Melting Of Ice Sheets Research Articles

An expert judgement assessment of future sea level rise from the ice sheets

This study uses a formalized pooling of expert views on uncertainties in the future contributions of melting ice sheets to sea-level rise, using a structured elicitation approach. The median estimate obtained is substantially larger than that found by previous studies. Expert opinion is shown to be both very uncertain and undecided on the key issue of whether recent ice-sheet behaviour is a long-term trend or due to natural variability.

Land water contribution to sea level from GRACE and Jason‐1measurements

AbstractWe investigate the effect of water storage changes in the world's major hydrological catchment basins on global and regional sea level change at seasonal and long‐term time scales. In a joint inversion using GRACE and Jason‐1 data, we estimate the time‐dependent sea level contributions of 124 spatial patterns (“fingerprints”) including glacier and ice sheet melting, thermal expansion, changes in the terrestrial hydrological cycle, and glacial isostatic adjustment. Particularly, for hydrological storage changes, we derive fingerprints of the 33 world's largest catchment basins, assuming mass distributions derived from the leading EOFs of total water storage in the WaterGap Global Hydrological Model (WGHM). From our inversion, we estimate a contribution of terrestrial hydrological cycle changes to global mean sea level of − 0.20 ± 0.04 mm/yr with an annual amplitude of 6.6 ± 0.5 mm for August 2002 to July 2009. Using only GRACE data in the inversion and comparing to hydrological changes derived from GRACE data directly using a basin averaging method shows a good agreement on a global scale, but considerable differences are found for individual catchment basins (up to 180%). Hydrological storage change estimates in 33 basins from the GRACE/Jason fingerprint inversion indicate a trend 46% smaller and an annual amplitude 43% bigger compared to WGHM‐derived storage changes. Mapping the hydrological trends to regional sea level reveals the strongest sea level rise along the coastlines of South America (max 0.9 mm/yr) and West Africa (max 0.4 mm/yr), whereas around Alaska and Australia, we find the hydrological component of sea level falling (min −2.0 mm/yr and −0.9 mm/yr).

Geochemical Monitoring for Potential Environmental Impacts of Geologic Sequestration of CO2

Carbon dioxide sequestration is now considered an important component of the portfolio of options for reducing greenhouse gas emissions to stabilize their atmospheric levels at values that would limit global temperature increases to the target of 2 °C by the end of the century (Pacala and Socolow 2004; IPCC 2005, 2007; Benson and Cook 2005; Benson and Cole 2008; IEA 2012; Romanak et al. 2013). Increased anthropogenic emissions of CO2 have raised its atmospheric concentrations from about 280 ppmv during pre-industrial times to ~400 ppmv today, and based on several defined scenarios, CO2 concentrations are projected to increase to values as high as 1100 ppmv by 2100 (White et al. 2003; IPCC 2005, 2007; EIA 2012; Global CCS Institute 2012). An atmospheric CO2 concentration of 450 ppmv is generally the accepted level that is needed to limit global temperature increases to the target of 2 °C by the end of the century. This temperature limit likely would moderate the adverse effects related to climate change that could include sea-level rise from the melting of alpine glaciers and continental ice sheets and from the ocean warming; increased frequency and intensity of wildfires, floods, droughts, and tropical storms; and changes in the amount, timing, and distribution of rain, snow, and runoff (IPCC 2007; Sundquist et al. 2009; IEA 2012). Rising atmospheric CO2 concentrations are also increasing the amount of CO2 dissolved in ocean water lowering its pH from 8.1 to 8.0, with potentially disruptive effects on coral reefs, plankton and marine ecosystems (Adams and Caldeira 2008; Schrag 2009; Sundquist et al. 2009). Sedimentary basins in general and deep saline aquifers in particular are being investigated as possible repositories for the large volumes of …

An Overlooked Term in Assessment of the Potential Sea-Level Rise from a Collapse of the West Antarctic Ice Sheet

As to sea level rise (SLR) contribution, melting and setting afloat make no difference for land based ice. Melting of West Antarctic Ice Sheet (WAIS) into water is impossible in the upcoming several centuries, whereas breaking and partially afloat is likely as long as sea waters find a pathway to the bottom of those ice sectors with basal elevation below sea level. In this sense WAIS may be disintegrated in a future warming climate. We reassess the potential contribution to eustatic sea level from a collapse of WAIS and find that previous assessments have overlooked a contributor: slope instability after the cementing ice is removed. Over loading ice has a buttressing effect on slope movements the same way ice shelves hinder the flow of non-floating coastal ice. A sophisticated landslide model estimates a 9-mm eustatic SLR contribution from subsequent landslides.

Central West Antarctica among the most rapidly warming regions on Earth

There is clear evidence that the West Antarctic Ice Sheet is contributing to sea-level rise. In contrast, West Antarctic temperature changes in recent decades remain uncertain. West Antarctica has probably warmed since the 1950s, but there is disagreement regarding the magnitude, seasonality and spatial extent of this warming. This is primarily because long-term near-surface temperature observations are restricted to Byrd Station in central West Antarctica, a data set with substantial gaps. Here, we present a complete temperature record for Byrd Station, in which observations have been corrected, and gaps have been filled using global reanalysis data and spatial interpolation. The record reveals a linear increase in annual temperature between 1958 and 2010 by 2.4±1.2 °C, establishing central West Antarctica as one of the fastest-warming regions globally. We confirm previous reports of West Antarctic warming, in annual average and in austral spring and winter, but find substantially larger temperature increases. In contrast to previous studies, we report statistically significant warming during austral summer, particularly in December–January, the peak of the melting season. A continued rise in summer temperatures could lead to more frequent and extensive episodes of surface melting of the West Antarctic Ice Sheet. These results argue for a robust long-term meteorological observation network in the region. The West Antarctic Ice Sheet is contributing to sea-level rise, but temperature trends in the region have remained uncertain. A complete temperature record for Byrd Station in central West Antarctica, spanning from 1958 to 2010, establishes West Antarctica as one of the fastest-warming regions globally.

Constraining Wind Stress Products with Sea Surface Height Observations and Implications for Pacific Ocean Sea Level Trend Attribution*

Abstract A number of global surface wind datasets are available that are commonly used to examine climate variability or trends and as boundary conditions for ocean circulation models. However, discrepancies exist among these products. This study uses observed Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) sea surface height anomalies (SSHAs) as a means to help constrain the fidelity of these products in the tropical region. Each wind stress product is used to force a linear shallow water model (SWM) and the resulting hindcast thermocline depth anomalies are converted to SSHAs. The resulting SSHAs are then assessed to see how well they reproduce the dominant EOF modes of observed variability and the regional (global mean removed) sea level trend (1993–2007) in each of the three ocean basins. While the results suggest that all wind datasets reproduce the observed interannual variability with reasonable fidelity, the two SWM hindcasts that produce the observed linear trend with the highest fidelity are those incorporating interim ECMWF Re-Analysis (ERA-Interim) and Wave- and Anemometer-Based Sea Surface Wind (WASWind) forcing. The role of surface wind forcing (i.e., upper ocean heat content redistribution) versus global mean sea level change (i.e., including the additional contributions of glacier and ice sheet melt along with ocean thermal expansion) on the recent dramatic increase in western equatorial Pacific island sea level is then reassessed. The results suggest that the recent sea level increase cannot be explained solely by wind stress forcing, regardless of the dataset used; rather, the global mean sea level signal is required to fully explain this observed recent abrupt sea level rise and to better explain the sea level variability of the last 50–60 years.

Mapping Greenland’s mass loss in space and time

The melting of polar ice sheets is a major contributor to global sea-level rise. Early estimates of the mass lost from the Greenland ice cap, based on satellite gravity data collected by the Gravity Recovery and Climate Experiment, have widely varied. Although the continentally and decadally averaged estimated trends have now more or less converged, to this date, there has been little clarity on the detailed spatial distribution of Greenland's mass loss and how the geographical pattern has varied on relatively shorter time scales. Here, we present a spatially and temporally resolved estimation of the ice mass change over Greenland between April of 2002 and August of 2011. Although the total mass loss trend has remained linear, actively changing areas of mass loss were concentrated on the southeastern and northwestern coasts, with ice mass in the center of Greenland steadily increasing over the decade.

Weighing the ocean with a single mooring

Scientists propose that it would be possible to measure changes in ocean mass with a single moored sensor. Changes in ocean mass, which can be caused by added water from melting ice sheets, are an important part of global sea level changes, which can also result from thermal expansion. Many estimates of changes in ocean mass currently rely on satellite‐based measurements of the regional gravitational field, which are used to calculate mass. However, satellites have limited spatial resolution and have difficulty distinguishing mass on land from ocean mass near coasts. They also have problems measuring the very largest scales, making interpretation difficult.

Greenland ice sheet melt, changes in oceanic circulation and European climate during the Last Interglacial

Greenland ice sheet melt, changes in oceanic circulation and European climate during the Last Interglacial

Stability of the Atlantic meridional overturning circulation: A model intercomparison

The evolution of the Atlantic Meridional Overturning Circulation (MOC) in 30 models of varying complexity is examined under four distinct Representative Concentration Pathways. The models include 25 Atmosphere‐Ocean General Circulation Models (AOGCMs) or Earth System Models (ESMs) that submitted simulations in support of the 5th phase of the Coupled Model Intercomparison Project (CMIP5) and 5 Earth System Models of Intermediate Complexity (EMICs). While none of the models incorporated the additional effects of ice sheet melting, they all projected very similar behaviour during the 21st century. Over this period the strength of MOC reduced by a best estimate of 22% (18%–25%; 5%–95% confidence limits) for RCP2.6, 26% (23%–30%) for RCP4.5, 29% (23%–35%) for RCP6.0 and 40% (36%–44%) for RCP8.5. Two of the models eventually realized a slow shutdown of the MOC under RCP8.5, although no model exhibited an abrupt change of the MOC. Through analysis of the freshwater flux across 30°–32°S into the Atlantic, it was found that 56% of the CMIP5 models were in a bistable regime of the MOC for at least part of their RCP integrations. The results support previous assessments that it is very unlikely that the MOC will undergo an abrupt change to an off state as a consequence of global warming.

Melting ice sheets 400,000 yr ago raised sea level by 13 m: Past analogue for future trends

Marine Isotope Stage (MIS) 11 was possibly the longest (∼423,000–362,000 yr ago) and warmest interglacial of the entire Quaternary Period. This resulted from a special arrangement of Earth's orbital parameters-similar to the present interglacial (MIS 1)-suggesting that MIS 11 provides an analogue for future natural climate forcing and sea levels. Although precise documentation of MIS 11 sea level history is, therefore, crucial – especially considering additional impetus from anthropogenic warming – the maximum MIS 11 sea level remains highly contentious. Estimates from onshore indicators have ranged from below present sea level to about +20m, resulting from uncertainties in reliability of sea level indicators, estimates of their subsequent displacement by vertical crustal motion and in dating. We used a clear and unambiguous sea level indicator (interface between subtidal and intertidal deposits) in well exposed, regressive raised shoreline deposits along South Africa's southern coast. The coast is stable in terms of tectonic setting and falls within a zone of low predicted glacio-isostatic adjustment (GIA) and low sensitivity for plausible model parameters. The sea level indicators were directly dated using thermally transferred optically stimulated luminescence (TT-OSL), which gave a mean age of ∼390ka, corresponding with MIS 11. We determined a precise maximum elevation of +14m for the MIS 11 sea level indicator, which corrected for minor crustal uplift and GIA yielded a eustatic sea level of +13m ±2m. The complete MIS 11 transgressive/regressive shoreline succession is preserved and the wave-cut platform extends 950m inland from the present shoreline, indicating a prolonged highstand. We have also documented sea level fluctuations during MIS 11, including an earlier (lower) highstand close to present sea level, which may explain the lower elevation range of some previous estimates. At one locality, MIS 11 deposits form a sea cliff against which MIS 5e sediments (at an elevation of +6.2m) abut. The +13m MIS 11 sea level tallies with total melting of the Greenland and West Antarctica ice sheets, regarded as most susceptible to melting. Our data predict notably higher sea levels in the future, regardless of anthropogenic influence on climate.

Holocene palaeoceanographic evolution off West Greenland

Benthic foraminiferal assemblages from a core southwest of Disko Bugt provide a Holocene perspective (last ~7 ka BP) on ice-sheet/ocean interactions between the West Greenland Current (WGC) and the West Greenland ice sheet. Changes in the fauna reveal significant variations in the water mass properties (temperature and salinity) of the WGC through time. From 7.3 to 6.2 ka BP, a relatively warm/strong WGC influences ice-sheet melt in Disko Bugt and causes enhanced meltwater production, resulting in low surface-water productivity. The most favourable oceanographic conditions occur from 5.5 to 3.5 ka BP, associated with ‘thermal optimum-like’ conditions, encompassing minimum ice sheet extent in the Disko Bugt area. These conditions are attributed to: (1) reduced meltwater influence as the ice sheet is land based and (2) enhanced contribution of warm/saline water masses from the Irminger Current to the WGC. The transition into the late Holocene (last ~3.5 ka BP) is characterized by a cooling of oceanographic conditions, caused by increased advection of cold/low-salinity water masses from the East Greenland Current. A longer-term late-Holocene cooling trend within the WGC is attributed to the onset of Neoglacial cooling within the North Atlantic region. Superimposed on this cooling trend, multicentennial-scale variability within the WGC matches reconstructions from a nearby coring site in Disko Bugt as follows: (1) cooling at ~2.5 ka BP, linked to the 2.7 ka BP ‘cooling event’; (2) a warm phase centred at 1.8 ka BP, associated with the ‘Roman Warm Period’; (3) slight warming between 1.4 and 0.9 ka BP, linked to the ‘Medieval Climate Anomaly’; (4) severe cooling of the WGC after 0.9 ka BP, culminating at 0.3 ka BP during the ‘Little Ice Age’. We show that multicentennial-scale palaeoceanography variability along the West Greenland margin is driven by ocean forcing, i.e. variations in the relative contribution of Atlantic (Irminger Current) and Polar (East Greenland Current) water masses to the WGC during the last ~7 ka BP, influencing ice sheet dynamics.

New estimates of secular sea level rise from tide gauge data and GIA modelling

SUMMARY During the last three decades, at least 30 independent estimates of the secular global mean sea level rise (GMSLR) have been published, based on sufficiently long tide gauge (TG) records. Despite its apparent simplicity, the problem of GMSLR is fraught with a number of difficulties, which make it one of the most challenging questions of climate change science. Not surprisingly, published estimates show considerable scatter, with rates ranging between 1 and 2 mm yr−1 for observations on the century timescale. In previous work, the importance of Glacial Isostatic Adjustment (GIA) upon the assessment of the GMSLR has been clearly demonstrated. In particular, starting from the 1980s, GIA models have been routinely employed to decontaminate TG observations from the effects of melting of the late-Pleistocene ice sheets, to fully highlight the sea level variations driven by climate change. However, uncertainties associated with the Earth’s rheological profile and the time history of the past continental ice sheets can propagate into the GIA corrections. After revisiting previous work and estimates, we suggest a significant modification of the criteria for the selection of the TGs which are most suitable for the robust assessment of the secular GMSLR. In particular, we seek a set of TGs for which GIA corrections are essentially independent of the parametrization of the rheological profile of the Earth’s mantle and of the detailed time chronology of surface loading. This insensitivity is established by considering predictions based upon three GIA models widely employed in the recent literature (namely, ICE–3G, ICE–5G and the one developed at the Research School of Earth Sciences of the National Australian University). Applying this approach and selection criteria previously proposed in the literature, we identify a set of 22 sufficiently evenly distributed TGs. By simple statistical methods, these records yield a ‘preferred’, GIA-independent GMSLR estimate since 1880, namely 1.5 ± 0.1 mm yr−1 (rms = 0.4 mm yr−1, wrms = 0.3 mm yr−1). This value is consistent with various previous estimates based on secular TG observations and with that proposed, for the 20th century, by the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (1.7 ± 0.5 mm yr−1).

Long-term ocean simulations in FESOM: evaluation and application in studying the impact of Greenland Ice Sheet melting

The Finite Element Sea-ice Ocean Model (FESOM) is formulated on unstructured meshes and offers geometrical flexibility which is difficult to achieve on traditional structured grids. In this work, the performance of FESOM in the North Atlantic and Arctic Ocean on large time scales is evaluated in a hindcast experiment. A water-hosing experiment is also conducted to study the model sensitivity to increased freshwater input from Greenland Ice Sheet (GrIS) melting in a 0.1-Sv discharge rate scenario. The variability of the Atlantic Meridional Overturning Circulation (AMOC) in the hindcast experiment can be explained by the variability of the thermohaline forcing over deep convection sites. The model also reproduces realistic freshwater content variability and sea ice extent in the Arctic Ocean. The anomalous freshwater in the water-hosing experiment leads to significant changes in the ocean circulation and local dynamical sea level (DSL). The most pronounced DSL rise is in the northwest North Atlantic as shown in previous studies, and also in the Arctic Ocean. The released GrIS freshwater mainly remains in the North Atlantic, Arctic Ocean and the west South Atlantic after 120 model years. The pattern of ocean freshening is similar to that of the GrIS water distribution, but changes in ocean circulation also contribute to the ocean salinity change. The changes in Arctic and sub-Arctic sea level modify exchanges between the Arctic Ocean and subpolar seas, and hence the role of the Arctic Ocean in the global climate. Not only the strength of the AMOC, but also the strength of its decadal variability is notably reduced by the anomalous freshwater input. A comparison of FESOM with results from previous studies shows that FESOM can simulate past ocean state and the impact of increased GrIS melting well.

Decadal fingerprints of freshwater discharge around Greenland in a multi-model ensemble

The recent increase in the rate of the Greenland ice sheet melting has raised with urgency the question of the impact of such a melting on the climate. As former model projections, based on a coarse representation of the melting, show very different sensitivity to this melting, it seems necessary to consider a multi-model ensemble to tackle this question. Here we use five coupled climate models and one ocean-only model to evaluate the impact of 0.1 Sv (1 Sv = 106 m3/s) of freshwater equally distributed around the coast of Greenland during the historical era 1965–2004. The ocean-only model helps to discriminate between oceanic and coupled responses. In this idealized framework, we find similar fingerprints in the fourth decade of hosing among the models, with a general weakening of the Atlantic Meridional Overturning Circulation (AMOC). Initially, the additional freshwater spreads along the main currents of the subpolar gyre. Part of the anomaly crosses the Atlantic eastward and enters into the Canary Current constituting a freshwater leakage tapping the subpolar gyre system. As a consequence, we show that the AMOC weakening is smaller if the leakage is larger. We argue that the magnitude of the freshwater leakage is related to the asymmetry between the subpolar-subtropical gyres in the control simulations, which may ultimately be a primary cause for the diversity of AMOC responses to the hosing in the multi-model ensemble. Another important fingerprint concerns a warming in the Nordic Seas in response to the re-emergence of Atlantic subsurface waters capped by the freshwater in the subpolar gyre. This subsurface heat anomaly reaches the Arctic where it emerges and induces a positive upper ocean salinity anomaly by introducing more Atlantic waters. We found similar climatic impacts in all the coupled ocean–atmosphere models with an atmospheric cooling of the North Atlantic except in the region around the Nordic Seas and a slight warming south of the equator in the Atlantic. This meridional gradient of temperature is associated with a southward shift of the tropical rains. The free surface models also show similar sea-level fingerprints notably with a comma-shape of high sea-level rise following the Canary Current.

Links between early Holocene ice-sheet decay, sea-level rise and abrupt climate change

The beginning of the Holocene interglacial was marked by ice-sheet melting and sea-level rise. A review of sea level and climate records identifies two sea-level jumps associated with the final drainage of glacial Lake Agassiz, and links them to an abrupt cooling event.

Seasonal Laurentide Ice Sheet melting during the "Mystery Interval" (17.5-14.5 ka)

The last deglaciation in the Northern Hemisphere was interrupted by two major stadials, the so-called “Mystery Interval” (17.5–14.5 ka) and the Younger Dryas (12.9–11.7 ka). During these events, the North Atlantic region was marked by cold surface conditions, yet simultaneous glacier and snowline retreat. Rerouting of Laurentide Ice Sheet meltwater from the Gulf of Mexico to an eastern or northern spillway may have reduced meridional overturning circulation at the onset of the Younger Dryas. However, this hypothesis has not been tested for the Mystery Interval. Paired Mg/Ca and δ 18 O measurements on foraminifera from laminated Orca Basin sediments in the Gulf of Mexico, constrained by 35 14 C dates, document the timing of meltwater input with subcentennial resolution. Isolating the δ 18 O of seawater (termed δ 18 O GOM ) reveals three major melting episodes from ca. 17.5 ka until 12.9 ka, followed by a rapid cessation, consistent with meltwater rerouting at the onset of the Younger Dryas. Conversely, inferred meltwater fl ow to the Gulf of Mexico during the Mystery Interval does not support a simple routing event, but is consistent with glacier and snowline retreat. We suggest that summer melting of Northern Hemisphere ice sheets during this stadial may have been an important mechanism for enhanced winter sea-ice formation, hypercold winter conditions, and enhanced seasonality in the North Atlantic region.

The impact of future changes in weather patterns on extreme sea levels over southern Australia

This study first compares two methods by which the global, variable resolution Cubic Conformal Atmospheric Model (CCAM) is forced by reanalysis over Australia. The methods are the spectral nudging and bias‐corrected sea surface temperature (SST) forcing. Surface winds and sea level pressure are compared since these influence coastal sea levels. SST forcing was found to better preserve the mean and standard deviation of these quantities. Second, a hydrodynamic model is used to model sea levels over southern Australia over 1980–1999 and 2080–2099 to investigate how changes in weather patterns affect extreme sea levels. Forcing from one Global Climate Model (GCM) and two CCAM simulations in which CCAM was used to downscale two GCMs over Australia with bias‐corrected SST forcing (including the GCM considered in this study) were used. While there are differences in the spatial patterns of change between seasons over the modeled coastline between the three models, extreme sea levels were mostly lower in the future period over the southern mainland coastline from autumn to spring due to reduced westerlies in the climate models. The sea level changes around Tasmania varied from positive to negative depending on the model and season. The projected extreme sea level changes were within 10 cm of current climate values. This suggests that over southern Australia extreme sea level changes will be dominated by changes in mean sea level due to thermal expansion and ice sheet and glacier melt rather than changes in weather patterns.

Impact of freshwater discharge from the Greenland ice sheet on North Atlantic climate variability

Using a coupled ocean–atmosphere general circulation model, we investigated the impact of Greenland ice sheet melting on North Atlantic climate variability. The positive-degree day (PDD) method was incorporated into the model to control continental ice melting (PDD run). Models with and without the PDD method produce a realistic pattern of North Atlantic sea surface temperature (SST) variability that fluctuates from decadal to multidecadal periods. However, the interdecadal variability in PDD run is significantly dominated in the longer time scale compared to that in the run without PDD method. The main oscillatory feature in these experiments likely resembles the density-driven oscillatory mode. A reduction in the ocean density over the subpolar Atlantic results in suppression of the Atlantic Meridional Overturning Circulation (AMOC), leading to a cold SST due to a weakening of northward heat transport. The decreased surface evaporation associated with the cold SST further reduces the ocean density and thus, simultaneously acts as a positive feedback mechanism. The southward meridional current associated with the suppressed AMOC causes a positive tendency in the ocean density through density advection, which accounts for the phase transition of this oscillatory mode. The Greenland ice melting process reduces the mean meridional current and meridional density gradient because of additional fresh water flux, which suppress the delayed negative feedback due to meridional density advection. As a result, the oscillation period becomes longer and the transition is more delayed.

Multiple early Holocene climate oscillations at Silver Lake, New Jersey and their possible linkage with outburst floods

Episodic discharges from the Laurentide Ice Sheet are considered to be one of the major causes of climate oscillations during the glacial to interglacial transition. These outburst floods disrupted thermohaline circulation and might have caused cooling events in the North Atlantic region and beyond, including the Younger Dryas, Preboreal Oscillation, and 8.2-ka events. However, few terrestrial sedimentary records show regional climate changes directly linked to outburst floods during the early Holocene. Here we present lithologic and isotopic data from Silver Lake in northern New Jersey to document temperature and moisture changes during the early Holocene and to discuss possible linkage with outburst flooding events. The lithologic record shows multiple intervals with coupled decreases in carbonate and increases in organic matter during the early Holocene, suggesting lower lake levels and drier climate conditions. Simultaneous with these changes were decreases in carbonate δ18O values, likely reflecting a decrease in air temperature during these dry periods. The apparent correlation of these sedimentary events at Silver Lake with documented outburst floods from the melting ice sheet suggests a possible causal connection, implying that the climate in the Mid‐Atlantic region was extremely sensitive to perturbations of ocean circulation.