Southern Ocean Stratification Research Articles

The Southern Ocean Freshwater Input from Antarctica (SOFIA) Initiative: scientific objectives and experimental design

Abstract. As the climate warms, the grounded ice sheet and floating ice shelves surrounding Antarctica are melting and releasing additional freshwater into the Southern Ocean. Nonetheless, almost all existing coupled climate models have fixed ice sheets and lack the physics required to represent the dominant sources of Antarctic melt. These missing ice dynamics represent a key uncertainty that is typically unaccounted for in current global climate change projections. Previous modelling studies that have imposed additional Antarctic meltwater have demonstrated regional impacts on Southern Ocean stratification, circulation, and sea ice, as well as remote changes in atmospheric circulation, tropical precipitation, and global temperature. However, these previous studies have used widely varying rates of freshwater forcing, have been conducted using different climate models and configurations, and have reached differing conclusions on the magnitude of meltwater–climate feedbacks. The Southern Ocean Freshwater Input from Antarctica (SOFIA) initiative brings together a team of scientists to quantify the climate system response to Antarctic meltwater input along with key aspects of the uncertainty. In this paper, we summarize the state of knowledge on meltwater discharge from the Antarctic ice sheet and ice shelves to the Southern Ocean and explain the scientific objectives of our initiative. We propose a series of coupled and ocean–sea ice model experiments, including idealized meltwater experiments, historical experiments with observationally consistent meltwater input, and future scenarios driven by meltwater inputs derived from stand-alone ice sheet models. Through coordinating a multi-model ensemble of simulations using a common experimental design, open data archiving, and facilitating scientific collaboration, SOFIA aims to move the community toward better constraining our understanding of the climate system response to Antarctic melt.

Sustained Deep Pacific Carbon Storage After the Mid‐Pleistocene Transition Linked to Enhanced Southern Ocean Stratification

AbstractChanges in ocean carbon inventory are considered the likely primary driver of declining glacial atmospheric pCO2 through the Mid‐Pleistocene Transition (MPT). Here, we present global core‐top calibrations of the “size‐normalized weight” (SNW) of planktonic foraminifera for estimating paleo‐deep‐water Δ[CO32−]. Then, we apply this approach to reconstruct deep‐water Δ[CO32−] in the western tropical Pacific since ∼1.4 Ma. At ∼1.0–0.9 Ma, a rapid weakening of North Atlantic Deep Water (NADW) resulted in a transient increase of ∼10 μmol kg−1 in deep‐water Δ[CO32−], after which deep‐water Δ[CO32−] declined at ∼0.9–0.7 Ma. Glacial and interglacial deep‐water Δ[CO32−] reveals stepwise declines of about 7 and 10 μmol kg−1, respectively, after MIS 20 (0.79–0.81 Ma) and MIS 19 (0.76–0.79 Ma), reflecting increased DIC content in the deep Pacific. We infer that a sustained increase in deep Pacific carbon storage following the MPT was linked to enhanced oceanic stratification and greater influence of CO2‐rich Southern Ocean‐sourced waters.

The southern amplifier.

Greater Southern Ocean stratification may have lowered the atmospheric CO 2 concentration and prolonged ice ages

Response of Atmospheric pCO2 to Glacial Changes in the Southern Ocean Amplified by Carbonate Compensation

AbstractAtmospheric carbon dioxide concentration (pCO2) varies by about 100ppm during glacial‐interglacial cycles. Previous studies suggest that the strongly stratified Southern Ocean at the Last Glacial Maximum increases the oceanic storage of carbon, but the glacial reduction of atmospheric pCO2 simulated by ocean general circulation models (OGCMs) does not reach 100ppm. One candidate for the underestimation is that carbonate compensation is not explicitly incorporated in the previous OGCM simulations. Therefore, we quantitatively evaluate the impact of carbonate compensation on the glacial atmospheric pCO2 by using an OGCM coupled with an ocean sediment model. As suggested by previous box model studies, our OGCM simulations show that the enhanced Southern Ocean stratification amplifies the decrease in atmospheric pCO2 due to carbonate compensation. Considering the enhanced stratification in the Southern Ocean, we obtain a 26‐ppm drawdown of atmospheric pCO2 by carbonate compensation, and the full reduction from our pre‐industrial simulation reaches 73ppm. Both the increase in ventilation ages in the deep Atlantic and Southern Oceans and the growth of export production in the subantarctic region reduce the bottom‐water carbonate ion and promote deposited carbonate dissolution. Consequently, a greater imbalance between the river inflow and burial loss of carbonate rises ocean alkalinity, lowering atmospheric pCO2. We suggest that the reproducibility of the Southern Ocean process is essential for controlling the magnitude of atmospheric pCO2 decline due to carbonate compensation.

Breakup of last glacial deep stratification in the South Pacific.

Stratification of the deep Southern Ocean during the Last Glacial Maximum is thought to have facilitated carbon storage and subsequent release during the deglaciation as stratification broke down, contributing to atmospheric CO2 rise. Here, we present neodymium isotope evidence from deep to abyssal waters in the South Pacific that confirms stratification of the deepwater column during the Last Glacial Maximum. The results indicate a glacial northward expansion of Ross Sea Bottom Water and a Southern Hemisphere climate trigger for the deglacial breakup of deep stratification. It highlights the important role of abyssal waters in sustaining a deep glacial carbon reservoir and Southern Hemisphere climate change as a prerequisite for the destabilization of the water column and hence the deglacial release of sequestered CO2 through upwelling.

Late Quaternary Deep Stratification‐Climate Coupling in the Southern Ocean: Implications for Changes in Abyssal Carbon Storage

AbstractThe Southern Ocean plays an important role in modulating Pleistocene atmospheric CO2 concentrations, but the underlying mechanisms are not yet fully understood. Here, we report the laser grain‐size distribution and Mn geochemical data of a 523 kyr‐long sediment record (core ANT30/P1‐02 off Prydz Bay; East Antarctica) to trace past physical changes in the deep Southern Ocean. The core sediments are predominantly composed of clay and silt‐sized material. Three grain size end‐members (EM) as well as three sensitive grain size classes (SC) were discerned, interpreted as Ice Rafted Debris (EM1 and SC1), and coarse (EM2 and SC2) and fine (EM3, SC3) materials deposited from bottom nepheloid layers, respectively. Ratios of EM2/(EM2 + EM3) and SC2/SC3 reveal changes in the local bottom current strength, which is related to the deep ocean diapycnal mixing rate, showing higher values during interglacial periods and lower values during glacial periods. MnO was enriched at each glacial termination, probably caused by abrupt elevations in Antarctic bottom water (AABW) formation rate. Lower AABW formation rate and reduced deep diapycnal mixing during glacial periods enhanced deep Southern Ocean stratification, contributing to glacial atmospheric CO2 drawdown. The elevated AABW formation and enhanced deep diapycnal mixing during glacial terminations alleviated such deep stratification, promoting deeply sequestered CO2 to outgas.

Contributions of Greenhouse Gas Forcing and the Southern Annular Mode to Historical Southern Ocean Surface Temperature Trends

AbstractWe examine the 1979–2014 Southern Ocean (SO) sea surface temperature (SST) trends simulated in an ensemble of coupled general circulation models and evaluate possible causes of the models' inability to reproduce the observed 1979–2014 SO cooling. For each model we estimate the response of SO SST to step changes in greenhouse gas (GHG) forcing and in the seasonal indices of the Southern Annular Mode (SAM). Using these step‐response functions, we skillfully reconstruct the models' 1979–2014 SO SST trends. Consistent with the seasonal signature of the Antarctic ozone hole and the seasonality of SO stratification, the summer and fall SAM exert a large impact on the simulated SO SST trends. We further identify conditions that favor multidecadal SO cooling: (1) a weak SO warming response to GHG forcing, (2) a strong multidecadal SO cooling response to a positive SAM trend, and (3) a historical SAM trend as strong as in observations.

Enhanced weathering and CO2 drawdown caused by latest Eocene strengthening of the Atlantic meridional overturning circulation

On timescales significantly greater than 105 years, atmospheric pCO2 is controlled by the rate of mantle outgassing relative to the set-point of the silicate weathering feedback. The weathering set-point has been shown to depend on the distribution and characteristics of rocks exposed at the Earth’s surface, vegetation types and topography. Here we argue that large-scale climate impacts caused by changes in ocean circulation can also modify the weathering set-point and show evidence suggesting that this played a role in the establishment of the Antarctic ice sheet at the Eocene–Oligocene boundary. In our simulations, tectonic deepening of the Drake Passage causes freshening and stratification of the Southern Ocean, strengthening the Atlantic meridional overturning circulation and consequently raising temperatures and intensifying rainfall over land. These simulated changes are consistent with late Eocene tectonic reconstructions that show Drake Passage deepening, and with sediment records that reveal Southern Ocean stratification, the emergence of North Atlantic Deep Water, and a hemispherically asymmetric temperature change. These factors would have driven intensified silicate weathering and can thereby explain the drawdown of carbon dioxide that has been linked with Antarctic ice sheet growth. We suggest that this mechanism illustrates another way in which ocean–atmosphere climate dynamics can introduce nonlinear threshold behaviour through interaction with the geologic carbon cycle. During the latest Eocene, declining atmospheric CO2 levels led to the inception of the Antarctic ice sheet. Simulations suggest that the deepening of the Drake Passage caused climate changes that enhanced continental weathering and CO2 drawdown.

Antarctic density stratification and the strength of the circumpolar current during the Last Glacial Maximum

The interaction between ocean circulation and biological processes in the Southern Ocean is thought to be a major control on atmospheric carbon dioxide content over glacial cycles. A better understanding of stratification and circulation in the Southern Ocean during the Last Glacial Maximum (LGM) provides information that will help us to assess these scenarios. First, we evaluate the link between Southern Ocean stratification and circulation states in a suite of climate model simulations. While simulated Antarctic Circumpolar Current (ACC) transport varies widely (80–350 Sverdrup (Sv)), it co-varies with horizontal and vertical stratification and the formation of the southern deep water. We then test the LGM simulations against available data from paleoceanographic proxies, which can be used to assess the density stratification and ACC transport south of Australia. The paleoceanographic data suggest a moderate increase in the Southern Ocean stratification and the ACC strength during the LGM. Even with the relatively large uncertainty in the proxy-based estimates, extreme scenarios exhibited by some climate models with ACC transports of greater than 250 Sv and highly saline Antarctic Bottom Water are highly unlikely.

Role of Southern Ocean stratification in glacial atmospheric CO2 reduction evaluated by a three-dimensional ocean general circulation model

Atmospheric carbon dioxide (CO2) concentration during glacial periods is known to be considerably lower than during interglacial periods. However, previous studies using an ocean general circulation model (OGCM) fail to reproduce this. Paleoclimate proxy data of the Last Glacial Maximum indicate high salinity (>37.0 psu) and long water mass residence time (>3,000 years) in the Southern Ocean, suggesting that salinity stratification was enhanced and more carbon was stored there. Reproducibility of salinity and water mass age is considered insufficient in previous OGCMs, which might affect the reproducibility of atmospheric CO2 concentration. This study investigated the role of increased stratification of the Southern Ocean in the glacial CO2 variation using an OGCM. We found that deep water formation in East Antarctica is required to explain high salinity in the South Atlantic. Saltier deep Southern Ocean resulted in increased atmospheric CO2 concentration against previous estimates. This is partly due to increased volume transport of Antarctic Bottom Water and associated decrease in the water mass age of the deep Pacific Ocean. On the other hand, weakening of vertical mixing contributed to increase of the vertical gradient of dissolved inorganic carbon and decrease of atmospheric CO2 concentration. However, we show that it is unable to explain all of the glacial CO2 variations by the contribution of the Southern Ocean. Our findings indicate that detailed understanding of the impact of enhanced stratification in the Southern Ocean on the Pacific Ocean might be crucial to understanding the mechanisms behind the glacial-interglacial ocean carbon cycle variations.

The Last Glacial Maximum at 44°S documented by a 10Be moraine chronology at Lake Ohau, Southern Alps of New Zealand

Determining whether glaciers registered the classic Last Glacial Maximum (LGM; ∼26,500–∼19,000 yrs ago) coevally between the hemispheres can help to discriminate among hypothesized drivers of ice-age climate. Here, we present a record of glacier behavior from the Southern Alps of New Zealand during the ‘local LGM’ (LLGM). We used 10Be surface-exposure dating methods and detailed glacial geomorphologic mapping to produce a robust chronology of well-preserved terminal moraines deposited during the LLGM near Lake Ohau on central South Island. We then used a glaciological model to estimate a LLGM glacier snowline and atmospheric temperature from the Ohau glacier record.Seventy-three 10Be surface-exposure ages place culminations of terminal moraine construction, and hence completions of glacier advances to positions outboard of present-day Lake Ohau, at 138,600 ± 10,600 yrs, 32,520 ± 970 yrs ago, 27,400 ± 1300 yrs ago, 22,510 ± 660 yrs ago, and 18,220 ± 500 yrs ago. Recessional moraines document glacier recession into the Lake Ohau trough by 17,690 ± 350 yrs ago. Exposure of an ice-molded bedrock bench located inboard of the innermost LLGM moraines by 17,380 ± 510 yrs ago indicates that the ice tongue had receded about 40% of its overall length by that time. Comparing our chronology with distances of retreat suggests that the Ohau glacier terminus receded at a mean net rate of about 77 m yr−1 and its surface lowered by 200 m between 17,690 and 17,380 yrs ago. A long-term continuation of ice retreat in the Ohau glacier catchment is implied by moraine records at the head of Irishman Stream valley, a tributary of the Ohau glacier valley. The Irishman Stream cirque glacier advanced to produce a set of Lateglacial moraines at 13,000 ± 500 yrs ago, implying that the cirque glacier was less extensive prior to that advance.We employed a glaciological model, fit to these mapped and dated LLGM moraines, to derive snowline elevations and temperature parameters from the Ohau glacier record. The modeling experiments indicate that a snowline lowering of 920 ± 50 m and temperature depression of 6.25 ± 0.5 °C below modern values allows for the Ohau glacier to grow to an equilibrium position within the LGM moraine belt. Taken together with a glaciological simulation reported from the Irishman Stream valley, snowlines and temperatures increased by at least ∼520 m and ∼3.6 °C, respectively, between ∼18,000 and ∼13,000 yrs ago.Climate parameters derived from the Ohau glacier reconstruction are similar to those derived from glacier records from Patagonia, to air temperature indicators from Antarctica, as well as to sea-surface temperature and stratification signatures of the Southern Ocean. We think that the best explanation for the observed southern LLGM is that southern winter duration modulated Southern Ocean sea ice, which in turn influenced Southern Ocean stratification and made the surface ocean cooler. Orbitally induced cooling of the Southern Ocean provides an explanation for the LLGM in the Southern Alps having been coincident with the northern LGM. We argue further that the global effect of North Atlantic stadials led to disturbance of Southern Ocean stratification, southward shifts of the subtropical front, and retreat of Southern Alps glaciers. Collapse of Southern Ocean stratification during Heinrich Stadial-1, along with attendant sea-surface warming, triggered the onset of the Last Glacial termination in the Southern Alps of New Zealand.

Human influence on extratropical Southern Hemisphere summer precipitation

Observations of extratropical Southern Hemisphere austral summer precipitation over recent decades show mid‐latitude drying and high‐latitude moistening. Here we show that the observed precipitation trends in two datasets are inconsistent with simulated internal variability, but are closely consistent with trends simulated in response to historical changes in anthropogenic and natural forcings. Simulations with individual anthropogenic and natural forcings suggest that the observed pattern of precipitation change is substantially forced by anthropogenic greenhouse gas and ozone changes, with an opposing influence from aerosols. Our results demonstrate that human influence had a significant impact on precipitation across the mid and high latitudes of the Southern Hemisphere, changes which are expected to have a profound impact on Southern Ocean stratification and hence on ocean‐atmosphere heat and carbon fluxes.

Glacial Southern Ocean freshening at the onset of the Middle Pleistocene Climate Transition

Changes in Southern Ocean hydrography may have played an important role in the Middle Pleistocene Transition (MPT), particularly through their impact on ocean circulation and atmospheric CO2 concentrations. Here we present foraminiferal Mg/Ca and δ18O results for the subsurface dwelling planktonic foraminifer Neogloboquadrina pachyderma (sinistral) at the Ocean Drilling Program (ODP) Site 1090. Results are used to reconstruct upper ocean temperatures and derive seawater δ18O in the Subantarctic Atlantic Ocean during the MPT. The new records indicate that, starting at ∼1250ka, glacial temperatures and local (ice volume corrected) seawater δ18O in the upper water column of the Subantarctic Atlantic Ocean decreased, pointing to cooler (∼2°C) and fresher (∼0.4‰) conditions than in the preceding glacial stages. These upper ocean hydrographic changes broadly coincide with the increase in the power of the 100ky glacial–interglacial cycle in both records and with a shift towards decreased deep ventilation in the glacial Southern Ocean. Our finding suggests that an increase in Southern Ocean stratification, driven by the observed freshening of the upper water column, may have reduced the exchange of carbon between the deep Southern Ocean and the atmosphere during glacial stages. This process may have contributed, in combination with other mechanisms, to lower glacial atmospheric CO2 concentrations during the MPT.

Deep ocean ventilation, carbon isotopes, marine sedimentation and the deglacial CO<sub>2</sub> rise

Abstract. The link between the atmospheric CO2 level and the ventilation state of the deep ocean is an important building block of the key hypotheses put forth to explain glacial-interglacial CO2 fluctuations. In this study, we systematically examine the sensitivity of atmospheric CO2 and its carbon isotope composition to changes in deep ocean ventilation, the ocean carbon pumps, and sediment formation in a global 3-D ocean-sediment carbon cycle model. Our results provide support for the hypothesis that a break up of Southern Ocean stratification and invigorated deep ocean ventilation were the dominant drivers for the early deglacial CO2 rise of ~35 ppm between the Last Glacial Maximum and 14.6 ka BP. Another rise of 10 ppm until the end of the Holocene is attributed to carbonate compensation responding to the early deglacial change in ocean circulation. Our reasoning is based on a multi-proxy analysis which indicates that an acceleration of deep ocean ventilation during early deglaciation is not only consistent with recorded atmospheric CO2 but also with the reconstructed opal sedimentation peak in the Southern Ocean at around 16 ka BP, the record of atmospheric δ13CCO2, and the reconstructed changes in the Pacific CaCO3 saturation horizon.

Glacial greenhouse-gas fluctuations controlled by ocean circulation changes

Earth's climate and the concentrations of the atmospheric greenhouse gases carbon dioxide (CO(2)) and nitrous oxide (N(2)O) varied strongly on millennial timescales during past glacial periods. Large and rapid warming events in Greenland and the North Atlantic were followed by more gradual cooling, and are highly correlated with fluctuations of N(2)O as recorded in ice cores. Antarctic temperature variations, on the other hand, were smaller and more gradual, showed warming during the Greenland cold phase and cooling while the North Atlantic was warm, and were highly correlated with fluctuations in CO(2). Abrupt changes in the Atlantic meridional overturning circulation (AMOC) have often been invoked to explain the physical characteristics of these Dansgaard-Oeschger climate oscillations, but the mechanisms for the greenhouse-gas variations and their linkage to the AMOC have remained unclear. Here we present simulations with a coupled model of glacial climate and biogeochemical cycles, forced only with changes in the AMOC. The model simultaneously reproduces characteristic features of the Dansgaard-Oeschger temperature, as well as CO(2) and N(2)O fluctuations. Despite significant changes in the land carbon inventory, CO(2) variations on millennial timescales are dominated by slow changes in the deep ocean inventory of biologically sequestered carbon and are correlated with Antarctic temperature and Southern Ocean stratification. In contrast, N(2)O co-varies more rapidly with Greenland temperatures owing to fast adjustments of the thermocline oxygen budget. These results suggest that ocean circulation changes were the primary mechanism that drove glacial CO(2) and N(2)O fluctuations on millennial timescales.

Quantitative interpretation of atmospheric carbon records over the last glacial termination

The glacial/interglacial rise in atmospheric pCO2 is one of the best known changes in paleoclimate research, yet the cause for it is still unknown. Forcing the coupled ocean‐atmosphere‐biosphere box model of the global carbon cycle BICYCLE with proxy data over the last glacial termination, we are able to quantitatively reproduce transient variations in pCO2 and its isotopic signatures (δ13C, Δ14C) observed in natural climate archives. The sensitivity of the Box model of the Isotopic Carbon cYCLE (BICYCLE) to high or low latitudinal changes is comparable to other multibox models or more complex ocean carbon cycle models, respectively. The processes considered here ranked by their contribution to the glacial/interglacial rise in pCO2 in decreasing order are: the rise in Southern Ocean vertical mixing rates (>30 ppmv), decreases in alkalinity and carbon inventories (>30 ppmv), the reduction of the biological pump (∼20 ppmv), the rise in ocean temperatures (15–20 ppmv), the resumption of ocean circulation (15–20 ppmv), and coral reef growth (<5 ppmv). The regrowth of the terrestrial biosphere, sea level rise and the increase in gas exchange through reduced sea ice cover operate in the opposite direction, decreasing pCO2 during Termination I by ∼30 ppmv. According to our model the sequence of events during Termination I might have been the following: a reduction of aeolian iron fertilization in the Southern Ocean together with a breakdown in Southern Ocean stratification, the latter caused by rapid sea ice retreat, trigger the onset of the pCO2 increase. After these events the reduced North Atlantic Deep Water (NADW) formation during the Heinrich 1 event and the subsequent resumption of ocean circulation at the beginning of the Bølling‐Allerød warm interval are the main processes determining the atmospheric carbon records in the subsequent time period of Termination I. We further deduce that a complete shutdown of the NADW formation during the Younger Dryas was very unlikely. Changes in ocean temperature and the terrestrial carbon storage are the dominant processes explaining atmospheric δ13C after the Bølling‐Allerød warm interval.

On the response of Southern Ocean water‐masses to atmospheric meridional moisture advection

We investigate the role of atmospheric moisture advection in determining Southern Ocean water‐mass properties in a coupled climate model. Two sensitivity experiments are presented in which the winds advecting moisture are either reduced or enhanced south of 45°S. It is shown that a variation in meridional winds in the Southern Ocean can generate large anomalies of subsurface potential temperature (T) and salinity (S). A reduction (increase) in southward atmospheric moisture advection tends to be balanced by a corresponding reduction (increase) in northward freshwater transport in Antarctic Intermediate Water. The response of both T and S is larger in the case of reduced southward moisture advection, as this corresponds to an overall reduction of Southern Ocean stratification. The interior ocean T–S response is not always density‐compensating, particularly in the Indian and Pacific Oceans. This is unlike zonal wind variations which have a tendency to change T–S in a density‐conserving manner. Our study suggests that variability in meridional winds over the Southern Ocean can alter local water‐mass formation rates significantly.

Model sensitivity in the effect of Antarctic sea ice and stratification on atmospheric pCO2

Several recent papers have demonstrated a decrease in atmospheric pCO2 resulting from barriers to communication between the deep sea and the atmosphere in the Southern Ocean. Stephens and Keeling [2000] decreased pCO2 by increasing Antarctic sea ice in a seven‐box model of the world ocean, and Toggweiler [1999] showed a similar response to Southern Ocean stratification. In box models the pCO2 of the atmosphere is controlled by the region of the surface ocean that fills the deep sea [Archer et al., 2000a]. By severing the Southern Ocean link between the deep sea and the atmosphere, atmospheric pCO2 in these models is controlled elsewhere and typically declines, although the models range widely in their responses. “Continuum models,” such as three‐dimensional (3‐D) and 2‐D general circulation models, control pCO2 in a more distributed way and do not exhibit box model sensitivity to high‐latitude sea ice or presumably stratification. There is still uncertainty about the high‐latitude sensitivity of the real ocean. Until these model sensitivities can be resolved, glacial pCO2 hypotheses and interpretations based on Southern Ocean barrier mechanisms (see above mentioned references plus Elderfield and Rickaby [2000], Francois et al. [1998], Gildor and Tziperman [2001], Sigman and Boyle [2000], and Watson et al. [2000]) are walking on thin ice.

Sensitivity of the Antarctic sea ice to the thermal conductivity of snow

The sensitivity of a global, coarse‐resolution ice‐ocean model to a decrease in the thermal conductivity of the snow overlaying Antarctic sea ice (ksant) is investigated. This study was motivated by recent observations made in the eastern sector of the Southern Ocean and in the Bellingshausen, Amundsen, and Ross Seas, which suggest that the value of ksant usually used in large‐scale sea ice models is about a factor two too high. When ksant is reduced by half in our model, the average thickness of the Antarctic ice pack decreases by 10 cm (10%) and the geographical distributions of snow and ice thicknesses become more realistic. A strengthening of the Southern Ocean stratification and a concomitant weakening of the Antarctic Bottom Water meridional overturning are also noticed. This ultimately impacts on the sensible heat flux from the ocean to the ice and thus on the rate of thermodynamic ice growth.