Heat Problems Associated with Genesis Flood Models—Part 2: Secondary Temperature Indicators

Introduction

The catastrophic global Flood at the time of Noah (described in Genesis 7 and 8) must have generated an enormous quantity of heat, thus raising the question of how environmental temperatures were kept within limits. This article is the second in a series aiming to identify, and where possible to quantify, the sources of Flood heat in order to provide boundary conditions and guidelines for creation scientists seeking to explain how the necessary cooling was accomplished.

The first article (Worraker 2018) considered boundary conditions relevant to modelling the earth’s thermal history including its internal temperature field, past and present ocean temperatures, surface heat flows and its inventory of heat-producing radionuclides. Of the various indicators of past ocean temperatures in current use by climate scientists, Worraker (2018) dealt only with the oxygen isotope ratio (¹⁸O/¹⁶O) in fossil shells and in ice, expressed as the ¹⁸O level or δ¹⁸O value (see Worraker 2018 for definitions). This is the longest-established and most widely used palaeotemperature indicator and has often been used for calibrating other, newer indicators. In the present article, we describe and assess the significance of several other temperature indicators including: (1) minor element ratio methods, notably Mg/Ca (magnesium/calcium) palaeothermometry, which can in principle be used to measure both the temperature and the oxygen isotope composition of seawater; (2) trace element methods, e.g. Sr/Ca and Li/Mg ratios, with particular application to corals; (3) biomolecular index methods, of which three are now commonly used in marine temperature reconstructions; (4) the carbonate clumped isotope index, which in principle can also give the temperature and, in conjunction with δ¹⁸O measurements, the seawater ¹⁸O level. These methods and their limitations are described in this order in the following subsections; Mg/Ca palaeothermometry, the most widely used of these, is given the most extensive and detailed analysis. The use of fossil assemblages as palaeoceanographic or palaeoclimate indicators is not addressed here, but deserves investigation from a creation science perspective at a later date.

Except where otherwise noted the implicit starting assumptions here are that (i) the conventional geological order of ocean floor deposits holds good within a Flood geology paradigm (Snelling et al. 1996), and (ii) the end of Flood deposits coincides approximately with the end of the Mesozoic (Austin et al. 1994). Whilst these are controversial points in Flood geology, most of our discussion does not critically depend on them. A short Nomenclature is also included.

Subsequent articles (Parts 3–6) in the series consider particular Flood heat sources and Part 7 will summarize our findings and suggest possible directions for future investigations which might reveal a solution to Flood heat problems or to clarify key related questions.

Mg/Ca Palaeothermometry

Introduction

Most planktonic and benthic foraminifera and other shell-forming marine invertebrates including ostracods (a class of small crustaceans, often known as “seed shrimps”), coccoliths and corals build their shells of calcium carbonate (CaCO₃) in the form of calcite or aragonite using calcium ions [Ca²⁺] and carbonate ions [CO₃^2-] from the seawater. In molar terms the magnesium concentration in seawater is typically ~5 times the calcium concentration (Mewes et al. 2014, de Nooijer et al. 2014; see also fig. 1), and during calcite shell formation magnesium ions [Mg²⁺], which are smaller than calcium ions, can substitute for them in the mineral lattice. In inorganic calcification this substitution is endothermic (Rosenthal and Linsley 2006, Lea 2014), such that the shell Mg/Ca ratio increases with temperature. Both experiments and thermodynamic analysis imply a sensitivity in the partition coefficient λ_Mg [≈ (Mg/Ca)_calcite/(Mg/Ca)_solution] of Mg²⁺ ions between inorganic calcite and solution of approximately 3.0% per °C across the range 10–50°C (Barker et al. 2005; Lea, Mashiotta and Spero 1999; Oomori et al. 1987; Rosenthal, Boyle and Slowey 1997). This suggests, in line with hints from early twentieth-century chemical analyses of marine invertebrate skeletons (Clarke and Wheeler 1922), that the atomic Mg/Ca ratio in marine invertebrate shell calcite might serve as a temperature indicator. From the 1950s onwards a few studies began to confirm this idea (e.g. Blackmon and Todd 1959; Burton and Walter 1987; Chave 1954; Chilingar 1962; Katz 1973; Savin and Douglas 1973). However only from the mid-1990s onwards has the Mg/Ca ratio become widely used in palaeothermometry (e.g. Dwyer et al. 1995; Lea 2014; Lea, Mashiotta, and Spero 1999; Nürnberg, Bijma and Hemleben 1996; Rosenthal, Boyle, and Slowey 1997).

The shells most commonly studied in Mg/Ca thermometry are those produced by planktonic and benthic foraminifera (e.g. Barker et al. 2005; Erez 2003, Lea, Mashiotta, and Spero 1999, Katz et al. 2010; Rosenthal, Boyle and Slowey 1997); see figs. 2, 3, and 4. Others include, for example, ostracods (Dwyer et al. 1995; Elmore et al. 2012; Farmer, Cronin and Dwyer 2012), mussels (Klein, Lohmann and Thayer 1996; Vander Putten et al. 2000) and brachiopods (Butler et al. 2015). The Mg/Ca ratio in belemnite calcite, however, does not generally seem to be a useful temperature indicator (Li, McArthur and Atkinson 2012).

Although far more magnesium is incorporated into inorganically precipitated calcite than into foraminiferal calcite (see fig. 1), the temperature sensitivity of the atomic Mg/Ca ratio measured in foraminiferal shells is generally much higher than the inorganic Mg/Ca temperature sensitivity (Lea 2014), and it differs significantly between species (Barker et al. 2005; Lea, Mashiotta, and Spero 1999; Rosenthal, Boyle, and Slowey 1997). Thus the incorporation of Mg into the shell calcite of these organisms, and of marine invertebrates generally, is biologically controlled (e.g. Erez 2003; Pérez-Huerta, Coronado, and Hegna 2018; Rosenthal, Boyle, and Slowey 1997; Sadekov, Eggins, and De Dekker 2005; Skinner and Elderfield 2005). The implications for Mg/Ca thermometry of vital (biological) effects, including environmentally induced habitat changes (e.g. seasonal or life cycle migration through the water column), are considered further below. Diagenetic changes also complicate interpretation of the Mg/Ca temperature signal in the marine sedimentary record. These effects are also discussed further below.

An important feature of Mg/Ca thermometry is that measurement of the atomic Mg/Ca ratio in shell calcite along with the δ¹⁸O value in the same sample can potentially give both the formation temperature and the seawater ¹⁸O level (Billups and Schrag 2002; Elderfield and Ganssen 2000; Lear, Elderfield and Wilson 2000; Stott et al. 2004), and in practice δ¹⁸O values are usually measured alongside Mg/Ca ratios; this information may then allow estimates to be made of salinity and global ice volume (Barker et al. 2005; Lear, Elderfield and Wilson 2000; Rosenthal and Linsley 2006). From a uniformitarian temporal perspective the Mg/Ca ratio is regarded as a useful palaeoclimate indicator because the oceanic residence times of Ca and Mg, 10⁶ and 10⁷ years respectively (Barker et al. 2005; Rosenthal and Linsley 2006) are much longer than typical oceanic mixing times of ~10³ years (Foster, Pogge von Strandmann, and Rae 2010). This means in the conventional chronology that the Mg/Ca ratio of seawater is practically constant over glacial/interglacial cycles. In a Flood scenario geochemical exchange and advection processes would occur on much shorter time scales, drastically reducing residence times. However no estimates of the reduced time scales are currently available.

Since ocean floors are geologically young (Müller et al. 2008), Mg/Ca palaeothermometry has mainly been employed on relatively recent fossil shells, mostly of Quaternary origin (e.g. Barker et al. 2005; Elmore et al. 2015; Nürnberg, Müller, and Schneider 2000; Sadekov et al. 2014). For example, of Mg/Ca data under the MARGO (‘Multiproxy Approach for the Reconstruction of the Glacial Ocean surface’, MARGO 2004) project, Barker et al. (2005) have undertaken SST (Sea Surface Temperature) reconstructions for the LGM (Last Glacial Maximum) using data from planktonic foraminifera. The LGM is dated at about 21 ka BP (before present) in the conventional chronology (Mix, Bard and Schneider 2001). Barker et al. (2005) conclude:

Most Mg/Ca reconstructions are concentrated in tropical regions and results consistently suggest LGM temperatures 2.0–3.5°C cooler than the Late Holocene for these regions. Results from northern latitudes are very scarce and some of them show inconsistencies with other proxies, particularly in those areas in which the temperature change associated with the last deglaciation is believed to be particularly large (> 4°C). Further data are required before any firm conclusions can be made regarding the origin of these disparities.

Mg/Ca data have also been used to trace temperature changes in the Indian Ocean through the last deglaciation (Levi et al. 2007). In another example, Mg/Ca data from the tests of the planktonic foraminifer Neogloboquadrina pachyderma have been used in conjunction with benthic foraminiferal δ¹⁸O data and faunal assemblage data to reconstruct North Atlantic hydrography and Greenland climate during the “last interglacial”, the relatively warm climate interval between the two most recent glacial maxima1 (Irvali et al. 2012, 2016).

However the use of Mg/Ca palaeothermometry is not confined to the Quaternary. By analysing benthic foraminiferal tests Lear, Elderfield and Wilson (2000) have produced a Cenozoic deep-sea Mg/Ca temperature and ice volume record covering the last 50 million years (Ma) in the conventional chronology, concluding that deep-ocean water has cooled by about 12°C since the early Eocene, and that although Antarctic ice first appeared in the earliest Oligocene, the deep water temperature was barely affected. A more sophisticated study by Cramer et al. (2011) extending back into the Cretaceous, using combined δ¹⁸O and Mg/Ca measurements on benthic foraminiferal tests and sea level data reached essentially the same conclusion. Southern Ocean cooling across the EOT (Eocene-Oligocene Transition, 35–32.5 Ma BP) has been traced using Mg/Ca data from southern hemisphere planktonic foraminifera (Bohaty, Zachos, and Delaney 2012).

Bice et al. (2006) have used combined Mg/Ca and δ¹⁸O data from planktonic foraminiferal tests to estimate upper ocean temperatures in the mid-Cretaceous, 102–82 Ma BP. Lea (2014) cites further results of Mg/Ca palaeothermometry through the Cenozoic.

Calibration

Empirical calibration of the Mg/Ca-temperature relationship is necessary because as already noted it is very different for organic precipitation (e.g. by foraminifera) compared with inorganic precipitation and it differs significantly between different organisms (Barker et al. 2005; Lea, Mashiotta, and Spero 1999; Rosenthal, Boyle, and Slowey 1997). In this section we consider several calibration exercises and their results. Complicating factors will be considered in more detail in the following section.

Calibration equations for planktonic foraminifera typically take the form

where T_c is the calcification temperature in °C and Mg/Ca is measured in units of mmol/mol. Examples from Lea, Mashiotta, and Spero (1999) are two species of cultured planktonic foraminifera, Globigerina bulloides, which does not host symbionts and for which the calibrations give A = 0.53 ± 0.17 and m = 0.102 ± 0.008 (temperature range 16–25°C), and symbiont-hosting Orbulina universa, for which A = 1.36 ± 0.24 and m = 0.085 ± 0.011 (17–27°C), corresponding to rates of increase in Mg/Ca with temperature of 10.2 ± 0.8% and 8.5 ± 1.1% per °C respectively.2 The standard error measures of these exponential data fits imply 1σ temperature uncertainties of ±1.13°C for each species.

Anand, Elderfield, and Conte (2003) produced Mg/Ca-temperature calibrations for several species of planktonic foraminifera based on paired Mg/Ca and δ¹⁸O measurements on samples taken in a 6-year sediment trap time series. Calcification temperatures were estimated from δ¹⁸O values, viz. measured δ¹⁸O_c (from shell calcite) and estimated δ¹⁸O_w for the seawater (based on salinity) using a standard palaeotemperature equation (Shackleton 1974) referenced to locally measured temperatures. Fig. 5 shows the data points and a combined calibration curve over the temperature range 14–28°C. In terms of the parameters of equation (1), this gives A = 0.38 ± 0.02 and m = 0.090 ± 0.003, which corresponds to a 1σ temperature uncertainty of ± 1.2°C. Barker et al. (2005, 825) state that:

The combined average deviation between calculated and isotopically derived temperatures for all species used in the generic calibration of Anand et al. (2003) increases from 0.9 to 1.5°C for specific and generic calibrations, respectively.

Thus uncertainties in reconstructed temperatures are smaller for species-specific calibrations than for combined calibrations, but to make practical use of the former in cored samples requires that the species represented are correctly identified; this is not necessarily straightforward for fossil material. The uncertainty in isotopic temperatures is not expressly quantified either by Anand, Elderfield and Conte (2003) or by Barker et al. (2005).

Subsequent temperature calibrations of Mg/Ca in planktonic foraminifera based on samples from a wider range of locations have produced similar calibration curves but with different constants. For example, Regenberg et al. (2009) distinguish between “warm water” shallow-dwelling species and thermocline species and two “cold water” deeper-dwelling species. Their results are summarised in table 1. Regenberg et al. (2009) cite an offset of ≈8°C between the “warm” and “cold” calibration curves,3 noting that this issue could cause problems in reconstructing temperatures from extinct species. The more recent investigation of δ¹⁸O and Mg/Ca values in eight living species of planktonic foraminifera by Jentzen et al. (2018) largely supports previous species-specific Mg/Ca-temperature calibrations whilst demonstrating known effects including depth migration and seasonal abundance variation.

Table 1. Calibration data for the planktonic foraminifera studied by Regenberg et al. (2009). A and m are the parameters derived for an exponential data fit (cf. equation 1). The warm water group comprises Globigerinoides ruber (pink), G. ruber (white), G. sacculifer, Globorotalia menardii, Neogloboquadrina dutertrei, and Globorotalia tumida, while the cold water group comprises Globorotalia truncatulinoides (dextral) and Globorotalia crassaformis. In the warm water 1 group annual T_c values are used for all species; the warm water 2 group is the same except that seasonal T_c values are used for G. ruber (pink) and G. ruber (white). The quoted depth ranges give the average calcification depths for the shallowest-dwelling and deepest-dwelling species in each group. T_c uncertainty values refer to propagated 2σ (95% confidence) intervals.

Species group	Depth range (m)	Temperature range (°C)	A	m	Tc uncertainty (°C)
Warm water 1	30–2600	19–280	0.220	0.1130	±0.24 (19ºC) ±0.29 (28ºC) 0
Warm water 2	30–2600	19–280	0.290	0.1010	±0.24 (19ºC) ±0.29 (28ºC) 0
Cold water	390–6300	8–150	0.840	0.0830	±0.39 (8ºC) ±0.49 (15ºC) 0

Von Langen et al. (2005) developed Mg/Ca-temperature calibrations for the non-spinose (spineless) planktonic foraminifera Neogloboquadrina pachyderma and N. dutertrei for use in temperate and polar regions. N. pachyderma are particularly valuable, being practically the only planktonic foraminifera living in polar waters; furthermore the coiling direction of their tests is temperature-sensitive (Bauch et al. 2003), although interpretation of this in the fossil record is not straightforward. The two types are now recognised as separate species: the left-coiling, cooler-water type is still N. pachyderma, while the right-coiling, warmer-water type is Neogloboquadrina incompta (Darling et al. 2006). Von Langen et al. (2005) used live culturing to establish the Mg/Ca-temperature relationship in neogloboquadrinid shells collected in plankton tows. Their calibration equation (cf. equation 1) gave constants A = 0.51(+0.23,−0.15), m = 0.10±0.02, temperature range 9–19.2°C. Comparing estimated temperatures with measured SSTs showed agreement within ±2°C (2σ confidence interval). However another study of Mg/Ca in N. pachyderma based on cores from the North Atlantic and Nordic Seas (Meland et al. 2006), where the present-day temperature range is 2–8°C, showed negligible sensitivity of Mg/Ca to temperature. Mg/Ca ratios in foraminiferal cells from the central Nordic Seas are ~0.4 mmol/mol higher than expected from established calibrations; sedimentation rates in this region are very low (

The main calibration methods for planktonic foraminifera are culture, core top, and sediment traps. A simple outline of their characteristic advantages and disadvantages as described by Barker et al. (2005) is shown in table 2; see also Katz et al. (2010). Barker et al. (2005) note that despite the expected differences between calibrations produced by these different methods, in practice they give largely consistent results (Anand, Elderfield, and Conte 2003). Intra-specific variability also occurs as planktonic foraminifera migrate vertically throughout their life cycle, often forming calcite at increasing depth as they mature. This migration in depth (and hence in temperature) results in heterogeneity of Mg/Ca ratios within the tests of individual forams. Further intra-test variability occurs in many species due to the secretion of a secondary crust of calcite at the time of gametogenesis (germ-cell production). The Mg/Ca ratio of “whole-test” samples therefore generally represents the integration of various depth habitats and (potentially) of biological controls (Barker et al. 2005). Since many species of planktonic foraminifera live at depths exceeding 50 m, temperatures deduced from Mg/Ca ratios do not necessarily represent the SST of prime interest to palaeoclimatologists. This issue does not seem to be critical for surface and mixed layer species such as Globigerinoides ruber (pink and white) and Globigerinoides sacculifer4, but is more serious for deeper-dwelling species (Anand, Elderfield, and Conte 2003; Dekens et al. 2002). These habitat and life cycle complications are discussed in more detail below.

The use of tests produced by benthic foraminifera for Mg/Ca thermometry is inherently difficult because, except in very shallow water (e.g. as in coral reef environments—see for example Raja et al. 2005), bottom water is cold, which means that the uptake of magnesium by the foraminifera is relatively small. Furthermore during climate changes the temperature variation of the deep water mass is smaller than the SST variation, leading to only small changes in Mg/Ca in the resulting tests. Sadekov et al. (2014) estimate that analytical methods capable of distinguishing differences of 0.1–0.15 mmol/mol are necessary to successfully record glacial-interglacial deep water temperature changes of order 1°C. This small range in Mg/Ca is close to the typical analytical precision reported in the literature (e.g. 1σ ≈ 0.08–0.02 mmol/mol), implying poor signal-to-noise ratio. Complicating effects, e.g. the suppression of Mg/Ca at high carbonate ion concentrations (Bryan and Marchitto 2008), are discussed below.

Rosenthal, Boyle, and Slowey (1997) and Lear, Rosenthal, and Slowey (2002) develop Mg/Ca-temperature calibrations for benthic foraminifera, the latter using samples from a wide range of sites. For Cibicidoides pachyderma from the Little Bahama Bank (LBB), Rosenthal, Boyle, and Slowey (1997) obtain a calibration equation of the same form as (1) with A = 1.36 and m = 0.044 for the temperature range 4.5–18°C; they cite a 2σ forecasting uncertainty of ±0.6°C at 12°C, increasing to ±0.85°C at 18°C. The result obtained by Lear, Rosenthal, and Slowey (2002) for three common Cibicidoides species is similar but with different constants, viz. A = 0.867±0.049 and m = 0.109±0.007, which they estimate gives a 2σ uncertainty in bottom water temperature of ±1°C.

Table 2.Summary of calibration methods for Mg/Ca thermometry. After Barker et al. (2005).

Method	Advantage(s)	Disadvantage(s)
Culture	– Known, controlled temperature0	– Laboratory conditions unrepresentative; – Calibration affected by changing biological controls 0
Core top	– Calibrations based on material forming part of sediment record0	– Temperature must be estimated; – Susceptible to post-depositional alteration, e.g. by calcite dissolution (which reduces Mg/Ca) 0
Sediment trap	– Growth season known, hence range of temperatures used in calibration well constrained; – Trap material best represents material about to enter sediment record0	– Temperature must be estimated0

These Cibicidoides calibrations rely solely on LBB samples. Using samples from the Florida Straits, Marchitto et al. (2007) and Curry and Marchitto (2008) found significantly lower Mg/Ca sensitivity to temperature over the range 5.8–18.6°C. Their best data fits were linear rather than exponential, giving statistically indistinguishable sensitivities of 0.12 and 0.13 mmol/mol per °C respectively. In these cases the reduced sensitivity is most noticeable at temperatures above ~12°C; the authors attribute the difference as possibly due to dissolution effects. The standard error (1σ) estimates for temperature reconstructions from these Mg/Ca calibrations are ±2.4°C (Marchitto et al. 2007) and ±2.6°C (Curry and Marchitto 2008). Bryan and Marchitto (2008) cite the results of numerous Mg/Ca-temperature calibrations for several genera of benthic foraminifera taken both from the literature and from their own study, in total covering the temperature range from –2 to 19.0°C. The temperature standard error (1σ) estimates in the newly investigated species were ±1.6°C for Uvigerina peregrina, ±2.5°C for Planulina ariminensis and P. foveolata combined and ±4.5°C for Hoeglundina elegans.

Kristjánsdóttir et al. (2007) developed cold water (0–7°C) Mg/Ca-temperature calibrations for three Arctic species of benthic foraminifera in order to reconstruct the north Iceland shelf temperature over the last 4,000 years. Using δ¹⁸O-based calcification temperatures for reference they derived calibrations with 2σ uncertainty margins of ±0.63°C (Islandiella norcrossi/helenae), ±1.10°C (Melonis barleeanus) and ±0.62°C (Cassidulina neoteretis).

Barrientos et al. (2018) investigated the Mg/Ca-temperature relationship in six living Arctic species of benthic foraminifera, three of them epifaunal (living on the sea floor) and three infaunal (living within the sea floor sediment); the overall range of bottom water temperatures was very small, approximately –1.9 to +0.9°C; for individual species the range was even smaller. The three infaunal hyaline species (i.e. with clear or translucent shells) showed the clearest Mg/Ca-temperature relationship and were deemed potentially useful for Mg/Ca palaeothermometry in cold regions; these are Elphidium clavatum, Nonionella labradorica, and Cassidulina neoteretis. The calculated sensitivities of two epifaunal species, Cibicidoides wuellerstorfi and Oridorsalis tener, although roughly consistent with previous findings, were based on very limited datasets. However the high-Mg porcelaneous epifaunal species Quinqueloculina arctica showed a strong Mg/Ca dependence on carbonate ion concentration and were deemed by Barrientos et al. (2018) unsuitable for use in Mg/Ca thermometry.

The superfamily Miliolacea of deep-water, high-Mg benthic foraminifera exhibits a practically unique Mg/Ca sensitivity to temperature; these organisms contain on average about 10 times as much magnesium as the benthic species used most often in palaeothermometry. Sadekov et al. (2014) found that in Pyrgo sp. (comprising P. sarsi and P. murrhina) living at various depths in the Timor Sea close to the north Australian coast, the correlation of test Mg/Ca with water temperature and carbonate ion concentration (temperature range –1 to +8°C) followed a linear relationship of the form

where T is the bottom water temperature, Δ[CO₃^2-] (≡ [CO₃^2-]_{in situ}–[CO₃^2-]_saturation) is the carbonate ion concentration referenced to the saturation state, A = 2.53±0.22, B = 0.129±0.023 and C = 4.63±0.53; B has units of mmol/mol per μmol/kg. The temperature sensitivity in equation (2) closely resembles the inorganic temperature sensitivity, implying that the magnesium content of Pyrgo sp. calcite is largely inorganically controlled. Since the magnesium uptake of Pyrgo sp. is so high (~18 mmol/mol at 4°C), Sadekov et al. (2014) note that the analytical precision of Mg/Ca measurements (2σ uncertainty margin 0.08 mmol/mol) is equivalent to an uncertainty in temperature estimates of only ±0.03°C; the approximate equivalent uncertainties for Cibicidoides sp. and Uvigerina sp. are ±0.5–1°C and ±1°C respectively. However the temperatures derived from the extremes of the Pyrgo sp. calibration curves (with the [CO₃^2-] dependency removed) are –0.7±0.27°C when Mg/Ca = 3 and 8.1±0.92°C when Mg/Ca = 25 (1σ uncertainty margins).

In these studies of benthic foraminifera the Mg/Ca calibrations were based on samples taken from cores; sediment traps are not relevant for benthic organisms. However Toyofuku et al. (2000) investigated Mg/Ca in high-Mg benthic foraminifera both in cultures and in specimens taken from natural environments in order to evaluate the effect of environmental factors on Mg/Ca thermometry; they concluded that Mg/Ca values in the foraminiferal tests clearly reflect growth temperatures in the range 10–25°C.

The ostracod Mg/Ca-temperature calibration used by Dwyer et al. (1995) based on core top samples from the North Atlantic (temperature range 2–14°C) was linear, the bottom water temperature being given by T = 0.854*(Mg/Ca)–5.75; they estimate a 2σ uncertainty in reconstructed temperature of ±1°C. Other calibrations are given by Farmer, Cronin, and Dwyer (2012) and by Elmore et al. (2012).

Klein, Lohmann, and Thayer (1996) grew mussels (Mytilus trossulus, also known as M. edulis) in their natural habitat while measuring the water temperature and analysing its chemistry and isotopic (¹⁸O/¹⁶O) composition. They established a linear Mg/Ca-temperature correlation for the mussel shell material (temperature range 5–25°C) with statistics implying an apparent 1σ uncertainty of approximately ±1.5°C. Vander Putten et al. (2000) conducted a similar investigation of M. edulis mussels grown in cages in the sea close to the Netherlands coast (approximate temperature range 8–20°C). They found a seasonal, temperature-related variation in the shell Mg/Ca ratio. However this covariation was abruptly interrupted after the spring phytoplankton bloom, implying that control of magnesium incorporation into the mussel shells was now mainly biologically controlled; hence Vander Putten et al. (2000) could not recommend the Mg/Ca ratio in these mussels as a high-resolution temperature proxy.

Complications

Sample cleaning methods have sometimes been implicated in partial dissolution leading to skewed Mg/Ca ratios (Barker, Greaves, and Elderfield 2003; Marr et al. 2011), and since methods differ between laboratories, comparability of results is often prejudiced. The basic need here is for inter-laboratory standardization.

Beyond this, complicating factors in Mg/Ca thermometry are often difficult to separate because they relate to the effect of environmental conditions on the calcifying organisms during their lifetime and on their shells after death. Furthermore individual environmental factors are often interrelated, for example salinity and seawater magnesium concentration, or pH and carbonate ion concentration. However for practical purposes we may consider them under three main headings: (1) diagenetic effects (Edgar et al. 2015; Kontakiotis et al. 2016); (2) environmental effects, i.e. seawater chemistry (including Mg/Ca ratio, salinity, pH and carbonate ion concentration); (3) vital effects, which arise from the way the calcifying organisms respond to environmental changes and control their own internal chemical environment.

(1) Diagenetic (post-depositional) effects. These include recrystallization and calcite encrustation of shells, which can add high-Mg calcite, and post-depositional dissolution. Of these processes, partial dissolution is widely regarded as the most serious problem in Mg/Ca-palaeothermometry. It generally occurs when the bottom or pore water concentration of CO₃^2- ions is below saturation, i.e. Δ[CO₃^2-]<0. Since Mg-rich calcite is preferentially removed by dissolution, the Mg/Ca ratio of the remaining calcite is reduced (Barker et al. 2005; Brown and Elderfield 1996; Dekens et al. 2002; Rosenthal et al. 2000; Rosenthal and Lohmann 2002; Savin and Douglas 1973), thereby depressing reconstructed temperatures.

The saturation level of CO₃^2- ions is primarily determined by temperature and (especially) pressure: calcite becomes more soluble with depth as the temperature falls and the pressure increases, the latter at a rate of approximately 100 bar per km. While near-surface waters are generally supersaturated with respect to calcium carbonate, at a depth known as the lysocline, the dissolution rate increases dramatically, and below this, at the carbonate compensation depth (CCD), the dissolution rate equals the calcite supply rate, and no more calcite is formed (Berger, Bonneau, and Parker 1982). Roughly speaking the CCD lies about 4.5 km down in the Pacific, 6 km down in the Atlantic, the difference arising because the Pacific has a lower pH and is cooler than the Atlantic, such that its lysocline and CCD are higher in the water column (Geosciences LibreTexts 2019). Within a particular ocean basin depth can thus serve as a proxy for Δ[CO₃^2-] as a calcite dissolution parameter. However sometimes calcite can dissolve well above the lysocline, for example as the degradation of sedimentary organic material releases CO₂ into sediment pore waters, thus acidifying the local environment (Brown and Elderfield 1996; Dekens et al. 2002; Regenberg et al. 2006; Tachikawa et al. 2008).

Several investigators have attempted to estimate the uncertainties introduced by partial dissolution of planktonic foraminiferal tests and if possible to correct for them (Dekens et al. 2002; Khider et al. 2015; Regenberg et al. 2006; Rosenthal et al. 2000; Rosenthal and Lohmann 2002; Tachikawa et al. 2008). Huang et al. (2008) found a seasonally dependent Δ[CO₃^2-] dissolution effect. The effect of partial dissolution on Mg/Ca in benthic foraminiferal tests seems to have received little attention.

The high-Mg crust found on planktonic foraminiferal tests from the very high-salinity Red Sea (Hoogakker et al. 2009) and from the Mediterranean Sea (Boussetta et al. 2011; Kontakiotis et al. 2011, Sabbatini et al. 2011; van Raden et al. 2011) seems to be diagenetic in origin, arising from direct inorganic precipitation of Mg-rich calcite; in the Mediterranean the degree of overgrowth increases from northwest to southeast (Kontakiotis et al. 2016). Such crust is not attributed primarily to high salinity, nor necessarily to the high carbonate saturation state of interstitial water, but possibly to a combination. Sabbatini et al. (2011) find a salinity effect on Mg/Ca in material from the western Mediterranean, and note evidence of recrystallization in some tests (see also Tribble and MacKenzie 1998). Fig. 6 shows an example of an obvious diagenetic overgrowth from an open-ocean site.

(2) Environmental effects. The most important
environmental variables seem to be magnesium concentration in the seawater, salinity, carbonate ion concentration and pH. Carbonate ion concentration and pH are linked via the balance of chemical species representing DIC (dissolved inorganic carbon), viz. aqueous CO₂, bicarbonate (HCO₃^–) ions and carbonate (CO₃^2-) ions. Increased levels of dissolved CO₂ (which
produces carbonic acid) tend to reduce both pH and carbonate ion concentration (Langdon et al. 2000, Russell et al. 2004).

Seawater magnesium concentration. Segev and
Erez (2006) investigated the effect of ambient Mg/Ca
(Mg/Ca_sw) on both calcification and shell composition
in two species of cultured benthic foraminifera. They
found a positive nonlinear correlation between shell
Mg/Ca and Mg/Ca_sw (Mg/Ca_sw range 0.53–10.1),
equivalent to a magnesium distribution coefficient
D_Mg which decreases with increasing Mg/Ca_sw. The
calcification rate in their experiments was sensitive
to Mg/Ca_sw rather than to the absolute Mg²⁺ or Ca²⁺ concentrations. Similar results were obtained by
Raitzsch et al. (2010). For pre-Quaternary times (i.e.
over time scales longer than the oceanic residence
times of calcium and magnesium ions) Evans and
Müller (2012) claim that previous calibrations of
foraminiferal Mg/Ca against both temperature and
Mg/Ca_sw were based on the incorrect assumption that
D_Mg was invariant with changes in Mg/Ca_sw; they
propose an alternative formulation.

Nehrke et al. (2013) investigated the transport
of calcium ions in the benthic species Ammonia
aomoriensis and developed a model to explain the
full range of Mg/Ca found in benthic foraminifera.
They deduced that the major transport mechanism
for calcium ions was trans-membrane transport, with a small PT (passive transport) contribution;
PT occurs through endocytosis (or vacuolization), an
established phenomenon in foraminifera, in which a
drop of seawater incorporated into a vacuole is then
transported to the calcification site. Nehrke et al. (2013)
conclude that this form of PT is key in determining
the trace element composition of the test, claiming
that their model predicts the effect of changing Mg/Ca_sw. Mewes et al. (2014) undertook a culture study in
two benthic foraminifera of calcification as a function
of seawater Mg²⁺ concentration and found that shell
Mg/Ca was positively correlated with Mg/Ca_sw; again,
D_Mg decreased with increasing Mg/Ca_sw. Mewes et al.
(2014) claim that their form of shell/seawater Mg/Ca
relationship is fairly robust and generic.

In terms of changing oceanic Mg²⁺ concentrations
over time, Fantle and DePaolo (2006) and Medina-Elizalde, Lea, and Fantle (2008) have suggested that
seawater magnesium and calcium concentrations
have changed significantly over the last few Ma,
Mg/Ca oscillating on top of a rising Mg/Ca trend.
Medina-Elizalde, Lea, and Fantle (2008) suggest
that allowance for this effect would mean that
early Pliocene SSTs in the tropical Pacific were
significantly higher than derived from models
assuming constant ocean Mg/Ca. Changes in ocean
magnesium inventory can potentially be traced
through its isotopic composition, manifested as the
δ²⁶Mg index,5 since this is unaffected by temperature
or pH but is sensitive to continental weathering
(representing a magnesium source) and to dolomite
formation (a magnesium sink); see Katz et al. (2010);
Pogge von Strandmann (2008).

Salinity. In culture studies of the planktonic
foraminifera Globigerinoides sacculifer, Nürnberg,
Bijma, and Hemleben (1996) found that temperature
was the key factor controlling magnesium uptake
when salinity was kept in a narrow range (33–36‰).
However at constant temperature (26.5°C) and
with widely varying salinity (22–45‰), test Mg/Ca was controlled by salinity, a 10% increase in S
(salinity) producing a 110% increase in Mg/Ca (and
vice versa). Lea, Mashiotta, and Spero (1999) found
in culture studies of Orbulina universa that the Mg/Ca ratio in their tests increased by 4±3% per psu
(1 psu ≈ 1‰—see Nomenclature) salinity increase.
Sadekov et al. (2009) studied the Mg/Ca-temperature
relationship in the final chambers produced by three
species of planktonic foraminifera in core tops from
southern equatorial regions. They used salinity
(taken from previous publications—range 33–38‰)
as a secondary input parameter in their calibration
equations, though without discussing how it might
influence magnesium uptake.

Kisakürek et al. (2008) investigated the Mg/Ca and
Sr/Ca ratios of cultured Globigerinoides ruber (white)
from the Gulf of Eilat as functions of temperature
(18–30°C), salinity (32–44 psu) and pH (7.9–8.4); since
these planktonic foraminifera generally live within
50 m of the sea surface, they are a favourite species
for use in SST palaeothermometry. At ambient pH
levels (8.1–8.3) they found no pH dependence, but
obtained the following calibration equation:

Here T is temperature in °C and S salinity in psu,
A = 0.08±0.02, B = 0.06±0.02, C = –2.8±1.0; quoted
uncertainties are 2σ values. Kisakürek et al. (2008)
suggest that sea surface salinity changes between
glacial/interglacial periods can give rise to overestimates
of Mg/Ca-based SST changes by roughly
0.7°C/psu. In a culture study of Globigerinoides
sacculifer collected from surface water near the
southwest coast of Puerto Rico, Dueñas-Bohórquez
et al. (2009) found that a salinity increase of 4 psu
was equivalent to a 1°C bias on Mg/Ca-based
temperatures, noting that this needs to be taken
into account when using Mg/Ca-based temperatures
in conjunction with foraminiferal δ¹⁸O to deduce
salinity.

In a study of cored samples of four species of
planktonic foraminifera from the Mediterranean
Sea, Ferguson et al. (2008) found salinity-related
Mg/Ca variations in the range 15–59% per psu (i.e.
much larger than in cultured foraminifera); they
concluded that this was not due to diagenetic high-Mg overgrowths. Groeneveld et al. (2008) studied
cored samples of G. sacculifer from Miocene/Pliocene
sediment in the Caribbean, combining both Mg/Ca
and δ¹⁸O measurements to deduce sea surface salinity
changes during the shoaling of the Isthmus of Panama
around 4.5 Ma BP (Bell et al. 2015). Groeneveld et
al. (2008) did not find diagenetic overgrowths with
especially high Mg/Ca, but concluded that there was a
significant salinity variation recorded in their Mg/Ca
data, and proposed a correction to Mg/Ca-determined
SST values for the period 4.5–3.9 Ma using the
Mg/Ca-S sensitivity found by Nürnberg, Bijma, and
Hemleben (1996). However part of the underlying
reasoning involves the assumption of orbitally forced
climate changes; creation scientists generally reject
this assumption (Hebert 2016a, b, c).

Sabbatini et al. (2011), working with cored G.
ruber tests from the western Mediterranean Sea,
found very little Mg/Ca-temperature correlation, but
rather a strong sensitivity of Mg/Ca to salinity, a
+1 psu change in S producing an apparent 1.7°C rise
in T estimated from the Anand, Elderfield, and Conte
(2003) calibration. This is similar to the sensitivity (+1.6°C Mg/Ca temperature bias for +1 psu change in S) found by Mathien-Blard and Bassinot (2009) in
G. ruber tests from open-ocean sites, though in the
latter case this is treated as a method of correcting
Mg/Ca SST estimates using for reference isotopic
(δ¹⁸O) temperature reconstructions based on the
Shackleton (1974) calibration.

Hönisch et al. (2013) undertook a culture study
of the effect of salinity variation on Mg/Ca in three
planktonic foraminifera (Orbulina universa, G.
sacculifer and G. ruber) and combined their results
with previously published culture studies. They
deduced respective Mg/Ca sensitivities to salinity of
4.4±2.3%, 4.7±1.2% and 3.3±1.7% per psu (2σ/95%
confidence intervals), noting that these are much
smaller than sensitivities derived from Atlantic coretop
studies, cited as 27±4% for G. ruber. Hönisch et
al. (2013) suggest that this discrepancy arises from
the dissolution correction often applied to Mg/Ca
data, which can lead to significant overestimation
of temperatures, and claim that combining evidence
of seasonality and latitude-specific habitat depth
preferences with corresponding variations in
environmental conditions enables reconciliation of
culture calibrations and core top observations.

Khider et al. (2015) applied a Bayesian calibration
model to G. ruber Mg/Ca data from 186 globally
distributed core tops in terms of three parameters,
viz. temperature, salinity and dissolution, the
latter expressed as deep-water Δ[CO₃^2-]. They report
resulting sensitivities of 8.7±0.9%/°C, 3.9±1.2%/psu
and 3.3±1.3%/μmol.kg^-1 (for Δ[CO₃^2-] -1)
respectively (2σ uncertainty margins). These results
are in good general agreement with previous studies.
Khider et al. (2015) also applied Bayesian modelling
to a published sedimentary record from the western
tropical Pacific (Stott, Timmermann, and Thunell
2007), concluding that systematic changes in sea
surface salinity and deep-water Δ[CO₃^2-] were the
main sources of bias in Mg/Ca palaeothermometry.

Gray et al. (2018) presented Mg/Ca-SST
calibrations for 440 G. ruber (white) sediment trap/plankton tow samples from the Atlantic, Pacific, and
Indian Oceans; 130 of these were newly collected.
They investigated two calibration models, assuming
(1) pH, and (2) [CO₃^2-], to be the controlling carbonate
system parameter. The resulting Mg/Ca sensitivities
(2σ uncertainty margins) in model (1) are 6.0±0.8%/°C
for temperature, 3.3±2.2%/psu for salinity and
–8.3±7.7%/0.1 pH unit, and in model (2), 6.7±0.8%/°C
for temperature, 5.0±3.0%/psu for salinity and
–0.24±0.11%/μmol.kg-1 for [CO₃^2-]. Gray et al. (2018)
note that in both models the temperature sensitivity
is smaller than in the commonly applied calibrations
of Dekens et al. (2002) and Anand, Elderfield, and
Conte (2003), commenting that estimates of salinity and carbonate chemistry (expressed either in terms of
pH or [CO₃^2-]) should ideally be combined with Mg/Ca
measurements to give reliable SST reconstructions.

In a core-top study of four species of planktonic
foraminifera from the Indonesian Throughflow
region (the region between Borneo, Celebes and the
eastward-extending Java island chain), Zhang et
al. (2019) did not find a significant salinity effect on
Mg/Ca. However they suggested that Mg/Ca-based
temperature differences between two of the species, G.
ruber (sensu stricto6) and G. sacculifer, could be used to
reconstruct the depth of the mixed layer in this region.

Kontakiotis et al. (2016) review the field of
foraminiferal Mg/Ca thermometry, focusing on the
distinction between field-based and culture-based
studies. Given some of the apparent discrepancies
(see, for example, comments above on the work
of Hönisch et al. 2013), they emphasize the need
for combining them to better understand how
foraminiferal Mg/Ca depends on temperature and
the effect of complicating factors, notably salinity.

Carbonate ion concentration. As already noted,
carbonate ion concentration can, if high, lead to
post-depositional calcite encrustation of shells or,
if low or negative, lead to calcite dissolution—in
both cases compromising the use of Mg/Ca as a
palaeothermometer. However it can also influence the
Mg/Ca ratio in calcite produced by living organisms.
Katz et al. (2010) note from various studies that
Mg/Ca in benthic foraminifera at temperatures below
3°C is more sensitive to carbonate ion saturation than
to temperature at low or undersaturated Δ[CO₃^2-] levels, citing a sensitivity of 0.0086 mmol/mol per
μmol/kg. Calibration of Mg/Ca in the deep-water
benthic foraminiferal family Miliolacea by Sadekov et
al. (2014) shows how it depends on both temperature
and carbonate ion saturation [see equation (2)].

Bryan and Marchitto (2008), who found that the
Mg/Ca-temperature relationship in four species
of benthic foraminifera flattens out at higher
temperatures, suggest (but without explanation) a
possible Mg/Ca-suppression effect at high Δ[CO₃^2-].
Lear, Mawbey, and Rosenthal (2010) used published
sensitivities of Mg/Ca and Li/Ca ratios to both
temperature and carbonate saturation state in
benthic foraminiferal calcite to deduce bottom water
temperatures and saturation states through the
Middle Miocene climate transition (16.6–11.6 Ma BP
in the conventional chronology). Dawber and Tripati
(2012) investigated the correlation between four
element/Ca ratios (B/Ca, Li/Ca, Mg/Ca and Sr/Ca)
and bottom water Δ[CO₃^2-] in the benthic foram
Oridorsalis umbonatus and inferred a mechanistic
cause for this correlation (i.e. it didn’t simply reflect the covariation of Δ[CO₃^2-] with other hydrographic
variables that influence element/Ca ratios). Weldeab,
Arce, and Kasten (2016) found that the infaunal
genus Globobulimina (more than one species)
produced calcite Mg/Ca sensitive both to temperature
and to pore water Δ[CO₃^2-], the latter being correlated
with bottom water Δ[CO₃^2-]. They claimed that after
correcting for Δ[CO₃^2-]_{pore water}, their calibrations were both sensitive and robust.

pH. As already noted, pH and carbonate ion
concentration are closely linked, and the effect of
seawater carbonate chemistry on calcification and on
the uptake of magnesium by calcifying foraminifera
can often be expressed through either parameter
(Gray et al. 2018).

As for the apparent effect of pH on shell calcite
Mg/Ca, Lea, Mashiotta, and Spero (1999) report
sensitivities in culture experiments of –6±2% for G.
bulloides and –6±3% for O. universa per 0.1 unit
increase in pH. Russell et al. (2004) report from
further culture experiments that below ambient pH
(pH G. bulloides
and by 7±5% for O. universa per 0.1 unit increase
in pH. Kisakürek et al. (2008), in experiments with
cultured G. ruber, tested the sensitivity of shell
calcite Mg/Ca to pH over the pH range 7.9–8.4. For the ambient pH range 8.1–8.3 the sensitivity was negligible, but reducing pH from 8.1 to 7.9 produced
an increase of 80±10% (2σ) in Mg/Ca, and increasing
pH from 8.3 to 8.4 produced a reduction in Mg/Ca of
35±11% (2σ). Evans et al. (2016), in another culture
study of G. ruber especially concerned with the effect
of seawater carbonate chemistry, argue that pH
rather than CO₃^2- is the key secondary control on
shell calcite Mg/Ca. They present new Mg/Ca-pH
calibrations showing how to correct for differential
modern and ancient pH. As already noted, Gray et
al. (2018) demonstrate how G. ruber Mg/Ca data
can be calibrated by either of two models, both
including temperature and salinity as independent
variables, one including pH and the second CO₃^2- as
the third independent variable; they express a slight
preference for pH to represent the effect of carbonate
chemistry. In support of this, recent studies have suggested the use of boron isotope measurements (δ¹¹B) as a seawater pH indicator (Henehan et al. 2016; Katz et al. 2010; Sosdian et al. 2018).

(3) Vital effects. These relate mainly to
foraminifera, especially planktonic foraminifera.
Included are interindividual variability; intra-test
magnesium distribution; seasonal changes; variation
in habitat depth with age (for planktonic organisms);
shell size; ontogeny (variation in calcification related
to maturity, especially during gametogenesis) and diurnal variation in calcification due to light level changes (e.g. Köhler-Rink and Kühl 2005), notably in the presence of photosynthetic algal symbionts; this last effect is considered below in the context of intratest magnesium banding.

Interindividual variability. Individual forams
within a single population can produce differing
test Mg/Ca ratios. This was demonstrated in a
culture study of G. sacculifer, from which Dueñas-Bohórquez et al. (2011) deduced a contribution from
interindividual variability (1σ) of 2.5±0.5°C to the
total apparent temperature variance, very similar
to the interindividual variability found in a core
top study of G. ruber (Sadekov et al. 2008). Dueñas-Bohórquez et al. (2011) suggest that interindividual
variability may be similar for many planktonic
foraminiferal species. Given a sufficient sample size
(Sadekov et al. 2008 suggest ~20 for G. ruber) from
a single-species population, this variability will have
no significant effect on the estimated mean Mg/Ca
value.

Intra-test magnesium distribution. Microscopic
examination of foraminiferal shells shows that
the distribution of magnesium at the sub-micron
scale is highly heterogeneous (Branson et al. 2013;
Eggins, Sadekov and De Dekker 2004; Fehrenbacher
et al. 2017; Geerken et al. 2018, 2019; Jonkers et
al. 2016; Kunioka et al. 2006; Spero et al. 2015). It follows a banded structure (see fig. 7) in which high
magnesium concentrations are associated with
high concentrations of organic molecules, sodium,
sulphur and other trace elements. However X-ray
absorption spectroscopy shows that magnesium is
uniformly substituted for calcium in an octahedral
coordination within the calcite crystal lattice
(Branson et al. 2013). These observations indicate
the action of continuous calcification and magnesium
uptake mechanisms in foraminifera, thereby
implying an inorganic thermodynamic connection
between seawater temperature and Mg/Ca in their
shells. This fundamentally supports the use of their
Mg/Ca ratio as a temperature indicator. Cusack et
al. (2008) investigated the magnesium distribution
in brachiopods, concluding that it was always
incorporated in the calcite mineral lattice, not in
the organic shell material; however they only found
support for using Mg/Ca as a temperature indicator
in rhynchonelliform brachiopod species, not in the
craniid species Novocrania anomala. Branson et
al. (2018) found that magnesium in the high-Mg
marine ostracod Krithe is hosted in organic shell
materials, not primarily in the calcite lattice; their
observations suggest a more complex biologically controlled
biomineralization mechanism. Unless
the relevant processes and their controls are better
understood, these observations cast doubt on Mg/Ca thermometry based on craniid brachiopod and Krithe ostracod shells.

High resolution microanalysis of Orbulina
universa tests from the Indian Ocean (Eggins,
Sadekov and De Dekker 2004) suggests that
magnesium banding in foraminifera arises, not
from temperature variations, but from the diurnal
variation of [CO₃^2-] concentration and hence of pH
within the foraminiferal microenvironment due to
the day-night photosynthesis-respiration cycle of
algal symbionts: thin high-Mg bands alternate with
broader, low-Mg bands. In this model the high-Mg
calcite would be deposited at night and the low-Mg calcite in the daytime. Later experiments on
the same species (Spero et al. 2015) confirm these
observations and show that Mg-banding is an
inherent feature of biomineralization in O. universa;
they also support the fundamental soundness of
Mg/Ca palaeothermometry. Banding in another
planktonic foraminifer, Neogloboquadrina dutertrei,
which has more complex test morphology, follows a
similar diurnal pattern (Fehrenbacher et al. 2017) in
which high-Mg calcite is also preferentially deposited
at night.

This diurnally paced mechanism does not appear
to be universally applicable. Erez (2003) argues that
calcification and photosynthesis are not necessarily
coupled in symbiont-hosting foraminifera, and that
light-enhanced calcification via photosynthetic
removal of CO₂ does not generally apply to these
organisms; he suggests that symbiotic algae may even
compete with their hosts for inorganic carbon. Erez
(2003) proposes a general model of biomineralization
in foraminifera based on the precipitation of two types
of calcite, high-Mg and low-Mg. However this model
was criticized by Sadekov, Eggins, and De Dekker
(2005), in particular as it applies to the symbionthosting
benthic foraminifera Amphistegina lobifera
and the planktonic species Orbulina universa,
Globigerinoides ruber, and G. sacculifer because it
predicts a pattern of Mg concentration within the
bands in conflict with their observations.

Hathorne, James, and Lampitt (2009) investigated
the detailed shell structure of two species of nonspinose
planktonic foraminifera from the midnortheast
Atlantic, Globorotalia inflata and G.
scitula; both are essentially symbiont barren. Again
they found banding of the Mg/Ca distribution through
the test walls, and concluded that this is due to
biomineralization. Although none of their suggested
models could individually explain the observed
patterns of variation, Hathorne, James, and Lampitt
(2009) found, using whole-test calibrations, that
temperatures based on mean Mg/Ca values from
individual analyses generally matched measured
growth temperatures; an exception was the Mg/Ca ratio in small G. scitula tests with only 3.5 chambers, which was higher than expected.

Geerken et al. (2018) found Mg-banding in the tests
of two benthic foraminifera, closely correlated with
Na-banding. Although a diurnally paced mechanism
for this banding was deemed possible, Geerken et al.
(2018) preferred some combination of other factors,
viz. vacuolization, trans-membrane transport,
a lattice strain effect and metastable precursor
phases. In another culture study of banding in the
same species, Geerken et al. (2019) established that
magnesium, sodium, strontium and potassium are
co-located in bands associated with organic linings
in their tests. Furthermore changes in temperature
and salinity induced coordinated changes in the
banding pattern, which implies that independent
changes in peak or trough height does not explain
interindividual variability in element/Ca ratios.

Seasonal changes. Planktonic foraminifera show
seasonal growth patterns, often becoming more
abundant in warmer conditions, as well as producing
seasonal temperature indications through their test
δ¹⁸O and Mg/Ca values; these temperature changes
are naturally smaller for thermocline-dwelling species
than for mixed-layer species (e.g. Anand, Elderfield,
and Conte 2003; Davis et al. 2016; Hönisch et al. 2013;
Huang et al. 2008; Jentzen et al. 2018; Pak, Lea, and
Kennett 2004; Regenberg et al. 2009; Weinkauf et
al. 2016). In a core-top study of benthic foraminifera
from the Arctic, Skirbekk et al. (2016) found seasonal
reproduction and growth patterns in three species:
Islandiella helenae/norcrossi reproduce and grow
during summer, Buccella frigida in summer and
autumn, and Nonionellina labradorica in autumn. In
the appropriate seasons Skirbekk et al. (2016) found
meaningful Mg/Ca-temperature correlations, which
implies that resulting temperatures were seasonal
rather than annual averages.

Several species of planktonic foraminifera are
characterised by lunar abundance and shell flux
variations, which have been attributed to a lunar-paced
reproductive cycle (Davis et al. 2016; Jonkers
et al. 2015). In sediment trap studies Weinkauf et al.
(2016) investigated the effect of seasonal changes in
temperature, productivity and growth conditions on
calcification intensity (measured by size-normalised
weight) in three species of planktonic foraminifera.
Carbonate saturation was kept effectively constant,
but they found significant inter-species differences in
response to these factors. More generally, although
seasonal effects are in one sense a complicating
factor, the results of relevant sediment trap and core
top studies can serve as a framework for interpreting
subtle details in downcore Mg/Ca data provided that
species are correctly identified and inter-species
differences accounted for.

Habitat depth changes. Several studies have
shown that planktonic foraminifera typically live at
different depths and so record different temperatures
whether based on δ¹⁸O or Mg/Ca; G. ruber generally
gives the closest approach to SST (Anand, Elderfield,
and Conte 2003; Barker et al. 2005; Dekens et al.
2002; Elderfield and Ganssen 2000; Regenberg et al.
2009; Sadekov et al. 2009). Thus an estimate of the
depth range in which sample tests grew is important
for interpretation of the temperature signal they
carry.

We have noted that planktonic foraminifera
often migrate vertically through the water column,
calcifying at greater depths as they mature (Barker
et al. 2005; Sadekov et al. 2009). For example,
Marr et al. (2011) found that Mg/Ca in Globigerina
bulloides from the southwest Pacific varied between
chambers, the smallest value being found in the
final (largest) chamber; this ontological change was
interpreted as due to the forams sinking into cooler
water during formation of the final (fourth) chamber.
Marr et al. (2011) recommended using Mg/Ca
from the penultimate or older chambers for SST
reconstructions.

Shell size and ontogeny. Shell size was investigated
by Elderfield, Vautravers, and Cooper (2002) for 17
species of planktonic foraminifera in six size fractions,
the smallest 212–250 μm and the largest >500 μm.
Apart from two globorotaliid species, Mg/Ca increased
with shell size. This increase is generally in line with
temperatures deduced from δ¹⁸O measurements,
but species which live near the surface show larger
Mg/Ca changes than is consistent with the
temperature changes. For calibration Elderfield,
Vautravers, and Cooper (2002) recommend the use
of a single size fraction, in most cases the largest, but
note that in absolute terms this will vary between
species.

As for ontogeny, Nürnberg, Bijma and Hemleben
(1996) found in cultured G. sacculifer specimens
that had undergone gametogenesis that the Mg/Ca
ratio increased from inner to outer layers of the final
chamber primary calcite. They also found that so-called
GAM calcite, a secondary layer deposited on
the test just before gametogenesis, was considerably
enriched in Mg/Ca relative to the primary calcite,
the enrichment exceeding the reduction naturally
due to calcification in a deeper, cooler environment.
Dekens et al. (2002) noted evidence of GAM calcite in
G. sacculifer but found none in G. ruber. Sadekov et
al. (2009) measured Mg/Ca profiles through the walls
of the final chambers in three species of planktonic
foraminifera. They found that Mg/Ca values in the
low-Mg layer in the final chamber in G. sacculifer
and G. ruber and in the cortex (outer) layer in the
final chamber in Pulleniatina obliquiloculata could be used as temperature indicators in addition to
whole-test values. We have already discussed (see
above) ontogenetic effects interwoven with depth
change effects in G. bulloides in the work of Marr et
al. (2011). Dueñas-Bohórquez et al. (2011) found in
cultured G. sacculifer that the calcite Mg/Ca value
decreased by an average of 0.43 mmol/mol between
successive chambers (four chambers in total).

Summary and appraisal of Mg/Ca
palaeothermometry. (1) Mg/Ca thermometry is
based on the temperature-dependent substitution of
magnesium for calcium in the calcite crystal lattice
in the shells of calcite-forming marine organisms
including foraminifera, ostracods, mussels and
brachiopods; of these, foraminifera, especially
planktonic foraminifera, are the most widely studied.
Since this element substitution is endothermic,
the shell Mg/Ca ratio is expected to increase with
temperature. In practice the Mg/Ca ratio in biogenic
calcite is lower than in inorganically precipitated
calcite, but is more sensitive to temperature. This
implies biological control over the calcification
process.

(2) The particular attraction of Mg/Ca thermometry
is that Mg/Ca ratios can be (and usually are)
measured in the same fossil samples as δ¹⁸O values.
Comparison of these two thermometers can be used
to reconstruct seawater δ¹⁸O values, which may then
permit reconstruction of salinity and continental ice
volume (Rosenthal and Linsley 2006).

(3) Many Mg/Ca-temperature calibrations have
been carried out since the mid-1990s, mostly for
foraminifera, on the basis of culture, sediment trap
and core top studies. Most of these have produced
exponential Mg/Ca-temperature curves, though a
few are better fit by a linear relationship. In terms
of temperature, quoted uncertainty margins are
typically within ±2.5°C. Species-specific calibrations
give smaller uncertainty margins than generic
calibrations.

(4) Most Mg/Ca temperature reconstructions
have focused on near-surface temperatures in the
Quaternary, but Mg/Ca palaeothermometry has been
extended as far back as the Cretaceous, and Mg/Ca
with δ¹⁸O from benthic foraminifera together with
sea level data have been used to reconstruct deep-sea
temperatures and cooling of ~12° since the early
Eocene (Cramer et al. 2011; Lear, Elderfield, and
Wilson 2000).

(5) Several factors complicate the application of
Mg/Ca thermometry. Although difficult to separate,
they may be considered under three headings, viz.
diagenetic, environmental and vital effects. Diagenetic
effects include shell dissolution, which tends to
reduce Mg/Ca values, and calcite encrustation, which
often adds high-Mg calcite. Environmental effects include the seawater magnesium concentration
(especially over long time scales), salinity, carbonate
ion (CO₃^2-) concentration and pH; some calibrations
include these factors explicitly. Vital effects include
interindividual variability, the intra-test magnesium
distribution (notably Mg-banding), seasonal changes,
habitat depth changes, shell size and ontogenetic
effects.

(6) Provided that complicating factors can be
reliably identified and quantified with sufficient
accuracy, Mg/Ca reconstructions of SST, thermocline
or deep water temperatures may be achieved within
a 2σ uncertainty within (sometimes well within)
±2.5°C. However all results obtained by this method
should be treated with caution: it is still subject to
development and refinement, and the pitfalls are not
always obvious.

Trace Element Ratios in Corals (Sr/Ca And Li/Mg)

The aragonite skeletons of scleractinian corals
are considered a sensitive and valuable source of
palaeoclimate data, especially as they are potentially
capable of providing subannual (seasonal) time
resolution (Alibert and McCulloch 1997; Beck
et al. 1992; Fowell et al. 2016; Gagan et al. 2000;
Lea 2014; Swart, Elderfield, and Greaves 2002;
Tierney et al. 2015). The various palaeotemperature
indicators associated with these corals include
δ¹⁸O, together with several based on the uptake of
auxiliary cations, notably Sr²⁺ (Beck et al. 1992),
Mg²⁺ (Mitsuguchi et al. 1996), Li⁺ (Marriott et al.
2004), and even U⁶⁺ (Felis and Pätzold 2004; Min et
al. 1995). Although the coral Mg/Ca ratio has been
used as a SST indicator (Mitsuguchi et al. 1996),
it is not generally regarded as reliable when used
independently of other element ratios (Montagna et
al. 2014). The element ratio most commonly used as
a coral temperature indicator is Sr/Ca (e.g. Alibert
and McCulloch 1997; Beck et al. 1992; DeLong et
al. 2014; Maupin, Quinn, and Halley 2008; Swart,
Elderfield, and Greaves 2002; Wu et al. 2013;
Zinke et al. 2019). Since Sr²⁺ ions are larger than
Ca²⁺ ions, strontium substitution into the aragonite
crystal lattice is exothermic and therefore the Sr/Ca
ratio should decrease with increasing temperature
(Rosenthal and Linsley 2006). As with Mg/Ca
and δ¹⁸O in foraminifera, Sr/Ca and δ¹⁸O can be
measured in the same coral samples to give the
seawater δ¹⁸O value.

However a number of studies have cast doubt on the
reliability and usefulness of the Sr/Ca thermometer.
Complications and uncertainties arise from various
sources, including: (1) algal symbiosis (Cohen et al.
2002; Lea 2014); (2) differing Sr/Ca-SST calibrations
between different coral species, different individuals
of the same species and even within the same colony (Alpert et al. 2016; Gaetani et al. 2011, Rosenthal
and Linsley 2006; Saenger et al. 2008); (3) kinetic
processes such as growth rate (Cohen et al. 2001; Lea
2014); (4) Rayleigh fractionation (which can affect all
element/calcium ratios in aragonite; Grove et al. 2013);
Gaetani et al. 2011; Kuffner et al. 2012; (5) differing
interlaboratory standards (Hathorne et al. 2013a).

These complicating factors have prompted a
search for alternative SST proxies, notably Li/Mg
ratios (Fowell et al. 2016; Hathorne et al. 2013b;
Marchitto et al. 2018; Montagna et al. 2014). The
potential of this indicator lies in the opposing
temperature controls on Li/Ca and Mg/Ca in the
coral skeleton, which amplify the sensitivity of Li/Mg
to SST. Also, Li/Ca and Mg/Ca respond similarly to
Rayleigh fractionation, implying that precipitation
progress does not significantly influence the Li/Mg
ratio of the calcifying fluid; coral calcification
involves a common seawater transport mechanism
for cations, notably magnesium, strontium and
boron (Gagnon, Adkins, and Erez 2012). Using cores
of twentieth-century growth, Fowell et al. (2016)
investigated the skeletal Sr/Ca and Li/Mg ratios of
the coral Siderastrea siderea from the forereef and
backreef zones of the Mesoamerican Barrier Reef
System in the Caribbean. From field calibrations
they found that Li/Mg and Sr/Ca ratios correlate well
with SST, although both ratios are three times more
sensitive to temperature change in the forereef than
in the backreef. This implies the influence of another
(unidentified) factor in addition to SST on element
uptake during coral skeleton formation. Fowell et al.
(2016) find that the use of a combined Sr/Ca and Li/Mg
multiproxy calibration improves the precision of these
SST reconstructions. However in a SST study based
on element ratios in modern Porites corals, Zinke et
al. (2019) found that Sr/Ca ratios gave a better match
than Li/Mg ratios to measured SST changes.

Summary and appraisal of coral Sr/Ca
palaeothermometry. The use of Sr/Ca in aragonitic
corals as a SST indicator is attractive because
of its potential for revealing seasonal changes.
However, along with related element ratios such
as Li/Mg, it is less well developed and understood,
and subject to greater uncertainties, than Mg/Ca
palaeothermometry. At present palaeo-SSTs based
on this method should be treated with great caution,
but improvements can be expected in the coming
decades.

Biomolecular Temperature Indicators

Some marine sediment contains biogenic
molecules, specifically cell membrane lipids (fats),
with measurable characteristics which depend on
their temperature of formation. On the assumption
that these molecules have not been degraded or otherwise modified since they were formed and
deposited, they can serve as temperature proxies.
The temperature in question is usually the SST
or the temperature of the uppermost part of the
water column to a depth of 200 m or less; for climate
scientists this is usually the most important ocean
temperature.

Biomolecular temperature reconstructions are
based on the principle that microorganisms adjust
the rigidity of their cell membranes in response to
environmental temperature (e.g. Ray, White, and
Brock 1971). By altering the number of double bonds,
rings, or branches in their phospho- or glycolipid
membranes, microbes raise or lower the melting point
of their cell structures and thereby adjust membrane
fluidity. Useful lipids for palaeotemperature
reconstructions must be: (1) well preserved and
abundant in ancient sediments; (2) relatively easy
to isolate and identify; and (3) reasonably specific
to an organism such that temperature calibrations
can be determined in both controlled experiments
and in the natural environment (Tierney 2012,
2014). Requirement (3) presumes that the organisms
responsible for producing the molecules of interest
are not extinct. The use of these lipid molecules
as temperature indicators is often linked in the
mainstream literature with the fossil record of the
organisms in view (Brassell 2014).

In order of discovery and usage we consider below
the temperature-sensitive lipids of interest in a
marine context, followed by a note of comparative
studies which help to elucidate when and where they
are applicable, and the uncertainties in the resulting
temperature values.

(1) Alkenones, a type of ketone, first identified in
sea floor sediments by Boon et al. (1978). Their use as
temperature indicators was pioneered by Brassell et
al. (1986). Alkenones are long single-chain molecules
produced by certain haptophyte coccolithophores
(single-celled marine green algae), notably Emiliania
huxleyi and Gephyrocapsa oceanica, which grow in
ocean surface waters. The relevant alkenones contain
37 carbon atoms in the central chain. The degree
of unsaturation, the proportion of doubled carbon-carbon
bonds, depends on the formation temperature:
more unsaturated molecules are produced in colder
water. Alkenone unsaturation thus serves as a
SST indicator, expressed formally as the alkenone
unsaturation index. This was initially denoted U^K₃₇
with an acknowledged temperature range of 11–28°C
(Brassell et al. 1986). However a simpler version
denoted U^K’₃₇ is now more commonly used; this has
a useful temperature range of 0–29°C (Müller et al.
1998). Both indices are defined and their calibrations
described in the Appendix. The upper limit of 29°C
on the use of U^K’₃₇ appears to be fundamental because U^K’₃₇ reaches saturation (its maximum possible value
of 1.0) at this temperature (Conte et al. 2006). Since
the response of U^K’₃₇ to temperature is nonlinear
above 24°C, declining towards its upper limit,
interpretation of alkenone index data in tropical
oceans is problematic. A statistical approach to this
problem using spline fits and Bayesian regression
has been proposed by Tierney and Tingley (2018).

Sachs et al. (2000), in seeking to provide
recommended standards and procedures for
the collection, preparation and use of alkenones
as palaeoceanographic proxies, note a range of
complicating factors. These include horizontal
advection, vertical mixing and the effect of diagenesis
on the unsaturation ratio. In order to ensure that
apparent temporal offsets of climate proxies are
correctly interpreted, Sachs et al. (2000) also suggest
that:

. . . differential mixing rates of alkenone-containing
particles and sand-sized foraminifera should be
quantified by independent dating of the two phases.

However, in a biblical timescale temporal offsets
are likely to be much smaller than envisaged by
Sachs et al. (2000), or practically non-existent,
which implies that the data may need a different
interpretation. Sachs et al. (2000) also suggest that,
at sites characterized by high deposition rates,
alkenone investigations should be combined with
other palaeoclimate proxy measurements. They
further suggest that, in upwelling regions and in the
vicinity of river plumes, salinity and nutrient proxies
should be measured since alkenone synthesis is
sensitive to changes in these parameters.

Herbert (2001) reviews alkenone calibrations
by culture, water column and sediment core-top
measurements. Culture studies show considerable
variation in the U^K’₃₇-temperature relationship and
suggest that growth rate as well as temperature can
influence unsaturation. Assemblages of regional water
column data sets give more consistent temperature
calibrations than culture studies, but results based
on basin-wide or global scales are not so useful.
Globally based sediment core-top data produces a
yet simpler picture in that sedimentary unsaturation
indices follow a linear trend; the best correlation
is that based on mean annual temperature in the
upper 10 m of the water column. Exceptions are seen
at high latitudes where highly seasonal production
and salinity may affect sediment unsaturation ratios.
Herbert concludes that much of the variance seen in
culture and water column calibrations is absent in
sediments, perhaps, he suggests, because of temporal
averaging.

A more comprehensive review of alkenone
palaeothermometry by Herbert (2003) suggests that
U^K’₃₇ is generally a more robust SST proxy than those derived from foraminifera (i.e. δ¹⁸O and Mg/Ca) in
that it survives extensive degradation in the water
column and sediments, although Mg/Ca is preferable
at temperatures above 25°C because of its higher
temperature sensitivity. He notes that the alkenone
index is generally a good proxy for mean annual SST,
although this is not a straightforward relationship
and can be distorted by regional variations in the
factors which control the depth and seasonality of
alkenone production. Herbert (2003) cites evidence
of advection by deep currents distorting alkenone
signals and their interpretation, but does not see this
as a widespread problem. He notes that alkenone
reconstructions of tropical SSTs at the LGM agree
with Mg/Ca results for planktonic foraminifera
in indicating a tropical cooling of 2–3°C (see also
Visser, Thunell, and Stott 2003); thus alkenone
palaeothermometry has contributed significantly to
the question of SSTs at the LGM.

Dekens et al. (2008) compare SST records based
on Mg/Ca and U^K’₃₇ from Pliocene and Pleistocene
sediments in the eastern equatorial Pacific (EEP).
They argue that these proxies can be meaningfully
compared here because they relate to different
organisms (Mg/Ca to planktonic foraminifera and
alkenone unsaturation to coccolithophores, both well
represented in the sediments here) and are subject
to different biases (Mg/Ca needs environments
with good calcite preservation while alkenone
unsaturation measurements need high organic
carbon preservation and temperatures K’₃₇ figure. There
was some uncertainty in the comparison arising
mainly from uncertainty in the Mg/Ca calibration.

Marlowe et al. (1990) identified a series of both
present-day and extinct coccolithophore species which
they considered to be likely producers of alkenones
and alkyl alkenoates found in ocean-floor deposits,
reaching back to ~45 Ma BP in the conventional
chronology. The oldest sediment in which alkenones
have hitherto been identified is early Cretaceous
porcellanite dated at 120.5 Ma (Brassell et al. 2004).
Applying the standard alkenone temperature
calibration to this material produces plausible values
of SST, though Brassell et al. (2004) disclaim this
as a meaningful temperature indication. At the
time of writing the oldest material with published
SST values derived from U₃₇ measurements is early
Eocene, conventionally dated at ~51 Ma (Brassell et
al. 2004).

Prahl and Wakeham (1987, 369) throw an
intriguing sidelight on the use of alkenones preserved
in sediment as palaeotemperature proxies. They ask:

How far back in the geological record do long-chain,
unsaturated ketones store palaeotemperature
information? And, why are the long-chain,
unsaturated ketones preserved in sediments at all?
Most unsaturated lipids of phytoplanktonic origin do
not survive passage through the pelagic food chain
and hence, never even enter the sediment record.
Long carbon chain length, unusual double bond
positions and possibly molecular geometry provide
at least partial explanations for the preservation of
these intriguing biological markers.

These questions could prove worth investigating
from a creationary perspective, since it is not clear
that these biogenic molecules can be preserved intact
in oceanic sediments for millions of years.

(2) GDGTs, iGDGTs or isoGDGTs (isoprenoidal
glycerol dialkyl glycerol tetraethers, Schouten
et al. 2002), for which the temperature indicator
is known as TEX₈₆, the TetraEther indeX of 86
carbons (Schouten et al. 2002; Tierney 2012, 2014).
The membrane lipids used to calculate TEX₈₆ are
86-carbon tetraethers produced by mesophilic marine
and lacustrine Thaumarchaeota (previously known
as Group I Crenarchaeota), such as Nitrosopumilus
maritimus, a practically ubiquitous marine archaeon
which oxidizes ammonia to nitrite. The tetraethers
consist of paired C₄₀ isoprenoid chains with varying
numbers of cyclopentane rings and one cyclohexane
ring connected by ether bonds to terminal glycerol
groups. The detailed molecular structure of the most
complex of these, crenarchaeol and its regioisomer,
have been elucidated by Damsté et al. (2002) using
NMR (nuclear magnetic resonance) imaging; see fig.
8. It appears that the cyclohexane ring here is crucial
for the cold-tolerance of the Thaumarchaeota. Thus
Damsté et al. (2002, 1649) state:

We have hypothesized that the formation of the
cyclohexane ring is an adaption of the membrane
lipids of hyperthermophilic archaea to relatively cold
conditions in the open ocean.

In a biblical creation context, this proposed
adaptation may have been included in the created
genetic potential for diversification among the
archaea.

The TEX₈₆ value is calculated from the proportions
of different numbers of these rings attached to each
tetraether core structure. It is usually correlated
with mean annual SST, but in some cases it reflects
the temperature of subsurface water masses
(Huguet et al. 2007). Tierney and Tingley (2015)
imply that TEX₈₆ may correlate equally well with
the averaged temperature down to 200 m depth; the
temperature range covered in their database is –3 to 30°C. Temperatures above 30°C were obtained by
Robinson et al. (2017), but different variants of TEX₈₆
and different calibrations produced temperatures
differing by several degrees. The definition and
temperature calibration of TEX₈₆ are described in
the Appendix, together with variant forms used in
special circumstances (Kim et al. 2010; Liu et al.
2009a). An associated index termed the RI (Ring
Index) was proposed by Zhang, Pagani, and Wang
(2016) to determine whether iGDGT distributions
from Mesozoic and Cenozoic sediments reflect SSTs
alone, or whether they are influenced by other factors,
e.g. production from terrestrial sources or within
sediments, or indeed by non-thermal factors such
as growth phase or nutrient level. RI is a weighted
average of cyclopentane moieties which can be
determined in the analysis used to determine TEX₈₆.
Zhang, Pagani, and Wang (2016) suggest that when
RI and TEX₈₆ indices deviate from the modern global
TEX₈₆-RI relationship, iGDGT distributions are not
solely temperature-controlled, in which case TEX₈₆-based temperature reconstructions are questionable.
The definition of RI and the reference TEX₈₆-RI
relationship are given in the Appendix.

TEX₈₆ has two acknowledged advantages over U^K’₃₇,
viz. (1) it can be used at temperatures outside the range
for alkenones, and (2) since GDGTs are produced by
archaea, which have a fossil record extending back
into the Precambrian, TEX₈₆ may be used further
down in the geological record (Tierney 2012, 2014).
However point (2) is based on uniformitarian deep-time
reasoning which assumes that the absence of a
particular fossil implies its absence from the earth;
this may not apply in a biblical paradigm. A further
possible advantage, though based on limited research,
is that GDGT distributions may be less affected by
advection than alkenones (Kim et al. 2009; Park et
al. 2014) such that the TEX₈₆ temperature signal is
generally more likely to relate to in-situ conditions. TEX₈₆ has been used as a temperature indicator for
middle Jurassic (Jenkyns et al. 2012) and even for
early Jurassic sediments, corresponding to ~191 Ma in
the uniformitarian chronology (Robinson et al. 2017).

(3) Long-chain alkyl (or alkane) diols. Rampen et
al. (2012) studied a sediment core from the South
Atlantic close to the Congo River outflow (West
Africa), which in uniformitarian terms provided a
43 ka SST record. The temperature indicator here is
LDI, the abundance of the C₃₀ alkyl 1,15-diol relative
to the combined C₂₈ 1,13-, C30 1,13- and C30 1,15-diol
abundance; see Appendix for the diol naming
convention, the definition of LDI and the annual
mean SST calibration adopted by Rampen et al.
(2012). The temperature range of the calibration is –3
to 27°C. Rampen et al. (2012) deduce that in a marine
context the diols of interest were probably generated
by photoautotrophic algae within the top 30 m of the
water column; however they could not unequivocally
identify the organisms responsible. In fresh water the
appropriate diols are produced by eustigmatophyte
algae, but the marine equivalent (Nannochloropsis)
produces long chain diol distributions dominated
by the C₃₂ 1,15-diol, which is relatively scarce in
marine sediments. Nannochloropsis is therefore not
considered to be a likely source of marine diols. Naafs,
Hefter, and Stein (2012) applied the LDI proxy to a
sediment core from the mid-latitude North Atlantic
(near the Mid-Atlantic Ridge) spanning an early Pleistocene section conventionally dated at 2.49–
2.41 Ma (i.e. a complete glacial/interglacial interval).
The results agreed well with U^K’₃₇ -based SST values
and followed a similar trend to benthic δ¹⁸O-based
temperatures. However, Naafs, Hefter, and Stein
(2012) also could not identify the source organisms.
A more recent study seeking to identify the biological
sources of the relevant lipids by comparing lipid and
genetic analyses of suspended particulate matter in
the tropical North Atlantic has so far also produced
inconclusive results (Balzano et al. 2018).

(4) Comparative studies involving biomolecular
temperature indicators. Apart from culturebased
or contemporary marine studies in which
temperatures can be measured directly, most
studies involving biomolecular temperature proxies
provide comparisons with more traditional proxies,
usually δ¹⁸O or Mg/Ca. Thus, for example, Brassell
et al. (1986) introduce the alkenone unsaturation
index via its correlation with δ¹⁸O values for the
planktonic foraminifera Globigerinoides sacculifer
and Globigerinoides ruber and the benthic
foraminifer Cibicidoides wuellerstorfi. Dekens et
al. (2008) compare results from Mg/Ca and U^K’₃₇
measurements from a site in the eastern equatorial
Pacific down to the early Pliocene, about 5 Ma BP
in conventional terms. They conclude that the temperatures recorded by these proxies generally
agree provided that a core-top Mg/Ca calibration
including a suitable dissolution correction is used;
U^K’₃₇ data is taken to represent SST. Liu et al. (2009a)
investigate a globally based set of SST records based
on U^K’₃₇ and TEX₈₆ data, together with corresponding
δ¹⁸O data from benthic foraminifera through the
Eocene-Oligocene transition. The U^K’₃₇ and TEX₈₆ SST
values are generally close together, but a few degrees
higher than the corresponding δ¹⁸O values. For highlatitude
and polar sites this is interpreted by Liu
et al. (2009a) as indicating that while benthic δ¹⁸O
records reflect deep-water production during winter
months, U^K’₃₇ and TEX₈₆ values capture mean annual
SSTs which are probably biased toward late spring/early autumn temperatures.

Richey and Tierney (2016) measured GDGT and
alkenone fluxes and U^K’₃₇ and TEX₈₆ indices in the
northern Gulf of Mexico over a 4-year (2010–2014)
sediment trap time series and compared the data
with core-top sediments at the same location. The
sediment trap sampled the sediment flux from the
overlying water column. The results show some
differences between the two proxies, the alkenone
signal reflecting the near-surface, mean annual
temperature in the region while TEX₈₆ indicates
an integrated mean annual subsurface (0–200 m)
temperature. Standard U^K’₃₇ calibrations are not fully
satisfactory at higher SSTs because of the nonlinear
U^K’₃₇ (T) relationship in this range (Conte et al. 2006).

Becker et al. (2015) developed and introduced
a laboratory protocol for producing rapid and
simultaneous U^K’₃₇, TEX₈₆, and LDI analyses on
samples taken from the same sediment core. Their
test core was taken from the Sea of Marmara, and
covered the period since the LGM (conventional date
21 ka BP). Major climatic changes took place during
this time, including the formation of sapropel S1, dated
according to Becker et al. (2015) at about 10 ka (see
fig. 9). Unit 1 represents lacustrine conditions, while
Unit 2 represents marine and Holocene conditions.
While the diols and iGDGTs were especially abundant
during sapropel S1, the authors concluded that there
were sufficient concentrations of all the relevant lipids
to construct meaningful SST plots throughout. Fig.
9b shows that these proxy-derived SST values are
in broad agreement in Unit 1 and afterwards, with
alkenones generally giving the lowest SST values and
diols the highest. However Becker et al. (2015) regard
the high alkenone-derived SSTs for the last glacial (up
to about 15 ka BP) as unrealistic; they reason that the
U^K’₃₇/SST transfer function is not applicable because
the alkenone-producing organisms in the lacustrine
environment are very different from Emiliania
huxleyi, being characterized by a very different proxy/SST relationship.

Rodrigo-Gámiz et al. (2015) investigated
the applicability of U^K’₃₇, TEX₈₆, and LDI to SST
reconstructions for the subpolar region around
Iceland. They found (i) anomalous LDI-SST values
in core top sediments and (ii) low mass fluxes of 1,13-
and 1,15-diols relative to 1,14-diols, inferring that
Proboscia diatoms, not eustigmatophyte algae, were
the main source of long-chain alkyl diols in that area
and concluding that the LDI index cannot be used
there. Flux-weighted average temperature estimates
had significant negative (approximately –2.3°C for
U^K’₃₇) and positive (up to +5°C for TEX₈₆) offsets against
satellite-derived SSTs and temperature estimates
derived from core top sediment. U^K’₃₇ estimates from
surface sediments around Iceland correlated well
with summer mean SSTs, while TEX₈₆-derived
estimates followed both annual and winter mean
0–200 m temperatures, suggesting a subsurface
temperature signal.

Summary and appraisal of biomolecular
temperature indicators. Temperature reconstructions
based on biomolecular proxies cannot easily be
compared since the residual lipid molecules are
produced by different organisms and are subject
to different biases (e.g. seasonality, the depth of
the water column sampled, diagenetic alteration
etc). Furthermore the alkenone index is limited
to temperatures not exceeding 29°C, and the
organisms which produce marine diols of interest
remain unidentified. In some cases alkenonebased
temperature signals may be compromised
by advection of the alkenone-bearing material; this
may be less of a problem for GDGTs. The use of
biomolecular indicators has largely been confined to
the upper part of the geological record, and none of
them indicates ocean floor or globally representative
temperatures. Although biomolecular temperature
reconstructions should be treated with great caution,
further developments can certainly be expected, and
the geological range of the archaea suggests that
GDGTs at least will be of great interest for research
into pre-Cenozoic ocean temperatures.

Clumped Isotope Palaeothermometry

This more sophisticated version of oxygen
isotope palaeothermometry has emerged within
approximately the last 13 years. It seeks to quantify
how ¹⁸O and ¹³C atoms are distributed in the
lattice of the carbonate crystal by distinguishing
“isotopologues”, molecules of similar chemical
composition but different isotopic composition. When
carbonates are reacted with orthophosphoric acid,
they produce CO₂ gas in isotopic equilibrium (subject
to a constant offset linked to acid temperature)
with the original carbonate. The technique involves
measuring the proportion in this CO₂ of the isotopologue with an atomic mass number of 47, viz. ¹³C¹⁸O¹⁶O, where the two “heavy” rare isotopes (¹³C and ¹⁸O) are substituted in the CO₂ molecule. This represents the amount of “clumping” of the heavy isotopes in the carbonate crystal lattice (Carbonate Research 2015), and depends on its formation temperature. The result is expressed as Δ₄₇‰, and its use is described by Ghosh et al. (2006) thus:

The abundance of the doubly substituted CO₂ isotopologue, ¹³C¹⁸O¹⁶O, in CO₂ produced by phosphoric acid digestion of synthetic, inorganic calcite and natural, biogenic aragonite is proportional to the concentration of ¹³C–¹⁸O bonds in reactant carbonate, and the concentration of these bonds is a function of the temperature of carbonate growth. This proportionality can be described between 1 and 50°C by the function: Δ₄₇ = 0.0592 · 10⁶ · T⁻² − 0.02, where Δ₄₇ is the enrichment, in per mil, of ¹³C¹⁸O¹⁶O in CO₂ relative to the amount expected for a stochastic (random) distribution of isotopes among all CO₂ isotopologues, and T is the temperature in Kelvin.

Ghosh et al. (2006) claim a 1σ temperature precision within ±2°C for Δ₄₇ thermometry. Its calibration up to 50°C has been reassessed and refined by Zaarur, Affek, and Brandon (2013) and its temperature range has since been extended up to 250°C (Kluge et al. 2015). In the experiments of Kluge et al. (2015) the temperature was set at a series of fixed values with quoted precision ±2°C, while resulting Δ₄₇ values were quoted with 1σ uncertainty of order ±0.01‰ (~2% of central values). Came, Brand, and Affek (2014) report a calibration based on modern brachiopods. Their results align well with those of Zaarur, Affek, and Brandon (2013), but they note significant discrepancies with other calibrations.

Δ₄₇ thermometry can be used in both biogenic and
non-biogenic carbonate systems and in marine and
terrestrial settings; for example, it has been used
to constrain the formation temperatures of eggs in
modern birds and in dinosaurs (Eagle et al. 2015);
Bernasconi et al. (2018) list other applications. A
valuable feature in the marine context is that it does
not depend on the δ¹⁸O value of the water in which
the carbonate grew. Hence measurements of Δ₄₇ in
a sample, which necessarily involves measuring
sample ¹⁸O, can in principle be used to reconstruct
both the temperature and δ¹⁸O value of the water.

The derivation of Δ₄₇ values from raw mass
spectrometer data depends on the absolute isotope
abundance ratios in reference materials, specifically
VSMOW (Vienna Standard Mean Ocean Water) and
VPDB (Vienna PeeDee Belemnite; see Ravelo and
Hillaire-Marcel 2007 for definitions). To appreciate
the extreme care in measurement and calibration
necessary to obtain meaningful Δ₄₇ data, note that:
(1) the full Δ₄₇ signal when the carbonate formation
temperature changes from 0 to 1000°C is only of order
1‰ (Schauer et al. 2016); (2) the VSMOW scale for
reporting oxygen isotope ratios of silicates and oxides
is subject to ambiguity of up to 0.5‰, mainly because
of differing procedures of oxygen extraction and
differing definitions of the VSMOW scale between
laboratories (Kusakabe and Matsuhisa 2008); (3) the
natural abundance of the ¹³C¹⁸O¹⁶O isotopologue in
analyte CO₂ is a mere 44.4 ppm (Davies and John
2017).

Meaningful Δ₄₇ measurements therefore require
both reliable contamination indicators and stringent
sample purification procedures. Davies and John
(2017) advocate a cold trap temperature as low as
–60°C to reduce contamination to acceptable levels.
Reliable Δ₄₇ temperature calibrations also require
an accurate figure for ¹⁷O fractionation (Schauer et
al. 2016); to accommodate this Kelson et al. (2017)
recommend the ¹⁷O correction proposed by Brand,
Assonov, and Coplen (2010). Daëron et al. (2016)
employ several approaches to investigate the
influence on measured Δ₄₇ values of the (¹³C/¹²C)
ratio in VPDB, the (¹⁸O/¹⁶O) and (¹⁷O/⁶⁷O) ratios
in VSMOW and λ, the slope of the “triple oxygen
isotope line”, which defines a mass-dependent
fractionation law (Brand, Assonov, and Coplen
2010). Having demonstrated that using different sets
of these parameters can produce systematic offsets
in Δ₄₇ values as large as 0.04‰, Daëron et al. (2016)
recommend using the parameter set proposed by
Brand, Assonov, and Coplen (2010); this includes
λ = 0.528, the observed value for natural waters
(i.e. ocean and precipitation). In short, reliable Δ₄₇
measurements demand extremely high laboratory
standards (Bernasconi et al. 2018)

Stolper, Eiler, and Higgins (2018) investigated
the effects on marine carbonate Δ₄₇ values of
balanced dissolution-reprecipitation reactions (i.e.
recrystallization without change in the total mass
of carbonate mineral) during diagenesis (burial and
lithification) in both deep- and shallow-water settings.
Their models are adaptations of 1D models developed
by Richter and DePaolo (1987), Schrag, DePaolo, and
Richter (1992) and others. Stolper, Eiler, and Higgins
(2018) assume that diagenetic carbonate (i.e. which
forms within the sediment column) forms in isotopic
equilibrium with the pore fluids. This assumption is
based on rates of carbonate precipitation in deep-sea
sediments of 10^-19 moles/m²/sec (Fantle and DePaolo
2007), which they note is 7 orders of magnitude lower
than theoretically estimated rates (Watkins et al.
2013, 2014; Watkins and Hunt 2015). Given such a
large discrepancy in carbonate precipitation rates in
the mainstream literature, the source of these figures
should be re-examined from the perspective of Flood
and post-Flood timescales.

Stolper, Eiler, and Higgins (2018) conclude
from their model that: (1) where the initial burial
temperatures differ significantly (by tens of °C) from
formation temperatures, both δ¹⁸O (carbonate) and
Δ₄₇ values are noticeably modified within the first km
of burial; (2) comparison of model predictions with
newly presented Δ₄₇ data from ODP (Ocean Drilling
Program; see IODP 2017) site 807 in the equatorial
Pacific serves to verify the model while at the same
time indicating, in line with previous studies, that
Palaeogene equatorial western Pacific surface waters
were warmer than they are today; (3) in shallow water
settings, the main sedimentary systems preserved
in Mesozoic and earlier rocks, the model predicts
only minor changes (~0.01‰) in Δ₄₇ values. This is
as expected because formation and initial diagenesis
occur at practically the same temperature.

Clumped isotope analysis of a suite of calcitic and
phosphatic fossil shells from late Cambrian to midlate
Ordovician strata was used by Bergmann et al.
(2018) in conjunction with petrographic and element
analysis to reconstruct both SSTs and seawater δ¹⁸O
levels in the early Palaeozoic. The modern brachiopods
used for calibration included both rhynchonelliform
(calcitic) brachiopods and both extant linguliform
genera, Lingula and Glottidia, which are phosphatic,
from a range of locations; the calibration suite covered
a temperature range of 2–35°C. A key aspect was the
use of paired calcitic and phosphatic fossil materials
taken from the same stratigraphic sections. The
point of this approach was that biogenic phosphates
behave differently from biogenic calcite during
diagenesis and thus serve as a valuable geochemical
archive of oceanic conditions before GOBE, the
“Great Ordovician Biodiversification Event” (Servais et al. 2009) in which apparent marine biodiversity
increased drastically, notably in organisms producing
thick-shelled calcitic skeletons.

Veizer and Prokoph (2015) cite reports of
unrealistically high Palaeozoic ocean temperatures
obtained by Δ₄₇ thermometry (e.g. Henkes et
al. 2014). Henkes et al. (2014) report apparent
temperatures derived from Δ₄₇ values in calcite from
late Mississippian (Carboniferous) brachiopods from
the Bird Spring formation, eastern Great Basin
province, Nevada, USA reaching up to 166±13°C (the
quoted uncertainty margin is 1σ/√n where n is the
number of samples, in this case 3); see fig. 10. They
infer that the fundamental problem is diagenetic
reordering of C-O bonds in the calcite crystal lattice
when residing for long periods at high temperature,
a process that cannot be detected via changes in
shell microstructure or trace element concentration.
Following Passey and Henkes (2012), Henkes et al.
(2014) undertook laboratory experiments involving
heating fossil brachiopod calcite at different
temperatures and times to observe directly rates of
¹³C-¹⁸O bond reordering. From the results they were
able to deduce the Arrhenius parameters which
characterise the reordering reaction, referring to
the first-order model7 of Passey and Henkes (2012)
and their own more sophisticated model, described
as a “transient defect/equilibrium defect” model. They concluded that calcite samples kept below
about 100°C for 10⁶–10⁸ years should not be affected
by solid state C-O bond reordering. The equivalent
figures for dolomite are an upper temperature limit
of 150°C for tens of millions of years (Lloyd, Ryb,
and Eiler 2018). From a biblical perspective these
timescales are unrealistic, which suggests that the
assumed thermal histories and underlying physics
should be reexamined with much shorter time scales
in view.

Breitenbach et al. (2018) have undertaken
coupled Mg/Ca and Δ₄₇ studies of core top samples of
planktonic foraminifera from several oceans, claiming
from their results that this combination can provide
reliable and consistent temperature estimates.

Summary and appraisal of clumped isotope
palaeothermometry. Although the clumped isotope
method looks very promising and is currently the
subject of vigorous development, results obtained to
date should be treated with caution. However the
method can be applied so widely using fossil and
mineral samples from the whole geological record
that it will inevitably be developed further. Creation
scientists are well advised to keep abreast of future
developments.

Interpretation of the Data in Terms of Flood Geology

Most of the commentary on the various
palaeothermometers discussed in this article would
apply either on conventional or biblical time scales.
Although the life spans of relevant fossil-producing
organisms are not generally well known, it is unlikely
that many species live for years; brachiopods are
an obvious exception. Weeks or months seem more
typical for foraminifera and ostracods; see, for
example, Nigam, Saraswat, and Mazumder (2003)
regarding the life spans of planktonic foraminifera.
This is short compared with expected timescales
of environmental change in a post-Flood scenario.
Violent rapid changes in ocean conditions during
the Flood year itself are most likely to be manifest
in sudden changes in faunal assemblages, which are
not considered here.

In general terms changes in ocean conditions
were probably much gentler after the Flood than from post-Flood sediment cores should, subject to
proper calibration and allowance for complicating
factors, fairly represent sequences of temperature
changes. During the Flood whole ecosystems were
probably transported, rapidly and often violently,
from their pre-Flood environments and may have
become mixed and buried with others. Consequently
fossil shells or tests within Flood sediments would
probably give relatively messy, perhaps confusing,
palaeotemperature signals. Thus where there
are both Flood and post-Flood sediments on the
ocean floor, temperature-related data from cores
penetrating the Flood/post-Flood boundary might
show a change in character from inconsistent and
confusing below the boundary to more consistent
above it. This in turn could serve to enable mapping
of the Flood/post-Flood boundary on the ocean floor.
However none of the literature considered in this
paper has presented results obviously following such
a pattern; the idea remains conjectural.

The temporal coverage of the proxy data of interest
is not sufficiently dense to construct plots of (say)
Mg/Ca-derived temperatures through the Cenozoic to
rival the δ¹⁸O plot presented by Veizer and Prokoph
(2015). A plot of Mg/Ca and δ¹⁸O-based deep-sea
temperatures since the early Eocene is presented
by Lear, Elderfield, and Wilson (2000), who used
data from six species of benthic foraminifera from
four well-separated sites to deduce an overall
cooling of 12°C since the early Eocene; see fig. 11.

A more sophisticated study, again based on benthic
foraminiferal Mg/Ca and δ¹⁸O together with sea-level
records (Cramer et al. 2011), produced similar results.
Although this study extended further back into the
Cretaceous, there was no Mg/Ca data from earlier
than the Palaeocene (~62 Ma BP in conventional
terms); see figs. 12 and 13. A puzzling feature of the
work reported by Cramer et al. (2011) is that cooling
episodes do not necessarily correlate with ice volume
growth, expressed thus in their Abstract:

Our reconstructions indicate differences between
deep ocean cooling and continental ice growth in
the late Cenozoic: cooling occurred gradually in the
middle-late Eocene and late Miocene-Pliocene while
ice growth occurred rapidly in the earliest Oligocene,
middle Miocene and Plio-Pleistocene.

However, Cramer et al. (2011) acknowledge their
ignorance of the mechanisms underlying these
episodes of rapid ice sheet growth. This apparent
timing mismatch should perhaps be investigated from
a Flood geology perspective. In terms of temperature
the results obtained by Lear, Elderfield, and Wilson
(2000) and by Cramer et al. (2011), although subject
to significant uncertainties, tie in closely with the
corresponding δ¹⁸O data and support the conclusion of
Worraker (2018) that deep ocean temperatures never
rose above 13°C during the Cenozoic. Post-Flood Ice
Age models which assume significantly higher bulk
ocean temperatures and in which Cenozoic deposits
represent the post-Flood period conflict with these
findings.

Other results from the use of the temperature
indicators discussed here relate to specific water
depths, specific regions and specific points in geological
history and do not add a great deal to the overall
picture of ocean temperatures through time. However,
there is considerable Mg/Ca coverage available of the
Quaternary, including for example SSTs in equatorial,
tropical and polar regions (Barker et al. 2005; Irvali
et al. 2012, 2016; Levi et al. 2007; Nürnberg, Müller,
and Schneider 2000), thermocline temperatures in
the South Atlantic (Groeneveld and Chiessi 2011),
Antarctic Intermediate Water temperatures (Elmore
et al. 2015) and bottom water temperatures in the
eastern equatorial Pacific (Sadekov et al. 2014). For
temperature-time plots from a selection of these
sources see figs. 14–19; in all cases the original
references should be consulted for more detailed
background information. Since the Quaternary is the
geological interval of special interest for modelling a post-Flood Ice Age, these Mg/Ca-based results serve as
useful ocean temperature data points against which to
check model predictions. Other coverage from Mg/Ca
results cited here includes Caribbean SSTs through
the Miocene-Pliocene transition (Groeneveld et al.
2008; see fig. 20), thermocline and intermediate deep
water temperatures in the Southern Ocean through
the Eocene-Oligocene cooling (Bohaty, Zachos and
Delaney 2012; see fig. 21) and mid-Cretaceous tropical
Atlantic upper ocean temperatures (Bice et al. 2006;
see figs. 22 and 23). Results from Bice et al. (2006)
may be problematic, e.g. because of conflicting trends
in δ¹⁸O and Mg/Ca data and the very high reported SSTs, but the others should again be treated as
providing useful data points when modelling Flood or
post-Flood environmental conditions. The literature
cited here, of course, is by no means exhaustive.

We have noted certain questions and inconsistencies
in the conventional literature which raise issues worth
investigating from a creation science perspective.
For example, we have cited a comment by Prahl
and Wakeham (1987) questioning the longevity
and integrity of alkenones, which have been used as
palaeotemperature indicators as far back as the early
Eocene, 51 Ma BP in the conventional chronology.
Investigation of the degradation of these and other
biogenic molecules (GDGTs and long-chain diols) in
ocean sediments over time seems a worthwhile creation
science exercise. The huge mismatch of 7 orders of
magnitude between (supposedly measured) rates of
carbonate precipitation in deep-sea sediments (Fantle
and DePaolo 2007) and theoretical estimates (Watkins
et al. 2013, 2014; Watkins and Hunt 2015) clearly
deserves reexamination from a biblical viewpoint.
The question of solid-state C-O bond reordering cited
by Henkes et al. (2014) as the cause of unrealistically
high Palaeozoic temperatures obtained by Δ₄₇
palaeothermometry, supposedly occurring over multi-million
year timescales, should also be reexamined.

Conclusions

1. All the ocean palaeotemperature indicators
reviewed here, specifically the Mg/Ca ratio in
calcite fossil shells, the Sr/Ca and Li/Mg ratios in
scleractinian corals, the biomolecular indicators
(the alkenone unsaturation index, the iGDGT index
or TEX₈₆, and the LDI or long-diol index) and the
clumped carbonate index, suffer from significant
complications and uncertainties. However all are
subject to active current research and development, especially the very widely applicable clumped
carbonate index, and improvements in accuracy and
reliability can be expected in the coming decades,
regardless of timescale assumptions. In many studies
two or more of these indicators are combined, which
can provide additional information (e.g. salinity and
continental ice volume from simultaneous δ¹⁸O and
Mg/Ca measurements) and facilitate assessment of
complicating factors. In Mg/Ca palaeothermometry, the most mature and widely used of these methods,
claims of an uncertainty of order ±2.5°C are
reasonable provided that complicating factors have
been assessed and accounted for.

2. Our most important conclusion, based on
extensive combined benthic foraminiferal δ¹⁸O-Mg/Ca data and sea level data, is that deep
ocean water has cooled by about 12°C
since the early Eocene. This reinforces
the conclusion in Worraker (2018) that
deep ocean temperatures never exceeded
13°C through the Cenozoic, an important
constraint on Flood and post-Flood
environmental models.

3. The temperatures derived from proxy
studies restricted to particular intervals in
the geological record, particular areas and
particular water depths (surface, thermocline,
bottom water etc.) can, subject to scrutiny
from a creation science perspective, be used
as reference data points against which
the predictions of Flood and post-Flood
environmental models may be checked;
examples are the extensive δ¹⁸O-Mg/Ca
coverage of the Quaternary, and the cooling
of thermocline and intermediate deep water in the
Southern Ocean across the Eocene-Oligocene transition
(Bohaty, Zachos, and Delaney 2012). The exact use of
such data points will depend on how a particular model
is chosen to relate to the geological record.

4. We have found some puzzling questions and
inconsistencies in the conventional literature
which merit investigation from a creation science
perspective. Most of these are related to time scales,
viz. the longevity and integrity of biomolecules in
ocean floor sediments over multi-million year time
scales, the rates of carbonate precipitation in deep-sea
sediment, and solid state carbon-oxygen bond
reordering over multi-million year time scales.
The puzzling apparent non-relationship between temperature and ice volume through the Cenozoic
noted by Cramer et al. (2011) also merits a creation
science investigation; this may prove of particular
interest for models of the post-Flood period.

Acknowledgments

Paul Garner (Biblical Creation Trust) provided
access to many of the references. I wish also to thank
the anonymous reviewers of this paper for their
suggestions, which I believe have enhanced its value.

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Nomenclature

Bayesian: Bayesian statistics is based on the Bayesian
interpretation of probability, in which probability expresses
a measure of belief or expectation of an event, which can
change in response to new information, in contrast to
the traditional frequentist interpretation which views
probability as the limit of the relative frequency of an event
after a large number of trials. It uses Bayes’ theorem to
compute and update probabilities after obtaining new data.
Bayes’ theorem describes the conditional probability of an
event based on data plus prior information or beliefs about
the event or conditions related to the event (e.g. MathPages
2019). For example, in Bayesian inference, Bayes’ theorem
can be used to estimate the parameters of a probability
distribution or statistical model.

Benthic: Benthic organisms (collectively benthos) live at the
bottom of an ocean or lake. Species living on the bottom
are described as epifaunal, while those living within the
surface layer or just below are termed infaunal.

Bølling/Allerød: A warm climate interval starting abruptly
following the Heinrich 1 event at the end of the Pleistocene
and ending with the start of the Younger Dryas, i.e.
occupying the interval ~14.5–12.9 ka BP in the conventional
chronology (Carlson et al. 2007; Liu et al. 2009b).

Coccoliths: Plates of calcite formed by single-celled algae
known as coccolithophores; coccoliths are the main
constituent of chalk deposits.

Diol: These are alcohols, hydrocarbon molecules characterized
by two hydroxyl groups attached to a central chain of
saturated carbon atoms. In the IUPAC naming convention
they are formally denoted alkane-n,n-diol, where alkane
corresponds to the number of carbon atoms in the chain, and
n,n give the numbers of the carbons in the sequence where
the hydroxyls are attached. The sequence is numbered so
as to give one of the hydroxyl groups the lowest possible
number. Thus, for example, propane-1,2-diol has 3 carbon
atoms in its chain, with hydroxyl groups attached to atoms 1 and 2 in the sequence. The diols of interest in temperature
reconstructions are based on considerably longer alkanes
than this.

Eustigmatophyte: Single-celled eukaryotic algae found in
marine and freshwater environments and soils. They are
photosynthetic autotrophs, i.e. their main energy source is
sunlight.

Gametogenesis: The production of gametes, the cells
involved in sexual reproduction to produce a new individual
organism. At this point in the life cycle of a calcifying
foraminifer it may deposit a significant amount of calcite in
its test (Köhler-Rink and Kühl 2005).

Heinrich 1 (or H1): The last of a series of events (H1-H6)
generally viewed as the production of large numbers of
icebergs in the Hudson Strait region of Canada. H1 is dated
in the conventional chronology at about 18 ka BP. The
defining diagnostic feature of Heinrich events in sediment
cores is the presence of detrital carbonate (limestone
and dolomite) from lower Palaeozoic basins of Northern
Canada. Heinrich events are also marked by high lithic
to foraminifer ratio and increased relative abundance of
the cold-water planktonic foraminifer Neogloboquadrina
pachyderma (Hodell et al. 2008).

Isomer: Molecules with the same chemical formula but
different chemical structures. Isomers do not necessarily
share similar chemical properties unless they also have the
same functional groups.

Mixed layer: When referring to the oceans, this is the near-surface
region which has been homogenized in temperature, density
and salinity by turbulence generated by (1) wind and wave
action, often generating or interacting with ocean currents,
and (2) Rayleigh-Taylor instability, a vertical instability due
to cooling at the surface or to injection of brine produced by sea
ice formation. Typically the mixed layer extends downwards
by 20–90 m, being deeper in winter than in summer. However
it may extend down much further (as in the Labrador Sea) if
a Rayleigh-Taylor instability occurs. Beneath the mixed layer
are the barrier layer and the thermocline, where temperature
falls rapidly with increasing depth.

Oil window: The geological environment in which petroleum
products are thought to form from kerogen (solid organic
material) as a result of thermal degradation and cracking
during burial. The typical range of depths is 760–4,880 m
and the range of temperatures 65–150°C.

Partition coefficient: The ratio of equilibrium concentrations
of a particular compound (atomic or molecular) between two
immiscible solvents, at least one of which is aqueous: the
second phase, although usually liquid, may be gas, liquid
or solid. In the case of magnesium in the context of Mg/Ca
thermometry, it is denoted D_Mg and refers to the ratio of
magnesium (Mg²⁺) concentrations in the shell calcite and
seawater respectively.

Pelagic: The pelagic zone of the oceans refers to the water
column of the open ocean. Thus the benthic zone and the
demersal zone immediately above it are excluded, as are
coastal and continental shelf regions.

Planktonic (or planktic): Planktonic/planktic organisms live
in open water, generally in the near-surface region, and are
unable to swim against a current. Hence in the oceans they
are carried along by the prevailing near-surface currents.
Most are microscopic in size, though larger organisms (e.g.
jellyfish) are included in the definition.

Porcelaneous: Benthic foraminifera can be agglutinated or
calcareous. Calcareous species are divided into those whose
shells have a clear or translucent appearance (hyaline) with
tiny perforations (pores) and those whose shells are white
and opaque and have no perforations (porcelaneous).

Primary Organic Membrane (POM): Most extant
planktonic foraminifera produce their tests by the sequential
addition of chambers. The walls of each chamber are initially
formed of two calcite layers (a bilamellar wall) secreted on
either side of an organic template or sheet known as the
Primary Organic Membrane or POM. Additional layers are
deposited on the outer surface of existing chambers as each
successive chamber is added to the test during ontogenetic
growth. Just prior to gametogenesis a final, often thick,
layer is deposited on the outside of each chamber exposed in
the last whorl of the test (Erez 2003; Sadekov, Eggins and
De Dekker 2005). Erez (2003) suggests that a better term
would be Primary Organic Sheet (acronym POS) as POM
can also be used to mean “particulate organic matter”, but
POM will be used in this article.

Rayleigh fractionation: This describes the chemical evolution of a system with multiple phases in which one phase is continuously removed from the system. Consider, for example, the case of coral skeleton aragonite formation in which the Sr/Ca ratio of the precipitate is the key variable of interest. Gaetani et al. (2011) explain the Rayleigh fractionation process in terms of the average concentrations of Sr and Ca in aragonite precipitated from a single “batch” of fluid, respectively C_Sr and C_Ca; the concentrations of Sr and Ca in the calcifying fluid as precipitation begins, respectively C_Sr⁰ and C_Ca⁰; the remaining mass fraction of the calcifying fluid FL; and the temperature-dependent Nernst partition coefficients between aragonite and seawater, D_Sr^{Aragonite-Seawater} and D_CA^{Aragonite-Seawater}; these partition coefficients express the equilibrium ratios C_i^Aragonite/C_i^Seawater for phase i. Given previously determined values of the Nernst partition coefficients for Ca, Mg, Sr and Ba between aragonite and seawater as functions of temperature, Gaetani et al. (2011) measured Mg/Ca, Sr/Ca and Ba/Ca ratios on the coral skeletons of interest and were then then able to estimate formation temperatures analytically from their Rayleigh fractionation equations.

Regioisomer: A type of constitutional isomer. In constitutional
isomers molecules with the same molecular formula are
bonded together in different orders. In a regioisomer, a
functional group or other molecular component changes
position on a parent structure. In long organic molecules
the parent structure is a basic “carbon skeleton” to which
various molecular groups can be attached.

Salinity: Ocean water salinity is the mass fraction of
dissolved salts (mostly but not exclusively sodium chloride),
typically about 3.5% or 35‰ in modern-day oceans. It is
relatively low in the Baltic Sea and can be very high in
enclosed inland seas subject to high evaporation (e.g. the
Dead Sea). Although conceptually simple salinity is not
straightforward to measure: the water has to be filtered
down to a pore size of 0.2 μm and pressure, temperature
and electrical conductivity all need to be measured.
Practical salinity units, or psu, give approximately the same
numbers as salinity defined in terms of mass fraction, but
are conceptually different; their use is formally incorrect
and officially discouraged (Pawlowicz 2013; see also fig. 1), but is still widespread in the literature.

Sapropel: A dark, organically rich sediment formed when
oxygen levels in bottom waters are very low, e.g. as in ocean
anoxic events. For a review see Rohling, Marino, and Grant
(2015).

Scleractinian corals: These are also known as stony or
hard corals, in which the individual animals or polyps
(phylum Cnidaria) build calcium carbonate skeletons by
active precipitation of calcium and carbonate ions from
the water. Individual skeletons are called corallites. Many
scleractinian corals live colonially and build reefs; these
are the hermatypic corals, which are of greatest interest to
climate scientists. All modern scleractinian coral skeletons
consist of aragonite, which is harder but chemically less stable than calcite. Scleractinian corals first appear in the
fossil record in the Middle Triassic.

Test: The exterior shell produced by a spherical or nearly spherical
marine organism. The organisms which produce
tests include sea urchins and many microorganisms
including foraminifera and radiolarians.

Younger Dryas: A cold interval in the Northern Hemisphere
during deglaciation after the LGM (Last Glacial Maximum);
in conventional terms the Younger Dryas is dated as
taking place between ~12.9 and 11.5 ka BP (Carlson et al.
2007), while the LGM is dated at ~21 ka BP (Mix, Bard,
and Schneider 2001). The Younger Dryas is thought to
have resulted from a change in the North Atlantic Ocean
circulation (Carlson et al. 2007).

Appendix: Definition and Calibration of Temperature Proxies
Alkenone unsaturation index

Brassell et al. (1986) introduce the alkenone unsaturation
index U^K₃₇, as

(A1)

where C_37:2 is the relative abundance of the molecule (C_37:2H₇₂O) with two carbon–carbon double bonds, C_37:3 the abundance of the molecule (C₃₇H₇₀O) with three double bonds, and so on (Eglinton and Eglinton 2008). In many cases there are very few C₃₇ molecules with four double bonds, so that to a good approximation C_37:4=0 and equation (A1) reduces to

(A2)

where U^K₃₇ is the index most often used in subsequent literature. The SST calibration given by Prahl and Wakeham (1987) for the index defined in equation (A2) is

(A3)

over the temperature range 11–28°C. This correlation refers specifically to the surface mixed layer. It is based on measurements on samples from a range of geographical locations. The correlation coefficient is close to unity, r=0.997. Brassell et al (1986) refer to sediments reaching down to 550kaBP in the uniformitarian timescale, while Prahl and Wakeham’s (1987) analysis is only cited for sediments down to 18kaBP. In a later calibration study covering the range 0–29°C, Müller et al. (1998) found a closely similar correlation, viz. U^K₃₇=0.033*T+0.044 (r²=0.958) for samples from a total of 370 sites between 60°S and 60°N in both Atlantic and Pacific oceans.

More sophisticated calibrations for present-day conditions are given by Conte et al. (2006). Using ocean surface C₃₇ alkenone unsaturation measurements from a wide range of locations (n=629 original data points reduced to 567, temperature range –1 to 30°C), they derive a single polynomial “global” surface water calibration of U^K₃₇ which predicts alkenone production temperatures over the diversity of modern-day ocean environments and alkenone synthesizing populations:

(A4)

Here the coefficient of determination r²=0.97, and the “mean standard error” of the estimate is 1.2°C. Two exceptions were found in sediments from the western Argentine Basin, which appeared to have been affected by lateral advection (transport), and, in contrast with previous measurements, from the upwelling region near Cape Verde. In both cases measured temperatures fell several degrees below values predicted by (A4). These exceptions highlight advection as a source of uncertainty. Thus ocean currents may have transported and deposited the measured alkenones an unknown, possibly long distance from the region where they were synthesized such that inferred temperatures are not representative of where they are found.

Conte et al. (2006) also derive a calibration for U^K₃₇ in surface (core-top) sediments against annual mean SST (denoted AnnO) in terms of a linear model (temperature in °C):

(A5)

Here r²=0.97, n=592 and the mean standard error of the estimate is quoted as 1.1°C. Conte et al. (2006) note that U^K₃₇ in surface sediments is consistently higher than that predicted from AnnO and the surface water temperature calibration. The magnitude of this offset increases as the surface water AnnO decreases; Conte et al. (2006) suggest that it may be due to (1) seasonality in production and/or thermocline production, (2) differential degradation of 37:3 and 37:2 alkenones, or some combination of these effects.

TEX₈₆

This index, originally defined by Schouten et al. (2002), is written more conveniently in the form

(A6)

following Tierney (2014). The terms [GDGT–1], [GDGT–2], and [GDGT–3] refer to the proportions of core isoGDGT structures containing 1, 2, and 3 cyclopentane rings respectively, and [cren′] to the proportion of Crenarchaeol regioisomer, which contains 4 cyclopentane rings and 1 cyclohexane ring. The linear SST correlation deduced by Schouten et al. (2002) for temperatures in the range 1–30°C is

(A7)

with r²=0.92; T is the annual mean SST in °C. On the basis of extended data sets Liu et al. (2009a) and Kim et al. (2010) have developed SST calibrations in terms of variants of TEX₈₆. Liu et al. (2009a) represent the SST calibration for five high-latitude sites in reciprocal form, viz.

(A8)

(range –3 to 30°C, r²=0.82, n=287) while Kim et al. (2010) define two distinct alternatives, viz. TEX^L₈₆ for annual mean SST in the range –3 to 30°C in subpolar oceans,

(A9)

and TEX^H₈₆ for warmer oceans where SST>15°C

(A10)

where TEX₈₆ is as defined in equation (A6). The calibrations given by Kim et al. (2010) are:

(A11)

(range –3 to 30°C, r²=0.86, n=396) and

(A12)

(range 5 to 30°C, r²=0.86, n=396). Since TEX₈₆ and its variants are treated as independent variables in these calibrations, it is possible to estimate the root mean square (RMS) predictive uncertainty associated with each, which Tierney (2014) gives as ±3.7°C in equation (A8), ±4°C in (A11) and ±2.5°C in (A12). There are other versions of TEX₈₆ SST calibrations in the literature, some of them relating to lacustrine rather than marine environments.

The Ring Index (RI) introduced by Zhang, Pagani, and Wang (2016) is defined by

(A13)

Zhang, Pagani, and Wang (2016) point out that although GDGT–0 has a weight of 0 here, it does contribute to a sample’s Ring Index (RI) value via its impact on the relative abundance of the cyclized GDGTs since by definition the sum of all GDGTs, including GDGT–0, is unity. The global RI-TEX₈₆ correlation cited by Zhang, Pagani, and Wang (2016) is

(A14)

with r²=0.87, n=531 and a 2σ uncertainty margin of ±0.30. This correlation includes data from Red Sea samples even though the TEX₈₆-SST relationship in these samples deviates significantly from the acknowledged global SST calibration.

LDI

The LDI (long diol index) as defined by Rampen et al. (2012) may be written in the form

(A15)

(Rodrigo-Gámiz et al. 2014) where the expressions in brackets denote the fractional abundances of the temperature-sensitive diols in the sediment samples (see Nomenclature for definition of the diol naming convention). The SST calibration derived by Rampen et al. (2012) is

(A16)

for which r²=0.969 and the number of points n=162. They report a residual error of

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