to have instigated a weakening of the SPG, and a consequent redistribution and warming of subtropical-origin waters in the SPG.  Upon entering the subsurface shelfbreak component of the EGC, the warm anomaly propagated north above the West Greenland Shelf on the WGC to Eastern Baffin Bay.  The 4-km Arctic Ocean ECCO2 simulation captures the warming around Greenland that is expected from a weaken SPG.  Simulated temperatures, however, are consistently warmer than observations in the interior SPG by about +0.4$^\circ$C --- probably due to a bias in the WOA05, which was used for
initial conditions.  Despite starting from a warmer state, the model reproduces the magnitude and timing of the successive warming of the SPG interior quite well, following the switch from 
NAO+ to NAO$-$ conditions.  In Eastern Baffin Bay, the magnitude of simulated warming is much greater than observed.  However, the WOA05, from which the model 
was initialized, appears to be colder in that region than the sparse observations from the late 1980's and early 1990's indicate.  Ultimately, the simulated Eastern Baffin Bay warming 
brings model temperatures closer to more recent observations.

Despite its limitations, the model is able to reproduce the observed patterns of warming around Southeast and Southwest Greenland and subsequent cooling in the Southeast Greenland when forced by JRA-25/JCDAS surface boundary conditions.  The model indicates widespread ocean warming, including in Northwest Greenland after 2005.

The rate of subaqueous melting of the glacier calving faces also depends on the flux of subglacial water at the glacier base. Using independent approaches, 
Jenkins (2011) and Xu and others (2012) find a linear dependence on thermal forcing and a 1/3 power law dependence on the flux of subglacial runoff. Runoff has roughly doubled in Greenland in 
1996--2006 compared to the colder 1987--1996 period (Ettema and others, 2009). A doubling in subglacial runoff should increase subaqueous melt by +25\% according to the model simulations. 
If we combine this result with the increases in melt rate discussed in Section 3.6 based on changes in ocean thermal forcing (Table 1), we obtain a total potential increase in 
subaqueous melt rate ranging from 40\% at SE$_S$ to 90\% at J$_S$ and M$_S$, if subsurface warm waters were transmitted to the glacier fronts. 

Enhanced subaqueous melting of the glacier fronts will undercut the glacier faces, increase calving and retreat the glacier fronts. Ice-front retreat will in turn reduce the buttressing force 
on the glaciers and engender speed up (Thomas and others, 2004). To investigate in detail whether the calculated melt rates justify the observed glacier acceleration is an effort 
well beyond the scope of this paper. Our analysis however indicates that the spreading of warm waters around Greenland must have significantly increased the glacier subaqueous melt rates in the
frontal regions.

\section{5.0 Conclusions.}

Our examination of subsurface ocean temperature estimates for the 1992--2009 time period in the 4-km ECCO2 solution shows widespread warming of the coastal waters around Greenland, not only in the southeast and the southwest, but also in the northwest. Despite model uncertainties, the spatial and temporal pattern of these oceanic changes is a prominent feature 
of the model solution, which is consistent with available, albeit sparse, hydrographic data. The results reported here and in a companion study (Xu and others, 2012) support the hypothesis 
that oceanic changes around Greenland have played a major role in the evolution of its glaciers and, in turn, the entire ice sheet mass balance. Further progress in investigating the detailed 
relationship between subsurface ocean conditions and glacier speed will require major advances in ocean modeling, bathymetry mapping, ice flow modeling, modeling of ice-ocean 
interactions, and oceanographic data collection in glacial fjords. Our results suggest that high-resolution ocean models will soon become a useful tool of analysis for the glaciological community to address this issue in a quantitative fashion.

Acknowledgments. This work was  performed under contracts with the  National  Aeronautics  and Space Administration's Cryospheric Science Program and Modeling Analysis and Prediction 
Program. We thank three anonymous reviewers and the guest Editor for their constructive comments. 

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\newpage
\renewcommand{\arraystretch}{1.0}\addtolength{\tabcolsep}{0pt}
\begin{table}    
\begin{tabular}{l c c c c c c c} \hline
Glacier                                 &  Main sill        & Fjord max         & GL            & Region        & Average T  92-94* &  $\delta$T & Calculated $\delta$B \\
                                        &  (m)                  &  (m)                  &  (m)          &                       & $^\circ$C           & $^\circ$C               &  \%             \\  \hline
Kangerdlugssuaq$^{1}$   &  500                  & 870                   & NA    & K$_S$         & 2.1           & +1.0                  &  24 \\
Helheim$^{2}$                   &  550                  & 920                   & 550           & SE$_S$        & 5.1           & +1.0                  &  14 \\
Kangiata Nunata$^{3}$           &   80                  & 600                   & NA            & N$_S$          & 3.6          & +1.0                  &  18   \\ 
Jakobshavn$^{4}$                &  350                  & 800                   & 600           & J$_S$         & 1.6           & +2.5                  &  68 \\
Torssukataq$^{5}$               &  285                  & 700                   & 450           & J$_S$         & 1.6           & +2.0                  &  54 \\
Store$^{6}$                     &  NA                   & 950                   & 550           & J$_S$                 & 1.6           & +2.0                  &  54 \\
King Oscar$^{7}$                &  NA                   & 900                   & NA            & M$_S$         & 1.0           & +2.0                  &  65 \\
Petermann$^{8}$         &  380                  & 900                   & 550           & P$_S$          & -0.25                & +0.25                         &  14 \\
79north$^{9}$                   & 70-200                & 900                   & 500           & 79N$_S$       & -1.7          & +1.0                  &    3 \\ \hline
\end{tabular}
\caption{Characteristics of several major glacial fjords in Greenland: Main sill (column 2) = depth in meters (NA = not available); Fjord (column 3) = maximum depth of fjord in meters; GL (column 4) = 
grounding line ice thickness in meters; region in Fig.\ 1 (column 5); temperature at 250 m depth in 1992-1994 (column 6) corrected by +0.4$^\circ$C in the south, -1$^\circ$C in the northwest and
based on {\em in situ} data in the north and north east; change in subsurface temperature in 1992-2009 (column 7) corrected by -1$^\circ$C for King Oscar, -0.25$^\circ$C for Petermann 
and unchanged for the other sites, and corresponding increase in subaqueous melt rates of the glaciers (column 8) assuming a linear dependence on thermal forcing from the ocean. 
$^{1}$ Dowdeswell and others (2010);  $^{2}$ Andresen and others (2010); $^{3}$ Mortensen and others (2010); $^{4}$ Holland and others (2008); $^{5}$ Rignot and others (2010); 
$^{6}$ Weinrebe and others (2009); $^{7}$ Jakobsson and others (2008); $^{8}$ Johnson and others (2010); $^{9}$ Mayer and others (2000).}
\label{table:locations}
\end{table}

\newpage

\renewcommand{\arraystretch}{1.0}\addtolength{\tabcolsep}{0pt}
\begin{table}    
\begin{tabular}{llc|c|c|c}         
Location Name     &    & Coordinates      & Area (km$^2$)  & Depths (m) & Mean shelf depth or \\         & & & [num cells] & & Off-shelf depth range (m) \\  \hline  \hline        
Kangerdlugssuaq shelf &K$_\textrm{s}$     & 31.2 W, 67.5 N & 1080 [55]           & 162-378         & 489                          \\         Kangerdlugssuaq off shelf& K$_\textrm{o}$ & 29.3 W, 65.4 N & 1090 [96]           & 162-378         & 323-1620                     \\ \hline        Southeast shelf& SE$_\textrm{s}$          & 41.3 W, 62.4 N & 597 [30]            & 146-323         & 493                          \\         Southeast off shelf &SE$_\textrm{o}$      & 40.0 W, 62.2 N & 798 [40]            & 146-323         & 592-1682                     \\ \hline        Nuuk shelf &N$_\textrm{s}$                & 52.2 W, 63.6 N & 357 [18]            & 162-441         & 385                          \\         Nuuk off shelf &N$_\textrm{o}$            & 52.9 W, 63.2 N & 1072 [54]           & 162-441         & 830-2312                     \\ \hline        Jakobshavn shelf&J$_\textrm{s}$          & 52.6 W, 69.2 N & 778 [40]            & 133-276         & 474                          \\         Jakobshavn off shelf &J$_\textrm{o}$      & 56.7 W, 66.7 N & 1299 [66]           & 133-276         & 182-677                      \\ \hline        Melville Bay shelf &M$_\textrm{s}$        & 60.3 W, 75.7 N & 456 [24]            & 110-207         & 177                          \\         Melville Bay off shelf&M$_\textrm{o}$    & 59.3 W, 74.8 N & 571 [30]            & 110-207         & 276-845                      \\ \hline        Petermann shelf &P$_\textrm{s}$           & 63.5 W, 81.3 N & 467 [25]            & 182-441         & 389                          \\         Petermann off shelf & P$_\textrm{o}$       & 64.6 W, 81.2 N & 374 [20]            & 182-441         & 276-441                      \\ \hline        
79N shelf &79N$_\textrm{s}$               & 16.9 W, 79.6 N & 751 [40]            & 133-207         & 197                          \\         79N off shelf &79N$_\textrm{o}$           & 5.19 W, 80.0 N & 1464 [78]           & 133-207         & 162-2130                     \\\hline    
\end{tabular}
\caption{Location of three-dimensional boxes used to plot average annual subsurface temperature in Figure 3.  ``Coordinates'' refers to the center of the volume used in the analysis while ``area'' and ``depths'' refers to the horizontal area and depth range of the averaging volumes, respectively.  ``Mean shelf depth'' indicates the mean bathymetric depth on the shelf for the shelf locations while ``off-shelf depth range'' indicate the range of bathymetric depths beneath the off-shelf averaging locations.  The off-shelf averaging regions generally span an area from shelfbreak to deeper waters.}
\label{table:locations}
\end{table}

\newpage

{\bf Figure 1.}  Subsurface ocean temperature from the 4-km ECCO2 simulation overlain on IBCAO isobaths (Jakobsson and others, 2008): (a) averaged for the time period 1992--2009 at 250-m 
depth (white areas are shallower than 250 m) with major locations discussed in the text. The AR7W, AR7E and Melville Bay evaluation boxes discussed in Figure 2 are dotted black lines; (b) 
water velocity (cm/s) at the 250-m depth with location of major ocean currents: Irminger Current (IC), East Greenland Current (EGC), Labrador Current (LC) and West Greenland Current (WGC); 
(c) 2001 mean temperature anomaly at 250 m from the model with respect to the 1992-2009 simulation period; and (d) as (c) but 2009 mean temperature anomaly. Diamonds (triangles) in (a) 
indicate the location of on-the-shelf (off-the-shelf) three dimensional boxes used to calculate the yearly-mean subsurface temperatures plotted in Figure 3. Sites are Kangerdlugssuaq Gletscher 
(K$_O$ and K$_S$), Southeast Greenland (SE$_O$ and SE$_S$), Nuuk (N$_O$ and N$_S$), Jakobshavn Isbrae (J$_O$ and J$_S$), Melville Bay (M$_O$ and M$_S$), Petermann Gletscher (P$_O$ and P$_S$) and 79north Glacier (79N$_O$ and 79N$_S$). 

{\bf Figure 2.} Comparison of subsurface temperature along the AR7W line (see Fig.\ 1a) in the central Labrador Sea from (a) {\it in situ} data and (b) ECCO2 4-km Arctic Ocean solution for the time period 1992--2009 minus an absolute offset of 0.4$^\circ$C. Similar plots are in (c) and (d), respectively, along the AR7E line in the Irminger Sea (Fig.\ 1a), and (e) and (f) in the Melville Bay evaluation box (Fig.\ 1a). 
Triangles in (a), (c), (e) denotes the availability of observations, which are linearly interpolated in between except in (e) between 1991 and 1996. 

{\bf Figure 3.} Regional changes in subsurface ocean temperature from the 4-km ECCO2 simulation for the time period 1992--2009 minus an absolute offset of 0.4$^\circ$C. Left column is for off-the-shelf 
sites (triangle in Fig.\ 1a); right column is for on-the-shelf sites (diamond in Fig.\ 1a). The size of the three-dimensional boxes used to calculate annual-mean subsurface temperatures is listed in Table 2. 
Left vertical axis of the plots indicates anomalies in subsurface temperature in reference to the average over the entire time period, between -1.5 and +1.5$^\circ$C, with vertical bars colored in red for 
positive anomalies and blue for negative anomalies. Right vertical axis in black is absolute subsurface temperature, with a scale that varies from site to site but not between on-the-shelf and off-the-shelf, 
except for K$_O$ and K$_S$.  Absolute temperature and anomaly calculations are insensitive to the particular trough or off shelf location near each region ($\pm$ 0.2$^\circ$C) but are somewhat sensitive to 
the depth range (shelf) and offshore extent (off shelf) over which the calculation is made.  Hence, both on and off-shelf averaging volumes use the same depth range - chosen to be below the seasonal 
mixed layer and above on-the-shelf waters without significant temporal variability.  The off-shelf volumes span the IW component of the boundary current where possible or comparably-sized regions 
off the shelf where not (P$_\textrm{s}$).
\end{document}