Modelling the effect of submarine iceberg melting on glacier-adjacent 1 water properties 2

12 The rate of ocean-driven retreat of Greenland’s tidewater glaciers remains highly uncertain in 13 predictions of future sea level rise, in part due to poorly constrained glacier-adjacent water properties. 14 Icebergs and their meltwater contributions are likely important modifiers of fjord water properties, yet 15 their effect is poorly understood. Here, we use a 3-D ocean circulation model, coupled to a submarine 16 iceberg melt module, to investigate the effect of submarine iceberg melting on glacier-adjacent water 17 properties in a range of idealised settings. Submarine iceberg melting can modify glacier-adjacent water 18 properties in three principleprincipal ways: (1) substantial cooling and modest freshening in the upper 19 ~50 m of the water column; (2) warming of Polar Water at intermediate depths due to iceberg melt- 20 induced upwelling of warm Atlantic Water, and; (3) warming of the deeper Atlantic Water layer when 21 vertical temperature gradients through this layer are steep (due to vertical mixing of warm water at 22 depth), but cooling of the Atlantic Water layer when vertical temperature gradients are shallow. The 23 overall effect of iceberg melt is to make glacier-adjacent water properties more uniform with depth. 24 When icebergs extend to, or below, the depth of a sill at the fjord mouth, they can cause cooling 25 throughout the entire water column. All of these effects are more pronounced in fjords with higher 26 iceberg concentrations and deeper iceberg keel depths. These iceberg melt-induced changes to glacier-


Introduction 34
Predicting the rates of ocean-driven retreat of Greenland's tidewater glaciers remains one of the largest 35 uncertainties in estimating future sea level rise (Edwards et al., 2021;Meredith et al., 2020). This 36 uncertainty is partly due to limited constraints on the ocean-driven thermal forcing of tidewater glacier 37 calving fronts, which reflects in part the difficulty in obtaining hydrographic observations in the 38 proximity of tidewater glacier termini (Jackson et al., 2017(Jackson et al., , 2020Sutherland et al., 2019). The few 39 observations of water properties in the inner part of glacial fjords demonstrate that there are typically 40 substantial differences between glacier-adjacent water properties and those near the fjord mouth (e.g. glacier-adjacent water properties will also vary both spatially (i.e. between fjords) and temporally. This 75 variability likely results in different thermal forcing of tidewater glaciers for a given set of far-field 76 ocean conditions. Constraining the effect of icebergs on glacier-adjacent water properties, and thus 77 glacier submarine melt rates, is therefore a necessary step in order to improve projections of ice sheet 78 mass loss. 79 Here, we use an ocean circulation model in a series of idealised fjord-scale simulations to examine how 80 icebergs affect glacier-adjacent water properties across a range of Greenland-relevant scenarios. We 81 first consider how iceberg concentration, keel depth and size-frequency distribution individually affect 82 glacier-adjacent water properties. We then consider a range of representative iceberg and ocean 83 scenarios, to examine how these parameters interact to determine water properties in the critical region 84 adjacent to tidewater glacier termini. Greenland's fjords are complex and varied in their geometry, 85 ranging from short, narrow inlets to those that are long and wide, each with varying sinuosity and 86 bathymetry, and often with several tributaries and sills of varying depth along their length. It would be 87 impractical to attempt to characterise all of these systems. Therefore, we focus here on two simple fjord 88 geometries: one with no sills and another with a single entrance sill, which we expect to be of particular 89 importance for iceberg-ocean interaction given the capacity of sills to concentrate fjord-shelf water   properties (here defined as the average properties of the water within 2 km of the ice wall; Fig. 1a) in 189 two main ways. Firstly, they cause substantial (6-7.5°C) cooling in the upper ~60 m of the water column, 190 relative to the initial conditions ( Fig. 3a-c). The amount of cooling in this near-surface layer depends 191 somewhat on iceberg concentration, with steady-state water temperature varying between ~-1.5°C and 192 ~0°C over the range of iceberg concentrations considered, but is otherwise relatively insensitive to 193 changing iceberg geometry and distribution (Fig. 3a-c). Secondly, warming of up to ~1°C occurs below 194 ~80 m because iceberg melting causes localised freshening at depth. The resulting iceberg melt-195 modified water (i.e. the mixture of iceberg freshwater and ambient water at depth) is less dense than the 196 surrounding water and rises buoyantly towards the fjord surface. The vertical extent and magnitude of 197 the resulting warming generally increase with maximum iceberg keel depth (Fig. 3b), because icebergs 198 with deeper keels cause upwelling of deeper AW (which in this case is also warmer (Fig. 1b)). This 199 warming effect does not extend to the fjord surface, because the stronger stratification near the surface 200 limits upwelling and because iceberg-ocean contact areas are much greater near the surface, so cooling 201 due to localised iceberg melting dominates. When subglacial discharge is included, the effect of iceberg 202 melt on glacier-adjacent water properties at depth (below 60 m) is similar to that in simulations without 203 subglacial discharge, but glacier-adjacent water temperatures in the upper ~60 m of the water column 204 display a greater range and the cooling of the near-surface waters is considerably reduced (Fig. 3d-f). 205 This is because the runoffsubglacial discharge causes strong upwelling of AW towards the fjord surface 206 and increases rates of fjord-shelf exchange, which counters some of the iceberg-induced cooling of 207 near-surface waters. 208  Table 1), ranging from a fjord with low iceberg concentration, shallow iceberg keels 217 and fairly uniform iceberg sizes (iceberg scenario one), to a fjord with high iceberg concentration, deep 218 iceberg keels and a large range of iceberg sizes (iceberg scenario five). For each of these scenarios, we 219 examine steady-state glacier-adjacent water temperature for a range of ocean boundary conditions, and 220 with and without a shallow (100 m) sill. We therefore consider three different PW and AW temperatures 221   Table 1). However, in 231 iceberg scenarios three to five, the PW layer is increasingly modified (Fig.s 4c-e). With PWcool, 232 icebergs in these scenarios cause on average a net warming of 1.02°C in the 80-200 m depth range, 233 compared to simulations without icebergs. Conversely, with PWwarm, the icebergs cause a net cooling 234 of 0.30°C over the same depth range, such that the steady-state temperature profiles for both sets of 235 initial conditions (PWcool and PWwarm) are similar. With BCstandard, the influence of icebergs on warming ( Fig. 4c-e). These changes arise due to differing balances between cooling due to iceberg 238 melting, and warming due to buoyancy-induced upwelling of relatively warm AW water. With PWcool 239 there is relatively little iceberg melting in the PW layer (because the PW is close to the in-situ freezing 240 point), and so warming due to upwelling of AW dominates (driven by iceberg melting at greater depth 241 in the warmer AW layer). In contrast, with PWwarm, iceberg melt rates in the PW layer are 242 comparatively high, and the temperature difference between the PW and AW layers is reduced, so 243 localised cooling offsets warming due to turbulent upwelling. In short, under the conditions represented 244 by these simulations, submarine iceberg melting acts to make glacier-adjacent water temperature more 245 uniform with depth ( Fig. 4c-e). 246 The addition of a 100 m deep sill near the fjord mouth serves to amplify the cooling effect of icebergs 247 ( Fig. 4f-j). Sills typically block external shelf waters below the sill depth from entering the fjord (unless 248 external forcing causes a shallowing of isopycnals seaward of the sill), causing the fjord basin bounded 249 by the sill to be replenished by waters sourced only from above the sill depth (e.g. Jakobsson et al., 250 2020). When icebergs reach down to the sill depth, all water entering the fjord may thus be subject to 251 melt-driven cooling. The result is that icebergs cause cooling throughout the water column, even below 252 the deepest iceberg keels and below the sill depth ( Fig. 4f-j). This cooling is increasingly pronounced 253 as the PW temperature increases and with more concentrated and deeper icebergs ( Fig. 4f-j). For  waters below 100 m, even in the presence of a sill (Fig. 5b). This is because the icebergs do not extend 268 to the sill water depth and so there is some unmodified exchange between the fjord and shelf. In iceberg 269 scenario five, icebergs cause on average 0.19°C warming of waters below 100 m when there is no sill, 270 and cooling of 0.61°C below 100 m when there is a sill (Fig. 5b). This cooling below the maximum 271 iceberg draught occurs in all iceberg scenarios in which icebergs extend to sill depth, but is most 272 apparent in the higher iceberg concentration scenarios (e.g. Fig. 5d). The simulated changes in water 273 properties arise due the combined effects of local iceberg melting and fjord circulation. Submarine 274 iceberg melting reduces the density of surrounding waters, causing upwelling until those waters 275 equilibrate at a new neutral buoyancy depth with respect to the fjord stratification. Within the 276 temperature-salinity space of Greenland's fjords, density is predominantly salinity controlled. 277 Therefore, the salinity stratification is little changed by iceberg melting, whilst the temperature changes 278 are much more pronounced. This means that the iceberg melt-induced migrations through temperature-279 salinity space that are often steeper than predicted by the submarine melt mixing line (Gade, 1979). 280 281

Changing Atlantic Water temperature 282
We also examine the interactions between iceberg scenarios and changes to AW temperature (Fig. 6). 283 As in the PW scenarios, there is always marked cooling in the upper ~60 m of the water column and 284 water modification below this is minimal for iceberg scenarios one and two. In iceberg scenarios three 285 to five, icebergs penetrate to a greater depth and thus into the AW layer, releasing freshwater which 286 causes upwelling of AW. In these cases, the net effect of icebergs on water properties between ~80 m 287 and the maximum iceberg keel depth depends on the balance between cooling due to localised iceberg 288 melting, and warming due to upwelling of AW. With AWwarm, there is a steep temperature gradient 289 between the cold PW and warmer AW layers. Consequently, upwelling of AW causes notable warming 290 in the PW layer that offsets localised iceberg-induced cooling. In the scenarios with greater iceberg 291 concentration (e.g. iceberg scenario five; Fig. 6e), the icebergs penetrate deeper into the AW layer and 292 so can induce upwelling of the deeper, warmer water, resulting in more warming and over a greater 293 depth range than in the lower iceberg concentration scenarios. However, with AWcool, the vertical 294 temperature gradient is reduced, so cooling due to localised iceberg melting dominates the signal 295 between the maximum iceberg draught and ~80 m. 296 This dependence of iceberg modification of glacier-adjacent water properties on the temperature 297 gradient through the AW layer is further illustrated by sensitivity tests in which the temperature of the 298 AW layer was modified in two ways relative to BCstandard. First, to examine whether the absolute 299 temperature of the water column affected the balance between upwelling and melting, the entire water 300 column was uniformly warmed by 1°C. With this uniform shift in temperature, the pattern of 301 temperature with depth is similar to that of BCstandard (compare dashed grey and red lines in Fig. 7b), illustrating that the additional upwelling-driven warming with AWwarm is due to the steeper 303 temperature gradient between the PW and AW layers, rather than the absolute temperature of the AW. 304 Secondly, to illustrate the importance of the temperature gradient within the AW layer, we made the 305 AW layer uniformly 3.5°C. With this set of boundary conditions, upwelling-driven warming dominates 306 in the PW layer, because of upwelling of warm AW, whilst melt-driven cooling dominates in the AW 307 layer because upwelling-driven warming is muted (Fig. 7c). Thus, the average warming below ~80 m 308 that we simulate with AWwarm is strongly sensitive to the vertical temperature gradient, and not only 309 the average or maximum temperature of the AW.

Comparison with observations and applicability to real fjords 317
Our simulations suggest that several changes to glacier-adjacent water properties can occur due to 318 submarine iceberg melting. In almost all simulations, we simulate pronounced (>2°C) cooling in the 319 upper several tens of metres of the water column. Deeper in the water column (between ~80 m and the 320 maximum iceberg keel depth), both iceberg-induced cooling and warming can occur (e.g. Fig. 4 and 6), 321 depending on the balance between cooling due local iceberg melting and warming due to melt-driven 322 upwelling. The balance between these processes depends on the iceberg contact area at depth available 323 for local melting (and therefore cooling) and on the temperature of the upwelling water. When vertical 324 temperature gradients are steep (e.g. with AWwarm; Fig. 6), icebergs can cause warming between their 325 Figure 6. Steady-state glacier-adjacent water temperature for a range of initial Atlantic Water conditions and with a flat-bottomed domain. In all plots, solid and dashed lines indicate simulations with and without icebergs, respectively. Grey, blue and red lines show scenarios using the BCstandard, AWcool and AWwarm boundary conditions, respectively (shown in Figure 1f). The horizontal grey lines indicate the maximum iceberg keel depth in each scenario. maximum keel depth and the surface layer. This is particularly apparent in the PW layer, where the 326 temperature difference between an upwelled parcel of water and that at the parcel's new neutral 327 buoyancy depth in the PW layer is greatest, and where iceberg melt rates (and therefore melt-driven 328 cooling) are generally smaller because of the low water temperatures. In contrast, when vertical 329 temperature gradients are shallower (e.g. with AWcool), cooling due to localised melting dominates 330 (blue lines in Fig. 7d6d,e and 7c). These effects tend to reduce vertical temperature variations of glacier-331 adjacent waters compared both to simulations without icebergs and compared to conditions at the fjord 332

mouth. 333
Detailed near-glacier hydrographic observations against which to make comparisons are sparse, but 334 those that do exist provide some useful insight into the applicability of our model results to Greenland's 335 fjords. The pronounced surface and near-surface cooling (relative to conditions at the mouth) that we 336 simulate is a common feature in Greenland's fjords. For example, a transect of conductivity,  Iceberg-induced changes to water properties below ~80 m are harder to identify in hydrographic 345 observations, most likely because they also contain the signature of glacial-plumes resulting from 346 subglacial discharge, or other external forcings. Our modelling suggests that, if vertical temperature 347 inIn keeping with our simulation design, we selected pairs of CTD casts acquired less than a week apart, 358 one near or outside the fjord mouth and the other as close as possible to the tidewater glacier at the head 359 of the fjord. These profiles (Fig. 8) show many of the characteristics that we have simulated here. 360 Specifically, the profiles show that near-surface water temperatures are substantially colder adjacent to 361 tidewater glaciers compared to those observed outside each fjord, and the observed temperature 362 simulations. Some of the profiles also show notable cooling at depth (e.g. Illulissat Isfjord, Fig. 8e), 372 which we are only able to reproduce in simulations including a shallow sill. (e.g. the red line in Fig. 4j). In our simulations, we have generally considered a glacier-fjord system in which the glacier face and 377 subglacial discharge interact with the entire water column, and with icebergs affecting a range of depths 378 between the surface and their keels, which is a coarse representation of many fjords in Greenland. In 379 many other fjords in Greenland, glacier grounding lines are shallower, such that the calving front and 380 subglacial discharge interact predominately with the surface and PW layers. Although our simulations 381 do not encompass this geometry, they still provide some insights into the potential effect of icebergs on 382 near-glacier conditions in these fjords. With this geometry, subglacial discharge is injected directly into 383 the PW layer. Therefore, plume outflow is relatively cool and we would expect, based the simulations 384 presented here, that iceberg-driven cooling of the surface layer to be significant (resembling Fig. 3a-c). 385 In addition, icebergs calved from such shallow glaciers would not be able to cause upwelling of warm 386 AW (as in our scenarios 1 and 2), and so we would not expect any iceberg melt-driven warming of the 387 melting, we first consider how iceberg-melt impacts subglacial runoffdischarge-driven plume dynamics 398 and then assess how the simulated temperature changes could affect melt rates across the parts of glacier 399 fronts that are not directly affected by runoffsubglacial discharge-driven plumes. 400 To examine the effect of icebergs on subglacial discharge plume-driven glacier submarine melting, we 401 evaluate plume properties for a single set of ocean boundary conditions (BCstandard; Fig. 1b-d) using 402 each of the five iceberg scenarios. We find that submarine iceberg melting has negligible influence on 403 plume vertical velocity and only modest influence on plume temperature, meaning plume-induced 404 glacier submarine melt rates appear relatively insensitive to the changes in temperature and salinity 405 induced by changes in iceberg geometry, concentration and size-frequency distribution (Fig. 9). 406 Although runoffsubglacial discharge-driven plume dynamics appear to be relatively insensitive to 407 iceberg-induced modification of glacier-adjacent water properties, submarine melting distal to glacial 408 plumes ('background melting' (e.g. Slater et al., 2018)) may be more directly affected. Qualitatively, 409 the iceberg-melt-induced changes to glacier-adjacent water properties presented above suggest that 410 iceberg melt will affect background glacier melt rates in three key ways: (1) at and near the fjord surface, 411 cooling will reduce background melt rates; (2) in the PW layer, background melting will usually 412 increase due to upwelling of warmer AW, and; (3) in the AW layer, iceberg melt-induced changes in 413 background melt rates are expected to be modest, with slight increases in fjords with steep vertical 414 temperature gradients, and slight decreases in other fjords (assuming icebergs penetrate into the AW 415 layer). These effects will be more pronounced in fjords with higher concentrations of larger (and thus 416 deeper keeled) icebergs. In some fjords, then, where icebergs cause cooling near the surface and 417 warming at depth, we expect icebergs will increase glacier undercutting through impacting submarine 418 melt rates, which may in turn influence the rate and mechanism of calving (Benn et   where the subscripts ib and nib indicate simulations with 'icebergs' and 'no icebergs', respectively, and 430 Tf is the in-situ freezing point, given by: 431 where λ1-3 are constants representing the freezing point slope (-0.0573 °C psu -1 ), offset (0.0832°C) and 433 depth (0.000761°C m -1 ), respectively. (Cowton et al., 2015). S is the local salinity (horizontally 434 averaged within 2 km of the terminus) and z is depth in the water column. It is worth noting that changes 435 in melt rate calculated using this method assume that all changes in heat supply are accommodated by 436 changes in submarine melt rates, and so this method provides an indication of the maximum relative 437 changes in submarine melt rates expected due to changes in ambient ocean temperature. 438 Using this approach, we find that the impact on water properties resulting from iceberg melt melting. In order to capture this near surface cooling, one relatively simple modification to such an 474 approach could be to reduce surface water temperature to close to the in-situ melting point during winter 475 periods, and proportionally to the iceberg surface area at the fjord surface during summer periods. 476 However, in fjords hosting icebergs with keel depth greater than or equal to 200 m and with average 477 concentrations of more than ~20% (i.e. our iceberg scenario three or higher), iceberg modification of 478 glacier-adjacent water properties becomes increasingly important. In such fjords that also exhibit 479 relatively shallow sills, icebergs act to cool glacier-adjacent water throughout the water column, with 480 the amount of cooling proportional to the draught and concentration of the icebergs, as well as to the 481 temperature of the ambient water at the fjord mouth (Fig. 4). In such fjords that do not have shallow 482 sills, the effect is more complicated, with both iceberg-melt-induced warming and cooling, depending

Transience vs steady-state 495
All of the results presented here were extracted from the final ten days of simulations that were run to 496 a quasi-steady state (i.e. the variable of interest had stabilised). In our domains without sills, steady-497 state of temperature and salinity was generally reached after just ten to thirty days. However, our 498 simulations with sills could take as many as one thousand days to reach such a steady state because Greenland drive fast shelf-forced flows (or intermediary currents) in glacial fjords, delivering coastal 509 waters to tidewater glaciers over just a period of a few days, and potentially reducing the magnitude of 510 iceberg-driven modification (Jackson et al., 2014(Jackson et al., , 2018. Such currents are strongest in winter, when 511 hydrographic observations are sparse, so this remains speculative. 512 513

Conclusions 514
We have used a general circulation model (MITgcm) to quantify the effect of submarine iceberg melting 515 on glacier-adjacent water properties in an idealised fjord domain. A large range of iceberg 516 concentrations, keel depths and size-frequency distributions were examined to represent the range of 517 iceberg conditions found in Greenland's marine terminating glacier fjords. We focused primarily on 518 iceberg-melt-induced changes to glacier-adjacent water temperatures throughout the water column, 519 because of their principal importance to glacier-submarine melting. 520 Our results suggest that icebergs can substantially modify glacier-adjacent water properties and that the 521 precise impact depends on iceberg size and on the temperature profile and stratification of water within is reduced by several degrees Celsius over a wide range of iceberg scenarios; (2) fjords with more and 524 deeper icebergs are subject to greater iceberg-melt-induced modification, which can result in either 525 cooling or warming at different depths depending on the balance between melt-driven cooling and 526 upwelling-driven warming, which in turn depends on fjord temperature stratification, and; (3) when 527 icebergs extend to or below the fjord mouth sill depth, they can cause significant cooling throughout 528 the water column. Particularly with regard to point (2), our results highlight that oceanic forcing of large 529 fast-flowing glaciers, which contribute the most to ice sheet dynamic mass loss, in existing projections 530 of tidewater glacier dynamics is strongly affected by ignoring the impact of icebergs on fjord water 531 properties. The iceberg-induced changes to the vertical temperature profile of glacier-adjacent waters 532 identified here are likely to reduce submarine melt rates at and near the fjord surface while increasing 533 them in the PW layer, which may influence the rate and mechanism of calving by exacerbating glacier 534 terminus undercutting. Our results therefore identify a critical need to develop simple parameterisations 535 of iceberg-induced modification of fjord waters, and other fjord-scale processes, to better constrain 536 oceanic forcing of tidewater glaciers. 537 538 539

Code availability 540
MITgcm is freely available at http://mitgcm.org/public/source_code.html. The IcePlume module is 541 available from Tom Cowton on request. The IceBerg module is available at 542 https://zenodo.org/record/3979647#.YWAayNrMKUk or from Benjamin Davison on request. 543 The authors declare that they have no conflict of interest. 556