# Assessment of Porites microatolls for paleothermometry: Calibration for French Polynesia

Nicholas Farley, Guillaume Antonioli, Nadine Hallmann, Gilbert Camoin, Anton Eisenhauer, Claude Vella, Glenn A Milne, Elias Samankassou

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## To cite this version:

Nicholas Farley, Guillaume Antonioli, Nadine Hallmann, Gilbert Camoin, Anton Eisenhauer, et al. "Assessment of Porites microatolls for paleothermometry: Calibration for French Polynesia." Palaeogeography, Palaeoclimatology, Palaeoecology, 2024, 642, pp.112146. 10.1016/j.palaeo.2024.112146 hal-04769903

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Submitted on 6 Nov 2024

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# Assessment of *Porites* microatolls for paleothermometry: Calibration for French Polynesia

Nicholas Farley<sup>a, *</sup>, Guillaume Antonioli<sup>a</sup>, Nadine Hallmann<sup>b</sup>, Gilbert Camoin<sup>b</sup>, Anton Eisenhauer<sup>c</sup>, Claude Vella<sup>b</sup>, Glenn A. Milne<sup>d</sup>, Elias Samankassou<sup>a</sup>

## ARTICLE INFO

Editor: Howard Falcon-Lang

### Keywords:

* Porites
* Microatoll
* Paleothermometry
* Calibration

## ABSTRACT

Massive dome-shaped coral *Porites* are the predominant choice for paleoclimate studies due to their consistent and reliable growth. When growing close to sea level, they become limited in their vertical growth and form so-called ‘microatolls’. Microatolls have not yet been extensively explored for paleoclimate reconstruction. Here, we investigate how reliable modern *Porites* microatolls are against empirical sea-surface temperature using Sr/Ca, δ¹⁸O, Li/Mg and Sr—U paleothermometry methods on samples from the Society Islands, French Polynesia. Our results show Sr/Ca ratios have the lowest Standard Error of the Inverse Prediction (SEIP) at 0.415 °C (N = 41) with a calibration of Sr/Ca (mmol mol⁻¹) = -0.082 ± 0.006 SST (°C) + 11.256 ± 0.170 and with high reproducibility across multiple corals. The reproducibility of δ¹⁸O was less good, with SEIP increasing to 0.829 °C (N = 41). Considering methods directly from the literature, Li/Mg ratio empirically corrected for Sr/Ca had the best balance between bias and precision where no local calibration could be available. This study independently evaluates and confirms the suitability of *Porites* microatolls from well-flushed environments for paleoclimate studies. Fossil dome-shaped *Porites* grow anywhere between near-surface and roughly 20 m depths which inherently incorporates uncertainty into any sea surface temperature reconstruction. This uncertainty is significantly reduced for microatolls due to their well-constrained bathymetry. The study represents a fundamental step in paleoclimate research targeting consistently near the water-air interface bringing reliability and, especially when combined with their ability to reconstruct past sea-level changes, microatolls have the potential to be central for future paleoenvironmental studies.

## 1. Introduction

The use of coral colonies as climate archives can extend the instrumental record, which reliably covers roughly 150 years (Parker et al., 2000). Unlike long-term deep-sea marine sediments, coral skeletons may record multiple centuries of past sea-surface conditions at a seasonal to monthly resolution under the right conditions. Coral records can therefore help to better understand the patterns and drivers of natural tropical climate variability, especially the El Niño Southern Oscillation (ENSO) in the Pacific Ocean, which has global environmental consequences (Smith et al., 2016) and massive socio-economic impacts (Cashin et al., 2017).

Concentrations of geochemical tracers incorporated into the coral

skeleton during its growth can provide valuable information on a range of environmental conditions. The Sr/Ca ratio is widely used to reconstruct sea-surface temperature (SST), with an inverse relationship first identified by Smith et al. (1979). The Mn/Ca ratios are a proxy for precipitation and runoff, as well as upwelling and wind speed (e.g. Inoue et al., 2014; Chen et al., 2015; Thompson et al., 2014; Yamano and Watanabe, 2016). Other proxies, such as Li/Ca (Marriott et al., 2004; Hathorne et al., 2013a, 2013b), have shown a correlation with temperature. Stable oxygen isotopes (δ¹⁸O) have also been regularly used to reconstruct SST. Still, it has been demonstrated that this proxy can be influenced by sea-surface salinity (SSS). Therefore, it must be used in combination with other proxies, such as Sr/Ca (see review in Corrège, 2006). The reliability and reproducibility of the Sr/Ca ratio and δ¹⁸O

<footnote><sup>a</sup> University of Geneva, Department of Earth Sciences, Rue des Maraîchers 13, CH-1205 Geneva, Switzerland</footnote>

<footnote><sup>b</sup> Aix-Marseille Université, CNRS, IRD, INRAE, College de France, CEREGE, Europôle Méditerranéen de l'Arbois, BP80, 13545, Aix-en-Provence cedex 4, France</footnote>

<footnote><sup>c</sup> GEOMAR Helmholtz-Zentrum für Ozeanforschung Kiel, Wischhofstraße 1-3, 24148 Kiel, Germany</footnote>

<footnote><sup>d</sup> University of Ottawa, Department of Earth and Environmental Sciences, Ottawa, Ontario K1N 6N5, Canada</footnote>

<footnote>* Corresponding author.
E-mail address: nicholas.farley@unige.ch (N. Farley).</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Location of sampled microatolls. On Bora-Bora sample BOB 47 and 48 from the North in Green (b) and BOB-108 from the South in Orange (c). On Maupiti in the North coloured Blue (e). The red dots mark the position of Météo-France weather stations on the respective islands. Base satellite images from Google Earth Pro, v 7.3.3.7699 Data SIO, NOAA, U.S. Navy, NGA, GEBCO. Images © 2020 CNES/Airbus. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

values have been questioned, as temperature reconstructions may vary considerably within the same reef or even within the same colony (Alibert and McCulloch, 1997; Alpert et al., 2017; Correge, 2006; D'Olivo et al., 2018; de Villiers et al., 1994). These variations have been attributed to biological and physiochemical controls in the calcification process, referred-to as “vital effects”, that are not yet fully understood (Gaetani and Cohen, 2006; Meibom et al., 2007). To overcome vital effects, Gaetani et al. (2011) proposed differential fractionation for different elements to extract the common temperature signal (for an overview see Sinclair, 2015). Two methods that propose to account for vital effects have recently been proposed: the Sr-U method (DeCarlo et al., 2016) and the Li/Mg universal thermometer (D'Olivo et al., 2018). While previous studies on Li/Ca and Li/Mg have been published (eg. Marriott et al., 2004; Hathorne et al., 2013a, 2013b; Montagna

et al., 2014), we examined D'Olivo et al. (2018) in detail as this has been proposed as a 'universal' paleothermometer.

*Porites* colonies are one of the most sampled corals for paleoclimate reconstructions due to their clear growth pattern and their growth in a wide range of environments. In very shallow-water environments, their vertical growth may be constrained by exposure at lowest tides (Stod-dart, 1969; McLean et al., 1978; Smithers and Woodroffe, 2001; Meltzner and Woodroffe, 2015; Hallmann et al., 2018) so that they continue to grow laterally to form so-called ‘coral microatolls’. Their lateral growth rates range from 5 to 25 mm yr⁻¹ (*Woodroffe and McLean*, 1990), comparable to those reported in dome-shaped *Porites* colonies. Coral microatolls have been used in sea-level reconstructions due to their strict environmental requirements (Hallmann et al., 2018; Smithers and Woodroffe, 2001; Woodroffe and McLean, 1990; Yu et al.,
<table><caption>**Table 1**
Summary of the geochemical measurements carried out on each coral.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">δ<sup>18</sup>O</th><th colspan="3">ICP-OES</th><th colspan="5">ICP-MS</th></tr><tr><th>Sr/Ca</th><th>Mg/Ca</th><th>Ba/Ca</th><th>Sr/Ca</th><th>Mg/Ca</th><th>Ba/Ca</th><th>U/Ca</th><th>Li/Ca</th></tr></thead><tbody><tr><td>MAU-140</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>BOB-108</td><td>X</td><td>X</td><td>X</td><td>X</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>BOB-478</td><td>X</td><td>X</td><td>X</td><td>X</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

2009). From a paleoenvironmental perspective, these requirements provide the unique advantage to obtain a record from a narrow depth range over extended periods. However, only a few studies have reported use of microatolls, namely on Kiritimati (Christmas) Island (McGregor et al., 2011; Schofield, 2011; Woodroffe et al., 2003) and the Great Barrier Reef (Roche et al., 2014).

This study aimed to assess the suitability and reliability of *Porites* microatolls for paleoclimate reconstructions. It relied on temperature reconstructions based on conventional geochemical analyses (element/Ca ratios and δ¹⁸O values) and methods to correct for vital effects (Li/Mg and Sr—U) obtained on microatolls from the Society Islands, French Polynesia. The evaluation of each method was then assessed based on the comparison between reconstructed temperatures and instrumental records with the primary goal to obtain a calibration that can be applied to fossil microatolls.

## 2. Methods

This study focused on microatolls from Bora Bora and Maupiti islands (French Polynesia, Central Southern Pacific), which are ~40 km apart on the Western end of Society Islands. Climate is tropical with two seasons, the austral summer from Nov-Apr being warm (28–29 °C) and rainy, and the austral winter from May-Oct with cooler (23–25 °C)

temperatures and drier (Delesalle et al., 1985; Boiseau et al., 1998). Tides are semi-diurnal with a mean amplitude of 0.5 m (Seard et al., 2011). The dominant wind patterns are the trade winds from the East/ South-East to the North-East (Rashid et al., 2020). The samples BOB-47 and BOB-48 originated from the same microatoll in the northern part of Bora Bora (16°26'27.60"S, 151°45'42.42"W), and BOB-108 (16°32'39.84"S, 151°41'56.88"W) from a microatoll in the southeast (Green and orange respectively in Fig. 1). MAU-140 (16°25'7.98"S, 152°15'44.70"W) was sampled on Maupiti (blue in Fig. 1). All micro- atolls were collected at present day sea level in 2014 and 2015 on the protected reef facing the open ocean. All studied microatolls originated from well-flushed sites with direct contact to the open ocean. In this study, the Maupiti coral was studied in detail, and then the corals from Bora-Bora were used to assess the reproducibility and reliability of the original findings. (See Table 1.)

In the laboratory, microatoll samples were sliced into 8 mm-thick slabs along the main growth axis and left 24 h in diluted NaClO. The outer biological surface was removed and subsequently rinsed with distilled water (Grove et al., 2015). Small pieces of the slab were observed under a Scanning Electron Microscope (SEM) (Jeol JSM7001F) to screen for any early diagenetic alterations that could affect the geochemical signals in coral skeleton (Sayani et al., 2011; Felis et al., 2012; Krause et al., 2019). Sampling was carried out using a frame- mounted Dremel with a 1.0 mm drill bit to achieve a 1 mm sampling resolution. Sample depth was fixed using the Dremel frame mount blocks such that enough sample for two analyses was collected, approximately 1 mg. Each sample was staggered to ensure each drill hole is clearly isolated making it traceable on the X-rays. This was done as part of a control during the method development and with confir- mation from personal communication with DeLong it is confirmed that with uniform nature of *Porites* growth it does not have a detrimental effect on the result. This extra control on sample traceability is not necessary for routine sampling where a continuous line would be easier. Sampling protocol was following the central axis of the corallite fan (DeLong et al., 2013). The coral slabs were x-radiographed at the

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** X-radiograph of MAU-140 with sampling path. The coloured lines show sample points in line with the corallite growth included in the analysis (green) and points excluded due to orientation of the corallite growth being unsuitable (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Results for coral MAU-140 for Sr/Ca (a), δ¹⁸O (b) and Li/Mg (c) against AVHRR-OISSTv2 (Reynolds et al., 2007a, 2007b; Banzon et al., 2016). The orange line is a WLS regression (Cantrell, 2008), the blue line is OLS regression, and the dashed lines are the inverse prediction confidence intervals for the expected value and single observation according to Demidenko et al. (2013). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

Quality Control SA (Lavaux, Switzerland) imaging facility using a D7Pb film, with 100 kV exposures for 525–750 mAs and a focal length of 1900 mm allowing to identify annual density bands and check exact sample positions along the growth axis.

The δ¹⁸O and δ¹³C values were measured on ThermoFinnigan Delta

Plus XL (Gas Bench II) at the University of Lausanne, Switzerland, standardised against a Carrara marble standard and expressed relative to Vienna Pee Dee Belemnite (VPDB). The methods were adapted from Spötl and Vennemann (2003). Average analytical precision was ±0.1‰.

For all the corals in this paper, the concentrations of Ca, Sr, Mg and Ba were measured by Inductively Coupled Plasma Optical Emission Spectrometer (ICP-OES) (iCAP 3000 Duo, ThermoFisher Scientific) at the University of Geneva using a method adapted from Cantarero et al. (2017). An amount of 0.4 mg of coral powder was dissolved in 5% nitric acid (HNO₃) to obtain a solution with Ca concentrations of roughly 40 ppm. Ba was measured on axial view allowing for greater sensitivity and lower detection limits. Internal yttrium standard was injected simultaneously to monitor machine stability and, with intermediate calibration samples (mixed from mono-element Agilent standards) inserted at regular intervals to monitor for drift in each relevant element. No such drift corrections were necessary for the corals presented in this paper. External JCP-1 standards (Hathorne et al., 2013b; Okai et al., 2002) were measured at regular intervals throughout the run. For the sample MAU-140 (n = 15) run JCP-1 results were Sr/Ca 8.860 (1SD = ±0.036), Mg/Ca 4.176 (1SD = ±0.032) and Ba/Ca 7.733 (1SD = ±0.949). Across all samples measured on ICP-OES the analytical precision showed somewhat higher variability in some runs: Sr/Ca (1SD = ±0.084), Mg/Ca (1SD = ±0.046) and Ba/Ca (1SD = ±0.927).

For coral MAU-140, trace elements of Li and U along with Ca, Sr, Mg and Ba were measured using ICP-MS (Agilent 7700×) at the University of Geneva. Samples were dissolved in 5% HNO₃ to obtain a solution including about 80 ppm Ca. Rhodium and rhenium internal standards were run in parallel, and similar to the ICP-OES method above, intermediate calibration samples were included regularly through the run to monitor, and if necessary correct, for drift in each relevant element along with JCP-1 standards (Hathorne et al., 2013a, 2013b; Okai et al., 2002). The uncorrected JCP-1 values from the MAU-140 run were Sr/Ca 8.682 (1SD = ±0.037), Mg/Ca 4.186 (1SD = ±0.153) and Ba/Ca 6.956 (1SD = ±0.336). A detailed comparison of the JCP-1 standard stability between the ICP-OES and ICP-MS is found in Supplementary S1.

Météo-France land and ship-based instrumental temperatures were evaluated against high-resolution satellite data (see detail in supplementary material S2). The chosen sea surface temperature dataset was the monthly resolution gridded 0.25° – 0.25° Advanced Very High Resolution Reconstructed Optimum Interpolation Sea Surface Temperature version 2 (AVHRR-OISSTv2) (Banzon et al., 2016; Reynolds et al., 2007a, 2007b).

For temporal correspondence between the OISST dataset and the geochemistry, peak matching and subsequent linear interpolation of the temperature values was carried out. The most recent datapoint was informed by the date of sample recovery with the outer edge surface of the coral skeleton, the living part during sample collection. The most recent turning point (maximum or minimum) in the analyte was matched to the most recent temperature turning point, while the oldest analyte turning point matched to the corresponding temperature turning point counting back in annual cycles. The tails either side of these two tie points were discarded from the calibration samples to reduce uncertainty and edge effects. As each tie point was added, the residual degrees of freedom in the linear regression analysis of the analyte on temperature was decreased by one. A Chi-Squared statistic and p-value were used, so the improvement in fit could be balanced with the loss of degrees of freedom to estimate residual error and avoid issues of overfitting. This was primarily carried out for the Sr/Ca as it has the most covariability with temperature. An assessment into calibration performance using other proxies was carried out to verify that it was not being overfitted for Sr/Ca but the effects were small and did not change the results (for more information see supplementary S3.2). The time assignment from the peak matching for Sr/Ca was kept and applied to the other proxies. This does not interfere with any assessment of potential lags between geochemical proxies. Results presented for the MAU-140 sample use the ‘reduced peak to peak’ dataset (n = 41), which
<figure><img src="image_8.png" /><figcaption>Fig. 4. X-radiograph image of the BOB-108 sample. The coloured lines show sample points in line with the corallite growth included in the analysis (green), points with uncertain alignment (orange) and points excluded due to orientation of the corallite growth being unsuitable (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

is down from the total 54 datapoints and eliminated possible edge effects
(more information in supplementary material S3.1).

Across the paleoclimate community there is discrepancy between the regression models to apply for a calibration. In this paper we compare Weighted Least Squares (WLS) (York et al., 2004; Cantrell, 2008) against an Ordinary Least Squares (OLS) linear regression of the proxy on temperature. For the OLS regression, the corresponding temperatures and 95% confidence intervals were estimated by inverse prediction from the fitted regression line (Draper and Smith, 1981, p 47; Neter et al., 1985). To make an inverse prediction, the estimated temperature is read horizontally and has an associated standard error of the inverse prediction (SEIP) (Demidenko et al., 2013). For more details and application of the equations, see supplementary material S4.

**3. Results**

**3.1. Temperature data**

A detailed comparison of the datasets from the Météo France land stations, ship data and OISST can be found in the appendix. For purpose of this study the dataset that was selected to generate the sea surface temperature record was the OISST from Reynolds et al. (2007a, 2007b) and Banzon et al. (2016).

**3.1.1. MAU-140 coral preservation**

X-radiography of the MAU-140 specimen showed good alignment of the corallites with the slab cut along the dominant growth axis (Fig. 2). The central axis of the corallite fan was easily identifiable with the corallite growth and density bands. An average growth rate of 14.3 ± 0.5 mm year⁻¹ was calculated based on measurements covering four years of continuous growth. The measured growth rate was consistent with previous data obtained on *Porites* microatolls (McGregor et al., 2011; Roche et al., 2014). SEM observations for MAU-140 reveal excellent preservation of the skeleton. No secondary aragonite or diagenesis was identified near the outer edge or in the coral’s internal structures and pores (for more detail and SEM images, see supplementary material S5.1).

**3.1.2. MAU-140 results and regression models**

Here we present the data for MAU-140 Sr/Ca (a), δ¹⁸O (b) and Li/Mg (c) against OISST with their associated errors. Errors for OISST as published in Banzon et al. (2016) in the supporting information that acc companies the raw data and the errors for the geochemical analysis come from variability in the Jcp-1 standard for each proxy. The orange line in Fig. 3 is the Cantrell (2008) weighted least squares (WLS) regression model and the blue regression line is the Ordinary Least Squares (OLS) regression with the 95% confidence limits for a new predicted value using the inverse prediction from the Demidenko et al. (2013) (calculations in Supplementary S4).

**3.1.3. BOB-108 coral preservation**

BOB-108 exhibited a more complex growth in multiple directions (Fig. 4). Slabbing was done along the dominant growth axis, but a single continuous sampling track could not be identified. The SEM images revealed a generally good preservation in the main part of the coral skeleton. There were issues of pore infilling visible near the upper sur face of the coral, a region with secondary Mg-rich crystal growth (brucite) related to algal growth (See SEM images, preservation, and discussion on brucite crystal in supplementary material S5.2). This part was discarded from the data analyses.

Figure 4 shows that many samples were taken in areas where the growth axis was no longer parallel to the slab cut axis. Those samples were excluded from the interpretation as they likely would produce unreliable results (e.g. DeLong et al., 2013). Combining the two transect lines would have been possible through estimation following barely visible annual density growth bands (Fig. 4) but could have brought significant uncertainties. The sample was therefore reduced to 28 data points, covering two years of reliable data.

After analysis, it was reconfirmed that applying the hinge points on peaks and troughs produced the best model for the temperature inter- polation, explaining most of variations without becoming overfitted.

**3.1.4. BOB-108 results and regression models**

See Fig. 5.

**3.1.5. BOB-478 coral**

BOB-47 and BOB-48 are sampled from the same larger microatoll in
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Results for coral BOB-108 for Sr/Ca (a), δ¹⁸O (b) against AVHRR-OISSTv2 (Reynolds et al., 2007a, 2007b; Banzon et al., 2016). The orange line is a WLS regression (Cantrell, 2008), the blue line is OLS regression, and the dashed lines are the inverse prediction confidence intervals for the expected value and single observation according to Demidenko et al. (2013). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

May 2014 so the outer living surfaces are contemporaneous meaning that the data could be combined as the growth occurred over the same time periods. No secondary diagenetic alteration was identified under the SEM (see supplementary material S5.3). From the sample BOB-48 the first 38 drilled spots were not parallel to the growth axis and were excluded from data analysis (Fig. 6). The data from BOB-47 and BOB-48 were combined by averaging contemporaneous samples to create the dataset BOB-478.

### 3.1.6. BOB-478 results and regression models
See Fig. 7.

## 3.2. Evaluation of stability and reproducibility of Sr/ca and δ¹⁸O

There are concerns about the reliability of the δ¹⁸O and Sr/Ca methods due to localised offsets and vital effects which may affect individual corals differentially (Corrège, 2006; de Villiers et al., 1995). To counteract this deficiency, slopes, and intercepts from multiple corals from the same area can be combined to create a regional calibration smoothing out the offsets (Felis et al., 2003; Sayani et al., 2019). However, when analysing a single fossil sample, it becomes impossible to

identify its specific offset.

To test the robustness and reproducibility of both δ¹⁸O and Sr/Ca, additional modern samples from the same region were assessed, particularly coral samples BOB-478 and BOB-108 from the North and South of Bora-Bora, respectively (Fig. 1).

### 3.2.1. Reproducibility of Sr/ca

Possible offsets of Sr/Ca ratios between corals driven by vital effects were evaluated. The linear regression fits of Sr/Ca on SST for all three corals are shown in Table 2 and Fig. 8. Coral MAU-140 resulted in a SEIP of 0.415 (±0.062)°C; the coral BOB-108 resulted in a SEIP of 0.840 (±0.200)°C and BOB-478 a SEIP of 0.724 (±0.143)°C. Importantly, despite the residual errors becoming larger on the two Bora Bora corals as the sample quality deteriorated, the fundamental relationship (slope and intercept) of the Sr/Ca to temperature remained very robust. There was no significant difference between the slopes or intercepts across the corals.

### 3.2.2. Reproducibility of δ¹⁸O

δ¹⁸O is affected by a combination of temperature and salinity (controlled in the present case by precipitation intensity). Data were collected on the four corals and combined into three coral records (same sampling points as for Sr/Ca). It was possible to observe an occasional lag in the δ¹⁸O curve compared to the Sr/Ca curve but adjusting the tie points for the temperature interpolation to optimise for δ¹⁸O did not significantly improved model fit (supplementary material S3.2).

Linear regression fits of δ¹⁸O against SST for each coral are presented separately along with a combined regression model (Table 3). The SEIP derived from sample MAU-140 was 0.829 (±0.165) °C. Data obtained on the BOB-108 sample revealed the smallest SEIP but relied on a reduced dataset (N = 28) with only sample points validated from the X-ray imagery (see Fig. 4). There was a significant difference between calibration curves produced by each of the three coral samples (Fig. 9 and Table 3). When combining the three corals into a single calibration model, purely statistically speaking, the quality of fit (residual mean square) was very similar for a model fitting a single slope but three different intercepts or a model fitting a single intercept but three different slopes. Considering the two, the model with a single common slope and three different intercepts, one for each coral, was more realistic and relevant. The variation (in intercept or can be read individual offset) across the three corals meant that the SEIP became considerably greater when combined into a single calibration (Table 3).

# 4. Discussion

## 4.1. Calibration model and error propagation

The graphs of the raw data presented in the results sections for each coral had both regression models, with York et al. (2004) and Cantrell (2008) Weighted Least Squares regression and compared against the Ordinary Least Squares regression. The key parameters of the calibrations are summarised in Table 4.

The argument for using a WLS regression model is that it can incorporate instrumental errors for each variable, that it is not sensitive to which is the dependent or independent variable and a simple inversion for reading off an estimated value. It is then generally considered more accurate as it accounts for the relative errors for each variable. Finally, it is worth noting that statistically a WLS regression minimises the ‘distance’ (the residuals) in both the X and Y dimensions according to the relative weights.

The OLS regression models however are sensitive and are therefore used as the dependent and independent variable (explored in supplementary material S4). Logically when we are considering a geochemical proxy that is controlled by the seawater temperature in which the coral grew the CaCO₃ skeleton we need to run the regression of the proxy (Y axis) onto temperature (X-axis). In terms of how OLS reduces the
<figure><img src="image_10.png" /><figcaption>Fig. 6. X-radiographs of BOB-48 and BOB-47. They are combined to produce dataset BOB-478 (see text). The coloured lines show sample points in line with the corallite growth included in the analysis (green), points with uncertain alignment (orange) and points excluded due to orientation of the corallite growth being unsuitable (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 7. Results for coral BOB-478 for Sr/Ca (a), δ¹⁸O (b) against AVHRR-OISSTv2 (Reynolds et al., 2007a, 2007b; Banzon et al., 2016). The orange line is a WLS regression (Cantrell, 2008), the blue line is OLS regression, and the dashed lines are the inverse prediction confidence intervals for the expected value and single observation according to Demidenko et al. (2013). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

residuals is purely in Y axis. For this reason, it cannot take into account the instrumental error in both the axes. The clear advantage of using the OLS regression is that there are well defined mathematical solutions for extrapolating an error estimate when using the regression for predicting new values and importantly that accounts for the distance from the mean values used in the calibration. This is important in case we are changing geographical location or time period and the temperatures we are estimating are outside or towards the extremes of the ranges we had for our calibration. We can still use that calibration but with the understanding that the certainty around that estimate will greatly reduced. For this we use the Demidenko inverse prediction, the full mathematics and description are laid out in the supplementary S4.

There is in fact little difference between the calibration curves that the WLS and OLS regression models produce with a percentage difference all below 0.1% (Figs. 3, 5 and 7 and Tables 4 and 5).

The conclusion we draw from comparing the regression models is to make the WLS regression results readily available as in theory they represent more the ‘true’ relationship and can be useful to compare against others in future studies. When the mathematical solutions for the error structure of a predicted value become clearer the priority should be put on using WLS regression. Considering how similar the calibration curves using the OLS regression models combined with the fact that then allows us to produce a predicted value with a mathematically sound error estimate for the purpose if this paper, to assess the methods and produce French Polynesian Porites microatoll calibration. From here-on out we will be using the OLS regression models. It is worth noting that despite in the paleoclimate community the use of WLS regressions are becoming more prevalent, the older studies used OLS regression (which goes some ways in explaining, albeit small, differences between calibration curves).

## 4.2. Sr/Ca Porites microatoll calibration from coral MAU-140 and comparison to published calibrations

For the analysed Porites microatoll sample, the fitted linear calibration for Sr/Ca was:

$$ \text{Sr/Ca (mmol mol}^{-1}\text{)} = -0.082 (\pm 0.006) \text{SST} + 11.256 (\pm 0.170) \quad (1) $$

To estimate temperature from a new Sr/Ca ratio, the resulting inverted fitted regression equation was:

$$ \text{SST} = -(\text{Sr/Ca} - 11.256)/0.082 \quad (2) $$
<caption>**Table 2**</caption>

Sr/Ca to temperature model analysis, for each coral (MAU-140, BOB-108 and BOB-478) and combined calibrations to Optimum Interpolation Sea Surface Temperature (AVHRR-OISSTv2) (Banzon et al., 2016; Reynolds et al., 2007a, 2007b).

<table><thead><tr><th></th><th>MAU-140</th><th>BOB-108</th><th>BOB-478</th><th>Combined 3 corals</th></tr></thead><tbody><tr><td>N</td><td>41</td><td>28</td><td>37</td><td>106</td></tr><tr><td><strong>Sr/Ca</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Mean</td><td>8.9842</td><td>9.0627</td><td>9.0178</td><td>9.0166</td></tr><tr><td>SD</td><td>0.0763</td><td>0.0975</td><td>0.0757</td><td>0.0872</td></tr><tr><td><strong>Temperature (°C)</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Mean</td><td>27.8321</td><td>27.7713</td><td>27.6716</td><td>27.7600</td></tr><tr><td>SD</td><td>0.8633</td><td>0.8747</td><td>0.8427</td><td>0.8538</td></tr><tr><td><strong>Regression</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Hinges</td><td>9</td><td>4</td><td>8</td><td>21</td></tr><tr><td>Intercept (±SE)</td><td>11.256 (±0.173)</td><td>11.402 (±0.432)</td><td>11.012 (±0.286)</td><td>11.229 (±0.195)</td></tr><tr><td>Slope (±SE)</td><td>-0.082 (±0.006)</td><td>-0.084 (±0.016)</td><td>-0.072 (±0.010)</td><td>-0.080 (±0.007)</td></tr><tr><td>R<sup>2</sup></td><td>0.852</td><td>0.571</td><td>0.644</td><td>0.609</td></tr><tr><td>RSS</td><td>0.0344</td><td>0.1101</td><td>0.0735</td><td>0.3124</td></tr><tr><td>RDF</td><td>30</td><td>23</td><td>27</td><td>83</td></tr><tr><td>MSE</td><td>0.0011</td><td>0.0048</td><td>0.0027</td><td>0.0038</td></tr><tr><td>Root MSE</td><td>0.0339</td><td>0.0692</td><td>0.0522</td><td>0.0613</td></tr><tr><td>SEIP (±SE) °C</td><td>0.415 (±0.062)</td><td>0.840 (±0.200)</td><td>0.724 (±0.143)</td><td>0.770 (±0.090)</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Fig. 8.** Sr/Ca to temperature relationship of the samples MAU-140, BOB-108 and BOB-478.</figcaption></figure>

with standard error of the inverse prediction (SEIP) 0.415 (±0.062) °C (See details on the calculation of SEIP in supplementary material S4).

The predicted temperatures from selected published models were compared (Fig. 10). Although several studies using Sr/Ca were reported in the literature (see summary in Ross et al., 2019), comparison was limited to four references: the most widely referenced Sr/Ca calibration developed by Corrège (2006), the Sr/Ca calibration developed by D'Olivo et al. (2018) who proposed a universal method based on a combination of Sr/Ca and Li/Mg ratio, and the studies of Cahyarini et al. (2008) and Felis et al. (2012) using samples from Tahiti. It is worth noting these were all performed on massive Porites colonies in contrast to Porites microatolls of the present study. The results of the present study showed a steeper (more inverse slope) relationship to temperature with a greater intercept recorded in microatolls than in massive colonies (Fig. 10).

The temperature reconstructions showed that the calibration curve of D'Olivo et al. (2018) displayed a good overlap for higher temperatures, but the shallower calibration slope meant the higher Sr/Ca values (inverse relationship) underestimated the temperatures (Fig. 11). Cahyarini et al. (2008) and Corrège (2006) reconstructed a very similar temperature range with a similar slope, but the absolute range was offset

(different intercepts). Our result is the most similar to the calibration from Felis et al. (2012), which was from massive Porites from the neighbouring Island of Tahiti.

### 4.3. δ¹⁸O Porites microatoll calibration on coral MAU-140 and comparison to the published calibrations

Using the MAU-140 reduced dataset (n = 41) for calibration the fitted regression line of δ¹⁸O on temperature was:

$$ \delta^{18}\text{O} (\text{‰}) = -0.166 (\pm 0.025) \text{SST (°C)} + 0.003 (\pm 0.689) \quad (3) $$

This produced a SEIP of 0.815 (±0.160) °C.

Our study confirmed within error a slope of -0.15 ‰/°C that was obtained on a Porites microatoll from Christmas Island (McGregor et al., 2011; Woodroffe et al., 2003). The comparison between microatolls and massive Porites from the same region indicated very similar slopes with -0.16 (±0.03) ‰/°C from Moorea (Boiseau et al., 1998), -0.19 (±0.019) ‰/°C from Tahiti (Cahyarini et al., 2008) and -0.168 (±0.012) ‰/°C from Tahiti (Felis et al., 2012) (Fig. 12 and Fig. 13). Each dataset overlapped within error, thus indicating regional reliability of the δ¹⁸O signal. The stability of the external standard analysed in parallel produced a value of -1.70 ‰ and σ = 0.09 (n = 12), providing reasonable confidence in the dataset.

### 4.4. Li/Mg Porites microatoll calibration on coral MAU-140 and comparison to the literature

The Li/Mg to temperature calibration produced from our microatoll was:

$$ \text{Li/Mg (mmol mol}^{-1}\text{)} = -0.073 (\pm 0.010) \text{SST} + 3.495 (\pm 0.285) \quad (4) $$

The regression model corrected for degrees of freedom produced a SEIP of 0.758 (±0.146) °C.

The methods proposed by Montagna et al. (2014) and D'Olivo et al. (2018) were applied and tested on the MAU-140 microatoll sample. The calibration curve from our sample was compared to that of the two previous studies (Fig. 14 and Fig. 15). The calibration curves were reasonably similar, where the curve of our study displayed the same trend as that of Montagna et al. (2014) with only a slight offset. The calibration curve for D'Olivo et al. (2018) was calculated followed their method.

The Li/Mg curve proposed by D'Olivo et al. (2018) underestimated the actual temperature by about 3 °C. The Li/Mg calibration of Montagna et al. (2014) was closer to our calibration, just over one standard error apart in temperature reconstruction. The nature of the Li/Mg data
<table><caption>**Table 3**

Summary of data used in statistics for the regression of δ¹⁸O to temperature for each coral and for a model where all three are combined.</caption><thead><tr><th></th><th>MAU-140</th><th>BOB-108</th><th>BOB-478</th><th>Combined 3 corals</th></tr></thead><tbody><tr><td>N</td><td>41</td><td>28</td><td>37</td><td>106</td></tr><tr><td><strong>δ¹⁸O</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Mean</td><td>-4.6129</td><td>-5.3107</td><td>-4.8207</td><td>-4.8698</td></tr><tr><td>St Dev</td><td>0.1862</td><td>0.2080</td><td>0.1822</td><td>0.3379</td></tr><tr><td><strong>Temperature (°C)</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Mean</td><td>27.8321</td><td>27.7713</td><td>27.6716</td><td>27.7600</td></tr><tr><td>St Dev</td><td>0.8633</td><td>0.8747</td><td>0.8427</td><td>0.8538</td></tr><tr><td><strong>Regression</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Hinges</td><td>9</td><td>4</td><td>8</td><td>21</td></tr><tr><td>Intercept (±SE) ‰</td><td>0.003 (±0.701)</td><td>0.756 (±0.544)</td><td>0.183 (±0.632)</td><td>0.070 (±1.078)</td></tr><tr><td>Slope (±SE) ‰ °C<sup>-1</sup></td><td>-0.166 (±0.025)</td><td>-0.218 (±0.020)</td><td>-0.181 (±0.023)</td><td>-0.178 (±0.039)</td></tr><tr><td>R<sup>2</sup></td><td>0.5914</td><td>0.8440</td><td>0.6992</td><td>0.2022</td></tr><tr><td>RSS</td><td>0.566562</td><td>0.182196</td><td>0.359586</td><td>9.565307</td></tr><tr><td>RDF</td><td>30</td><td>23</td><td>27</td><td>83</td></tr><tr><td>MSE</td><td>0.0189</td><td>0.0079</td><td>0.0133</td><td>0.1152</td></tr><tr><td>Root MSE</td><td>0.1374</td><td>0.0890</td><td>0.1154</td><td>0.3395</td></tr><tr><td>SEIP (±SE) °C</td><td>0.829 (±0.165)</td><td>0.407 (±0.070)</td><td>0.638 (±0.118)</td><td>1.908 (±0.442)</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>**Fig. 9.** δ¹⁸O values against temperature for sample MAU-140 in blue, BOB-478 in orange and BOB-108 in green, along with the respective regression curves.</figcaption></figure>

did reconstruct the temperature trends; however, it did not clearly pick out smaller scale features such as the double austral summer peak in 2012. Most of the prediction was within one standard error except for overestimating temperatures during the austral summer of 2013.

The universal calibration from D'Olivo et al. (2018) whereby Li/Mg was empirically corrected with Sr/Ca produced the best result. However, Zinke et al. (2019) found that, although the universal Li/Mg result worked well, using just the Sr/Ca ratio alone produced a better result. Our results confirmed these findings.

### 4.5. Sr—U Porites microatoll calibration on coral MAU-140 and comparison to the literature

Here, we applied the method proposed by DeCarlo et al. (2016) using the U/Ca ratio to adjust for potential vital effects in the Sr/Ca signal.

Measured Sr/Ca ratios in the sample MAU-140 ranged from 8.80 to 9.09 mmol mol⁻¹ with an average value of 8.93 and SD 0.07 mmol mol⁻¹. U/Ca ratios ranged from 1.08 to 1.29 µmol mol⁻¹, mean 1.20 and SD 0.05 µmol mol⁻¹. These were similar to the values obtained by DeCarlo et al. (2016) from massive Porites corals from four different locations (Red Sea, Western Pacific and two in the Central Pacific) (See Fig. 16 where our data were plotted on the same scale and shown alongside Fig. 1a from DeCarlo et al., 2016).

The reverse regression equation from DeCarlo et al. (2016):

$$ \text{SST (°C)} = (-11 \pm 1) (\text{Sr-U}-9) + (28.1 \pm 0.1) \quad (5) $$

with their median value for U/Ca of 1.1 µmol mol⁻¹ applied on the reduced dataset of MAU-140 as per the Sr/Ca, δ¹⁸O and Li/Mg methods. The mean temperature was estimated to 29.97 (±0.46)°C. This compared poorly to the actual mean temperature throughout growth as measured from the OISST data of 27.81 °C (SD 0.86).

The mean Sr/Ca value at 8.93 mmol mol⁻¹ was similar to the value derived from corals studied in DeCarlo et al. (2016) (see Fig. 16b). However, when the U/Ca value of 1.1 µmol mol⁻¹ was used to normalise Sr/Ca and calculate the Sr—U value, the resulting temperature prediction overestimated the SST and was outside of the range of DeCarlo et al. (2016) (Fig. 16c). This result clearly showed that directly applying that method to our coral data did not improve the temperature estimate. To be applicable to our material, a U/Ca value of 1.29 µmol mol⁻¹ would have been required in DeCarlo et al. (2016)'s equation.

We ran a multivariate ANOVA analysis to understand the relationship between Sr/Ca, U/Ca and SST. Fitting a regression model of temperature against Sr/Ca resulted in an R² of 0.668. This increased to 0.715 when the U/Ca term was added which was a statistically significant improvement in fit (p-value 0.017). The pattern observed in our

<table><caption>**Table 4**

comparing slope and intercept for each coral using Cantrell (2008) WLS regression and OLS regression with their standard errors in brackets.</caption><thead><tr><th rowspan="2">Coral</th><th rowspan="2"></th><th colspan="3">MAU-140</th><th colspan="3">BOB-108</th><th colspan="3">BOB-478</th></tr><tr><th>Sr/Ca</th><th>δ¹⁸O</th><th>Li/Mg</th><th>Sr/Ca</th><th>δ¹⁸O</th><th>Li/Mg</th><th>Sr/Ca</th><th>δ¹⁸O</th><th>Li/Mg</th></tr></thead><tbody><tr><td rowspan="2">WLS</td><td>m</td><td>-0.0838 (±0.0053)</td><td>-0.1744 (±0.0222)</td><td>-0.0828 (±0.009)</td><td>-0.0947 (±0.0146)</td><td>-0.2227 (±0.0185)</td><td>-0.0746 (±0.0091)</td><td>-0.1875 (±0.0201)</td><td>-0.1875 (±0.0201)</td><td>-0.1875 (±0.0201)</td></tr><tr><td>b</td><td>11.2865 (±0.1473)</td><td>0.2404 (±0.6170)</td><td>3.7686 (±0.2569)</td><td>11.6940 (±0.4061)</td><td>0.8751 (±0.5128)</td><td>11.0825 (±0.2515)</td><td>0.3685 (±0.5568)</td><td>0.3685 (±0.5568)</td><td>0.3685 (±0.5568)</td></tr><tr><td rowspan="2">OLS</td><td>m</td><td>-0.0820 (±0.0053)</td><td>-0.1659 (±0.0221)</td><td>-0.0729 (±0.0089)</td><td>-0.0842 (±0.0143)</td><td>-0.2185 (±0.0184)</td><td>-0.0721 (±0.0091)</td><td>-0.1808 (±0.0200)</td><td>-0.1808 (±0.0200)</td><td>-0.1808 (±0.0200)</td></tr><tr><td>b</td><td>11.2383 (±0.1469)</td><td>0.0032 (±0.6147)</td><td>3.4954 (±0.2490)</td><td>11.4017 (±0.3978)</td><td>0.7560 (±0.5117)</td><td>11.0116 (±0.2510)</td><td>0.1832 (±0.5550)</td><td>0.1832 (±0.5550)</td><td>0.1832 (±0.5550)</td></tr></tbody></table>
<table><caption>**Table 5**
Difference in temperature reconstructions in °C and as a percentage between Cantrell (2008) WLS regression and OLS regression.</caption><thead><tr><th>Coral</th><th>Proxy</th><th colspan="2">Sr/Ca</th><th colspan="2">δ<sup>18</sup>O</th><th colspan="2">Li/Mg</th></tr></thead><tbody><tr><td rowspan="2">MAU-140</td><td>Min</td><td>0.06 °C</td><td>0.19%</td><td>0.10 °C</td><td>0.35%</td><td>0.28 °C</td><td>0.94%</td></tr><tr><td>Mean</td><td>0.02 °C</td><td>0.08%</td><td>0.00 °C</td><td>0.01%</td><td>0.03 °C</td><td>0.10%</td></tr><tr><td rowspan="4">BOB-108</td><td>Max</td><td>0.02 °C</td><td>0.07%</td><td>0.12 °C</td><td>0.47%</td><td>0.24 °C</td><td>0.92%</td></tr><tr><td>Min</td><td>0.26 °C</td><td>0.88%</td><td>0.02 °C</td><td>0.06%</td><td></td><td></td></tr><tr><td>Mean</td><td>0.01 °C</td><td>0.02%</td><td>0.01 °C</td><td>0.04%</td><td></td><td></td></tr><tr><td>Max</td><td>0.23 °C</td><td>0.87%</td><td>0.04 °C</td><td>0.15%</td><td></td><td></td></tr><tr><td rowspan="4">BOB-478</td><td>Min</td><td>0.03 °C</td><td>0.10%</td><td>0.06 °C</td><td>0.22%</td><td></td><td></td></tr><tr><td>Mean</td><td>0.02 °C</td><td>0.09%</td><td>0.00 °C</td><td>0.00%</td><td></td><td></td></tr><tr><td>Max</td><td>0.10 °C</td><td>0.39%</td><td>0.07 °C</td><td>0.27%</td><td></td><td></td></tr></tbody></table>

<figure><img src="image_15.png" /><figcaption>**Fig. 10.** Sr/Ca ratios against temperature (AVHRR-OISSTv2) (Reynolds et al., 2007a, 2007b; Banzon et al., 2016) for sample MAU-140 of this study, along with the linear regression compared to a representative selection of linear regressions from the literature consisting of D'Olivo et al. (2018) and Corrège (2006) – universal. Cahyarini et al. (2008) and Felis et al. (2012) – local, Tahiti.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 11.** Temperature reconstruction using the different calibration curves and methods proposed in the most relevant literature for Sr/Ca and including the satellite temperature AVHRR-OISSTv2 (Reynolds et al., 2007a, 2007b; Banzon et al., 2016). The calibrations from D'Olivo et al. (2018) and Corrège (2006) are proposed to be universal while Cahyarini et al. (2008) and Felis et al. (2012) are used as local calibrations from Tahiti.</figcaption></figure>

data when regressed this way round did indeed confirm that including the U/Ca signal improved the proportion of variance explained (R²). As discussed in the methods section on the standard versus reverse regression (further detailed in supplementary material S4), the use of the dimensionless R² metric will mislead into believing that the prediction is better. However, it is simply showing that the model explains more of the percentage of variability. Using the correct regression of Sr/Ca and

<figure><img src="image_17.png" /><figcaption>**Fig. 12.** δ¹⁸O values against temperature (AVHRR-OISSTv2) (Reynolds et al., 2007a, 2007b; Banzon et al., 2016) of sample MAU-140, along with the linear regression compared to linear regressions published in McGregor et al. (2011) – microatoll, Boiseau et al. (1998) – Moorea and Cahyarini et al. (2008) and Felis et al. (2012) – Tahiti.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Fig. 13.** Sea Surface Temperature reconstruction using the calibrations from our Maupiti sample against (AVHRR-OISSTv2) (Reynolds et al., 2007a, 2007b; Banzon et al., 2016). The curve for Maupiti is compared to different δ¹⁸O calibration curves proposed in the representative literature with McGregor et al. (2011) being a microatoll and Boiseau et al. (1998) from neighbouring island Moorea and Cahyarini et al. (2008) and Felis et al. (2012) both from another neighbouring island Tahiti.</figcaption></figure>

U/Ca on temperature, we can estimate temperature by inverse prediction. The inverse prediction is essential when considering the error structure of the regression model and its effect on an estimated temperature. When the inverse prediction was performed on our ICP-MS dataset, the SEIP for the model Sr/Ca against temperature was 0.618 (±0.100) °C. When the U/Ca variable was added to the model, in other words, the regression of Sr/Ca on temperature was adjusted for U/Ca as a covariate, the proportion of variance in the Sr/Ca ratio accounted for (R²) increased, but the standard error of the inverse prediction increased to 0.808 (±0.153) °C which was not desirable.

## 4.6. Polynesian Porites microatoll calibrations for MAU-140 coral – Methods compared

Key summary statistics for each of the optimised methods on the MAU-140 sample are presented in Table 6. The results showed that δ¹⁸O, Li/Mg and Sr/Ca adjusted for U/Ca all showed a similar SEIP value around 0.8 °C, but the Sr/Ca method stood out with a considerably lower SEIP of 0.41 °C. The detailed analysis of all methods optimised for our local sample clearly showed that the Sr/Ca method produced the calibration with the smallest error and best temperature estimate. For Li/Mg signal, we did not apply an empirical combination of Li/Mg and Sr/Ca as per D'Olivo et al. (2018). Instead, we refer to section 3.2 where
<figure><img src="image_19.png" /><figcaption>**Fig. 14.** Li/Mg ratios against temperature (AVHRR-OISSTv2) (Banzon et al., 2016; Reynolds et al., 2007a, 2007b) from this study, along with the linear regression for the sample MAU-140 compared to the regression curves of D'Olivo et al. (2018) and Montagna et al. (2014).</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. 15.** Temperature reconstruction for sample MAU-140 using the Li/Mg data along with Optimal Interpolation Sea Surface Temperature (OISST) values. Data from D'Olivo et al. (2018) and Montagna et al. (2014) were included for comparison.</figcaption></figure>

we applied calibration equations directly from the literature. We explored the consequences of adding U/Ca values to Sr/Ca results to obtain a temperature estimate using the regression with inverse prediction. The R² value was high (meaning the variance was largely explained); however, it was misleading as the SEIP in °C was less accurate than the Li/Mg method.

### 4.7. Thought experiment – Applying calibrations from the literature on massive Porites

We have a unique opportunity to evaluate the methods considered universal proposed in the literature. This would apply when arriving to a new region with fossil corals and specifically in this case *Porites* microatolls and no modern calibration is possible – which method should be applied? To answer this, the calibration equations from various authors were applied directly to our data and compared using the mean and standard deviation of the difference between the fitted and measured SST (AVHRR-OISSTv2) (Banzon et al., 2016; Reynolds et al., 2007a,

2007b), results are presented in Table 7. In addition, the results from the ‘universal’ calibrations (i.e. applicable in any tropical region) and, for Sr/Ca and δ¹⁸O local calibrations from neighbouring island of Tahiti (roughly 300 km away), French Polynesian (Cahyarini et al., 2008) were included. Cahyarini et al. (2008) was used as local given the study included both Sr/Ca and δ¹⁸O. The best fit was found with Cahyarini et al. (2008) with δ¹⁸O outperforming the universal calibrations with a mean difference of 0.17 °C and a standard deviation of 0.64 °C. For the Sr/Ca model, however, the local Cahyarini et al. (2008) was intermediate between the ‘universal’ calibrations of Corrège (2006) and D'Olivo et al. (2018). In detail, the local French Polynesian Sr/Ca calibration of Cahyarini et al. (2008) was not as accurate as the universal Sr/Ca equation of D'Olivo et al. (2018) (larger mean difference); but note that the local calibration produced a more precise result (lower standard deviation). The best universal calibration model was that of D'Olivo et al. (2018) using the Li/Mg method. While this method did not have the smallest mean or standard deviation of the difference of all the methods assessed, it had the best balance between bias and precision as shown by the two metrics.

## 5. Conclusion

This study demonstrates that Sr/Ca in *Porites* microatolls is a precise and reliable proxy for reconstructing sea-surface temperatures, with a standard error of the inverse prediction of 0.415 (±0.062) °C. The Sr/Ca to temperature relationship remained very consistent across multiple corals independent of sample quality. The precision and reliability across multiple corals were remarkable and merit to be repeated on microatolls growing in similar environmental conditions from other regions. The nature of microatolls continually growing at the same water depth most likely plays a role in the consistency and reproducibility of the signal. The local calibration that we obtained in French Polynesia can be used as a reliable calibration for the tropical Pacific, and the reconstruction of Holocene sea-surface temperatures based on *Porites* microatolls.

δ¹⁸O resulted in a reasonable confidence for the reconstructed relative temperature range (seasonality), but outliers and significant local offsets meant large errors in absolute temperature predictions. The δ¹⁸O-SST relationship was similar to that of previously studied French Polynesian massive *Porites*. The local offset between our samples needs
<figure><img src="image_21.png" /><figcaption>**Fig. 16.** Sr—U data of sample MAU-140 from Maupiti. For comparison, data of various sites to compare and evaluate the method on a microatoll are reproduced from DeCarlo et al. (2016).</figcaption></figure>
<table><caption>**Table 6**
Comparison of δ¹⁸O, Li/Mg, Sr/Ca adjusted for U/Ca and Sr/Ca for estimating temperature by inverse prediction for coral MAU-140.</caption><thead><tr><th></th><th>δ¹⁸O</th><th>Li/Mg</th><th>Sr/Ca adjusted for U/Ca</th><th>Sr/Ca</th></tr><tr><th>N</th><th>41</th><th>40</th><th>40</th><th>41</th></tr></thead><tbody><tr><th>Slope (±SE)</th><td>-0.166 (±0.025) ‰ °C<sup>-1</sup></td><td>-0.073 (±0.010) mmol mol<sup>-1</sup> °C<sup>-1</sup></td><td>-0.051 (±0.012) mmol mol<sup>-1</sup> °C<sup>-1</sup></td><td>-0.082 (±0.006) mmol mol<sup>-1</sup> °C<sup>-1</sup></td></tr><tr><th>Intercept (±SE)</th><td>0.003 (±0.701) ‰</td><td>3.495 (±0.280) mmol mol<sup>-1</sup></td><td>9.879 (±0.514) mmol mol<sup>-1</sup></td><td>11.256 (±0.170) mmol mol<sup>-1</sup></td></tr><tr><th>R<sup>2</sup></th><td>0.591</td><td>0.636</td><td>0.715</td><td>0.852</td></tr><tr><th>RSS</th><td>0.56656</td><td>0.088709</td><td>0.063759</td><td>0.034435</td></tr><tr><th>RDF</th><td>30</td><td>30</td><td>37</td><td>31</td></tr><tr><th>MSE</th><td>0.0189</td><td>0.00296</td><td></td><td>0.00111</td></tr><tr><th>Root MSE</th><td>0.1374</td><td>0.05438</td><td></td><td>0.03333</td></tr><tr><th>SEIP (±SE) °C</th><td>0.829 (±0.165)</td><td>0.745 (±0.141)</td><td>0.809 (±0.153)</td><td>0.415 (±0.062)</td></tr></tbody></table>

<table><caption>**Table 7**
Compilation of the mean difference between calibrations applied directly from the literature and Sea Surface Temperature (AVHRR-OISSTv2) (Banzon et al., 2016; Reynolds et al., 2007a, 2007b) in °C.</caption><thead><tr><th rowspan="3"></th><th colspan="3">Universal</th><th colspan="3">Local</th></tr><tr><th colspan="2">Li/Mg</th><th>Sr-U</th><th colspan="2">Sr/Ca</th><th>Sr/Ca</th></tr><tr><th>D'Olivo et al. (2018)<br>Empirical</th><th>Montagna et al.<br>(2014)</th><th>DeCarlo et al.<br>(2016)</th><th>Corrège<br>(2006)</th><th>D'Olivo et al.<br>(2018)</th><th>Cahyarini et al.<br>(2008)</th></tr></thead><tbody><tr><th>Mean diff.<br>°C</th><td>1.967</td><td>1.908</td><td>-2.089</td><td>4.913</td><td>1.620</td><td>2.250</td></tr><tr><th>SD °C</th><td>1.230</td><td>3.828</td><td>n.a.</td><td>0.817</td><td>4.059</td><td>0.902</td></tr><tr><th>Std err °C</th><td>0.194</td><td>0.605</td><td>n.a.</td><td>0.128</td><td>0.634</td><td>0.141</td></tr></tbody><tfoot><tr><td colspan="3"></td><td colspan="3">δ¹⁸O</td><td>0.169</td></tr></tfoot></table>

further investigation to explain whether a single universal calibration can be applied to microatolls. Replication in other locations will be necessary to gain further insight into this proxy.

Assessing the key coral paleothermometry techniques established in the literature, we found, where no local calibration is available, the Li/Mg ratio empirically corrected for Sr/Ca was the method that best balanced bias and precision. The Sr-U method did not produce an accurate result on our microatoll sample despite the Sr/Ca and U/Ca values being within the expected range. Exploring in detail showed that the method itself with the regression model used was the most likely source of error.

Our study shows that *Porites* microatolls accurately and reliably record sea-surface temperatures. Our regional calibration (Sr/Ca = -0.082 ± 0.006 SST + 11.256 ± 0.170) for the French Polynesian islands in the Tropical South Pacific applies to sea surface, the targeted proxy for paleoclimate reconstruction. This is a fundamental and significant step towards reconstructing sea-surface temperature because *Porites* microatolls grow close to the sea-air interface, whereas dome-shaped *Porites* corals grow in a wide range between near surface and roughly 20 m water depth.

### CRediT authorship contribution statement

**Nicholas Farley:** Writing – review & editing, Writing – original draft, Visualization, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Guillaume Antonioli:** Formal analysis, Data curation. **Nadine Hallmann:** Resources. **Gilbert Camoin:** Resources. **Anton Eisenhauer:** Resources. **Claude Vella:** Resources. **Glenn A. Milne:** Resources. **Elias Samankassou:** Writing – review & editing, Supervision, Resources, Project administration, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

The data at time of publication will be available through PANGEA (https://pangaea.de/). For submission it is attached as supplementary. The temperature data obtained for this study is the AVHRR OISST v2 dataset (Banzon et al., 2016; Reynolds et al., 2007). The data is available at doi:10.7289/V5SQ8XB5 or through https://www.ncdc.noaa.gov/oisst. For figures featuring in the Appendix, we also used MétéoFrance station data which is accessible directly from them upon request through https://donneespubliques.meteofrance.fr.

### Acknowledgements

Field campaigns and sampling were conducted in the frame of the HOLOREEFS project. The support of the Department of Earth Sciences, University of Geneva, is acknowledged. The support of Serge Planes and his team at CRIOBE in Moorea, French Polynesia, is thankfully acknowledged. The study benefited from funding through the Swiss National Science Foundation (Project 133771). The authors would also like to thank C. Delong for her time and expertise discussing *Porites* coral growth and sampling methodologies.

### Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.palaeo.2024.112146.

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