Paired δ18O and Mg/Ca measurements on the same foraminiferal shells offer the ability to independently estimate sea surface temperature (SST) changes and assess their temporal relationship to the growth and decay of continental ice sheets. The accuracy of this method is confounded, however, by the absence of a quantitative method to correct Mg/Ca records for alteration by dissolution. Here we describe dissolution-corrected calibrations for Mg/Ca-paleothermometry in which the preexponent constant is a function of size-normalized shell weight: (1) for G. ruber (212–300 μm) (Mg/Ca)ruber = (0.025 wt + 0.11) e0.095T and (b) for G. sacculifer (355–425 μm) (Mg/Ca)sacc = (0.0032 wt + 0.181) e0.095T. The new calibrations improve the accuracy of SST estimates and are globally applicable. With this correction, eastern equatorial Atlantic SST during the Last Glacial Maximum is estimated to be 2.9° ± 0.4°C colder than today.
 Accurate knowledge of past sea surface temperatures (SST) is crucial for understanding the sensitivity of the climate system to radiative perturbations. There is a growing body of evidence to suggest that tropical SST were colder by about 2 to 6°C during the last glacial maximum (LGM) [Guilderson et al., 1994; Bard et al., 1997; Hastings et al., 1998; Lea et al., 2000]. However, it is a matter of debate as to what part of this large range in temperature estimates reflects real oceanographic conditions and how much is attributable to inaccuracies associated with different paleotemperature proxies [De Villiers et al., 1995; Martin et al., 2000]. A better understanding of the oceanographic, ecological and geochemical processes affecting these proxies certainly will lead to more accurate estimates of sea surface temperature.
 Recent studies suggest that foraminiferal Mg/Ca provides a new proxy for estimating seawater temperature [Nürnberg et al., 1996; Rosenthal et al., 1997; Hastings et al., 1998; Lea et al., 1999; Elderfield and Ganssen, 2000]. Because Mg/Ca is measured on the same phase as δ18O, and therefore gives the actual temperature at which the foraminifera shell calcified, it is possible to use Mg/Ca measurements to adjust for the temperature-dependency of 18O/16O and isolate the record of δ18Owater [Mashiotta et al., 1999]. Records of δ18Owater can then be used to reconstruct local changes in evaporation-precipitation (and by inference salinity) and provide valuable information about changes in continental ice volume. Paired δ18O and Mg/Ca measurements on the same shells have the additional advantage of allowing for reconstruction of the temporal relationships between changes in SST and continental ice sheets' growth and decay [Lea et al., 2000]. However, the accuracy of Mg-based SST reconstruction is confounded by evidence from core top studies showing that planktonic foraminiferal Mg/Ca is susceptible to postdepositional alteration by dissolution on the seafloor [Brown and Elderfield, 1996; Rosenthal et al., 2000]. Dissolution is also the likely cause for significant inconsistencies among the available calibrations for Mg/Ca-paleothermometry. Most current calibrations of Mg/Ca vs. temperature are based on culture and to a larger extent core top studies, in which measured Mg/Ca ratios are compared with the overlying surface temperatures, prescribed from modern climatological data [Nürnberg et al., 1996; Lea et al., 1999; Mashiotta et al., 1999]. Although these calibrations are very useful for paleoceanographic studies (since they are aimed at reconstructing SST), they are sensitive to the effects of postdepositional dissolution and therefore are typically accurate only when applied to the specific region and time from which they were obtained. To circumvent these problems, Elderfield and Ganssen  use a calibration of core top Mg/Ca against the shell's calcification temperature derived from measurements of δ18O on the same shells. Whereas this may be the correct approach for obtaining a “dissolution-free” calibration, it is not very useful for paleoclimate reconstructions since we are primarily interested in obtaining estimates of sea surface, rather than calcification temperatures.
2. Dissolution Effects
 We have studied two species of planktonic foraminifera, G. ruber (white variety, 212–300 μm size fraction) and G. sacculifer (355–425 μm), which live near the ocean surface and are often used for reconstructing tropical SST. Core top samples of both species along a depth transect (~2700 to 5300 m) on the Sierra Leone Rise (SLR), in the east equatorial Atlantic, show a linear decrease in the size-normalized shell weight and Mg/Ca composition when plotted against pressure-corrected carbonate ion concentration (i.e., CO32−* = CO32− + 20(4 - z), where z is the water depth in kilometers; Figure 1). The results suggest a decrease in weight of 0.06 and 0.31 μg per 1 μmol kg−1 of CO32− for G. ruber and G. sacculifer, respectively. The Mg/Ca data suggest a concomitant decrease of 0.023 and 0.010 mmol mol−1 per 1 μmol kg−1 of CO32− for G. ruber and G. sacculifer, respectively. The tight relationships reflect the preferential dissolution of the shell's primary calcite, which is formed in shallow, warm surface water and therefore is more susceptible to dissolution [Lohmann, 1995]. Thus dissolution shifts the shell’s bulk Mg/Ca toward the chemistry acquired in deeper and colder water, in accord with its dependence on the calcification temperature. Paired measurements of δ18O and Mg/Ca show that the initial relationship between Mg/Ca and temperature is maintained during postdepositional dissolution [Rosenthal et al., 2000]. Also, a depth transect of glacial sediments along the SLR (Y. Rosenthal, unpublished results, 2002) exhibits the same Δ(Mg/Ca)/Δ(wt) trend in shells from the last glacial maximum (LGM) interval as that observed in surface sediments, thus supporting the idea that the relationships depicted in Figure 1 might be applicable to other times in the past. Consequently, we suggest that extrapolating these trends back to the initial shell weight, which is the weight the shell presumably had when it sank to the seafloor, may provide the means for correcting postdepositional dissolution effects on Mg/Ca-based reconstructions of sea surface temperatures [Lohmann, 1995; Rosenthal et al., 2000].
3. Temperature Calibration
 The relationship between foraminiferal Mg/Ca and temperature is best described by an exponential curve (Mg/Ca)shell = BeAT, where A specifies the Mg/Ca dependency on temperature and T is the water temperature. Calibration of planktonic foraminifera, using both culture and field studies, suggests that A ranges from 0.09 to 0.11; i.e., a 10 ± 1% increase in Mg/Ca per 1°C [Nürnberg et al., 1996; Lea et al., 1999; Mashiotta et al., 1999; Lea et al., 2000; Nürnberg et al., 2000]. These results are not significantly different considering the analytical precision and accuracy of the methods and statistical constraints (e.g., low number of samples and replicates). It seems, however, that the lower value is more typical of calibrations using core tops affected by dissolution, whereas higher values are found in studies of culture and well-preserved core top samples. The core top calibration of foraminiferal Mg/Ca against δ18O-derived calcification temperatures of Elderfield and Ganssen  is currently the best published data set to examine the temperature dependency of Mg/Ca. These authors adopted a unique value of A = 0.10 as the exponent for the temperature calibration of multiple species of planktonic foraminifera. Using this value, they obtain species-specific preexponent values, which provide the best fit to each individual species data set. We have adopted a different approach. We use a geometric mean regression of the natural Log of (Mg/Ca) against calcification temperature. This method normalizes the results with respect to the average and standard deviation of each species' data set. Geometric regression offers two distinct advantages: (1) by normalizing to zero intercept for all the species it allows us to obtain the exponent for the entire data set regardless of the species-specific preexponent value, and (2) the standard deviations for both variables (i.e., Mg/Ca and temperature) are weighted equally in the regression. Using this approach we obtain an exponent of A = 0.095 for all the planktonic species used in the Elderfield and Ganssen  calibration. This value is identical with the value recently obtained from a sediment trap time-series calibration of planktonic foraminifera from the Sargasso Sea [Jha et al., 2001]. Therefore we adopt a value of A = 0.095 as the exponent in our temperature regression.
 When plotted against sea surface temperatures, Mg/Ca ratios in foraminifer shells collected from surface sediments at different water depths but underlying the same surface temperature (e.g., SLR) deviate from the exponential calibration line because of postdepositional dissolution (Figure 2). This is due to the fact that dissolved shells no longer reflect the surface temperature; dissolution shifts the bulk shell chemistry towards that acquired in deeper water. Evidently, Mg/Ca ratios in core top samples reflect the combined effects of changes in both SST and the varying degree of alteration of each sample by post depositional dissolution. Consequently, temperature calibrations using core top samples may lead to data aliasing, resulting in apparently different exponential values. To circumvent this problem, Elderfield and Ganssen  used δ18O-derived calcification temperatures rather than SST in their calibration. Using data from different depth transects, similar to those presented here, Dekens et al.  suggest using the core depth or the bottom water carbonate ion concentration for correcting the exponential constants (i.e., the apparent temperature dependency). We suggest, however, that a more accurate mathematical expression of dissolution on the Mg/Ca-temperature calibration, in which sea surface rather than calcification temperatures are used, is a change in the preexponent constant (B) as depicted in Figure 2. Adjusting B to account for dissolution yields a family of calibration curves, all with the same temperature dependence (A = 0.095), but with varying preexponent constants (Figures 3a and 3b). Here we show that B is linearly correlated with the size-normalized shell weight of two planktonic species (Figures 3c and 3d). Therefore we propose new equations for Mg/Ca-thermometry in which the preexponent constant is a function of shell weight: (1) G. ruber (Mg/Ca)rubber = (0.025 wt + 0.11)e0.095T (size range of 212–300 μm) and (2) G. sacculifer (Mg/Ca)sacc = (0.0032 wt + 0.181) e0.095T (size range of 355–425 μm).
4. Variations in Shell Weight/Size Ratio
 The Achilles heel of the new calibration is the assumption of constant initial size-normalized shell weight (wt). Although there is evidence for spatial and temporal variability among morphotypes of the same species of planktonic foraminifera, the variability in size-normalized shell weight has not yet been quantified. Based on a study of G. sacculifer shells from modern shallow sediments in Little Bahama Banks (LBB), Rosenthal et al.  suggested that shells within a restricted size range may have a relatively constant initial weight, which is the weight the shell presumably had before sinking to the seafloor. Thereafter, dissolution shifts the shell weight along a predictable wt/CO3* slope (e.g., Figure 1). Preliminary data suggest, however, that the initial size-normalized shell weight may be more variable than previously anticipated. A recent study shows that changes in the shell weight (wt) of G. sacculifer samples from the Atlantic and Pacific Oceans fall along the same (wt)/CO3* regression [Broecker and Clark, 2001a]. In contrast, samples of the planktonic species, P. obliquiloculata and N. dutertrei, from Atlantic and Pacific sediments fall along different (wt)/CO3* slopes, suggesting that shells from different oceanic basins start with distinctly different weight/size relationships [Broecker and Clark, 2001a]. Some indications as to what factors might control the weight/size relationships come from recent culture and field studies. Culture studies of planktonic foraminifera found that the shell weight of Orbulina universa strongly depends on the CO3 concentrations of the calcifying solution [Bijma et al., 1999]. The data suggest an increase of 10–15% in shell weight for 50–100 μmol kg−1 increase in the CO3 concentration; a similar increase in seawater CO3 ion content is expected from a glacial decrease of atmospheric pCO2 of 100 ppmV. Furthermore, a recent study of North Atlantic surface sediments shows a significant increase in the weight/size ratio of several planktonic species along a north–south transect, suggesting a strong dependence between the shell density and calcification temperature [Elderfield, 2001]. Considering the concomitant effect of temperature on the solubility of CO2 in surface waters, the latter data argue for greater dependence of shell weight on CO3 concentrations. Clearly, this issue needs to be better understood. At this time we estimate that a ±10–15% uncertainty with respect to the initial weight/size ratio will lead to errors of about ±0.7°–1.0°C and ±0.4°–0.6°C in temperature estimates based on our calibrations for G. ruber and G. sacculifer, respectively.
5. Application for Down Core Records
 The new approach is demonstrated in Figure 4, which shows down core records of the planktonic foraminfer G. sacculifer from two cores at different water depths (3152 and 3995 m) on the Sierra Leone Rise, where the overlying mean annual SST is 26.7°C. Although both cores are above the modern hydrographic lysocline, shells from the Holocene (HL) section are significantly dissolved in both sites. Glacial shells from the shallow core at 3152 m are significantly heavier than Holocene shells, whereas in the deeper core at 3995 m the weight of glacial and Holocene shells is very similar. Taken at face value, the down core records of variations in foraminiferal shell weight suggest higher degree of shell preservation during the last glacial maximum in the shallow site and very little LGM-HL change in foraminiferal shell preservation in the deeper site. These results are consistent with recently published shell weight data by Broecker and Clark [2001b], who also argue for increased glacial shell preservation at mid-depths in the Atlantic Ocean. The possibility that some of the down core variation is due to changes in the initial weight/size ratio needs, however, to be considered. Nonetheless, the substantial difference between the general shape of the Mg/Ca and shell weight records (Figures 4a and 4b) supports the hypothesis that variations in Mg/Ca are primarily driven by temperature. The difference in dissolution intensity between the two cores is clearly reflected in the Mg/Ca records. Particularly, glacial samples from the deeper site have significantly lower Mg/Ca than in the shallow core, as expected from the shell weight records. Without correcting for the dissolution effects, the two records suggest different glacial SST and, consequently, different LGM-HL temperature changes. Using the currently available calibration [Nürnberg et al., 2000], we calculate LGM-HL change of −2.5° ± 1°C and −3.1° ± 1°C for the shallow and deeper cores, respectively. These are consistent with previous Mg/Ca-derived estimates of 2.6° ± 1.3°C and 2.2° ± 1°C glacial cooling relative to late HL SST in the eastern equatorial Atlantic [Hastings et al., 1998; Nürnberg et al., 2000]. If we assume that the down core variations in shell weight are primarily driven by changes in the extent of shell dissolution, and using the dissolution-corrected equation described here, we calculate that both cores indicate that SST in the east equatorial Atlantic, above the Sierra Leone Rise, was 2.9° ± 0.4°C colder during the LGM than today (the error includes 1σ S.D. on Mg/Ca and weight measurements, and a 10% uncertainty on the initial shell weight). In conclusion, we suggest that the new equations not only provide more accurate SST estimates, but because they account for dissolution effects, they are applicable globally and back through time, which for the first time allows the comparison of paleoclimatological data from different oceanic regions and preservational settings.
 We thank Suzanne Perron-Cashman for technical help in the lab. Critical reviews from W.S. Broecker, H. Elderfield and Larry Peterson greatly improved the manuscript. This study was supported by the NSF grant OCE9986716 to Y.R.