Calibration of Sr/Ca Ratio and In Situ Temperature Using Hawaiian Corals

The Sr/Ca ratio of modern coral skeletons can record local seawater temperature (T) and is an important tool for reconstructing past environments. However, site‐specific calibrations are required to ensure accurate temperature reconstructions. Here, we examine three modern coral skeletons collected at contrasting sites on the island of Oahu, Hawaii to establish the first accurate calibrations for this region and investigate site specific influences on the calibration process. Satellite T data, which is used for many calibrations, may not be able to derive an accurate thermometer. For our shallow lagoonal sites, satellite T had smaller seasonal T ranges, which resulted in significantly higher slopes of Sr/Ca‐T compared to using in situ T. The traditional age model based on aligning only min/max values can lead to errors in the Sr/Ca‐T calibration due to variable growth rates. An enhanced age model which adds midpoint alignments between the min/max peak values can account for seasonal changes in growth rate and reduce the error. On the same island, site‐ and time period specific conditions can cause notable differences in the Sr/Ca‐T calibrations. The coral from an estuarine embayment showed a high Sr/Ca offset, likely due to high Sr/Ca in ambient seawater. For corals which experienced thermal stress, lower slopes were observed probably due to elevated Sr/Ca values during the period of thermal stress.

The relationship between Sr/Ca and temperature could be disturbed by other factors such as local seawater characteristics, biological effects, and environmental stresses.The inverse relationship between Sr/Ca in the aragonite skeletons of reef building scleractinian corals and seawater temperature is based on the thermodynamic partition coefficient and the Sr/Ca ratio of ambient seawater (De Villiers, 1999;de Villiers et al., 1994;Shen et al., 1996) and must be calibrated with temperature (T) for a given coral taxon at each location due to inter-taxa differences (Weber, 1973).While largely consistent throughout the world oceans, seawater Sr/Ca ratios can vary geographically due to local processes that add or remove dissolved Sr and Ca from seawater (Lebrato et al., 2020).The relationship between Sr/Ca in coral skeletons and temperature has been reported to be influenced by "vital effects" such as skeletal growth rates (De Villiers et al., 1995) and Rayleigh fractionation in calcification fluids (Cohen & Gaetani, 2010).However, an absence of correlation between Sr/Ca and growth rates (Alibert & McCulloch, 1997;Hayashi et al., 2013;Hirabayashi et al., 2013) and an insufficient explanation of Sr/Ca variability by the Rayleigh model have also been reported (Inoue et al., 2015).Thermal stress can cause a breakdown of the Sr/Ca-T relationship by decreasing biomineralization and causing higher Sr incorporation (Marshall & McCulloch, 2002).Along a latitudinal gradient, increasing mean seasonal T has been shown to decrease the sensitivity of Sr/Ca to higher T, resulting in a lower Sr/Ca-T slope (Murty et al., 2018).
To establish an accurate Sr/Ca-T thermometer, the referenced seawater temperature should be representative of in situ T and the age model must accurately pair the correct T with each Sr/Ca measurement.Many previous studies have used satellite-based (hereafter, satellite T) data or gridded reanalysis temperature data (e.g., Linsley et al., 2000;Zinke et al., 2004).However, satellite observations limited to the "skin" (roughly a micron in depth) surface layer (Huang et al., 2021) may underestimate vertical water column dynamics (Gomez et al., 2020).Additionally, there are large uncertainties in satellite observations at shallow water depths (∼40 m) (Xie et al., 2008), and biases due to contamination from land in land-masking grids (Brewin et al., 2017;McClanahan et al., 2007;Merchant et al., 2019;Smit et al., 2013;Tang et al., 2003).Traditional age models have been obtained by aligning the extreme values of Sr/Ca and seawater temperature and assuming that the skeletal extension rate is constant between these alignment dates.However, skeletal extension rates can vary across time (Barnes et al., 1995;Shimamura et al., 2005;Taylor et al., 1993).Intra-annual difference in coral growth rate can cause the chronological uncertainty (Gagan et al., 1994;T. Watanabe et al., 2003).DeLong et al. (2014) applied an adjustment for the season bias by adding midspring and midautumn alignment points which improved the Sr/Ca-T correlation.
To date, an acceptable Sr/Ca calibration has not been established for the Hawaiian Archipelago.A prior calibration study using Hawaiian corals reported an anomalously high Sr/Ca-T slope (de Villiers et al., 1994), possibly caused by subsampling that did not follow the optimal growth line affecting the age model (Alibert & McCulloch, 1997;Marshall & McCulloch, 2002).Within a region, there are many reports of inter-colony differences in Sr/Ca variation and its relationship to T (Abram et al., 2007;Alpert et al., 2016;Cahyarini et al., 2009;Fallon et al., 2003;Felis et al., 2004;Gagan et al., 1998;Linsley et al., 2004;Marshall & McCulloch, 2002;Pfeiffer et al., 2009).In cases where Sr/Ca could not be solely explained by local T (Linsley et al., 2004) or environmental stress (Fallon et al., 2003;Marshall & McCulloch, 2002), the inter-colony variability is often attributed to vital effects (Alpert et al., 2016;Felis et al., 2004;Grove et al., 2013;Pfeiffer et al., 2009).Composites of multiple coral Sr/Ca have been used to reduce intrinsic variance due to small-scale spatial environment heterogeneity or vital effects.Averaging the multiple-core data reduces the error with instrumental "regional" temperature (Cahyarini et al., 2009;Pfeiffer et al., 2009).However, lack of understanding of actual in situ T, and its relationship to Sr/Ca makes accurate interpretation of how well the composite T reflects local seawater temperature difficult (Grove et al., 2013).
This study establishes a Sr/Ca-T calibration for Hawaii by examining the variability associated with contrasting locations on the same island (shallow lagoon vs. deeper forereef, estuary vs. non-estuary, and windward vs. leeward).The use of satellite SST as a proxy for in situ T is examined, and the implications of variable growth rate are also investigated.

Study Sites and Coral Sampling
Oahu (21°N, 158°W) is one of the main Hawaiian Islands located in the center of the North Pacific Subtropical Gyre (Figure 1).On the east facing side of the Hawai'i Island, the North Hawaiian Ridge Current bifurcates from North Equatorial Current at the flow northward (Castillo-Trujillo et al., 2019).Northeast trade winds dominate the airflow, which produces orographic rain along the windward side of the island (Hsiao et al., 2021).On the west facing side of the island, Hawaiian Lee Current flows northwestward.Trade wind shadow results in drier and warmer weather along the leeward side of the island (Kolivras & Comrie, 2007).Oahu is partially exposed to large Northwest swells in winter and south swells in summer, which ventilate inshore waters (Li et al., 2016).The south and west part of Oahu are also exposed to M 2 semidiurnal tides, which can bring sub thermocline waters onto the insular island shelves (Chavanne et al., 2010;Smith et al., 2016).
Three contrasting study sites on Oahu Island were used for collecting coral samples and using both in situ T and remotely sensed SST for comparative geochemical calibrations: Makai Pier, Kaneohe Bay CRIMP2, and Ko'Olina.The Makai Pier site (21.320°N,157.669°W) is a shallow inshore lagoon buffered from the open ocean by a fringing reef on the windward side of Oahu but located in an area with very minimal terrigenous influence due to the watershed characteristics.The Ko'Olina site (21.327°N,158.129°W) is a deeper offshore forereef site representative of the leeward side of the island.The CRIMP2 buoy site in Kaneohe Bay (21.46°N, 157.80°W) is in a large urban estuary and embayment sheltered from the open ocean by a fringing reef and characterized by long residence times (Lowe et al., 2009).
At each study site, temperature loggers (HOBO U22-001) recording temperature at 15-30 min intervals were deployed next to a Porites coral colony, which was targeted for the subsequent calibration sampling.After ∼18 months, the temperature loggers were retrieved, and colonies were sampled on the same date.Additional in situ T was observed at the CRIMP2 buoy (Sutton et al., 2016) at 3-hr intervals.At Makai Pier and Ko'Olina, the top of a massive Porites colony was sampled along its vertical growth axis on 16 March 2019 at a depth of 2-3 m (depending on the tidal height) and on 23 February 2021 at a depth of 7 m respectively.An additional massive Porites coral nubbin (sampled from Makai Pier) was sequentially outplanted onto an oceanographic buoy at Kaneohe CRIMP2 at 0.6 m depth on 5 November 2017, and sampled on 11 December 2019.For supporting information, a coral core was sampled at Waialua (21.592°N, 158.114°W, depth 5 m), Oahu on 16 September 2019.Unfortunately, in situ T data was not available at Waialua, so the Sr/Ca of a coral from Waialua was only used to present the results of the Sr/Ca-T calibration using satellite T.

Comparison With Satellite T Data
The SST data, based on satellite observations, was obtained from OISST version2p1 AVHRR Daily SST from NOAA NCDC (Huang et al., 2021).The satellite SST product is available for retrieving daily SST data from 1981 on a 0.25° × 0.25° grid.To avoid land effects on satellite observation, seawater temperatures at the adjacent grid from the coral sampling site were selected.A grid centered at (21.375°N, 157.375°W), (21.125°N, 158.125°W), and (21.625°N, 157.625°W) were selected for Makai Pier, Ko'Olina and Kaneohe, respectively.
To evaluate the difference between in situ T and satellite T, each data set along the common overlapped time series were compared.The seasonal maximum and minimum temperature values and timing of these values were compared for the three sampling sites.

Coral Sr/Ca
Coral skeletal cores were cut into 5 mm thick slabs using a rock cutter.The sampling paths were set along the optimal growth axis that was determined based on X-ray image scans (NAOMI, RF).Two millimeter thick ledges were prepared along the sampling line, then cleaned in ultrasonic cleaning (Smurt NR-50M, MICROTEC) with ultrapure water to remove the microstructures in the skeleton, leaving only the skeletal structures that grow continuously along the time series.Powder samples were collected for trace element analysis using an electric microdrill every 0.2 mm.Sr/Ca ratio measurements were performed using an inductively coupled plasma optical emission spectrometer (ICP-OES, iCAP6200 Thermo Fisher Scientific) at Hokkaido University.Elemental emission signals were simultaneously collected and subsequently processed following a technique described by T. K. Watanabe et al. (2020).The analytical precision of Sr/Ca measurements as estimated from multiple JCp-1 standard measurements using this instrument is 0.07% RSD (T.K. Watanabe et al., 2020).

Coral Extension Rates
The Sr/Ca midpoints were defined as the Sr/Ca value halfway between the Sr/Ca maxima and subsequent minima during the warming season, and halfway between the Sr/Ca minima and subsequent maxima during the cooling season.Skeletal extension rates were calculated based on the distance (mm) between the Sr/Ca midpoints to determine the relative growth rates during the warm and cold seasons.

Coral Chronology
We tested two age models.First, the traditional chronologies were developed based on the seasonal minima/ maxima of Sr/Ca and temperature.High resolution in situ T data were averaged for daily resolution.The highest (lowest) measured Sr/Ca value was aligned with the lowest (highest) temperature.The Sr/Ca time series was linearly interpolated between these alignment points to obtain the date for each coral sample point.
Second, additional date alignment points were applied by pairing each Sr/Ca midpoint with a corresponding T midpoint.The temperature midpoints were defined as the T halfway between the T minima and subsequent maxima during the warming season and T halfway between the T maxima and subsequent minima during the cooling season.The date of midpoint temperature was determined by taking the minimum number of running averages (13 days for Makai Pier and Kaneohe, 5 days for Ko'Olina) to monotonize T fluctuations and prevent midpoint T from appearing more than once.

Statistical Analyses for Coral Sr/Ca-T Calibration
Regression equations were calculated for the coral skeletal Sr/Ca ratio and seawater temperature data using the ordinary least squares (OLS) method.Correlation coefficients r were calculated using the OLS method for the strength of correlation between coral Sr/Ca ratios and seawater temperature.To fairly compare how the Sr/Ca-T calibration differs between using in situ and satellite T, we tested Sr/Ca-T calibration using satellite T for a limited period (1∼2 years) of in situ T observations.The precision (error) of coral Sr/Ca-T calibration results, was evaluated by calculating root mean square error, defined as where T est,i is the i'th term from the coral derived temperature record and T ref,i is the i'th reference temperature, was used.

Results
The average in situ Ts used for Sr/Ca-T calibrations were 25  2a).The seasonal range differences between in situ T and satellite T were 1.8°C at Makai Pier, 3.1°C at Kaneohe, and 0.1°C at Ko'Olina.In inshore lagoonal environments, the timing of the seasonal changes in temperature also occurred earlier in the in situ T compared to the satellite T. At Makai Pier, in situ T recorded annual maximum (minimum) seawater temperature that were 41 (and 25) days on average earlier than satellite T. Similarly, at Kaneohe, in situ T recorded annual maximum (minimum) seawater temperature that were 32 (and 14) days on average earlier than satellite T. Between the peak timings, in situ T exceeded satellite T mainly during the period of warming in situ T (around April to September), while in situ T were lower than satellite T mainly during the period of cooling in situ T (October to March).The difference between in situ T and satellite T (Figure 2) showed discrepancies of ±2°C (warmer in situ T during warming season and cooler in situ T during cooling season) appeared in the shallow lagoonal sites of Makai Pier and Kaneohe (Figure 2b).
The Sr/Ca-T calibration lines using satellite T data consistently had lower slopes than those using in situ T data (Table 1 and Figure 4), with the largest differences occurring at the inshore lagoonal sites.The correlation factors (r) were the same or higher for satellite T compared to in situ T (traditional calibration) for all sites.
The skeletal extension rate for the corals varied between warm and cold seasons but not in a consistent manner (Table 2, Figure S1 in Supporting Information S1).At Ko'Olina, the extension rate was twice as fast during the warm season (7.6 mm/season) compared with the cold season (3.8 mm/season).
By adding midpoint alignment of Sr/Ca and T, an improvement in the correlation between Sr/Ca and in situ T was observed for all sites (Table 1).For Ko'Olina, the correlation coefficient (r) increased from 0.79 for the traditional age model to 0.88 for the enhanced age model (Table 1).Higher slopes and intercepts were observed in the enhanced age model for all sites.
Comparison of our Sr/Ca-in situ T calibration (enhanced age model) at the three sites (Figure 5) showed notable differences between the three sites.
The Kaneohe site had a high Sr/Ca offset equivalent to an approximately 2°C compared to the other two calibrations for the same Sr/Ca value.Both Kaneohe and Ko'Olina sites had lower slope values than the Makai Pier site (Figure 5).

Discussion
Using satellite T can cause the error of Sr/Ca-T calibration to have a steeper slope than actual.As noted in previous studies, the referenced temperature must accurately reflect in situ T, which may not be the case when satellite T data are used (Corrège, 2006;DeLong et al., 2007;Marshall & McCulloch, 2002).Results from previous studies (Table S1  Note.RMSE (°C) represents the error between the seawater temperature estimated by the linear regression and each reference seawater temperature (see text).Information S1) show that Sr/Ca-T calibrations using satellite-based T have higher slopes than those using in situ T, although not statistically significant.For the shallow inshore study sites located inside the fringing reef (Makai Pier and Kaneohe), seawater temperatures can warm during the day and cool at night compared to offshore open ocean waters, resulting in temperature gradients and heat exchange (Monismith et al., 2006).During prolonged warming (cooling) periods, since the shallow lagoons are partially thermally isolated from offshore waters with deeper mix layers, the seasonal changes of in situ T occur earlier than offshore satellite T and have higher seasonal extremes.The closer alignment between in situ T and satellite T at the exposed Ko'Olina forereef site is likely due to more frequent mixing with offshore waters and lower residence times.For the inshore sites thermally isolated from offshore waters, the use of satellite SST can underestimate the magnitude of the seasonal temperature range.Calibrating the same Sr/Ca values with a smaller temperature range (i.e., satellite SST) results in an errantly higher Sr/Ca-T slope (Figure 6).The anomalously high Sr/Ca-T slope (−0.07952 mmol/mol°C −1 ) reported by de Villiers et al. (1994) from nearshore Koko Head in eastern Oahu may have been influenced by this effect.Their use of weekly open ocean temperature data from another location may have underestimated the actual inshore seasonal temperature range, thereby causing an artificially high Sr/Ca-T slope.

Table 1 Linear Regression Equations Between Coral Sr/Ca and Temperature (Sr/Ca [mmol/mol] = a [mmol/ mol/°C −1 ] × Temperature [°C] + b [°C]) and Correlation Factors (r) for Each T Source (In Situ T or Satellite T) and Age Models Used (Traditional or Enhanced Age Model). n Is the Number of Coral Sr/Ca Results Used in the Calibration
Differences in growth rates between warm and cold seasons can cause traditional age models (only aligning extreme values) to systematically distort the Sr/Ca-T relationship between the peak values.This is caused by extrapolating a constant extension rate between extreme values (spring/autumn samples).For example, if coral has a consistently higher extension rate during the warm season than the cold season, the traditional age model would systematically shift the dates of each Sr/Ca sample backwards during the warming season and forwards during the cooling season.This age model distortion would systematically align the Sr/Ca samples between the peaks to a lower than actual temperature (Figure S2 in Supporting Information S1).The histograms of Sr/Ca datapoints showed distribution from that of in situ T for Ko'Olina (Figure S3 in Supporting Information S1), which had more numbers of samples in summer (low Sr/Ca) than winter (high Sr/Ca).Similar patterns of Sr/Ca data points, which are distinctive from in situ T, were reported in previous reports for corals in Shikoku (32°N), Japan (Fallon et al., 1999) and Kikai Island (29°N), Japan (Kawakubo et al., 2017).Although our limited coral records for Makai Pier and Kaneohe prevented us from determining the constant higher (lower) extension rate during the warm (cool) season, the histogram of Sr/Ca data points showed distinctive patterns from that of in situ Ts (Figure S3 in Supporting Information S1).While the growth variability in our coral samples was more complex, adding date alignment at the midpoint values of Sr/Ca and T between min/max values improved the Sr/Ca-T correlation and increased the slope and intercept values (Table 1 and Figure 7).This improvement was particularly pronounced for our Ko'Olina sample due to more variable growth characteristics (Figure 7).The Sr/Ca-T slopes and intercepts obtained in Hawaii (Figure 5) were within well the middle of the range reported in previous calibrations around the world (e.g., Alibert & McCulloch, 1997;Corrège, 2006;Gagan et al., 2000; Table S1 in Supporting Information S1).Result Sr/Ca-T using a coral sampled on 16 September 2019 at Waialua (5 m depth forereef), North Shore of Oahu, calibrated by satellite T for 3.5 years instead of in situ water temperature showed similar results to Sr/Ca-in situ T of Makai Pier and Ko'Olina (Figure S4 in Supporting Information S1).
The high Sr/Ca offset observed for Kaneohe is likely due to the unique local seawater chemistry.The high Sr/Ca offset observed for Kaneohe is not likely caused by vital effects, as the extension rate was not clearly different compared to the other two corals during the calibration period (Table 2), but likely caused by higher ambient seawater Sr/Ca within the embayment.Although not measured at our study sites, Sr/Ca in ambient seawater can be elevated by both riverine input and marine calcification (Lebrato et al., 2020).Dissolved Sr can be released via the diagenesis of subaerial aragonite (high Sr/Ca ratio) to low-Mg calcite (low Sr/Ca ratio) when exposed to meteoric water (Marshall & McCulloch, 2002).The Kaneohe shoreline has exposed Pleistocene and Holocene coral reefs from prior periods of higher sea level (Fletcher et al., 2008) and is exposed to regular orographic rain supplying riverine discharge into the bay (De Carlo et al., 2007;Drupp et al., 2011).A similar high Sr/Ca  offset compared to other regions was reported from Sanya Bay and Hainan Island in the South China Sea (Wei et al., 2000).The corals in that location are also subject to heavy riverine discharge of dissolved elements from the continent.Marine calcification has also been associated with elevated seawater Sr/Ca ratios (Lebrato et al., 2020).Since net community calcification includes the precipitation of both aragonite with slightly higher Sr/Ca ratio than seawater and calcite with very low Sr/Ca (1.80-5.69mmol/mol (Ulrich et al., 2021)), the net community calcification effect on seawater Sr/Ca ratio may be dominated by the calcite calcification influence raising the Sr/ Ca of ambient seawater.To assess the net ecosystem calcification rate, total alkalinity (TA) is a good indicator because it changes with calcification and dissolution of CaCO 3 in coral reefs.In Kaneohe Bay, the diel depletion of TA compared to incoming open ocean waters from outside the bay was observed, which indicates a strong diel calcification signal inside the bay (Shamberger et al., 2011).The long residence times characteristic of the CRIMP2 location in southern Kaneohe Bay (Lowe et al., 2009) may accumulate the effect of calcification on the ambient seawater Sr/Ca ratio.However, the nTA (TA normalized to a constant salinity of 35) in Kaneohe Bay is largely restored every night from dissolution.Since the dissolution component is believed to be largely associated with more soluble forms of CaCO 3 such as high-Mg calcite from coralline algae (Sr/Ca ratio 3.23 mmol/ mol (Ulrich et al., 2021)) in the sediments (Shamberger et al., 2011), the net community effect on seawater Sr/Ca ratio in Kaneohe Bay remains uncertain in the absence of direct measurements.Furthermore, pCO 2 in Kaneohe Bay is known to be higher than open ocean waters entering from outside the bay (Shamberger et al., 2011).The pCO 2 in Kaneohe Bay increases throughout the night, with a daily pCO 2 range of 200 μatm.It was reported that higher pCO 2 increased Sr/Ca in cultured coral skeletons (Cole et al., 2021).Based on the relationship reported by Cole et al., 2021 that a pCO 2 increase of 100 μatm results in an increase of 0.02 mmol/mol change in the coral skeleton, elevated pCO 2 levels in Kaneohe Bay can only explain 0.04 mmol/mol increase in coral Sr/Ca.Although the elevated pCO 2 in Kaneohe Bay cannot explain all of the high Sr/Ca offsets in Kaneohe corals, it may partially explain the offset.
The slightly lower Sr/Ca-T slopes of Ko'Olina and Kaneohe corals compared to that of Makai Pier are possibly due to thermal stress experienced at the former sites but not the latter (Figure 3).When corals are stressed and calcification is decreased (e.g., bleaching), lowering active Ca 2+ transport to the calcifying fluid whereas Sr 2+ is less affected, causing higher coral skeletal Sr/Ca and the breakdown of the Sr/Ca-T relationship (Cohen & McConnaughey, 2003;Marshall & McCulloch, 2002).Thermal stress during the period of maximum seasonal T could elevate Sr/Ca, thereby causing a lower Sr/Ca-T slope.At both Kaneohe and Ko'Olina, in situ T exceeded the NOAA Coral Reef Watch (2019)'s bleaching threshold (28.0°C) for a significant number of days during their respective growth periods.Also, the Ko'Olina site characteristic of leeward Oahu experienced a higher time averaged T than the other two windward sites.In a comparison of sites across a latitudinal gradient, Murty et al. (2018) reported that the slope of coral Sr/Ca-T decreases as the mean annual temperature increases due to a large noise-to-signal ratio during summer high temperatures.The lower slope at Ko'Olina compared to Makai Pier is consistent with this average temperature effect.During the growth period of the Ko'Olina coral, only one of the two warm seasons experienced thermal stress, which can possibly explain the higher variability in the Sr/Ca-T relationship at high T and lower r values.The standard deviation (1σ) of residuals of reconstructed T over 28.0°C and in situ T was 0.39°C, which was 8.8% of the average in situ T seasonal range (4.39°C) of Ko'Olina.During periods of rapid calcification, Rayleigh fractionation has been reported to cause Sr/Ca depletion in the semi-closed calcification fluid, thereby reducing the Sr/Ca in the skeleton (Cohen & Gaetani, 2010).The linear extension rates for our coral samples were variable (Table 2) but slightly lower than the average extension growth rates reported for Porites in Oahu (Grigg, 1982) with one exception.During the 2020 warm season, the Ko'Olina coral experienced a high extension rate.If there was a Rayleigh fractionation effect, lower than expected Sr/Ca during this warm period would have increased the Sr/Ca-T slope.Our data are not consistent with this effect.

Conclusions
By our comparison of Sr/Ca-T, using satellite T can cause Sr/Ca-T slope steeper than actual due to its smaller seasonal T range, which can be common in shallow lagoonal environments.Also, the coral age model should be enhanced by aligning additional points to min/max profiles to correct the chronology associated with variable growth rates.
When calibrating Sr/Ca-T coral thermometers, the local environmental characteristics affecting the calibration can vary on relatively small geographic scales.Therefore, corals and calibration equations from similar environments, especially seawater Sr/Ca characteristics, must be matched when reconstructing paleoenvironmental conditions.The potential nonlinear effect of thermal stress on the Sr/Ca-T slope is also an important factor when matching corals to a calibration equation.Since the coral reef environment of Kaneohe Bay with its estuarine effects and high residence time is uncharacteristic of the coral reef habitats along the Hawaiian Archipelago, the calibration equations for the Makai Pier and Ko'Olina, which are most regionally relevant, can be applied to windward and leeward corals respectively.The corals were collected under the State of Hawaii DLNR Special Activity Permits 2017-07, 2019-61, and 2021-56.Special thanks to the Andrew Rossiter, the Director of the Waikiki Aquarium; his staff Mark Dimzon, John Casey, Helene Meehl; and student interns Lara Boudinot, Michelle Rincon, and Hannah Fietcher for their assistance in prepping and maintaining the coral nubbins prior to outplanting.We also thank Eric DeCarlo and Christopher Sabine of the University of Hawaii at Manoa and their students Lucie Knor, Noah Howins, Caroline Jackson, and Kyle Conner for assistance with outplanting and maintaining the corals on the NOAA/PMEL CRIMP2 carbon monitoring buoy.We also thank Kaho Tisthammer, Masataka Ikeda, and Motoya Odajima, for assistance with finding and sampling the corals.This study was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grants JP 15KK0145, 17H04708, 22H01313, and 20KK0236, and JSPS Invitational Fellowship for Research in Japan (Fellowship ID L20527), and Research Institute for Humanity and Nature (RIHN: a constituent member of NIHU) Project RIHN 14200157, and the Hokkaido University Ambitious Doctoral Fellowship (Information Science and AI).

Figure 1 .
Figure 1.(a) Coral sampling sites at Makai Pier, Ko'Olina, and Kaneohe in Oahu.From (b) to (d), white triangles represent the coral locations and show a closer look at Ko'Olina, Kaneohe, and Makai Pier, respectively.

Figure 2 .
Figure 2. Comparison of daily in situ Ts and satellite Ts at Makai Pier, Ko'Olina, and Kaneohe.(a) Daily in situ Ts (red) and satellite Ts (blue).(b) Difference between in situ Ts and satellite Ts.Note that the vertical axis ranges are different.

Figure 3 .
Figure 3.In situ Ts for Makai Pier (red), Kaneohe (blue), and Ko'Olina (green) used for Sr/Ca-in situ T calibration.The black dotted line represents the coral bleaching threshold (28.0°C) for the Main Hawaiian Islands by NOAA Coral Reef Watch (2019).There were 55 and 46 days above the bleaching threshold in summer 2019 at Kaneohe and Ko'Olina, respectively.

Figure 4 .
Figure 4. Comparisons of Sr/Ca-in situ T with the traditional calibration method at Makai Pier, Ko'Olina, and Kaneohe.Plots of Sr/Ca and in situ Ts (red) and satellite Ts (blue) are shown.Ordinary least squares regression lines are shown.Analysis error (0.07%RSD) is the same size of the plots.

Figure 5 .
Figure 5.Comparison of Sr/Ca-in situ T with enhanced calibration age model at Makai Pier (red), Ko'Olina (green), and Kaneohe (blue).Linear regression lines (dotted lines) and each error bar (95% significance) are shown.

Figure 6 .
Figure 6.(a) Comparison of Sr/Ca (black) and seawater temperature (in situ: red and satellite: blue) at Makai Pier.Traditional age models of Sr/Ca were applied using in situ T. Note that the peak dates of two sets (black and red/blue) are different.Seasonal ranges are shown with the vertical lines.(b) Schematic showing how satellite T with a small T range causes a higher slope of Sr/Ca-T than in situ T with a large T range.The arrows indicate the direction to the larger T range.

Figure 7 .
Figure 7. (a) Comparison of two age models of peak-only alignment (orange) and adding midpoint (green) and 5 days running averaged in situ T (blue) for Ko'Olina.(b) Scattering plots for both age models.Black arrows indicate the direction of improved fitting by the enhanced age model.
in Supporting

Table 2
Extension Rates for Warm/Cold Seasons Calculated as the Distance Between Two Midpoints