5.1. Size of the Discharge
 Alley and MacAyeal  estimated the mass and volume of a typical Heinrich IRD layer to be 1.0 ± 0.3 × 1015 kg or 370 ± 120 km3. Their estimate was based on combining the total glacial IRD flux estimate of 9.8 × 1015 kg from Ruddiman  with the area fractions under the SU90-08 magnetic susceptibility curve that are Heinrich fluxes as opposed to background glacial values [Grousset et al., 1993]. A consistent estimate of 100–400 km3 is derived from simple mapping of the layer thickness across the North Atlantic (Figures 7 and 25 and Table 5), but more importantly the mapping of Heinrich layer area allows assessment of water volumes derived from the icebergs. The area covered by Heinrich layers, with average thickness of ∼10–15 cm, is 1 × 106 (H1) to 2.4 × 106 km2 (H4). Accordingly, the volume (VIRD (km3)) is estimated by
where A is the area covered by HS Heinrich layer debris (km2), t is the average thickness (cm), and 10−5 is the conversion factor for centimeters to kilometers. This is smaller than the estimate of Dowdeswell et al.  of 3.4 × 106, where the thickness of H1 and H2 north of the IRD belt appears to be overestimated.
Figure 25. Equal area maps of H1-H4 used to estimate area covered by Hudson Strait-derived IRD: (a) H1, (b) H2, (c) H3, and (d) H4. Data sources are reported in Table 1. Numbers are estimated thickness for each location. Values of “0” are used where the position where the layer would be is understood but the layer was not identified. Rectangles surround the areas estimated for the layers, and the results are reported in Table 5.
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Table 5. Area and Volume Estimates of Heinrich Layer IRD
|H Layer||Area Covered, km2||Average Thickness, cm||Volume Detritus, km3|
|1||1.0 × 106||10||100|
|2||2.0 × 106||15||300|
|3||0.7 × 106||15||99|
|4||2.4 × 106||15||350|
 Estimates of the volume of water released during Heinrich events can be made using the assumptions provided in Table 6. The minimum volume of water (Vwat(min) (km3), i.e., a one-shot instantaneous addition) diluted by fresh water during a Heinrich event is
where A is the same area as defined above and tml is the ocean mixed layer thickness in kilometers. The fraction of water derived from the melting of Heinrich event icebergs can then be calculated from this volume using the fraction of meltwater, calculated from the corrected δ18O excursion (Table 6), and an assumed average δ18O of ice of approximately −31. This is probably an extreme estimation of the ice composition for the Laurentide ice sheet (D. P. Schrag, personal communication, 2003), and thus the meltwater fraction calculated this way is a minimum.
Table 6. Parameters Used to Calculate Water Volumes From Hudson Strait Heinrich Events
|Parameter Used||Value||Source or Calculation|
|δ18O of ice||−28 to −34‰||Duplessy et al.  and Schrag et al.  (note that the Laurentide is likely heavier, so this yields minimum volumes (D. P. Schrag, personal communication, 2003))|
|Magnitude of δ18O excursion (δ18OHeinrich −18Oambient)||−1 to −2‰||Cortijo et al. |
|Temperature lowering (ΔT)||3° to 4°C||Cortijo et al. |
|δ18O excursion of water||−1.7 to −2.9‰||(δ18OHeinrich − δ18Oambient) − (ΔHeinrich − Δambient)a|
|Area of Heinrich layers A||0.7 to 2.3 × 106 km2||Table 3 and Figure 24|
|Mixed layer depth (MLD)||0.02 to 0.1 km||Kara et al. |
|Volume of water (minimum)(b)||1.4 × 104 to 2.3 × 105 km3||from A times mixed layer depth|
|Duration t||1 to 500 years||timing and duration section|
|Replenishment of NAC||14 to 21 Sv||Lynch-Stieglitz et al.  and Schmitz and McCartney |
|Flux of water to maintain dilution F||0.6 to 1.9 Sv||(4.5% of 14 Sv) to (9% of 21 Sv)c|
|Volume of water(d)||1.9 × 104 to 3 × 107 km(e)||Vwater(km3) = F(Sv) × 1 × 106(m3 s−1 Sv−1) × t(years) × 3.15 × 107(s yr−1) × 10−9 (km3 m−3)|
 The minimum estimate described above does not take into account the strong flows within the sea, which would have tended to dissipate the low-salinity lens. This flow requires that the actual glacially derived water volume depends on the duration of the event. It is clear from the pattern of distribution of Heinrich layer IRD with the distinctive Hudson Strait provenance that a strong eastward flow existed along the latitude of about 45°N (Figures 6 and 7), consistent with an iceberg transport rate close to that of today and/or a lower melting rate resulting from reduction of water temperatures in the North Atlantic [Matsumoto, 1997]. Lynch-Stieglitz et al.  estimated that the flow of the Gulf Stream was reduced by about 30% to between 14 and 21 Sv (1 Sv = 106 m3 s−1) in the LGM. It appears that today a large fraction of the Gulf Stream goes to form the North Atlantic Current [e.g., Schmitz and McCartney, 1993; Schmitz, 1996]. Input values ranging from 4.5% glacial water and 14 Sv Gulf Stream contribution to 9% glacial water and 21 Sv Gulf Stream contribution require a flux of 0.6–1.9 Sv of glacial water (Table 6).
 The amount of ice required to maintain the dilution implied by the δ18O values depends on the duration of the event and the fraction of the North Atlantic Current flow that is contaminated by the ice-derived water (approximately the mixed layer thickness). The volume of water (Vwat(flow) (km3)) is
where F is the ice-water flux (m3 s−1), t is time (seconds), and 10−9 is the conversion from cubic meters to cubic kilometers (a longer version with more normal units is presented in Table 6). For 1 year and a fully contaminated flow the volume is similar to the minimum limit (Table 6). For 1000 years, ∼4 × 107 m3 would be required. Under these conditions, if the average ice thickness from which the bergs were derived is 1 km, the areas occupied by the ice that produced the layers are between 3 × 104 km2 and 4 × 107 km2. This maximum number is very large. For reference, the area occupied by Hudson Bay is about 8 × 105 km2, and MacAyeal  and Matsumoto  estimated the area of the Hudson Strait catchment to be about 1 × 106 and 2 × 106 km2, respectively. A best estimate area for a possible Hudson Bay catchment of 1.66 × 106 km2 results from the following input values: the duration estimate discussed above of about 500 years, a 14 Sv Gulf Stream contribution, 4.5% glacial water, a 50 m mixed layer, and a 1.5 km ice thickness. (I have assumed here that reducing the thickness of the mixed layer reduces the volume required linearly, but this ignores a decrease in rate with depth.) Accordingly, it appears that a mechanism to add 3 × 104 to >5 × 106 km3 of ice must be invoked to account for the δ18O recorded in the Heinrich layers. The range in estimated ice volume corresponds to a range of scenarios for its entry to the ocean. At the fastest the entry would last about 1 year and imply about 0.1 m of sea level rise and 1 Sv of freshwater flux (or 0.025 m and 0.25 Sv for 50 m mixed layer). At the slowest the entry would last about 500 years and imply 10–20 m of sea level rise and 0.15–0.3 Sv of freshwater flux (for 50 and 100 m mixed layer). These estimates are comparable to those of Alley and MacAyeal , who used a similar strategy to estimate ∼0.01 m yr−1 sea level rise and a 200–300 year duration (2–3 m total rise, if duration was 500 years, then their estimate would be a 5 m sea level rise). On the basis of estimates of IRD concentration in the ice and glacialogical processes, and using their mapped volume of H1 and H2, Dowdeswell et al.  suggested 1.4 × 105 to 1.4 × 106 km3 of water released over 250–1250 years (0.39–3.9 m sea level rise).
5.2. What Caused the Heinrich Layers?
 A successful Heinrich layer model, that is, specifically for the Hudson Strait Heinrich layers, must produce sufficient IRD and distribute it across the North Atlantic [Hulbe, 1997]. It must explain the limited source region for the terrigenous sediments and the presence of abundant detrital carbonate only within the Heinrich layers. It must account for the apparent association with the cold phases of the D-O cycles, with the dramatic ocean circulation changes, and with the rapid warming that directly follows them. Finally, if Hudson Strait Heinrich events accompanied global mountain glacier advances [e.g., Denton et al., 1999], then they must be interpreted in the context of global climate change. Three proposed mechanisms to model the IRD and freshwater delivery of Hudson Strait Heinrich layers are reviewed here: catastrophic ice sheet purging, jökulhlaup activity, and ice shelf buildup/collapse. An additional model that involves a sea ice switch to trigger the abrupt warming (Y. Kaspi et al., A ‘triple sea-ice state’ mechanism for the abrupt warming and synchronous ice sheet collapses during Heinrich events, submitted to Nature, 2003, hereinafter referred to as Kaspi et al., submitted manuscript, 2003) is described briefly after the discussion of glacialogical mechanisms.
 MacAyeal  formulated an internally driven “binge-purge” model. The premise of a binge-purge model is that a large ice sheet will build up gradually during the binge stage, dependent on air temperature and moisture supply. Some combination of geothermal heat, advection of heat from the upper surface, and internal friction in the bottom boundary zone at the base of the ice sheet will act to eventually destabilize the ice sheet, resulting in a rapid purge phase, also known as Heinrich events. MacAyeal  assumed geothermal heating is the driving force for purging the interior of the ice sheet, while Verbitsky and Saltzman  found friction and heat advection from the surface to be more important parameters. Marshall and Clarke  provided a continuum mixture model between sheet ice, which deforms by viscous creep, and stream ice with fluxes dictated by basal sliding and sediment deformation. They used this model to test the sensitivity of a Hudson Strait ice stream and concluded that it is unlikely for an ice stream in Hudson Strait to drain the interior portions of the ice sheet. Clarke et al.  concluded that it is likely that the onset of a Heinrich event occurs when glacier flow instability is triggered, and they favor episodic surging of an ice stream in Hudson Strait. An alternative purge mechanism was proposed by Hunt and Malin , that is, that ice-load-induced earthquakes may have destabilized the Laurentide ice sheet (although they call for successively shorter intervals between the Heinrich events, whereas my reassessment of the timing (Table 4) suggests a nonchanging, 7 kyr spacing).
 The volume MacAyeal  estimated is 1.25 × 106 km3 of fresh water (he estimated an area of 1 × 106 km2 with an average thickness of 1250 m), introduced into the North Atlantic over about 250–500 years, implying a 0.16–0.08 Sv flux. Dividing the volume by the area of the world ocean, 3.61 × 108 km2, MacAyeal estimated a sea level rise of about 3.5 m. If the Heinrich events represent a purging of a very large part of the Laurentide ice sheet, then it would take an interval considerably longer than a single D-O cycle to rebuild the ice sheet and create the conditions necessary to trigger a purge. The binge interval estimated from MacAyeal's model was about 7 kyr (remarkably close to the recurrence time of Heinrich layers, see Table 4). The water volumes and event durations calculated by MacAyeal  abide by the maximum constraints discussed above. Marshall and Clarke  modeled the behavior of an ice stream in Hudson Strait using mixed bed conditions, and they were able to produce a maximum flux of 0.03 Sv of icebergs, which is about 10 times lower than that implied by the δ18O-based calculations given above. One possible explanation they proposed is that their ice streams do not tap deep enough into the core of the ice sheet. However, because the maximum ice stream velocity in their simulations is 900 m yr−1, ice originating at the head (750 km in) takes 833 years to get to the outlet. Accordingly, Marshall and Clarke  concluded that it is unlikely for an ice stream in Hudson Strait to drain the interior portions of the ice sheet. They left open the possibility that their omission of hydrological conditions under the ice sheet may have led to an underestimation, and this theme was extended by Clarke et al. . The Verbitsky and Saltzman  model implies that the formation of the Heinrich events depends on climate; however, Marshall and Clarke  concluded that the response time of the Laurentide ice sheet to climate change is quite long. Large ice streams tend to take on oscillatory behavior without the need for climate forcing [Marshall and Clarke, 1997], and rapid climate change is integrated into the buildup of the ice sheet (S. J. Marshall, personal communication, 2002). However, hydrologically controlled ice streams might have a more direct influence from climate change [Marshall and Clarke, 1997], and Clarke et al.  speculated that during the buildup to a Heinrich event, phase locking between an atmospheric forcing applied to the ice surface and subglacial meltwater production can be achieved if the ice bed contact is at the melting temperature and strain heating is appreciable. The apparent interhemispheric symmetry of mountain glacier advances and their coincidence in timing with Heinrich events [e.g., Lowell et al., 1995; Denton et al., 1999] favors a climate control on the Heinrich layers but does not eliminate the binge-purge behavior.
 Johnson and Lauritzen  proposed an alternative hypothesis for Heinrich layers: Repetitive jökulhlaups from a Hudson Bay lake may have produced major freshwater pulses into the North Atlantic when the ice dams at the mouth of the Hudson Strait failed. A jökulhlaup is a massive flood that occurs when the height of the dam is exceeded by lake level because of rising lake level or reduced flow of glacial ice into the dam [Johnson and Lauritzen, 1995]. As noted in section 5.1, the area of Hudson Bay is about 8 × 105 km2, and if it was overfilled by 100 m, the amount of water that would spill into the ocean in this process is around 8 × 104 km3, about twice the minimum estimate based on the area occupied by H4 and assuming a 200 m mixed layer. The Johnson and Lauritzen  mechanism would be very rapid, and thus a number approaching the minimum estimate is reasonable based on the volume constraints alone. It is clear that a large fraction of the precursor fine carbonate sediment deposited near the Hudson Strait is brought by meltwater not icebergs [e.g., Hesse and Khodabakhsh, 1998; Rashid et al., 2003b]. This model could produce a sea level change of only ∼0.2 m or less, and it would be virtually instantaneous. In the distribution of continental ice proposed by the Johnson and Lauritzen  mechanism, Hudson Bay is filled with water and surrounded by glacial ice flowing into it rather than being a glacial dome itself. During early phases of the ice sheet buildup (stage 5) and possibly for H3, an ice-damned lake in Hudson Bay is possible; however, during the LGM it is unlikely that a lake occupied Hudson Bay (J. Andrews, personal communication, 2003). J. Andrews (personal communication, 2003) is considering the possibility of large, subglacial lakes under the Laurentide ice sheet. If large subglacial lakes existed under the Laurentide ice sheet, this would provide scope for large bursts of meltwater, accompanied by dramatic destabilization of the ice sheet.
 Hulbe  proposed a model for Heinrich events in which the Hudson Strait ice stream flows into the Labrador Sea from a Hudson Bay dome and forms an ice shelf in the Labrador Sea, in other words with an ice sheet configuration similar to that assumed by MacAyeal . The ice shelf model proposed by Hulbe  would operate under extreme cold conditions, consistent with the observations of Heinrich layers in DSDP609 and V23-81 [e.g., Bond et al., 1992; Broecker et al., 1992]. Ice shelves form where grounded ice flows into the sea and floats on the surface. In this model, sediment would be enriched in the basal zone of the ice shelf by basal freezing due to large slopes in the basal topography. Hulbe's  model appears to produce an acceptable volume of ice of 800 × 1200 km, with ∼500 m average thickness (4.8 × 105 km3 of ice). However, there is not a Heinrich event for every cold interval in Greenland, and the δ18O excursions coincident with Heinrich events do not stand out in magnitude (Figure 24). Nonetheless, Heinrich events do appear to occupy relatively long cold intervals, and the model shelf needs about a thousand years of cooling to build up the ice shelf volume noted above [Hulbe, 1997]. Hulbe's model should predict detrital carbonate events for every cold phase of the D-O cycles in the vicinity of Hudson Strait. Indeed, it appears that there might be such events [Andrews and Barber, 2002], although the greatly reduced amplitudes that are implied are puzzling unless the freezing-on process in the ice shelf model operates effectively only when the shelf is fully developed. Sea level should not rise because of ice shelf collapse because the ice is already floating in the Labrador Sea prior to its release. However, perhaps small sea level rise from surges of other ice sheets could be a trigger for Hudson Strait collapse. Additionally, the collapse of the ice shelf could allow enhanced ice stream activity in Hudson Strait (although this does not appear to provide appropriate amounts of ice in the required time interval according to the work of Marshall and Clarke ).
 Hulbe et al.  suggest a revision of the ice shelf hypothesis. In the new scenario the ice shelf is fringing the Laurentide ice sheet margin rather than extending across the Labrador Sea, and the events are formed by explosive disintegration of the ice shelf such as recently witnessed along the Antarctic Peninsula. The proposed ice shelf was fed by several ice streams, which have been identified by geomorphic studies. Each of the suggested ice streams is underlain by dominantly Churchill Province basement, consistent with the provenance constraints. The ice-derived water volume estimated in this study is 2.8 × 104 to 2 × 105 km3, consistent with volume constraints shown in Table 6 as long as the duration is very short.
 The three mechanisms described above, (1) purging of the Laurentide ice sheet [MacAyeal, 1993; Verbitsky and Saltzman, 1995; Hunt and Malin, 1998; Clarke et al., 1999] or episodic activity of an ice stream in Hudson Strait [Marshall and Clarke, 1997], (2) jökulhlaup activity [Johnson and Lauritzen, 1995], and (3) ice shelf buildup/collapse [Hulbe, 1997; Hulbe et al., 2004], all appear to be capable of producing the first-order features of the Heinrich layers, including the large injection of fresh water into the North Atlantic Current (with volume depending on duration, see Table 7) and the large volume of sediment deposited rapidly in these events. In the purging and jökulhlaup scenarios the best way to get IRD-enriched icebergs appears to be a glaciohydraulic supercooling mechanism [e.g., Alley et al., 1997, 1998; Lawson et al., 1998; Roberts et al., 2002], which would allow the limited sediment provenance of Heinrich layer sediments [Bond et al., 1992; Gwiazda et al., 1996a; Hemming et al., 1998, 2002]. In this mechanism, ice accretes to the bottom of the glacier ice from water that is supercooled due to flowing up large topographic features such as the Hudson Strait sill. In the case of binge-purge behavior, basal debris entrainment mechanisms described by Alley and MacAyeal  will also yield appropriate sediment loads. Glaciohydraulic supercooling may not apply to the ice shelf model. According to R. Alley (personal communication, 2003) the detritus from the mouth of Hudson Strait is most likely melted out. This is because the ice shelf is likely to be thickest in the mouth of Hudson Strait where the bed is deep. Freeze-on would be expected down flow, where the ice shelf is thinner, but after the debris has melted out. Alternatively, the freeze-on could be transverse to flow, which would tend to preserve sediment incorporated in the slower moving ice from the sides of the strait rather than in the main ice coming out of the strait (or other ice streams in the modified ice shelf model of Hulbe et al. ). Additionally, it is likely that warming, rather than sea level rise, drives the retreat of the ice shelf [e.g., Parizek et al., 2002; Hulbe et al., 2004], although the revised ice shelf model may not require very substantial warming [Hulbe et al., 2004].
Table 7. Vital Statistics of Heinrich Layers
|Duration||495 ± 255 years (1σ)|
|Freshwater flux||∼3 × 104 km3 (1 year, 200 m mixed layer)|
| ||∼1 × 107 km3 (500 years, 4.5% ice water, and 14 Sv flow); if assumption of 100 (or 50) m mixed layer halves (quarters) volume, then 5 (or 2.5) × 106 km3|
|Sea level rise||0 m (ice shelf)|
| ||0.2 m (jökulhaup)|
| ||3–15 m (Laurentide ice sheet purge)|
|Size of Hudson Strait catchment||1.66 × 106 km2 (for 5 × 106 km3 volume and 3 km ice thickness or for 2.5 × 106 km3 volume and 1.5 km thickness)|
|Average ice thickness for 500 year duration||≥1.5 km|
|Volume of over-deepened Hudson Strait||∼2 × 103 km3|
|Volume of IRD||100–350 km3|
|Concentration of IRD in ice||0.01–10%|
 Taking everything together, glacialogical instability (episodic purging) seems to be the most likely explanation for the Hudson Strait Heinrich layers unless it can be demonstrated that these events are substantially shorter than the apparent 500 year duration or that the mixed layer is extremely thin (∼0.5–1 m). Such a thin mixed layer seems unlikely given the (probably) more vigorous atmospheric circulation that accompanies Heinrich events. Interestingly, a scenario that involves components of all three proposed end-members may have some appeal. Buttressing by an ice shelf during cold periods could lock up the Hudson Strait ice stream. If the low area of Hudson Bay contains subglacial water, release of the ice shelf could set off a chain of events, ending in a massive purging of the Laurentide ice sheet. Kaspi et al. (submitted manuscript, 2003) have modeled a triple sea-ice state to produce the pattern of variability found in North Atlantic records. In their model, phase locking ties the behavior of Northern Hemisphere ice sheets together. I am not convinced that this locking is necessary, but it is an interesting theory that can presumably be tested if paleoceanographers can come to better understand the meaning of changes in the content of IRD in marine sediment cores (see section 2.1 for a discussion of defining IRD). In addition to the phase locking mechanism, Kaspi et al. (submitted manuscript, 2003) propose that rapid melting of sea ice following a Heinrich event is what leads to the abrupt warming recorded in sediment cores, inferred to be the product of ice-albedo feedback.
 Further examination of hydrographic changes in the North Atlantic (reviewed in section 6) may provide additional constraints on the ice-derived water volume by documenting the mixed layer thickness. The combined application of 230Thexcess with 3He from interplanetary dust particles and 10Be offers promise for constraining the volume of ice involved in the events [Higgins, 2001]. However, to achieve this promise, significant development work is necessary, as well as mapping of the intervals in space and time with these methods. Additionally, further examination of detailed sedimentology and hydrography proxies in the Labrador Sea provides constructive ways to decide among the proposed possibilities. It may be that much of the hydrographic and sedimentological data from Labrador Sea cores are available [e.g., Andrews and Tedesco, 1992; Andrews et al., 1994a, 1994b, 1998; Hillaire-Marcel et al., 1994; Jennings et al., 1996; Hesse and Khodabakhsh, 1998; Hillaire-Marcel and Bilodeau, 2000; de Vernal and Hillaire-Marcel, 2000; de Vernal et al., 2000; Rashid et al., 2003b], and a synthesis with the goal of testing the alternative hypotheses for Heinrich events could be what is most needed.