A database of biological and geomorphological sea-level markers from the Last Glacial Maximum to present

The last deglacial was an interval of rapid climate and sea-level change, including the collapse of large continental ice sheets. This database collates carefully assessed sea-level data from peer-reviewed sources for the interval 0 to 25 thousand years ago (ka), from the Last Glacial Maximum to the present interglacial. In addition to facilitating site-specific reconstructions of past sea levels, the database provides a suite of data beyond the range of modern/instrumental variability that may help hone future sea-level projections. The database is global in scope, internally consistent, and contains U-series and radiocarbon dated indicators from both biological and geomorpohological archives. We focus on far-field data (i.e., away from the sites of the former continental ice sheets), but some key intermediate (i.e., from the Caribbean) data are also included. All primary fields (i.e., sample location, elevation, age and context) possess quantified uncertainties, which—in conjunction with available metadata—allows the reconstructed sea levels to be interpreted within both their uncertainties and geological context.


Methods
All data have been obtained from peer-reviewed papers and books. Authors were contacted where information was missing or clarification was needed. Samples that still fail to reach a complete set of database fields have been excluded from our relative sea-level reconstructions. However, such samples are retained in the database because they may be important for other analyses. Figure 2 summarises the treatment of datasets within the database, and a brief outline of data acquisition and processing is given below.

Location
Each data point in the database has been assigned a unique identifier, along with the original sample or analysis identifier. Sample locations are as originally reported. Where this information was lacking or insufficiently detailed, the latitude and longitude were estimated.

Tectonic setting
The tectonic setting of a sample affects the reconstructed sea level through the interaction of uplift or subsidence with the measured elevation. Ideally, uplift/subsidence rates should be independently constrained. However, only Tahiti 16,17 and Mururoa Atoll 18 have such independent constraints. For most sites, the rates are often determined using the maximum elevation of the fossil coral terrace corresponding to the Last Interglacial, and an assumed age and relative sea-level position for the Last Interglacial. Occasionally, independent data (e.g., radiometrically dated lava flows) constrain the uplift/ subsidence rate and we use these constraints where available (Mururoa Atoll 19 ; Tahiti 17,20,21 ). Where no independent constraints are available, we have recalculated the uplift rates from the elevation of the maximum Last Interglacial terrace and an assumed Last Interglacial age and sea level (Table 2 (available online only), as per Hibbert et al. 12 ). Figure 2. Simplified schema of the deglacial sea level database giving an overview of data acquisition and processing. The numbered boxes are the four essential components needed to reconstruct former sea levels: (1) location; (2) elevation; (3) age and; (4) sample information and other contextual information (including how the sample dated relates to sea level at the time of formation). Within each of these boxes we list the primary information recorded. Grey boxes indicate additional processing of data from original publications and new outputs (also included in the database, Data Citation 1).

Sample elevation and uncertainty
The elevation uncertainty of a sample falls into two broad categories: (i) the measurement uncertainty related to the method used for establishing the elevation of the outcrop or core and (ii) sampling uncertainties associated with both the method of sample acquisition (e.g., core stretching or shortening errors), which is dependent upon the method, and uncertainties that arise from sampling a core or section. Where information is missing in the original publication, we allocate a method-appropriate uncertainty. For example, where there is no mention of how the elevation was obtained or where only the method is given (e.g., levelling), we allocate a ± 0.5 m and ± 0.03 m (cf. ref. 22) uncertainty (2σ),

Elevation determination:
Auto-level not reported not reported 0.03 cf. levelling uncertainty (Törnqvist et al. 22 ; Hijma et al. 296   respectively. Table 3 details the allocated uncertainties used in the database. The elevation uncertainty therefore is the root mean square of: (i) uncertainty associated with the method of establishing the elevation (e.g., levelling); (ii) uncertainties accounting for any distortion in obtaining the record (i.e., those resulting from coring methods) and; (iii) sampling uncertainties. In order to compare elevations, a common datum is required. Within the database, we note the datum to which all measurements relate and, where possible, we reference all elevations to mean sea level (MSL) using appropriate tidal parameters (e.g., when converting elevations referenced to mean low water springs (MLWS) to MSL). We do not include any tidal errors; the modern tidal range often is not reported and variations in the past are poorly constrained.

Sample age and uncertainty
The database incorporates samples dated using U-series and radiocarbon methods. Detailed descriptions of the systematics of both these techniques are available elsewhere (e.g., for U-series dating [23][24][25] ; for radiocarbon dating [26][27][28]. A brief summary of data type and processing is given in the following. U-series analyses. We record the instrument, method of spike calibration, decay constants, activity ratios, and detrital thorium correction used in the original age determination (also included). For samples where the spike was calibrated gravimetrically, we recalculate the activity ratios using the most recent decay constants 29 . For all samples, we then iteratively recalculate ages (equation 1) and δ 234 U intial (equation 2) assuming a closed system and using the most recent decay constants 29 (calculations were made using Isoplot v. 3.5 ref. 30). The reported uncertainties include the error associated with the decay constants. We make no attempt to account for any open-system behaviour (i.e., the remobilisation of nuclides) within the U-series dated datasets because the identification and correction of open system behaviour continues to be complex and debated (e.g., ref. 24). In addition, we do not screen the recalculated ages for reliability; there are multiple approaches to assess age reliability and the inclusion of all metadata and the original reported ratios etc., allows users to determine appropriate age-reliability screening criteria (e.g., the bounds of acceptable δ 234 U initial values, % calcite etc.).

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Ages are reported as ka BP in order to ensure that they are comparable to the radiocarbon ages, which are by convention reported as years before 1950 AD. We adjust the age for the time elapsed since analysis. Where no date of analysis is given, we have assumed this was the year of publication. We recognise that this may introduce additional age uncertainty but anticipate that this only a few years and typically less than a decade.
Radiocarbon analyses. We record the laboratory, instrument, publication code, any corrections applied by the laboratory (i.e., background and δ 13 C corrections) and both the conventional and calibrated ages and associated uncertainties for each sample (including any regional marine reservoir age correction, ΔR, applied by the authors). We also report the δ 13 C values for samples, and the calibration dataset and programme where provided. Where no background and/or δ 13 C correction was applied by the laboratory, we apply a sample-specific normalisation (terrestrially derived organic material δ 13 C = − 25 ± 2 ‰; marine carbonates δ 13 C = 0 ± 2 ‰). The conventional age can then be calculated using the appropriate (instrument dependent) 14 C/ 12 C or 14 C/ 13 C equations 32 . Age uncertainty is reported at the 1σ level in accordance with standard radiocarbon reporting protocols [33][34][35] .
We assume that sample materials obtained their carbon from only one reservoir (i.e., atmospheric or marine). Additionally, we assume that estuarine bivalve and mollusc samples are fully marine because additional information, such as δ 18 O and δ 13 C analyses, that would help establish the environment in which the sample was living is often not available. We recognise that there may be considerable variation in the regional marine reservoir correction (ΔR) for estuarine bivalve and mollusc samples due to the varying mixing of marine and freshwater [36][37][38][39] which potentially results in an older apparent age for specimens living in estuarine environments.
A radiocarbon measurement requires an additional step of calibration to obtain an age estimate due to the non-linear nature of the 14 C timescale 40 . Both the calibration procedure itself (given the complexity of the calibration dataset) and the choice of software and parameters (such as the use of Bayesian statistics to construct age-depth models) 41,42 influence the final calibrated age of a sample.
The calibration curve may affect the statistical inference of time because the relationship between the radiocarbon age and the calendar age changes through time, due to variations in the radiocarbon concentration (e.g., refs 43,44). In addition, the shape of the calibration curve (non-monotonic with www.nature.com/sdata/ SCIENTIFIC DATA | 5:180088 | DOI: 10.1038/sdata.2018.88 inversions) means that calibration is non-commutative and directional 45 , with distortions due to the structure of the curve itself 43 , the potential for the production of artificial peaks 46 , and the amplification of the output probability density function by steep sections of the calibration curve 45,47 . This can result in the summed probability density function of a calibrated date exceeding the 'true' time interval of the event 48 .
Different calibration algorithms may affect the final calibrated age probability distribution, particularly when comparing results from software packages that do, or do not apply Bayesian statistics, i.e., where the age-depth model uses different depositional models to mimic sediment deposition processes. For example, OxCal 49 , BChron 50 , and Bacon 51 utilise Bayesian statistics to incorporate stratigraphic and other chronological information to formulate prior distributions for the calibrated dates, and to provide 'bestestimate' age-depth models with uncertainties. In the database, we have chosen not to implement such age-depth modelling routines for datasets with stratigraphic ordering when recalibrating the radiocarbon dates, for several reasons: (1) to ensure consistency within the database; (2) because not all samples in the database have simple stratigraphic relationships, for example, coral reefs are complex 3-dimensional structures that do not necessarily accumulate monotonically like sediment cores, and; (3) to refrain from imposing any structure on future analysis. Overviews and comparisons of the main age-depth modelling routines are available 41,42 , should users wish to apply these on appropriate, individual subsets of the database. Samples with stratigraphic ordering are clearly identified in the database with a numeric identifier for each group, and ordering given by subdivision of that number, smallest/topmost to largest/ lower-most sample.
The conventional radiocarbon age and uncertainty for each sample were recalibrated using OxCal For marine samples, we apply a local marine reservoir correction (ΔR 55 ) to account for regional variations in the offset between the marine and terrestrial carbon reservoirs (the marine reservoir effect). The marine reservoir effect (i.e., the offset in the radiocarbon age of marine materials compared to materials deriving their 14 C from the atmospheric at the same time) is spatially and temporally variable. The spatial variation from a calculated global average is accounted for by using a regional offset (ΔR). A consistent value of ΔR was applied for each coherent geographical region (i.e., for all sites influenced by the same surface oceanographic circulation) and estimated from the online database 56 , double checked with previous ΔR determinations (Table 4 (available online only)). The online database 56 of values (and calculations of ΔR 57 ) is used to ensure both the correct and consistent calculation of ΔR. Note that the method used to calculate ΔR in the online database incorporates the full probability distribution unlike 'classical' intercept methods, so that the resulting ΔR uncertainties are more accurate (full discussion of the methodology 57 ). Where more than one ΔR value is used, we calculated an error weighted mean and uncertainty. We apply the pre-industrial calculated ΔR, but recognise that ΔR is also temporally variable [58][59][60] . Applying a pre-industrial ΔR does not account for any variations through time as a result of changing climatic and surface-ocean conditions, or variations in the production of 14 C in the atmosphere with variations in the Earth's magnetic field e.g., ref. 61. In general, there are few locations in the database and a limited number of studies where the temporal variability in ΔR has been investigated. As this variability is largely unconstrained at present, we do not attempt to account for this uncertainty in the database but the effect would be most pronounced for sites with data spanning the transition from the glacial to interglacial, when reorganisations of ocean circulation and of carbon stores within the ocean may have led to potentially large variations in ΔR. It should be noted that any such age uncertainty may additionally affect the resulting P RSL reconstruction of some sites through interaction with uplift or subsidence rates.
The output of a calibrated radiocarbon date is a probability density function. The calculated posterior probability distributions are often multimodal and difficult to summarise, except via graphical representations 41 . Reporting of the 68 and 95% confidence interval has become common, although not universal, in part due to the ease of plotting a point estimate. Point estimates (such as the mean, mode, median etc.) do not fully account for the variation in the output of calibration (i.e., the resulting multimodal distributions), and none of these point-based estimates can be considered a good estimate of the full complexity of the calibrated date 44,62 . It is difficult within a database to accurately record the outcome of calibration. However, because all information required for calibration of a date is included in the database (inter alia: conventional radiocarbon date and uncertainty; material dated; ΔR for marine samples; calibration curve, programme and version), users can recalibrate the data and obtain the same probability density function as captured by the 68 and 95% confidence intervals listed in the database. The complete documentation also allows recalibration of the dates following future refinements of the calibration datasets, etc.
In our recalculation (where appropriate) and recalibration of radiocarbon samples, we take care to ensure that we round the calibrated age (to nearest whole number) only at the end of the process. However, we are unable to guarantee that is the case of the reported values used in each of the processing steps.

Sample information and context
Detailed information on both the sample and its geological context is vital. We record available information from the publications including: what material was dated (and species, if given); the facies context and/or other outcrop and unit information; whether the authors determined the sample to be in growth position and/or in situ; and the growth form (e.g., branching or massive corals, if given).
In addition, to reconstruct past sea levels, we must establish the relationship between the sample and sea level at the time of its formation (i.e., the 'indicative meaning' which describes the range of elevations, with respect to a specified tidal datum, that a particular indicator forms 13,14,63 ). This is often achieved using a modern analogue, i.e., looking at the modern elevation range of a sea-level indicator in relation to present sea level (or some tidal datum). This approach is subject to key assumptions: (i) that the modern depth distribution is the most appropriate analogue; (ii) that the relationship is stable through time and; (iii) that the fossil record is a faithful approximation of the living diversity and distribution (i.e., minimal loss of detail due to taphonomic processes).
We use two different approaches for representing these relationships. The first uses a specific probability distribution for each taxon (e.g., the modern depth distribution of a coral species; following the methodology of Hibbert et al. 12 ), and the second assumes a uniform probability distribution because the sea-level indicator forms somewhere within an altitudinal range but we have no further information as to the most likely depth or elevation (e.g., an oyster living somewhere within the intertidal to lowsupratidal range at a given site).
Using a specific probability distribution of a species. For coral sea-level indicators, we are able to define a probability distribution for the depth-habitat (using the methodology detailed in Hibbert et al. 12 and summarised here). In this iteration of our analysis, we update the datasets used to define each taxonspecific depth distribution using the latest release from the Ocean Biogeographical Information System (www.iobis.org). The data in the OBIS dataset have been rigorously quality controlled. We use only observational and live-collected data with a vertical precision of ≤0.25 m. In some instances, there are insufficient observations ( o150) to constrain the depth distributions and so the depth precision criterion was relaxed: Alveopora sp. has a depth precision of ≤0.5 m (n = 171); Favia fragum and Porites solida have a depth precision of ≤ 2 m (n = 183 and 149 respectively) and; Acropora abrontanoides has a depth precision of ≤ 5 m (n = 132). For some fossil species used to reconstruct past sea levels (Goniopora lobata and Gardinerosis planulata), little or no modern observational data were available and, in these instances, we use the modern genus depth distributions. We urge caution where fewer than 150 observations constrain the depth distributions.
For each taxon, we derive an estimate of the median water depth in which the modern species lives (Fig. 3). We have chosen the median rather than the mean because the depth distributions are not Gaussian or symmetrical and because the mean is more sensitive to outliers. The lower and upper bounds of the 95 and 68% confidence intervals were also determined using the 2.5, 97.5, 16 and 84 percentiles, respectively (Table 5 (available online only); all depth observations used can be found in Data Citation 2 so that users may 'draw' directly from the distribution, if desired). We compile depth distributions at a 'global' scale (i.e., using all information available for the species) as well as geographical subsets: ocean basin, sub-basin and, where sufficient information is available, regional subsets (for example, Atlantic, Caribbean, Belize or Pacific, SW Pacific, Great Barrier Reef). These regional distributions are included as a first-order approximation of the modern variability (both geographically and with depth) of coral taxon distribution 64,65 . Our ecological depth distributions are especially useful for sites lacking site-specific assemblage work that would constrain the modern relationship between coral depth and sea level.
In general, there are very few observations in the Indian Ocean and so it was not possible to further constrain the depth distributions for this region.
In the Pacific, there are significant numbers of observations but once sub-divided into sub-basin and regional locations, only the Great Barrier Reef (GBR) has sufficient, systematic observations (i.e., regular recording of data to depths of~10 m and greater) to allow determination of robust regional depth distributions. For the most of the Pacific region, despite large numbers of observations, there appears to be a shallow-water bias, with observations concentrated within the upper couple of meters (for example using Porites sp., Fig. 4). Additionally, there are too few observations to allow determination of regional depth distributions with any confidence, particularly for the east and southeast of the basin. The depth distributions determined for the GBR region are based on numerous observations and span a greater depth range than other Pacific observations. However, collating observations from such a large geographical area likely masks the modern complexity of coral distribution within the reef system e.g., refs 66-68. Nonetheless it represents a first step in refining sea-level reconstructions, by incorporating a first-order approximation of the geographic variation in coral diversity and distribution. It should be noted that at present there are relatively few fossil corals in the database from the Great Barrier Reef (GBR) itself (n = 27 but, of these, 15 have been determined only to the genus level). The similarity between reef ecology, distributions and growth forms between Vanuatu and the GBR 69 also allows us to use the GBR depth distributions to refine sea-level reconstructions for Vanuatu. This is especially useful given that most (~70%) fossil corals from Vanuatu do not have original water depth determinations from modern biozonation of corals, coralline algae etc. In the Atlantic, there is a substantial number of observations, including for the Caribbean sub-basin and for many regional sites. This allows definition of several taxon-specific, regional depth distributions. Most of these regional depth distributions are constrained by at least 100 observations, with most regions having > 300 observations (see summary statistics in Table 6 (available online only)). For many regions within the Caribbean sub-basin, there are distinct differences in species depth preference (e.g., Acropora palmata, Fig. 5), with notable offsets to deeper or shallower habitats evident relative to the 'global' depth distributions. This likely represents spatial variations in the depth habitat of the species (given the sitespecific factors governing coral distributions and diversity; see review of Hibbert et al. 12 ) but may also be an artefact of sampling bias (i.e., shallow-water bias in sampling). For some Caribbean fossil samples (e.g., those from St Croix in the US Virgin Islands, Belize, and Panama), modern constraints on the relationship between (tectonically corrected) coral elevation and sea level at the time of formation (i.e., a palaeo-water depth relationship) are lacking. As such, the regional depth distributions generated here allow us to both reconstruct sea level, and to incorporate the modern complexity in the geographic variation in taxon depth preference. Without this information on the relationship between the sample and sea level at the time of its formation, only a (tectonically) corrected elevation could be calculated, not sea level.
It should be noted that both the 'global' and regional depth distributions are a 'maximum' representation of the vertical uncertainties associated taxon-specific depth distributions. Additional biological (e.g., associated species with a narrower depth range) or geomorphological (e.g., designation as reef crest facies) information might be used to reduce the total vertical range associated with the reconstructed sea levels, if such additional data were provided. Unfortunately, most samples currently lack such information.
The use of modern analogues (including our OBIS-derived depth distributions) to define the palaeowater depth relationship has three primary caveats. First, for some sites the present may not be the most appropriate analogue due to human influences 70,71 . For example, the modern coral fauna of Barbados is not representative of the Pleistocene reefs due to reef destruction and loss of coral species, particularly the mass mortality of once dense populations of Acropora palmata 72,73 . Fortunately, given the number of fossil corals from Barbados in the database, the similarity between the recurrent patterns in species dominance and diversity observed between the raised reef terraces of Barbados and the living reefs of Jamaica 74,75 , first recognised by Mesolella 76 , justifies the use of modern regional depth distributions of Jamaica as an analogue for Barbados. Second, the fossil record may not faithfully capture the living reef assemblage and structure due to the potential for non-preservation and selective removal/alteration of material by physical, chemical and/or biological processes (i.e., taphonomic processes [77][78][79][80][81] ). Third, a key assumption is the constancy and stability of the palaeo-water-depth relationship through time and, although difficult to determine, there is some evidence from the Caribbean that the large stands of branching A. palmata that dominated for the last 0.5 Ma are the same as those documented in the Caribbean until the early 1980's, when human-induced habitat changes forced major changes in community structure 72,73 .
Using a facies formation range or biological indicative range. For the non-coral subset of samples, we use the depth range or facies formation depth range as determined by the original authors. Where this information is missing, we are unable to reconstruct past relative sea level. We assume a uniform distribution for the relationship, in that the indicator may occur equally anywhere within the given altitudinal range. Note, the original coral palaeo-water depth determinations would also have a uniform distribution, and could be treated in the same manner, if desired.
Limiting data. For some samples, we are only able to say confidently that sea level was above or below the (tectonically corrected) elevation of the sample at the time of its formation. For example, a fossilised tree provides an upper limit on sea level at the time of growth, in that sea level must have been lower than the elevation of the sample. This subset of data is included, although we are unable to confidently reconstruct relative past sea levels, as such data can be very useful for constraining models of glacioisostatic processes.

(Tectonically) Corrected position (Z cp )
Where appropriate, the modern elevation of the sample is corrected for uplift or subsidence since the time of formation, ensuring consistency between sites. For each sample, we are able to calculate the (tectonically) corrected position 12 (Z cp ) (equation 3) where, Z cp is the tectonically corrected elevation in m, and negative values are below sea level, E sam is the elevation of the sea-level indicator referenced to mean sea level (MSL), ΔH/Δt is the recalculated uplift or subsidence rate in m/ka, with increasing positive ages in kilo-years before present and; t sam is the recalculated (and recalibrated in the case of radiocarbon analyses) age of the sample in ka, with increasing positive ages in kilo-years before present (ka BP).  Figure 5. An example of regional depth distributions for Acropora palmata from the Caribbean sub-basin.
(a) map of the fossil Acropora sp. samples (red open circles) and A. palmata observations used to constrain the depth distributions (grey, filled circles); (b) Caribbean depth distributions for Acropora palmata (green) and regional subsets (orange) represented as relative probability (normalised histograms, left panels) and cumulative frequency distributions (right panels).

Reconstructed Probability of Sea Level (P RSL )
We combine elevation uncertainties (including any uplift/subsidence correction) with the information relating the indicator to sea level at the time of formation (i.e., the modern altitudinal distribution for that indicator in relation to mean sea level) using the methodology of Hibbert et al. 12 . A schematic of this procedure is given in Fig. 6. We use a Monte-Carlo approach of 350,000 simulations to derive a probability maximum (P RSL ) associated with each sea-level indicator position (Z cp ) and a confidence interval around that point. For each sea-level indicator, we obtain a set of randomly sampled values from the corrected position (Z cp ) uncertainty, and a set of randomly sampled values from the depth distribution (arising from either the empirically derived depth distributions for coral samples or a uniform distribution within a given formation range) and sum across the two errors. For each individual sea-level indicator, we then have multiple instances across a combined error distribution. From this set we can generate the probability distribution, and extract a probability maximum and the associated 1, 2-and 3-sigma equivalent levels (68%, 95%, and 99% probability intervals) (the code used is provided, Data Citation 3). Note, these are typically asymmetrical for fossil coral samples when our modern, taxon-specific depth distributions are used to calculate P RSL . Users of the database (Data Citation 1) are free to choose the relationship they deem most appropriate as we include the palaeo-water depth determined by the original authors, our OBIS-derived depth distributions (Data Citation 2), and the code (Data Citation 3) used to calculate P RSL . The result is a probability distribution of relative sea level (P RSL ) that incorporates both a eustatic, an isostatic and other (e.g., hydro-isostacy, compaction etc.) components. Note, we do not account for any glacio-isostatic processes as this is outside the scope of the present study. Additionally, we do not include any tidal corrections to our reconstructed sea levels to account for past variability in the magnitude and spatial variation of past tidal regimes. In many publications, the modern tidal range is not reported and variations in the past are poorly constrained at present.

Data Records
The database (Data Citation 1) is designed to include all available data, for example we include all information relating to dating to enable users to recalculate the age, and associated metadata. 'Data descriptors' details all fields used in the database and can be found in Table 7 (available online only). The modern taxon-specific depth distributions (Data Citation 2) and the code (Data Citation 3) used to reconstruct past sea levels from fossil samples are also available from Figshare. A summary of the treatment of each the dataset in the database (Data Citation 1) can be found in 'Supplementary Data'.

Technical Validation
In addition to ensuring consistency of data processing and any recalculations (age recalculation, recalibration etc.), we have attempted to validate various data-processing steps, where appropriate, and details for this are given below.

Age
Reported ages from the original publications are included in the database in addition to our recalculated ages (and recalibrated ages in the case of radiocarbon). This provides a first check of our age recalculations/recalibration. Note, that any uncertainty in the age determinations may propagate into our reconstructions of past relative sea-level through the interaction with uplift/subsidence. U-series. All geochemical data are included in the database to enable users to recalculate the ages, if so desired. It should be noted that we do not screen the U-series ages for reliability. Users may select their own screening criteria (limits on acceptable δ 234 U initial values, calcite content etc.) from the fields  Radiocarbon. Regional deviations from the global offset between the atmosphere and the surface mixed layer (i.e., the marine reservoir effect) are dealt with using an offset (ΔR) during calibration, with ΔR often assumed to be constant through time. The resulting final calibrated probability distribution of the sample therefore includes the uncertainty in the construction of the marine calibration curve (currently Marine13 53 ), but not the uncertainty in the variation in ΔR through time 57 . The effect on resulting calibrated age of: (i) spatially and temporally variation of the regional marine reservoir correction (ΔR) and; (ii) the effect of assuming a uniform, rather the Gaussian distribution for ΔR is explored further here. The examples provided are for illustrative purposes only. In order to investigate the possible magnitude of this effect-i.e., potentially disparate modern and glacial values of ΔR for the same region-we explore the effect of using different values for ΔR, different error distributions for ΔR (Gaussian and uniform distributions) for a marine dataset that possesses both radiocarbon and U-series age determinations (corals from Barbados 82,83 ). The calibrated ages (calibrated using the OxCal calibration software, version 4.3 (ref. 52).) are compared to the U-series dates for the same samples (recalculated assuming a closed system and the decay constants of 29 ) (Fig. 7). Note, this exercise is an example only; for sea-level reconstructions, we would use U-series ages in preference to radiocarbon ages for these samples, in order to negate both calibration issues and the unconstrained variable ΔR. Additionally, for this example, we assume that the U-series ages for the samples are reliable, i.e., that there has been no addition or loss of isotopes from the system (i.e., no open system behaviour) and negligible diagenetic alteration.
We recalibrate the radiocarbon ages using the following ΔR values: (i) those used by the original authors (R = 400 years, therefore ΔR = −5 years 82 ; R = 365 ± 60 years, therefore ΔR = − 40 years 83 ); (ii) the values used by the original authors ± 100 year uncertainty (assuming a Gaussian distribution); (iii) the preindustrial ΔR estimated for the Caribbean 56 (ΔR = − 27 ± 11 years, n = 8; note, there are currently no observations from Barbados in the online ΔR database 56 ); (iv) using model output values 84 (using an iterative approach of transient, 3-dimensional simulations) that suggest variations in ΔR of 200 and 900 years for the Caribbean during the last deglacial. We use the upper and lower limits of their simulations with an arbitrary uncertainty of 100 years (i.e., ΔR = 200 ± 100 years and ΔR = 900 ± 100 years) using both a Gaussian and uniform distribution during calibration. Finally, we recalibrate the ages using temporally varying estimates of ΔR a b c d Figure 9. An example from the Caribbean (using the species Acropora palmata) of the effect of using different palaeo-water depth relationships on the resulting sea-level reconstructions. (a) the elevation uncertainties for the fossil A. palmata data; (b) the reconstructed sea level assuming a uniform distribution and a palaeo-water depth of 0 to 5 m; (c) the reconstructed sea level using our OBIS derived, 'global' species specific depth distribution and; (d) the reconstructed sea level using our regional depth distributions. P RSL is reconstructed using a Monte-Carlo simulation of samples; coloured shading indicated the 99th (pale blue), 95th (yellow), 85th (orange), 70th (red) and 50th (black) percent probability intervals. This example is for illustrative purposes only and is not intended as a reinterpretation of the Caribbean A. palmata dataset. (derived from Butzin et al. 84 ). Few of the of the recalibrated ages match the U-series ages for the samples, although the calibrated ages using the authors original estimates, preindustrial ΔR and those with no ΔR applied, offer a reasonable first approximation (Fig. 7). Using the modelled deglacial values for the Caribbean does not improve the match, although a variable ΔR does approximate the U-series ages slightly better than either of the model extremes (using both the Gaussian and uniform distributions). In this example, we are fortunate that the samples also possess U-series ages but it does illustrate the magnitude of the effect that choices regarding the ΔR value may have on the resulting age. This effect would be most acute during time intervals such as the last deglaciation, as major reorganisations in ocean circulation (as well as variations in 14 C production and sequestration by the various reservoirs) are documented [85][86][87] . The sites in the database (i.e., primarily mid to low latitudes) should mitigate the magnitude of these effects because the scale of the oceanic changes (and hence ΔR) at those latitudes is smaller than at the higher latitudes 88 . The 'distortion' in age due to variations in ΔR is likely greater than the effects of uncertainties in both the tectonically corrected elevation (Z cp ) and reconstructions of sea level probability (P RSL ) for this interval of time, given the relatively low rates of both subsidence and uplift for most sites in the database, and the relatively young ages of the samples. The example illustrates the current difficulty in constraining ΔR through time. Therefore, we apply only the preindustrial estimates 56 for the marine fossils when recalibrating ages in the database. Refinements in both the age determinations and reconstructed sea-level probability (P RSL ) for radiocarbon-dated marine sealevel indicators could be achieved as more robust constraints on both the spatial and temporal variation in ΔR through time become available.

Coral depth distributions
We compare our ecologically derived depth distributions of modern corals to: (i) other estimates/ observations of the maximum depth of coral species at both global 89,90 and local geographic scales 75,91-97 (Fig. 3) and; (ii) palaeo-water depth determinations of the original publications (Fig. 8). The median and 95% confidence limits derived compare favourably with both the global and regional (where available) modern observations of the maximum depth observed for most species (Fig. 3). This lends confidence that the use of our ecological depth distributions is reasonable and, that use of a modern-analogue approach provides a first-order approximation of the relationship between the elevation of the fossil coral and sea level at the time of formation. The global, ecologically derived depth distributions also compare favourably with palaeo-water depth estimations, originally derived using a variety of methodologies (e.g., modern assemblage, coral diversity/ distribution) and geographical scales (site-specific to ocean basin scale comparisons). Figure 8 illustrates for each of three commonly dated coral taxa our ecological depth distributions and the palaeo-water depths. The modern 'global' estimates broadly replicate the palaeo-water depths. However, our depth distributions are unlikely to capture the full complexity in species distribution and diversity observed in modern coral reefs, nor are they able to capture all details of the site-specific relationship between corals and sea level. Therefore, these ecological depth distributions should be considered as 'maximum', firstorder approximations of the relationship between the elevation of the coral and sea level at the time of formation. The effect of using different depth distributions on reconstructed sea-level probability (P RSL ) is illustrated for fossil Acropora palmata using data from the Caribbean (i.e., using the sub-basin and regional depth distributions) (Fig. 9). Once the elevation uncertainties are combined with either the palaeo-water depth estimates (assuming a 0 to 5 m depth preference and a uniform distribution, Fig. 9b) or the taxon-specific depth distributions (Fig. 9c), the regional depth distributions (Fig. 9d) result in 'tighter' P RSL estimates for Barbados than either the palaeo-water depth or the Caribbean sub-basin depth distribution. Therefore, using a well-constrained, regional ecological depth distribution offers some promise of refining the vertical precision of reconstructed sea levels, and allows past sea levels to be reconstructed for samples where no information is available to define the relationship between the elevation of the fossil coral and sea level at the time of formation. Modern site-specific assemblage studies (i.e., documenting modern reef biota, facies and environmental characteristics) provide perhaps the best description of this relationship but our ecologically derived depth distributions (i.e., where only taxa and depth occurrence is given) offer a reasonable first-order approximation. Users of the database are able to use either the authors' original palaeo-water depth determinations or our taxon depth distributions (at the 'global' or regional scale, Data Citation 2).

Tectonic corrections
The only independent (i.e., not constrained using the fossil sea-level indicators themselves) tectonic corrections are those for Tahiti and Mururoa Atoll (both French Polynesia [16][17][18] ). Hence, we are unable, so far, to validate the uplift/subsidence terms used in the database. This remains one of the main outstanding issues that hindering reconstructions of past sea level.

Code availability
We make the code used to calculate P RSL available as a separate text file (Data Citation 3). This contains significant modifications from that given as a supplement 12,98 to incorporate a uniform facies formation depth distribution and non-Gaussian age uncertainties.

Usage Notes
This release comprises 4 files (details of the file formats are within the square brackets): We welcome contributions from authors of additional or clarifying information. These will be incorporated into any subsequent iteration of the database. When using data in this compilation, the original data collector(s) as well as the data compiler(s) should be credited 99 .
Users are welcome to use either the original authors' (included in the database, Data Citation 1) or our ecologically derived depth distributions (Data Citation 2) to relate the elevation of the coral and sea level at the time of formation. Both are included in the database release, in addition to the code for reconstructing P RSL (Data Citation 3).
No attempt has been made to correct for U-series open system behaviour, nor do we screen for age reliability. The inclusion of all metadata enables users to determine their own appropriate age reliability screening criteria. For simplicity, we record only the 68%, 95% confidence intervals, mean and sigma of the calibrated radiocarbon output. Again, the inclusion of all data and metadata relating to each radiocarbon determination enables users to both replicate our outputs and adapt the input into calibration software, if so desired. We do not attempt to account for temporal variations in ΔR.
The reconstructed P RSL is a function of both eustatic and glacio-isostatic (GIA) processes. No correction has been made for GIA processes as this is outside the scope of this study.