4.1. A Mean Paleotemperature Estimate for the Late Maastrichtian Deep Ocean
 The mean temperature of the deep ocean can be estimated from the mean δ18Owof seawater and the δ18Oc of calcite in equilibrium with the average deep ocean. The stable isotopic signals of Gavelinella and Nuttallidesappear close to equilibrium values [Shackleton et al., 1984]. Hence, although we do not know the exact δ18Ocof calcite in equilibrium with the mean late Maastrichtian ocean, we can approximate it with the mean δ18Oc of benthic foraminifera from the 16 sites analyzed for this study (0.51‰).
 Estimates of the mean δ18Owof Late Cretaceous seawater typically assume that there was no globally significant Late Cretaceous ice volume and that the mean δ18O value of the terrestrial surface hydrosphere has not changed over the last 100 million years [Shackleton and Kennett, 1975]. This assumption results in a mean δ18Owvalue of about −1.0‰ for late Maastrichtian seawater. Given mean δ18Owof −1.0‰ and benthic foraminiferal tests in equilibrium with their paleoenvironments, a mean benthic foraminiferal δ18Ocvalue of 0.51‰ indicates a mean deep-ocean paleotemperature of 10.2°C.
4.2. Paleotemperature and Paleosalinity Estimates for Late Maastrichtian Deep Water at Individual Sites
 Extending paleotemperature estimates to individual sites requires another level of assumption. Since different deepwater masses have different evaporative histories, the effects of evaporation and precipitation on the δ18Owvalues and salinities of deep waters are not constant from site to site. For example, the mean δ18Ow value of deepwater masses in the modern open ocean ranges from 0.12‰ (North Atlantic Deep Water) to −0.45‰ (Antarctic Bottom Water) [Craig and Gordon, 1965]. Similarly, mean deepwater salinity in the modern open ocean ranges from 34.6 psu in the North Pacific to 35.0 psu in the North Atlantic [Levitus et al., 1994]. Deep waters entering the open ocean from the Red Sea and the Mediterranean Sea are much more 18O-enriched and much more saline. The Red Sea is characterized by a deepwater δ18Owvalue of 1.95‰ and deepwater salinity of 40.6 psu [Craig, 1966]. The Mediterranean basin contains deep water with δ18Ow values of 1.55–1.9‰ [Thunell et al., 1987] and salinity of ∼38.4–38.7 psu [Sverdrup et al., 1942] (deep Mediterranean δ18Owand salinity decrease to ∼1.45‰ and 37.75 psu, respectively, in the Strait of Gibraltar where Mediterranean deep water mixes with North Atlantic waters during formation of Mediterranean Overflow Water). Hence estimation of paleotemperatures at different sites requires consideration of evaporation-precipitation balances.
 To a closer approximation the deep ocean has about the same potential density everywhere. In the modern open ocean, potential density (at 1 atmosphere of pressure) ranges from 1027.7 kg m−3(North Pacific) to 1027.9 kg m−3 (North Atlantic) (based on temperature data from Levitus and Boyer  and salinity data from Levitus et al. ). In semienclosed basins, potential density deviates further from open ocean values. For example, it averages 1028.7 kg m−3 in the Red Sea and reaches an extreme of 1029.1 kg m−3 in the eastern Mediterranean. These interbasinal differences in potential density are dwarfed by the interbasinal differences in deepwater salinity. Hence, given an estimate of the relationship between δ18Oc and paleosalinity (Δδ18Ow/ΔS), the average paleotemperature and paleosalinity of any individual site can be most closely approximated by calculating the paleosalinity and paleotemperature values at which the mean δ18Ocof Gavelinella and Nuttallidesfrom that site corresponds to the potential paleodensity of mean deep water at 1 atmosphere of pressure.
 An estimate of mean paleosalinity is necessary in order to calculate the potential paleodensity of mean Maastrichtian deep water. The mean paleosalinity of the late Maastrichtian ocean can be provisionally estimated by assuming that there was no globally significant late Maastrichtian ice volume and that the mean salinity of the terrestrial surface hydrosphere has not changed over the last 70 million years (similar to the standard δ18Ow assumption). Given a lack of significant ice volume and a constant salt balance in the surface hydrosphere, late Maastrichtian oceans were characterized by a mean paleosalinity of ∼34 psu. If the late Maastrichtian deep ocean was characterized by a mean paleotemperature of 10.2°C and a mean paleosalinity of 34 psu, its mean potential density was 1026.13 kg m−3 (equivalent to a σt of 26.13).
 The relationship between δ18Ocand paleosalinity (Δδ18Ow/ΔS) must be estimated before we can use paleodensity to infer the average paleotemperature and paleosalinity of any individual site. For an isolated deepwater mass this relationship is determined by effects of evaporation and precipitation that occurred during the surface water history of the deepwater mass. Mixing considerations aside, the salinity of a surface marine water mass is simply determined by the mean salinity of seawater and the local balance between evaporation and precipitation. In contrast, the δ18Owvalue of a surface water mass is controlled by the mean δ18Owof seawater, the degree of evaporation from the water mass, the degree of precipitation to the water mass, the δ18Owvalue of the evaporated water, and the δ18Owvalue of the precipitated water. The lighter isotope (16O) is preferentially evaporated and the heavier isotope (18O) preferentially rains out (resulting in atmospheric concentration of 16O by Rayleigh distillation); consequently, the δ18O value of early stage precipitation is relatively close to that of seawater, whereas subsequent precipitation is progressively depleted in 18O [Dansgaard, 1964; Craig and Gordon, 1965]. The relative rain out of 16O and 18O is strongly dependent on temperatures of evaporation and condensation for two reasons. First, the equilibrium ratio of 18O/16O in liquid to 18O/16O in water vapor increases with decreasing temperature [Dansgaard, 1964]. Second, a cold atmosphere holds less water vapor than a warm atmosphere and consequently is generally characterized by greater relative atmospheric “distillation.” These effects lead to strong positive correlations between atmospheric temperature and the δ18O values of water vapor and precipitation. For example, at mean air temperatures approaching 30°C, the δ18O value of precipitation approaches that of mean seawater (0‰), whereas at a mean air temperature of −50°C the δ18O value of precipitation approaches −50‰ [Dansgaard, 1964].
 Low-latitude waters of the modern open ocean and marginal seas define a Δδ18Ow/ΔSwslope of ∼0.35 [Railsback et al., 1989]. The slope of Δδ18Ow/ΔSw is as low as 0.11 in much of the low-latitude open Atlantic [Craig and Gordon, 1965]. At these latitudes the Δδ18Ow/ΔSw relationship is defined by the low level of isotopic fractionation undergone by the surface ocean during early stage evaporation and precipitation at relatively high temperatures [Craig and Gordon, 1965]. In contrast, midlatitude and high-latitude waters of the modern open ocean define a Δδ18Ow/ΔSw slope of ∼0.5 [Railsback et al., 1989]. The steepest surface water Δδ18Ow/ΔSwslope in the modern ocean (0.6) is defined by midlatitude and high-latitude Atlantic surface waters [Craig and Gordon, 1965]. In these regions the slope of Δδ18Ow/ΔS is primarily controlled by the high level of isotopic fractionation undergone by late stage precipitation at low condensation temperatures [Craig and Gordon, 1965]. A world with warmer high-latitude waters (i.e., the late Maastrichtian) would probably have been characterized by high-latitude precipitation with δ18O values more positive than that of the present (due to decreased isotopic fractionation at higher temperatures). Consequently, the steepest Δδ18Ow/ΔSw slopes of the late Maastrichtian ocean were probably <0.5.
 On the assumption that tropical evaporation was a dominant cause of deepwater formation in ancient oceans (Cretaceous and Ordovician), a Δδ18Ow/ΔSw slope of 0.35 has been used to develop estimates of deepwater paleotemperatures [Railsback et al., 1989; Woo et al., 1992]. In previous studies we assumed the same Δδ18Ow/ΔSw slope to estimate late Maastrichtian surface water paleotemperatures [D'Hondt and Arthur, 1995, 1996]. Given a Δδ18Ow/ΔSw slope of 0.35, a late Maastrichtian deepwater potential density of 1026.13 kg m−3 allows deepwater paleotemperature and paleosalinity as low as 6°C and 33.2 psu (DSDP Site 577: mean δ18Oc value of 1.2‰) and as high as 13.7°C and 34.8 psu (DSDP Site 357: mean δ18Ocvalue of 0.0‰) (Figure 6 and Table 2).
Figure 6. Estimates of mean late Maastrichian paleotemperature and paleosalinity values for the 16 DSDP and ODP sites. These estimates assume a mean deep-ocean density of 1026.13 kg m−3 (Table 2).
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Table 2. Estimates of Mean, Minimum (Site 577), and Maximum (Site 357) Deep-Sea Paleotemperatures and Paleosalinities Given Different Assumptions of Mean Oceanic Paleosalinity, Mean Oceanic δ18OWand Δδ18OW/ΔS
|Mean Oceanic δ18O, ‰||Mean Oceanic Paleosalinity, psu||Δδ18O/ΔS||Mean Deep Ocean (16 Sites)a||Site 577a||Site 357a|
|Paleotemperature, °C||Paleodensity, kg m−3||Paleotemperature, °C||Paleosalinity, psu||Paleotemperature, °C||Paleosalinity, psu|
4.3. Sensitivity of Paleotemperature and Paleosalinity Estimates to Estimates of Mean Paleosalinity, Mean δ18Ow, and Δδ18Ow/ΔS
 Section 4.2suggests that estimation of ancient seawater temperatures from δ18Ocvalues is fraught with assumptions. The sensitivity of paleotemperature estimates to most of those assumptions can be readily assessed by calculating paleotemperature estimates under different conditions of mean paleosalinity, mean δ18Ow, and Δδ18Ow/ΔSw. Such calculations demonstrate that over the range of δ18Ocvalues found in this study, deepwater paleotemperature estimates are insensitive to the assumed mean paleosalinity (given standard estimates of Maastrichtian δ18Ow) (Table 2). In contrast, on the scale of 3°–4°C, deepwater paleotemperature estimates are sensitive to 1.0‰ differences in the estimate of mean oceanic δ18Ow. On the scale of 1°–2°C, intersite differences in paleotemperature estimates are also sensitive to 1.0‰ differences in the estimate of mean oceanic δ18Ow (Table 2).
 Changes in the estimates of mean oceanic paleosalinity and mean oceanic δ18Owaffect paleotemperature estimates similarly throughout the range of δ18Ocvalues. For example, with an assumed mean oceanic δ18Owof 0.0‰, all δ18Oc values correspond to higher paleotemperature estimates than with an assumed mean oceanic δ18Owof 1.0‰ (Table 2). In contrast, a change in the assumed slope of Δδ18Ow/ΔSwleaves mean estimates of paleosalinity and paleotemperature unchanged but changes end-member estimates in opposite directions. For example, an assumed Δδ18Ow/ΔSwslope of 0.5 results in negative δ18Ocvalues corresponding to warmer paleotemperatures and higher paleosalinity values than the standard Δδ18Ow/Δ Sw slope of 0.35. However, the same difference in assumed Δδ18Ow/Δ Swslopes results in positive δ18Oc values corresponding to cooler paleotemperatures and lower paleosalinity values than the standard Δδ18Ow/Δ Sw slope of 0.35. In any case, the dependence of deepwater paleotemperature and paleosalinity estimates on the slope of Δδ18Ow/Δ Sw is relatively low for Δδ18Ow/Δ Sw values in the range of 0.2–0.5 (Table 2).
 Barring a relatively large (= 1.0‰) error in the standard assumption of mean oceanic δ18Ow[Shackleton and Kennett, 1975], the preceding calculations suggest that the most positive mean δ18Oc value in our study corresponds to a paleotemperature estimate of 5°–7°C (Site 577A), the most negative mean δ18Oc value corresponds to a paleotemperature estimate of 13°–15°C (Site 357), and the average value of all 16 sites corresponds to a paleotemperature estimate of ∼10°C.