3.2.1 Evidence for material-specificity in regression models
Given the finding that the calibration slope of Anderson et al. (2021)
does not statistically match the larger composite calibration of
freshwater carbonates assembled here (Figure 3; Table 3) and also does
not fit well with data from freshwater carbonates from certain latitudes
and environments (Figure 2), we proceed by testing the hypothesis that
there could be material-specific calibrations. We derive calibrations
for biologic carbonates (bivalves and gastropods), biologically-mediated
carbonates (microbialites and tufas), micrites, and travertines, and
test whether regression parameters differed between these groups of
materials (Table 2; Figure 3).
3.2.1.1 Biogenic Carbonates
Our biogenic carbonate calibration was developed using 137 analyses from
23 samples with Δ47 values and independently constrained
water temperatures ranging from 0.573-0.643‰ and 7 - 29°C, respectively.
This dataset includes 16 new samples, alongside reprocessed data from
Huntington et al. (2015) and Wang et al. (2021) that have been brought
onto the I-CDES reference frame. Our calibration shows a significant
temperature dependence (Figure 4a; p = <0.0001) between the
clumped isotope signal and temperature and samples demonstrate agreement
with our linear model (r2 = 0.7811).
Our results show that biogenic carbonates record more depleted
Δ47 values relative to other freshwater samples in this
study (Fig. 3) and the resulting calibration line has a lower intercept
relative to the Petersen and Anderson calibrations (Figure 4A). Despite
visually appearing to be offset from the rest of the data (Figure 3), we
find no statistical difference in slopes between our
Δ47-T regression of biogenic carbonates and other
carbonate groups within this study (Table 3). However, an ANCOVA
analysis finds significant differences in intercepts between biogenic
carbonates and micrite (pintercept = <0.0001)
and biologically mediated carbonates (pintercept =
0.0047) (Table 3). When comparing our calibration results to the
calibrations presented in Anderson et al. (2021), H. Li et al (2021),
Bernasconi et al. (2018), and Petersen et al. (2019), our ANCOVA
indicates shows no difference in slope between our biogenic carbonate
calibration, but differences in intercept between our study and the
authigenic carbonate calibration presented in H. Li et al. (2021)
(pintercept = 0.0215) and the ‘universal’ calibration
derived by Petersen et al. (2019) (pintercept = 0.0728)
(Table 3). We find no differences in either slope or intercept between
biogenic carbonates and the recent I-CDES calibration of Anderson et al.
(2021)
The depletion in Δ47 observed within these biologic
samples relative to micrites, travertines, tufas, and microbialites
could stem from changes in growth rate as a function of season, or other
unidentified factors. As the sample size requirements for clumped
isotopes is relatively large, it often requires the analyses of a
complete shell or the majority of a shell for analyses, effectively
integrating seasonal signals recorded in the shell and potentially
leading to a more muted temperature sensitivity of the calibration than
if seasonally resolved sampling could be carried out. Additionally,
there is potential for a mismatch of temperature between in-situ
measured temperatures, which is representatitve of a multi-year average,
and the temperature range experienced by biologic samples considering
that the lifespan when shell growth would occur is limited to a mush
shorter timeframe. Another possibility is that kinetic isotope
fractionations may manifest in freshwater gastropod and bivalve shells,
as have been constrained in other biocarbonates such as coral skeletons
(Ghosh, Adkins, et al., 2006; Saenger et al., 2012). However, more
research is needed to draw this conclusion for freshwater biologic
carbonates including potentially performing culturing experiments at
controlled temperatures as well as examining other geochemical
indicators such as Δ48 measurements. We note that
although in-depth study of clumped isotope fractionations in aquatic
freshwater gastropods is limited to this study, work with modern land
snails has shown that a majority of these samples also are offset to
lighter Δ47 values than the Petersen et al. (2019)
calibration (Dong et al., 2021). Culture experiments on species of
freshwater gastropods and bivalves may help to better constrain the
origin and impact of these effects.
3.2.1.2 Micrites
In our study we present 2 new samples of micrite, and reprocess data
from 33 samples from Li et al. (2021) and 3 samples from Huntington et
al. (2010) to be on the I-CDES reference frame. Micrites in this study
include water temperatures between 9.8 and 29.0°C and
Δ47 values from 0.596 to 0.682‰. Micrites evaluated in
this study demonstrate a significant temperature dependence
(p<0.0001; Figure 4b), however, our samples demonstrate
significant variability (r2 = 0.5736).
Comparing our derived micrite parameters to other carbonate groups in
this study, we find no significant difference in slopes between
materials, but find significant differences in intercept between
micrites and biogenic carbonates (pintercept =
<0.0001), biologically mediated carbonates
(pintercept = 0.0379), and travertines
(pintercept = 0.0050). Visually, we find that the
micrite regression is positively offset relative to both the Anderson et
al. (2021) and Petersen et al. (2019) calibrations (Figure 4b). In
contrast to the agreements in slope, our ANCOVA analysis finds
significant differences in intercept between a published travertine
calibration (Bernasconi et al., 2018; pintercept =
0.0264), an authigenic carbonate calibration (H. Li et al., 2021;
pintercept = 0.0014), a large calibration dataset
(Petersen et al., 2019; pintercept = <0.0001),
and a recently published calibration on the I-CDES scale (Anderson et
al., 2021; pintercept = <0.0001).
Prior work analyzing clumped isotope composition suggests that
Δ47 values of authigenic carbonates precipitate near
equilibrium, and are not impacted by disequilibrium fractionations
related to carbonate precipitation rate or water chemistry (H. Li et
al., 2020). Thus, the variability in Δ47 that we observe
for micrite is potentially due to uncertainty in the timing of surface
carbonate precipitation events at each site. Micrite precipitation is
enhanced by biological processes such as algal blooms and temperature
effects which can peak at different times throughout the year, and
behavior of precipitation events varies depending on characteristics of
the lake (i.e. open or closed; location; stratification/ventilation;
etc.)(Hren & Sheldon, 2012). Additionally, we note that the samples
from UCLA were sieved through 212 μm mesh, which may include juvenile or
fragments of mature ostracodes, and it is unclear if any screening for
additional fossil material occurred for samples first published in
Huntington et al. (2010) was performed. However, the majority of the
samples recalculated in this synthesis from H. Li et al. (2021) were
filtered through a 45 μm mesh and screened for ostracode valves.
Ostracode valves in the sediment may bias temperature estimates derived
by clumped isotope analysis, given that different factors control
organism growth, thus, the inclusion of potential fragments of
fossilized material may be a source of the increased scatter we see in
the Δ47-temperature dependence for micrites.
3.2.1.3 Biologically Mediated Carbonate
The calibration for biologically mediated carbonates is constructed with
255 analyses of 24 samples, including 7 new samples, 13 reprocessed
samples from Santi et al. (2020), Petryshyn et al. (2015), Huntington et
al. (2015), Huntington et al. (2010), and Bernasconi et al. (2018) that
were converted into I-CDES, and 4 samples taken from Anderson et al.
(2021). Water temperatures for biologically mediated samples span 18.9°C
(10.1 - 29.0°C) and Δ47 values range between
0.585-0.666‰. We find significant variability in our dataset (Figure 4c;
r2 = 0.5669) and a significant relationship between
Δ47 and temperature (p = <0.0001).
Although we do not see statistically significant differences in slopes
between biologically-mediated carbonates and other freshwater carbonate
types, an ANCOVA detects differences in intercept between biologically
mediated carbonates and biogenic carbonates (pintercept= 0.0047) and micrite (pintercept = 0.0379). We also
find significant differences in intercept between the biologically
mediated regression and the I-CDES calibration of Anderson et al. (2021)
(pintercept = <0.0001).
Overall, the biologically-mediated regression results in warmer
temperature predictions, in particular at higher temperatures, relative
to biogenic carbonates and travertines analyzed in this study as well as
the Anderson calibration (Table 2; Supplemental Table 3), suggesting
that biologic processes may influence observed
Δ47-temperature relationships (also could be a source of
scatter; r2 =0.5669). Similar discrepancies between
tufa and synthetic samples were observed in Kato et al. (2019), who
reported values from tufa samples predicted by synthetic calibrations
that were higher than modern environmental temperatures. However, the
modern tufa data from Kato et al. (2019) is not included in this
synthesis due to discrepancies between standard values for Carrara
Marble and NBS-19 relative to what was reported by Bernasconi et al.
(2021) and Uphadhyay et al. (2021), although we note their calibration
falls within our 95% confidence interval of our biologically-mediated
calibration.
3.2.1.4 Travertines
Although we did not add new data, we created a regression for travertine
samples containing 543 analyses from 23 samples. The travertine dataset
includes data from 15 recalculated samples from previous publications to
be on the I-CDES reference frame (Bernasconi et al., 2018; Kele et al.,
2015) following methodology in Bernsconi et al. (2021) and 8 new
published measurements (Anderson et al., 2021), to analyze them within
the same statistical framework used here. Travertine samples encompass
the largest range of independently measured water temperatures (5 -
95°C) and Δ47 values (0.409-0.637‰). Similarly to the
other groups of carbonate considered in this study, we find a
significant temperature dependence (slope; p = <0.0001) and a
high degree of agreement between the fitted values and calibration data
points (r2 = 0.9487). Travertines display the highest
r2 values relative to biogenic carbonates,
biologically mediated carbonates, and micrites, which may arise if they
have the least complex precipitation mechanism with little biological
influence relative to the other groups.
ANCOVA tests indicate the travertine linear regression did not have a
statistically significant slope compared to other groups of freshwater
carbonates in this study, but does indicate a statistically different
intercept to the micrite regression (pintercept =
0.0050; Table 3). The newly-derived regression on the updated I-CDES
reference frame is statistically indistinguishable from the previous
travertine calibration presented in Bernasconi et al. (2018), but has
significant differences in intercept from the calibration presented in
Petersen et al. (2019) (pintercept = 0.0354), suggesting
that applying a ‘universal’ calibration may not be appropriate.
Additionally, we find no significant differences in either slope or
intercept between travertines and the Anderson et al. (2021) calibration
or authigenic lacustrine carbonate calibration of H. Li et al. (2021)
(Table 3).
3.2.1.5 Comparison of material-specific and composite calibrations
Overall, we observe no statistically significant difference between the
calibration slopes derived from different materials and previously
published calibrations (Table 3) when freshwater carbonates are divided
into groups to account for differences in their precipitation (e.g.
seasonality, ecology, etc.), calibrations converge on a common
temperature dependence (slope) for clumped isotope measurements. A
similar convergence of slopes was found in Petersen et al. (2019) when
comparing 14 different clumped isotope studies of both biogenic and
abiogenic carbonates using updated parameter values for
Δ47 calculation. Anderson et al. (2021) also found a
convergence of slopes between their new data, the Petersen calibration,
and recalculated calibration lines using updated carbonate
standardization procedures for 4 recent calibration studies. However,
our ANCOVA analyses also indicate statistically different intercepts for
most of our calibrations from groups of freshwater carbonates (Table 3).
Our findings are unchanged if we only consider samples that were
analyzed at UCLA.
In order to evaluate goodness of fit between the two types of models
presented in this study, we use root mean square error (RMSE) to
evaluate the differences between our directly measured and
Δ47-derived measurements. Applying our composite
calibration to biogenic samples results in a RMSE of 4.4°C, while
applying the biogenic calibration results in a RMSE of 2.9°C, showing a
better fit when using the material-specific calibration. Temperatures
derived from a micrite-specific calibration results in a lower RMSE than
a composite calibration (3.9°C and 4.6°C, respectively). Contrastingly,
the composite calibration outperforms the material specific calibrations
for biologically mediated carbonates and travertines, resulting in a
lower RMSE than their material specific counterparts (tufa: 4.4°C and
5.1°C, travertine: 6.5°C and 7.1°C). Figure 5 shows the impact of the
applied calibration on temperature reconstructions using both the
composite and material specific calibrations derived in this study,
showing a decrease in residuals when utilizing material-specific
regressions for all material types. Thus, it may be more appropriate to
use material-specific calibrations when reconstructing
paleotemperatures. However, we also note that the application of
material-specific calibrations will necessitate using fewer data points
(minimum n = 22) over a more limited temperature range in most cases
(except for travertines), both factors of which could increase
uncertainty in the calibration. We recommend using material specific
calibrations for samples that fall within the original observation
range, given that application of material specific calibrations to
samples from more extreme temperatures could necessitate calibration
extrapolation.