Technical note: A new online tool for δ 18 O–temperature conversions

. The stable-oxygen-isotopic composition of marine carbonates ( δ 18 O c ) is one of the oldest and most widely used paleothermometers. However, interpretation of these data is complicated by the necessity of knowing the δ 18 O of the source seawater ( δ 18 O w ) from which CaCO 3 is precipitated. The effect of local hydrography (the “salinity effect”) is particularly difﬁcult to correct for and may lead to errors of > 10 ◦ C in sea-surface temperatures if neglected. A variety of methods for calculating δ 18 O w have been developed in the literature, but not all are readily accessible to workers. Likewise, temperature estimates are sensitive to a range of other calibration choices (such as calibration species and the inclusion or exclusion of carbonate ion effects), which can require signiﬁcant effort to intercompare. We present an on-line tool for δ 18 O–temperature conversions which provides convenient access to a wide range of calibrations and meth-ods from the literature. Our tool provides a convenient way for workers to examine the effects of alternate calibration and correction procedures on their δ 18 O-based temperature estimates.


Motivation
The stable-oxygen-isotopic composition of carbonates (δ 18 O c ) is one of the oldest and most widely used paleothermometers and undergirds a wide variety of paleoceanographic research (for recent reviews, see Pearson, 2012, andSharp, 2017).Converting δ 18 O c to temperature is typically done using an empirical calibration in either a linear form, such as (Bemis et al., 1998), or in a quadratic form, such as T = 16.0 − 5.17 (2) (McCrea, 1950, as reformulated by Bemis et al., 1998), where T is temperature (in • C), δ 18 O c is the oxygen isotope composition of the carbonate (as ‰ VPDB, or parts per thousand relative to the Vienna Pee Dee Belemnite standard), and δ 18 O w is the oxygen isotope composition of the water in which the carbonate was precipitated (as ‰ VS-MOW, or parts per thousand relative to the Vienna Standard Mean Ocean Water standard).Much of the complexity of using δ 18 O as a paleothermometer arises from the need to know δ 18 O w , which may vary both globally as a function of ice volume and locally at the sea surface as a function of regional hydrography (Rohling, 2013).Global variation can be estimated using independent records of sea level, so the global record of deep-water δ 18 O-based temperatures has been relatively well established (Zachos et al., 2001;Cramer et al., 2009;Westerhold et al., 2020;Rohling et al., 2021;etc.).However, local variations in surface δ 18 O w are more difficult to predict, rendering sea-surface temperature (SST) estimates from δ 18 O less reliable than deep-water temperature estimates.To address this, a variety of methods have been developed in the literature to estimate surface δ 18 O w .Since modern surface δ 18 O w broadly covaries with latitude, a common approach has been to apply the modern latitudinal variation to a sample's paleolatitude (typically using Figure 1.Effect of estimating SST using measured/modeled local δ 18 O w rather than the latitude-based approximation of Zachos et al. (1994, Eq. 1 therein).Modern: comparison with mean annual δ 18 O w < 50 m depth (after LeGrande and Schmidt, 2006).Last Glacial Maximum (LGM): comparison with inferred annual surface δ 18 O w at the LGM (Tierney et al., 2020).Miocene: comparison with CESMv1.2_CAM5model run at 400 ppm CO 2 with Miocene paleogeography (Gaskell et al., 2022).Eocene: comparison with CESM_1.2_CAM5model run at 6 times the preindustrial CO 2 with Eocene paleogeography (Zhu et al., 2020).Temperatures are calculated assuming a slope of 4.80 • C ‰ −1 (Bemis et al., 1998).
the relationship fit from Southern Ocean data in Eq. 1 of Zachos et al., 1994, or more recently the updated method of Hollis et al., 2019).However, this approach performs particularly poorly in the North Atlantic and other high northern latitudes, where local δ 18 O w can deviate significantly from the latitudinal mean (Fig. 1; Zachos et al., 1994;Gaskell et al., 2022; see also generally Tindall et al., 2010).It also as-sumes that the latitudinal gradient in δ 18 O w has not changed through time, which is contradicted by modeling.In warmer climates with an altered hydrological cycle, models predict that regional salinity contrasts should change due to alterations in the local ratio of evaporation to precipitation (Richter and Xie, 2010;Singh et al., 2016), with an analogous effect on δ 18 O w (Zhou et al., 2008;Tindall et al., 2010;Roberts et al., 2011;Zhu et al., 2020).In particularly extreme cases such as the Eocene, the theoretical difference between modern latitude-derived δ 18 O w (after Zachos et al., 1994, Eq. 1 therein) and modeled local δ 18 O w at 6 times the preindustrial pCO 2 (Zhu et al., 2020) yields a mean temperature error of 5 • C in the Southern Ocean (60-90 • S) or an astonishing mean temperature error of 41 • C above the Arctic Circle (66.5-90 • N; Fig. 1).
An alternative approach is to obtain δ 18 O w more or less directly from isotope-enabled climate models (Zhou et al., 2008;Roberts et al., 2011;Gaskell et al., 2022).Several approaches have been adopted: drawing local δ 18 O w directly from model output (Roberts et al., 2011); using modeled zonal mean δ 18 O w for a particular paleolatitude (Zhou et al., 2008); using models as input to fit a generalized equation for predicting δ 18 O w from latitude and bottom-water temperature (Gaskell et al., 2022 Eq. S9); or, recently, a generalized method which uses bottom-water temperature to interpolate local δ 18 O w between models run at different pCO 2 (Gaskell et al., 2022).While some authors have avoided these approaches altogether due to the uncertainty in modeled δ 18 O w (e.g., Hollis et al., 2012) or the possibility of introducing circularity into data-model comparisons (e.g., Hollis et al., 2019), model-derived δ 18 O w clearly captures information lost by simpler approaches and is therefore appropriate for some use cases (Roberts et al., 2011).
Here, a new online tool for δ 18 O temperature conversion is presented which automates a range of methods for δ 18 O w reconstruction and correction from the literature, improving the accessibility of advanced methods to workers generating δ 18 O c data.

Description
We present a new online tool for performing δ 18 O ctemperature conversions which automates a range of methods from the literature.This tool is available at https:// research.peabody.yale.edu/d180/(last access: 7 June 2023).The general workflow for using the tool is summarized in Fig. 2; details on the methodology and reasoning behind each option are given below.
Where applicable, we use the standardized reformulations of Bemis et al. (1998) and Willmes et al. (2019) or exact algebraic rearrangements of the original equations.For the bayfox core-top calibrations of Malevich et al. (2019), the standard bayfox tool re-fits the calibration coefficients with every run.Since this is computationally expensive, we instead use the linear calibration coefficients fit by runs of the R package bayfoxr 0.0.1 directly in linear functions of the form of Eq. (1) (see Table 1).These yield results equivalent to the full fitting process within numerical error (mean residual = ±0.02• C, identical to the mean scatter between replicates of the full bayfox fit).

Global δ 18 O w estimation
Users may specify global δ 18 O w manually or choose to draw δ 18 O w by sample age from 12 different time series of global δ 18 O w from the literature (from Cramer et al., 2011;Henkes et al., 2018;Meckler et al., 2022;Miller et al., 2020;Modestou et al., 2020;Rohling et al., 2021;and Veizer and Prokoph, 2015).These records are typically constructed by assuming that the benthic δ 18 O record reflects a combination of temperature and ice volume and then subtracting out an independent record of temperature (e.g., using Mg/Cabased bottom-water temperatures; Cramer et al., 2011) or ice volume (e.g., using a multi-proxy sea level reconstruction; Rohling et al., 2021) to determine the residual δ 18 O w .Which global δ 18 O w record is most realistic remains a contentious topic in the literature, with sea-level and Mg/Cabased records (e.g., Cramer et al., 2011;Rohling et al., 2021) predicting up to ∼ 1 ‰ lower δ 18 O w for much of the Cenozoic than records based on clumped isotope paleothermometry (Meckler et al., 2022; see also Agterhuis et al., 2022).We provide both classes of record here for comparison by the user.
Records are mapped to the user data's ages by linear interpolation.The 47-based δ 18 O w records of Meckler et al. (2022) included in our tool were generated by interpolating the authors' original results to 0.1 Myr resolution using the Monte Carlo LOESS method and parameters described in the original publication (Meckler et al., 2022).
All built-in δ 18 O w and temperature records are internally converted to four different timescales, so the user can select the timescale consistent with their data: GTS2004 (Gradstein et al., 2005), GTS2012 (Gradstein et al., 2012), GTS2016 (Ogg et al., 2016), and GTS2020 (Gradstein et al., 2020).These timescale conversions are performed by linear interpolation between magnetochron boundaries; dataset files can be found on the project GitHub.

Local δ 18 O w estimation
The user may select a method for estimating local δ 18 O w .These are as follows: performing no local correction, using modern δ 18 O w from each sample's location and a specified depth (after LeGrande and Schmidt, 2006), using reconstructed Late Holocene or Last Glacial Maximum surface δ 18 O w from each sample's location (model output from Tierney et al., 2020), using δ 18 O w estimated from latitude alone (after Eq. 1 in Zachos et al., 1994, or   .The temperature solution for this form (in • C) is T = a×10 3 1000 ln δ 18 Oc+1000 δ 18 Ow+1000 +b − 273.15,where the relationship δ 18 O VPDB = 0.97001 δ 18 O VSMOW − 29.99 (Brand et al., 2014)   provided using the datasets of Miocene and Eocene paleogeography used in that publication).For methods which draw from an existing dataset of δ 18 O w , the user may specify a number of degrees latitude/longitude or great-circle radius to average over in order to capture a regional mean when the exact paleocoordinates or local hydrography may not be known.To help determine site locations at the time of deposition, an option is also provided to automatically perform paleocoordinate rotations using the GPlates Web Service (Müller et al., 2018).Ages passed to GPlates are rounded to the nearest 100 ka to reduce the number of calls to the web service.
Our tool does not currently implement any automated consideration of seasonal variation in local δ 18 O w , as this is generally treated as negligible by standard methodologies or implicitly baked into the calibration by calibrating against mean annual temperatures and δ 18 O w values (e.g., Malevich et al., 2019).

Carbonate chemistry effects
Because δ 18 O c is known to vary with aqueous carbonate chemistry (the "carbonate ion effect"; Spero et al., 1997;Bijma et al., 1999;Ziveri et al., 2012), users may also specify a carbonate ion correction factor.This is performed by adjusting δ 18 O c with the linear relationship where δ 18 O c is the uncorrected oxygen isotope composition of the carbonate, δ 18 O c is the corrected oxygen isotope composition of the carbonate, s is the selected slope of the effect (in ‰ VPDB per µmol L −1 CO 2− 3 ), and [CO 2− 3 ] is the concentration of carbonate ion in solution (in µmol kg −1 ).This relationship yields no correction when [CO 2− 3 ] = 200 µmol kg −1 , an approximation of the mean modern surface value (after the long-term record of Zeebe and Tyrrell, 2019).The user may specify [CO 2− 3 ] manually or select a published long-term record of [CO 2− 3 ] (Tyrrell and Zeebe, 2004; Zeebe and Tyrrell, 2019).

Tool output
On completion, the tool presents a formatted table of the resulting temperatures, along with any intermediate values (such as estimated δ 18 O w ) which were required to generate them.Any rows with potential errors (e.g., paleocoordinates which do not yield a valid δ 18 O w estimate or temperatures which exceed the data range of the calibration) are highlighted in color and flagged with warning text, which appears in an adjacent column.For reference, a short summary of methods is also generated, including relevant equations and a complete bibliography of citations in both text and BibTeX formats for the methods employed in each run.
It should be noted that, while the tool automates the process of applying a given calibration method, the user is still responsible for pre-screening their data for diagenetic alteration or other external biases.For example, use of δ 18 O data from foraminifera must consider factors such as diagenetic recrystallization, depth habitat, shell size, and the presence of gametogenic calcite (for a review, see Pearson, 2012).

Concluding remarks
Our tool provides a convenient way for workers to perform δ 18 O-temperature conversions and explore the sensitivity of their results to different calibrations, corrections, and δ 18 O w reconstruction methods by successively trying different options in the interface.By allowing data generators to rapidly generate multiple temperature estimates for their records with different underlying assumptions, our tool allows workers to quickly understand and quantify the effects of different assumptions on the resulting temperature estimates.
Review statement.This paper was edited by Marit-Solveig Seidenkrantz and reviewed by Brett Metcalfe and one anonymous referee.

Figure 2 .
Figure 2. General workflow for using the tool.(Each box may reflect multiple sub-options.) //doi.org/10.5281/zenodo.7946599;Gaskell and Hull, 2023b).Author contributions.DEG and PMH conceptualized the tool.DEG wrote the software.DEG and PMH contributed to the manuscript writing.Competing interests.The contact author has declared that neither of the authors has any competing interests.Disclaimer.Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
. Gaskell and P. M. Hull: Technical note: A new online tool for δ 18 O-temperature conversions stitutional support from the Yale Peabody Museum and assistance from Nelson Rios in hosting the tool.

Table 1 .
Hollis et al., 2019)et al., 2019), using δ 18 O w estimated from latitude and bottomwater temperature (afterGaskell et al., 2022 Eq.S9), or using δ 18 O w estimated from isotope-enabled climate models (GCMs; after the method ofGaskell et al., 2022, presentlyLinear and quadratic δ 18 O: temperature calibrations of the form T = a + b 18 O c + c( 18 O c ) 2 , where 18 O c = δ 18 O c − δ 18 O w , with the given VSMOW conversion factor first added to δ 18 O w to convert VSMOW into the format expected by the calibration.

Table 3 .
δ 18 O: temperature calibrations in other forms.18Oc = δ 18 O c − δ 18 O w ; the VSMOW-VPDB conversion is included in the equations below, with no further conversion required.