The Mg/Ca ratio of foraminifera tests is increasingly being utilized as a paleotemperature proxy. Deep time (pre-Pleistocene) Mg/Ca paleothermometry is complicated by the fact that the Mg/Ca ratio of seawater (Mg/Casw) has undergone considerable secular variation over the Cenozoic. Previous studies have corrected for this by assuming an invariant Mg distribution coefficient (DMg) with Mg/Casw. More recent laboratory culturing has shown that this is not the case, demonstrating that a power relationship best describes the variation in test Mg/Ca (Mg/Catest) with Mg/Casw. Therefore, previous corrections are likely to have led to inaccurate temperature reconstructions. Here, we show how the systematics of such a correction should be applied and demonstrate why this provides good evidence that the Mg/Ca ratio of Paleogene seawater was lower than previously implied by foraminiferal constraints, in agreement with the majority of the proxy Mg/Casw evidence. We also demonstrate how it is indirectly possible to constrain the value of H, the power component of a Mg/Catest–Mg/Casw calibration, potentially enabling the appropriate correction of results derived from species where this relationship has not been calibrated. However, this technique should not be treated as a substitute for culturing. The previous erroneous assumptions regarding both (1) the relationship between Mg/Catest and Mg/Caswand (2) the Mg/Ca ratio of seawater at a given time in the past may counteract each other to differing extents. As a result, previous absolute pre-Pleistocene paleotemperature estimates derived from Mg/Ca ratios in foraminifera should be treated with caution, although relative temperature changes over short (<1 Ma timescales) are likely to be reliable.
 The Mg/Ca ratio of foraminifera tests is increasingly being utilized as a paleotemperature proxy. Since the first detailed laboratory culture studies demonstrated a systematic relationship between Mg/Ca and temperature [Nürnberg et al., 1996], the potential of this technique for paleoclimate reconstruction has been reflected by its growing popularity. Although most work has so far focused on the Quaternary, examining oceanic temperature changes over glacial-interglacial cycles, the most relevant periods of Earth's history with respect to the oceanic response to anthropogenic greenhouse gas emissions are thought to lie deeper in geological time. Becauseδ18O-derived temperatures suffer from uncertainties due to assumptions made regarding the pastδ18O of seawater [e.g., Norris et al., 2002; Tripati and Zachos, 2002], it was initially thought that the Mg/Ca ratio of foraminifera tests may be a more promising paleothermometer [Klein et al., 1996]. However, more recent work has identified several potential complications in the Mg/Ca paleothermometer, including salinity [e.g., Arbuszewski et al., 2010] and test size [Elderfield et al., 2002]. It also appears that the Mg/Ca ratio of at least some benthic foraminifera are largely controlled by the carbonate ion saturation state (ΔCO32−) at temperatures below ∼5°C [e.g., Yu and Elderfield, 2008], potentially rendering the bottom water temperature proxy unreliable in some species during cooler intervals. There is currently limited evidence for the effect of ΔCO32− on test Mg/Ca (Mg/Catest) at higher temperatures.
 A significant advantage of the Mg/Ca-paleothermometer overδ18O-derived results is that trace element data may be obtained by plasma-based analytical techniques which, particularly when sampling by laser ablation, are faster and offer intraspecimen spatial resolution [Evans et al., 2011; Eggins et al., 2003]. For these reasons, the Mg/Ca paleothermometer represents the best possibility of simultaneously extracting detailed temperature information while also rigorously assessing sample preservation. Continued refinement of this proxy is therefore of great importance to our knowledge of paleo-ocean temperatures.
 When comparing data over timescales greater than several million years, the most significant source of inaccuracy inherent in this technique is that the Mg/Ca ratio of seawater (hereafter Mg/Casw) has not remained constant. Mg/Casw may be modified by changes in the rate of dolomite/carbonate precipitation and oceanic crust formation, as well as the Mg/Ca ratio and flux of riverine input (Mg and Ca have ocean residence times of ∼14 Ma and ∼1 Ma, respectively). All or some of these parameters have varied over geological time, resulting in a broad increase in Mg/Casw over the Cenozoic [e.g., Sandberg, 1983; Coggon et al., 2010]. The majority of studies utilizing foraminiferal Mg/Ca as a pre-Pleistocene paleotemperature proxy [e.g.,Billups and Schrag, 2003; Creech et al., 2010; Dutton et al., 2005; Lear et al., 2000, 2002; Tripati and Elderfield, 2004; Tripati et al., 2003] have applied or considered a correction for secular Mg/Caswvariation. However, it is increasingly becoming apparent that the method employed by previous foraminifera-based reconstructions is inaccurate, demonstrated in detail below. This is because the basic assumption made by these studies is that the Mg distribution coefficient (DMg = [Mg/Catest]/[Mg/Casw]) remains constant irrespective of varying Mg/Casw. Recent work has shown that this assumption is incorrect [Raitzsch et al., 2010; Segev and Erez, 2006], demonstrating that a power law describes the relationship between DMg and Mg/Casw more appropriately [Hasiuk and Lohmann, 2010]. The implications of this are that (1) previous Paleogene temperature reconstructions are likely to be inaccurate to varying degrees dependent on the specific assumptions made and (2) the discrimination against certain Mg/Caswmodel and proxy data in the literature for the correction of Mg/Ca-derived temperatures is a consequence of assuming DMgto be invariant. Therefore, suggested foraminiferal constraints on the Mg/Ca ratio of early mid-Cenozoic oceans require reconsideration. We stress that these comments are not intended as criticism of previous work, which were largely published before this aspect of Mg/Ca paleothermometry was under investigation. As a result of recent culturing experiments, leading to a significant advance in our understanding of this topic, this issue can now be properly addressed in all future studies attempting accurate temperature reconstruction via this technique.
 Based on a synthesis of existing data from both foraminifera culturing studies and applied foraminifera temperature reconstructions, we demonstrate that previous assumptions regarding the relationship between DMg and Mg/Caswhave produced inaccurate results. We then show how such corrections should be applied in future. While all previously published Mg/Ca-derived temperatures are potentially unreliable because of previous erroneous assumptions,relative reconstructed temperature variations over timescales shorter than ∼1 Ma are not necessarily subject to change following this new method. This is because the maximum potential rate of Mg/Caswvariability is dominantly controlled by the shortest elemental residence time. Furthermore, previous assumptions (a relatively high paleo-Mg/Caswand an invariant DMg with Mg/Casw) may cancel out, and it is therefore possible that some estimated paleotemperatures will undergo limited change when adjusted properly. We demonstrate that reliable paleo-oceanic temperature information can only be obtained when an accurate correction for temporal change in the Mg/Casw ratio have been applied.
2. Results and Discussion
 The majority of foraminifera Mg/Ca-temperature calibrations are presented in the form Mg/Ca =BeAT, where B and A are constants to be defined for a species, genera or group of foraminifera (referred to as the preexponent and exponent component of the calibration, respectively), and Tis temperature. The majority of studies that apply such calibrations to fossil material to reconstruct paleo-ocean temperatures have recognized that Mg/Casw exerts a control on Mg/Catest and therefore a correction is required, even though until the study of Segev and Erez  only preliminary information was available regarding the relationship between test and seawater Mg/Ca in foraminifera [Delaney et al., 1985]. Virtually all studies so far have assumed that the relationship between Mg/Casw and Mg/Catest is linear, equivalent to a horizontal straight line on a DMg–Mg/Casw plot. Expressed as an equation, this requires DMg to be constant irrespective of Mg/Casw:
where t = 0 is the present and t = t is some point in the past. It then follows that for a fossil sample
 Therefore, because the fossil foraminifera Mg/Ca ratio is a function of both temperature and the Mg/Ca ratio of seawater at some point in the past, equation (2) can be combined with the preexponent component of a temperature calibration derived from recent foraminifera to give
This is the method that has been used by virtually all deep time foraminifera Mg/Ca paleotemperature reconstructions so far to correct for the secular variation in Mg/Casw over the Cenozoic (see introduction for references).
 More recent work attempting to quantify the relationship between Mg/Casw and Mg/Catest has demonstrated that equation (1) is not applicable to virtually all marine organisms studied so far. Hasiuk and Lohmann  provide a synthesis of data from abiogenic calcite, echinoids, crabs, shrimps and coccoliths (amongst others) and show that DMg is not invariant with Mg/Casw; in almost all cases the least squares regression results from a power function curve fit. There are currently only three studies that have investigated this relationship in foraminifera, that of Delaney et al. , who cultured the planktic foraminifera Globigerinoides sacculifer, Segev and Erez , who cultured two symbiont-bearing benthic species;Amphistegina lobifera and A.lessonii, and most recently Raitzsch et al. , who cultured Heterostegina depressa. All of these studies demonstrate that a power best fit between Mg/Catest and Mg/Casw gives the least squares regression (Figure 1), with the implication that this is also the case for the relationship between DMg and Mg/Casw. Therefore, in the general form, the relationship can be described as
where F and H are constants to be calibrated for a specific group or species. H is hereafter referred to as the power component of such a calibration. Equation (4) can be alternatively expressed in terms of the Mg distribution coefficient (cf. equation (1)):
Segev and Erez  not only calibrated this relationship in two benthic foraminifera species but also examined the effect of absolute Mg and Ca concentrations on test Mg/Ca. This study demonstrated that Mg/Catest is dependent only on the Mg/Caswratio; foraminifera grown in seawaters with the same ratio but different Mg and Ca concentrations produced equivalent test Mg/Ca ratios. This experiment therefore appears to preclude the absolute concentrations of ions in seawater as a further source of Mg/Ca-temperature reconstruction inaccuracy.
 Based on these culture studies, a more appropriate correction that should be applied to future pre-Pleistocene Mg/Ca-derived temperature reconstructions is to combineequation (4) with an exponential temperature calibration to give
An obvious implication of this is that the nonpower component of the Mg/Catest–Mg/Casw calibration (the constant F) cancels out and is therefore irrelevant when correcting for secular variation in Mg/Casw. Thus the magnitude of such a correction depends entirely upon the age of the samples and on the value of the constant H (the power component of a Mg/Catest–Mg/Casw calibration).
Figure 2 shows the Mg/Catest–Mg/Casw calibration data for the four species previously referred to Figure 1 along with two hypothetical data sets with H = 0 and H = 1, with the constant Fremoved. As previously discussed, almost all Mg/Ca-based paleotemperature studies have assumed DMg to be invariant with Mg/Casw, i.e., H = 1. The consequence of this is that any correction applied to Mg/Ca data in this way is more extreme than necessary, because the magnitude of difference between and increases as H increases (Figure 2). Therefore the correction applied to the preexponent component (the constant B) of a temperature calibration will necessarily be larger if H is assumed to be 1 compared to H < 1, which is the case in all Mg/Catest–Mg/Caswcalibrations so far. There is one published foraminifera-based study which has not made the same assumption (thatH = 1), namely Medina-Elizalde et al. , who for the first time applied a nonlinear correction to their Mg/Ca results based on the Mg/Casw curve of Fantle and DePaolo  and the Mg/Cacalcite–Mg/Casw calibration for inorganic calcite given by Mucci and Morse . While this study represents a significant advance because it is the first to recognize that a linear correction is not appropriate when adjusting results for paleo-Mg/Casw, Figure 2shows that the power component of such a calibration is highly group or species specific. Therefore, utilizing the inorganic calcite calibration when correcting foraminifera-derived results is also likely to result in inaccuracies.
Figure 3 compares the effect of using a power correction (H < 1) and a linear correction (H = 1) on the preexponent component (the constant B) of a Mg/Ca-temperature calibration. Here, the correction applied is expressed as the fraction reduction (Fr) of this component (i.e., B × Fris the modification that would be applied to a Mg/Ca-temperature calibration), while the error in the linear correction (Figure 3b) previously applied is expressed as the absolute difference between the dashed line H = 1 and the species specific calibrations shown above it in Figure 3a:
where ΔFr denotes the fraction difference in the correction applied between a linear and power law Mg/Catest–Mg/Caswcalibration to the preexponent component of a Mg/Ca-temperature calibration.
 For a given Mg/Casw value the linear correction greatly overestimates the necessary adjustment, or alternatively, a linear calibration requires a higher Mg/Casw value in order for an equivalent correction to be applied (Figure 3a), and therefore an equivalent paleotemperature estimate to be derived. The lower the H value of the Mg/Catest–Mg/Casw calibration for a given species, the greater the error in the method previously utilized by most studies. This is of particular concern as the single (albeit preliminary) data set available for a planktic foraminifera (G. sacculifer [Delaney et al., 1985]) suggests a relatively low value of H (0.41). If this is common to many, or most, planktic foraminifera species then previous absolute temperature estimates derived from these are likely to be particularly unreliable. For comparison, Figure 3b also shows the total range in reconstructed Paleogene Mg/Casw reconstructions, including all model and proxy data. This shows that previous corrections to the constant B may be a factor of up to 40% too great (e.g., at Mg/Casw = 2, FrH = 1 = 0.39 whereas FrH = 0.4 = 0.68).
 The difference between assuming a linear Mg/Catest–Mg/Caswrelationship and the method outlined here will be illustrated using the Mg/Ca-temperature calibration ofDekens et al. , along with a range of assumptions regarding the value of the constant H for this species. Dekens et al.  determined the constants B and A to be 0.38 and 0.09 for the planktic species Globigerinoides ruber (white), respectively. Figure 4 explores the effect of hypothetically changing the value of H, while also varying Mg/Casw to cover the total range of values reconstructed for the Paleogene.
 Increasing H shifts the calibration downward, while increasing Mg/Casw shifts the calibration relatively upward. Therefore, an incorrect assumption regarding the value of H in species where this parameter remains unknown (i.e., assuming H = 1) could be largely counteracted by assuming a Mg/Casw value that is too high. Because H < 1 in all Mg/Catest–Mg/Casw calibrations so far, it seems likely that constraints placed on Mg/Casw by results derived from foraminifera, particularly in the Paleogene, tend toward values that are high, because such values are required to produce sensible temperature estimates. This is because assuming H = 1 shifts the original calibration so far downward that a high Mg/Casw value is needed to counteract this. Compare, for example, on Figure 4 the solid blue line (assuming H = 0.5, Mg/Casw = 2.5 mol mol−1) with the red dashed line (assuming H = 1, Mg/Casw = 3.5 mol mol−1, i.e., the correction applied by previous studies). These two different sets of combined Mg/Casw and H values produce corrected calibration lines to be applied to fossil measurements that are almost identical, because the higher H value of the red dashed line is almost exactly counteracted by the lower Mg/Casw value of the solid blue line. Thus, apparently sensible paleotemperature reconstructions were derived from these two (counteracting) incorrect assumptions.
 One major assumption of this correction technique, even if the power relationship between Mg/Catest and Mg/Caswis taken into account, is that the exponential component of a Mg/Ca-temperature calibration remains constant, irrespective of Mg/Casw (i.e., that the constant A does not change whatever value of H or Mg/Casw is used). For this reason, relative temperature changes (over periods <1 Ma) derived in this way are not at all affected by any conjecture regarding either Mg/Casw or any inaccuracies in the determination of the value of H for a specific species or group of organisms. The validity of this assumption remains to be proven and would require comparative Mg/Catest–Mg/Casw calibrations to be carried out over a number of temperatures.
2.3. Application: Paleogene Seawater Mg/Ca
2.3.1. Proxy and Model Data
 For the reasons outlined above it is now clear that both a Mg/Ca-temperature calibration and a Mg/Catest–Mg/Caswcalibration are required in order for the Mg/Ca paleotemperature proxy to produce accurate results. However, a further requirement is a well-constrained Mg/Casw value for the age of the fossil samples under study. Several proxy and model reconstructions for Cenozoic Mg/Casw are available and while most of these agree on the broad trend of Mg/Casw variation over the Phanerozoic, there is disagreement in the detail of these estimates within the Cenozoic, where accurate data at million year resolution is required. Paleogene proxy reconstructions are available using fluid inclusions in halite [Horita et al., 2002; Lowenstein et al., 2001], from the analysis of ridge flank vein carbonates [Coggon et al., 2010] and by comparing the Mg/Ca ratio of fossil and modern echinoderms [Dickson, 2004] (Figure 5). All of these techniques are associated with (in some cases large) uncertainties but are generally in good agreement with each other, suggesting early mid-Cenozoic values of 1.5–2 mol mol−1followed by a rise over the last ∼20 Ma to the present-day value of 5.2 mol mol−1. In the Paleogene, these proxy data are in agreement with the models of Stanley and Hardie , Demicco et al.  and Berner  (Figure 5) but contrast the overall much higher Cenozoic Mg/Casw values suggested by the model of Wilkinson and Algeo . If an error of ±0.5 mol mol−1 is added to the model of Stanley and Hardie  then almost all of the proxy data fall within this range suggesting that it is much more likely to be representative of Cenozoic Mg/Casw than the models suggesting relatively higher Paleogene Mg/Casw values (>3 mol mol−1).
2.3.2. Constraints on Paleogene Mg/Casw: Coupled δ18O-Mg/Ca Data
 Some previous studies [e.g., Broecker and Yu, 2011; Creech et al., 2010; Lear et al., 2000, 2002] have argued that higher Cenozoic Mg/Casw values are more realistic, specifically in some cases that the model of Wilkinson and Algeo  is more likely to be correct than all other model and proxy data arguing for lower values, particularly in the Paleogene. As discussed above, this conclusion results from an incorrect assumption regarding the value of H in a Mg/Catest–Mg/Casw calibration.
 In principle, coupled δ18O-Mg/Ca measurements from foraminifera allow both temperature and to be evaluated: an approach taken by many previous studies to calculate changes in global ice volume over both the Cenozoic and the Quaternary [Elderfield and Ganssen, 2000; Lear et al., 2000; Billups and Schrag, 2002, 2003]. It is now apparent that there are in fact six variables to be constrained: , , temperature and the value of the constant H, as well as δ18Otest and Mg/Catestwhich can be analyzed in well-preserved samples. In an ice-free world, the assumption that deep waterδ18O was −1.2 or −0.9% (Lear et al.  and Cramer et al. , respectively), allows either or H to be calculated if the other is known. Because H is known for only a few species of foraminifera, while almost all of the proxy and model Mg/Casw evidence for the Paleogene suggests low (<2.5 mol mol−1) values (Figure 5), we show how the value of H can be calculated for a species where a calibration is not yet available, thereby fully reconciling Cenozoic Mg/Casw values lower than that of Wilkinson and Algeo  with δ18O-derived temperatures from foraminifera.
Oridorsalis umbonatusis an extant benthic foraminifera which is also present throughout the Cenozoic, enabling direct comparison of recent and fossil material without the need for species-specific corrections. There are several Mg/Ca-temperature calibrations available for this species, which are not all in agreement. It is also unclear whether a linear or exponential fit more appropriately describes the data.Lear et al.  used an exponential calibration, whereas the data of Lear et al.  and Bryan and Marchitto  suggest a linear fit is more appropriate. In particular, calibrations focusing on low temperatures show that a linear fit is equally or more suitable. A linear or exponential best fit appear to represent the data of Rathmann et al.  equally well.
Lear et al.  suggest that early Paleogene Mg/Casw values are likely to be in the region suggested by Wilkinson and Algeo , around 3.6 mol mol−1. This is because when H is assumed to be 1, lower Mg/Casw values shift the calibration to much higher temperatures for a given Mg/Catest value (or rather Mg/Catest values are shifted downward for a given temperature) and therefore produce reconstructed paleotemperature estimates in very poor agreement with comparative δ18O-derived results.
 At 49 Ma the Earth is assumed to be ice free, which, along with the aforementioned assumption of ocean bottom water δ18O on an ice-free planet and depending on whichδ18O-temperature calibration is used, has led to a range in reported temperatures for this time of 12.4–13.4°C [Lear et al., 2002; Cramer et al., 2011]. An uncertainty in the value of δ18Osw of 0.1% results in a temperature error of ∼0.4°C. By using the measured δ18O and Mg/Ca ratio of O.umbonatus at 49 Ma (2.9 mmol mol−1), the constant H can be calculated by combining both these data and respective temperature calibrations; at one specific value the Mg/Ca temperature will match precisely the δ18O-derived temperature. Because the model ofStanley and Hardie  is within error of the majority of the Mg/Casw data currently available (Figure 5), and an independent temperature estimate is available from δ18O measurement, the value of H for this species can be calculated. Specifically, we derive H by iteratively solving equation (6) so that T = 13.4°C when Mg/Casw = 1.6 mol mol−1 (the value given by Stanley and Hardie  at 49 Ma). This gives a value of Hfor this foraminifera species of 0.52 or 0.54 based on the Mg/Ca-temperature data ofRathmann et al.  and Lear et al. , respectively (Figure 6). This value of H is for δ18Osw = − 0.9%, a value of −1.2% would result in H = 0.44 or 0.48, respectively. Following Cramer et al.  a correction has been applied to those lines in Figure 6relating to paleo-Mg/Casw values for changes in the calcite compensation depth (CCD), using a CCD depth at 49 Ma of 3.25 km [Van Andel, 1975]. Such a correction is necessary as a relatively higher CCD lowers ΔCO32− for a given depth.
 In the absence of any calibration study this result should be treated as preliminary, particularly as Mg/Casw is not very well constrained throughout much of the Cenozoic. In section 2.3.1 we noted that with one exception all of the Mg/Casw proxy evidence lies within ±0.5 mol mol−1 of the model of Stanley and Hardie . However, propagating this error through to our calculation of Hresults in an uncertainty of ∼±0.14, therefore until early mid-Paleogene Mg/Casw is better constrained, this methodology can be used as a guide only. Furthermore, an uncertainty in of ±0.1% results in an error in H of approximately ±0.04.
 Despite considerable uncertainties in the calculation of H, we demonstrate how it is possible to reconcile low Mg/Casw values with δ18O-derived temperatures from foraminifera. Given that for all species studied so farH < 1, the possibility of high (>2.5 mol mol−1) Paleogene Mg/Casw values are precluded. Previously, constraints have been placed on Paleogene Mg/Casw by assuming H = 1. This resulted in the exclusion of estimates from the lower range of Mg/Casw values, as a Paleogene ratio of 3.6 mol mol−1 was required to match the δ18O with the Mg/Ca-derived temperatures, despite the available proxy evidence suggesting that such higher values were unlikely. The reasons for this result are discussed above, however it should again be noted that this aspect of Mg/Ca paleothermometry was only understood after the publication of the majority of studies that assumeH = 1. Because virtually all of the paleo-Mg/Casw direct proxy evidence lies reasonably close to the model of Stanley and Hardie  and H < 1 for all foraminifera species studied so far, it is not possible that the model of Wilkinson and Algeo  is representative of the magnitude of increase in Cenozoic Mg/Casw.
 Recently, Cramer et al.  calculated a Cenozoic Mg/Casw record by combining the Cenozoic benthic foraminifera Mg/Ca and δ18O records with a sea level record (used as a proxy for ice volume). We outline in this contribution the inaccuracy in previous Mg/Casw corrections and the associated assumptions and constraints placed on Paleogene Mg/Casw. The recent reconstruction of Cramer et al.  is therefore not assessed in detail here, as such a discussion is outside the intended remit of this paper. Briefly, however, the Cramer et al.  Mg/Casw reconstruction is not included in Figure 5 because it is not entirely independently derived. The record was produced by matching the Cenozoic Mg/Ca and δ18O temperature curves by varying Mg/Casw at each time interval and therefore requires some assumption of the value of H or Mg/Casw at one or several tie points. Given that H is not known from culturing for any deep benthic foraminifera species, the assumption is of Mg/Casw and it is therefore not independent of the reconstructions shown in Figure 5. This is important because the relatively high Mg/Casw values that Cramer et al.  reconstruct (broadly >3 mol mol−1) are a result of their assumption regarding Mg/Casw at some point in the past. Assuming a lower Mg/Casw value at this time would shift the entire reconstruction downward and it therefore does not provide independent evidence that lower Mg/Casw estimates are incorrect.
 Although the discussion has so far focused on the Paleogene, because seawater Mg/Ca ratios were significantly different before ∼20 Ma in comparison to the present day, it is also important to appropriately adjust Mg/Ca data from fossil material younger than this. The model of Fantle and DePaolo  (Figure 5), based directly on high-resolution proxy evidence, suggests that the Mg/Ca ratio of seawater may have undergone fluctuation on submillion year timescales significant enough to greatly increase the inaccuracy in Mg/Ca-derived temperatures. If Mg/Caswhas indeed undergone far more short-term fluctuation than previously accounted for, then any study based on samples older than 0.5 Ma reporting absolute temperatures should take the correction outlined here into account [seeMedina-Elizalde et al., 2008]. Furthermore, any high-resolution study spanning more than 0.5–1 Ma should consider the effect of potential changes in Mg/Casw. While the majority of the Mg/Casw proxy data agree well with the model of Stanley and Hardie , further high-resolution model and proxy reconstructions of secular variation in Cenozoic Mg/Casw are clearly a priority.
 We demonstrate here that previous assumptions regarding the correction of Mg/Ca analyses of fossil foraminifera for secular change in Mg/Casw are incorrect. Studies have hitherto assumed that the Mg distribution coefficient is invariant with Mg/Casw, which is equivalent to H = 1 on a Mg/Catest–Mg/Casw calibration in the form . Recent calibration studies that have quantified this relationship have shown that this is not the case. The implication is that previous studies have overcorrected their Mg/Ca-derived results, leading to the conclusion that the Mg/Ca ratio of (in particular) Paleogene seawater was much higher than suggested by proxy or model evidence. We detail how future corrections should be applied, highlighting the need for further culturing studies that calibrate this relationship (specifically the value ofH) in species that are more routinely used for paleotemperature reconstruction. However, given that temperature information is independently available from δ18Otest analyses, the value of H for a given species can also be calculated because Mg/Catest can be measured and Mg/Casw is known from proxy evidence. Caution should be exercised when indirectly assessing H in this manner because there are uncertainties associated with both the oxygen isotopic composition of paleoseawater and the exact value of Mg/Casw for any given time. By applying this technique to the benthic species O.umbonatus we calculate a range of H based on certain clear assumptions, which are compatible with previous culture experiments demonstrating that H < 1 for all foraminifera species studied so far. Using the same species, we demonstrate that Paleogene Mg/Casw > 2.5 mol mol−1 are not possible, in line with almost all independent proxy evidence.
 For this approach to be valid, a reasonable assumption of δ18Osw is required. It is more difficult to reasonably assess a likely δ18Osw value for ocean surface waters, particularly away from the tropics, as evaporation and freshwater input broadly increase and decrease δ18Osw, respectively. An indirect assessment of the value of the constant Hin planktic foraminifera species using this technique is therefore likely to be inherently less accurate, but may still provide some constraint. The use of well-preserved samples from or before the early Paleogene (>48 Ma), when the world is considered to have been ice free [Lear et al., 2000; Zachos et al., 2008], may lessen the error in whatever assumption regarding δ18Osw is made.
 There are two potential approaches to solving this problem via culturing. The first is based on the assumption made here, that the exponential component of a temperature calibration (A) is not dependent on Mg/Casw, in which case only a temperature calibration and a Mg/Catest–Mg/Casw calibration are required. However, this hypothesis requires confirmation, which could be implemented by calibrating the Mg/Catest–Mg/Casw relationship at several different temperatures. The second approach is to choose a relevant value of Mg/Casw and to calibrate the Mg/Catest-temperature relationship at this value. While this approach is advantageous in that it makes no assumption regarding the behavior of the exponent component of the calibration, it is disadvantageous because it is inflexible and therefore time consuming, as a large number of such calibrations would be necessary in order to be useful for correcting long-term data sets that cover a wide range of Mg/Casw values. It also would not allow data to be updated if new information of the Mg/Casw ratio at a particular time became available.
 D.B.J.E. acknowledges a NERC postgraduate research studentship at Royal Holloway University of London. We thank two anonymous reviewers, whose constructive comments have greatly improved this paper.