WALIS is built as a series of tables embedded in a MySQL database. The central concept is that the description of a single sea-level index point must include data and metadata describing its stratigraphy and relationship with the former sea level and must be tied to a series of tables reporting on dated samples and details on how both samples and index points have been measured. The techniques used to measure elevation (including the vertical datum) and geographic positioning must relate to sea-level index points and dated samples. Also, studies reporting details on each site, sample, or technique used must be referenced where necessary (Fig. 2). The WALIS database structure (i.e., the mandatory or optional columns that need to be filled when describing a given entity) was drafted by several scientists (coordinated by the authors of this paper), including experts on different subfields (e.g., geomorphology, stratigraphy, dating techniques, earth modeling). A complete list of tables, fields and associated descriptors is available via the project documentation (Rovere et al., 2020). An overview of the database in terms of the number of fields and records contained in each table is shown in Fig. 2.

WALIS has a complex structure, with a series of one-to-many and many-to-many links between tables (Fig. 3). One example of a one-to-many relationship is the one between the tables “RSL stratigraphy” (containing the stratigraphic descriptions of sea-level index points) and “Elevation measurement technique” (including details on the techniques used to measure site or sample elevation). Each record in the elevation measurement technique table can be associated with many RSL stratigraphy data points, as the same measuring technique can be applied to many sites. However, each RSL stratigraphy record can be associated with only one elevation measurement technique. The relationship between the RSL stratigraphy and any table containing dated samples (e.g., amino acid racemization, electron spin resonance, and U-series) is an example of a many-to-many relationship. Multiple dated samples can characterize one RSL stratigraphy data point (e.g., replicates of the same dated material or different samples within the same stratigraphic layer).

It is also possible, under certain conditions, that a single dated sample can be used within various RSL stratigraphy records. This can happen when different sites containing sea-level index points correlate with a single stratigraphic unit dated elsewhere with, for example, U-series. In such cases, the WALIS structure allows connecting one or more sea-level index points with one stratigraphic unit but also with one or more radiometric ages that have been used to assign an age to that unit. The distance between the sea-level proxy and the closest dated sample is calculated and stored in a column of the exported spreadsheet. This kind of many-to-many relationship between sea-level proxies and dated samples allows retaining not only the age information for a given sea-level proxy but also information about how that age has been established. This is a crucial difference with previous Last Interglacial sea-level databases (Hibbert et al., 2016; Pedoja et al., 2014; Ferranti et al., 2006). The relationship between samples and sea-level proxies in these databases is always one-to-one.

The links between database tables are shown in Fig. 3. One key aspect of WALIS is that the links are not defined in MySQL but are managed in the PHP interface. Taking the examples of the one-to-many and many-to-many relationships described above, in the RSL stratigraphy, there is an elevation measurement technique type integer field, which is filled via the PHP interface with the corresponding ID in the Elevation measurement techniques table. Similarly, in the RSL stratigraphy table, there is a U-series type varchar field (i.e., an indeterminate string length data type) that, upon selection in the PHP interface, is filled with the corresponding ID(s) in the U-series table as comma-separated values. Unique constraints and orphans are managed via the PHP interface, and all relationships are coded into the Python scripts used to extract the data (Fig. 1). While we recognize that this makes WALIS an “unorthodox” database from the SQL standpoint, we have found that this is the most effective way to manage the inter-table relationships' complexity without affecting the interface's usability.

The interface to the MySQL database was built in PHP 7.3 using Scriptcase, a rapid application development software. The main components of the interface (current version: 1.8.0) are shown in Fig. 4. On the left side, a menu allows navigating the different pages of the application. Windows for data insertion can be browsed in a tab space in the central part of the application. Below the tab space is the main window, where the active tab is shown. The data insertion is done inside the active tabs in the main window, where a data compiler can find the fields to fill and help tips to guide the compilation of the database.

To ensure rapid access to the data in WALIS, we also prepared a map interface that allows end users to browse the contents of the database (Garzón and Rovere, 2022). This visualization interface is built with the R package Shiny and uses a simplified database version exported via a Python script (Table 1). The interface's main page allows an end user to select data from different filters or geographic queries. The chosen data on the first page can be browsed and downloaded in CSV format on the second page of the interface (Fig. 5). On the third page of the visualization interface, it is possible to run a script implementing a Monte Carlo elaboration that allows plotting a probability density distribution of RSL in space and time, as indicated by the selected indicators. It is also possible to download the results of the Monte Carlo elaboration for further analysis or plot outside the interface. Within the visualization interface, it is possible to apply different filters to the selected data.

With the release of WALIS 1.0, we prepared a repository that includes several Python scripts that can be executed via Jupyter notebooks. The scripts allow querying WALIS by selecting data compilers by name or geographic boundaries. Then, they connect records via one-to-one and many-to-many links and associate database column names with formatted labels. After these scripts are run, it is possible to export the queried data in different formats (CSV, XLSX, GeoJson) or make exploratory plots, such as maps or histograms for various fields (Table 1).

The documentation associated with WALIS is maintained in GitHub and served via a ReadTheDocs web page built with Sphinx (Brandl, 2021). The documentation contains details on the main tables of WALIS and a description for each field of the database, with guidelines on which values or details are expected to be included by the data compiler. Via the ReadTheDocs page, the documentation may be searched and exported as a PDF file.

WALIS 1.0 includes 4545 sea-level proxies (Fig. 6). The papers listed in Table 2 contain data and metadata standardized from 2130 references, spanning more than one century of published scientific literature. The sea-level proxies in WALIS 1.0 consist of 3311 sea-level index points from coastal sites (containing, for example, fossil beach deposits or marine terraces), for which it is possible to identify a relationship with the paleo sea level via the “indicative meaning” (Shennan et al., 2015). Other points indicate that paleo sea level was above (“marine limiting” points, n=285) or below (“terrestrial limiting” points, n=410) the measured stratigraphy. Examples of marine limiting points are fossil subtidal sands, while terrestrial limiting points are, for example, fossil dunes. The database also contains 463 sea-level index points from fossil corals (most of them compiled by Chutcharavan and Dutton, 2021a), which can be correlated to paleo sea level when there is enough information on paleo water depth given. In WALIS are also included 76 phreatic overgrowths on speleothems, which are a particular morphotype of cave deposits formed in association with paleo sea level (Dumitru et al., 2021).

Each sea-level index point is associated with one or more dated samples or with non-radiometric chronological constraints, such as, for example, biostratigraphic markers. In total, WALIS 1.0 includes 4110 dated samples. These include corals, cave deposits, mollusks, or oolites dated via U-series (n=2717). Upon selecting the material dated by U-series techniques, the interface requests the compiler to fill in different fields specific to the material chosen. WALIS 1.0 also contains a relevant number of samples dated with luminescence (n=597), amino acid racemization (n=583), and electron spin resonance (n=213). Additional chronological constraints include 120 chronostratigraphic or biostratigraphic records (e.g., pollen zones) and 160 age determinations of “other” type. Examples of the latter are tephra layers or finite radiocarbon ages, or ages inferred to be beyond the range of the radiocarbon method. Each sea-level proxy must be correlated with at least one chronological constraint. There is no upper limit on the number of chronological constraints associated with a single sea-level proxy. The choice of how to calculate final-age uncertainties for a sea-level proxy associated with several chronological constraints is left to the end user. However, in the data visualization interface, we propose an approach where each age within the same sea-level proxy is sampled using a Monte Carlo method within a random or uniform distribution (depending on the type of constraint), and a synthetic age is calculated by combining the samples available for the proxy.

In the interface, it is also possible to select minimum or maximum ages, indicating if a sea-level proxy is older or younger than a given sample. This option may be chosen when, for example, only infinite radiocarbon ages are available as an age constraint for a beach deposit, indicating thus that the deposit is older than 50–60 ka, but it is impossible to assign a radiometric age. In summary, in WALIS 1.0, there are nine possible combinations (Fig. 7) to define a sea-level proxy (sea-level index point, marine or terrestrial limiting) and its associated age (older/younger than, or with defined age).

In WALIS 1.0, paleo sea levels are interpreted from 30 different types of sea-level indicators. In Fig. 8, we group them into four general categories. In the current version, the most represented category is geomorphological sea-level indicators (such as marine terraces, shoreline angles, or tidal notches). The high number of records for this category is driven by the data from Freisleben et al. (2020). They used a tool called TerraceM (Jara-Muñoz et al., 2016) to systematically map the inner margin of marine terraces along the Pacific coasts of South America, reporting 1953 marine terraces, representing more than 80 % of the data points of this kind in WALIS (and 43 % of the data points in WALIS 1.0). Biological indicators (i.e., single corals or coral reef terraces) and limiting points (marine or terrestrial) contain relatively fewer records. The lowest occurrences in the database are indicators of depositional origin. This category includes several proxies, ranging from widely defined fossil beach deposits and beach rocks (Mauz et al., 2015), to beach ridges (Otvos, 2000) or lagoonal deposits.

Data and metadata on elevation measurement and the vertical datum used are essential to describe a sea-level proxy, as they affect the uncertainties associated with paleo RSL. For this reason, WALIS includes two tables containing information on elevation measurement methods and vertical datums used to report the elevation of samples and sea-level proxies in the field. Each sea-level proxy and each sample in WALIS 1.0 must relate to one record in these two tables. Looking at broad categories of elevation measurement techniques (Fig. 9), it is evident that only a fraction of sea-level proxies in WALIS 1.0 have been measured with techniques with sub-meter (or better) vertical accuracy (e.g., differential GNSS or total station). Elevations for almost half of the sea-level proxies in WALIS 1.0 were gathered from digital elevation models or topographic maps. This high percentage is driven by the 1953 marine terraces measured on digital elevation models by Freisleben et al. (2021). Also, elevation measurement methods are often labeled in WALIS as “not reported”, meaning that there was insufficient information in the literature to discern how the elevation of a sea-level proxy was initially measured.

Looking at broad categories of vertical datums to which elevation measurements have been attributed (Fig. 9), a large number of data referred to either orthometric or geodetic datums. The high frequency of the latter is driven by the large number of terraces reported by Freisleben et al. (2021), who referred their measurements to the global EGM08 geoid. If this source is excluded, the vertical datum for most records in WALIS is either not reported or referred generally to “mean sea level” with no further specifications. Only a small fraction of data are referred to a tidal datum, and very few data points were referred to a vertical biological datum (e.g., the height of living coral microatolls).

As shown above, in Fig. 8, sea-level proxies in WALIS 1.0 can be divided into four broad categories. However, there are differences in how relative sea-level (RSL) information is inserted in the WALIS interface for three common types of index points: stratigraphic (including geomorphological proxies), speleothems, or corals (Fig. 10). For any sea-level index point, regardless of the type, the WALIS interface requests as mandatory information the elevation of the proxy and the associated 2σ error, which should also include datum uncertainty.

Regarding RSL index points from stratigraphy, the WALIS interface calculates paleo RSL from the upper and lower limits of occurrence of the proxy in modern analogs, which are requested as mandatory fields. Using the concept of indicative meaning (Shennan, 1982; Shennan et al., 2015) and associated formulas (Rovere et al., 2016), the interface calculates paleo RSL and 2σ uncertainties, which are then saved in the database. In the case of sea-level index points from speleothems, in WALIS 1.0 represented by phreatic overgrowth on speleothems (POS), the compiler is required to insert the values of paleo RSL and associated ±1σ uncertainty. In the case of sea-level index points from single corals, the WALIS interface requests the insertion of upper, lower, and modal depth range of occurrence of living specimens. For corals, the interface does not calculate paleo RSL. However, in the code used to prepare data for the ShinyApp interface (Rovere et al., 2022), we include scripts to compute a gamma distribution from the upper and lower limits of occurrence of corals used as index points (shown in Fig. 10), an approach similar to that proposed by Hibbert et al. (2016).

In several tables within WALIS, there are fields to help end users understand the quality of the data. In this context, quality does not necessarily refer to accuracy or precision but is a subjective measure that can reflect, for example, more information associated with the data point that leads it to be considered more robust. In the RSL from stratigraphy table, data compilers were asked to score, on a scale from 0 to 5, the age and RSL information quality of each data point inserted. A general guide on how to score the records was given by Rovere et al. (2020) and is here reported in Table 3. However, its use was not strictly enforced within the WALIS special issue. Although the guidelines are designed to facilitate objective data analysis, we recognize there is still potential for subjective interpretation.

For studies following this suggested ranking scale, comparing quality scores among areas is possible. Examples are the records of Argentina (Gowan et al., 2020) and Brazil (Rubio-Sandoval et al., 2021a), shown in Fig. 11. Comparing the scores in these two datasets shows that, on average, records in Argentina have slightly higher age quality than those in Brazil. However, the RSL information for some sites in Brazil reaches the “excellent” score, which is not achieved by any record in Argentina. Ideally, those sites might be targeted to gauge whether it may be possible to improve their age control.

Samples dated with radiometric techniques have a mandatory field where data compilers indicate whether the data point is “accepted” or “rejected”. The rationale of this field is to allow the data compiler to insert samples rejected by original authors and retain unsuccessful dating attempts for future reference. Such fields were expanded in the U-series ages on corals template thanks to the input by Chutcharavan and Dutton (2021a). These authors proposed inserting fields in the database to report different screening protocols applied to existing ages. Investigating whether U-series approach on corals might also be used for other radiometric dating techniques represents potential ground for future WALIS versions.

In compiling data for WALIS 1.0, the aim was to include as many sites as possible globally, including all relevant information related to sea-level proxies and associated dating methods. While we achieved both goals, comparing the data included in WALIS 1.0 with the sites reported in the extensive review by Pedoja et al. (2014), it is possible to highlight areas where Last Interglacial sea-level proxies might be present but are not available in the WALIS standard format. These areas are shown in Fig. 12 and are discussed below, together with relevant or most recent works, which may be used as a starting point for the inclusion of these areas in the subsequent versions of WALIS.

Starting from the northernmost part of the North American continent, the areas not included in WALIS 1.0 include the Last Interglacial shorelines reported in Alaska along the coasts of the Lisburne and Seward peninsulas, the latter including the Nome coastal plain where sea-level records left by several sea-level highstands have been reported (Brigham-Grette and Hopkins, 1995; Goodfriend et al., 1996). On the Russian side of the Bering Strait, in the Chukotka Peninsula, the Last Interglacial sequences are reported by Khim et al. (2001) and Brigham-Grette et al. (2001). South of this area, Quaternary marine and coastal sequences were also reported on the eastern side of the Kamčatka Peninsula (Pedoja et al., 2013).

Another data gap in WALIS 1.0 is evident on the Pacific coasts of North and Central America. Potential sites in this area (including the Mexican states south of Sonora and the Pacific coast of Central America) are discussed in Muhs (2022), who highlights that some studies on these locations are present but do not contain enough details to be inserted in WALIS. We also emphasize that WALIS 1.0 does not include the data reported by a recent paper detailing the marine terraces of Santa Cruz Island, California, which appeared in the literature during the compilation of the atlas (Muhs et al., 2021b).

There are virtually no Last Interglacial shorelines along the South American Pacific coasts extending south of 75∘ S latitude. The absence of such features in this vast area is probably due to the presence of the Patagonian ice sheet during the Last Glacial Maximum, which has likely eroded most, if not all, Last Interglacial coastal sections in this area. Going southwards, surfaces of marine origin, likely of Pleistocene age, are reported on the South Shetland Islands (Navas et al., 2006; López-Martínez et al., 2016) but not included in WALIS 1.0. It is unclear whether the chronological constraints on those landforms are robust enough to be inserted in WALIS.

On the western coasts of the Central Atlantic, another vast area with a substantial lack of records in WALIS 1.0 includes the shores of northern Brazil, French Guiana, Suriname, Guyana, Venezuela, and the Caribbean Sea coasts of Colombia, Panama, Costa Rica, Nicaragua, and Honduras. Rubio-Sandoval et al. (2021a) discuss potential sites in this vast area. However, studies with enough metadata are missing, except offshore Colombia, on the San Andrés and Providencia Islands. Regarding the Caribbean Sea, WALIS 1.0 includes the most relevant data from this region. However, additional sites that may be inserted in WALIS are present in Jamaica (Mitchell et al., 2001, 2006) and Cuba (Muhs et al., 2017; Schielein et al., 2020).

For the US Atlantic coast (excluding the Florida Keys), the only data included in WALIS 1.0 are those related to MIS 5a/5c (Thompson and Creveling, 2021b). Former studies suggested that these stages attained similar elevations to MIS 5e in this area due to glacial isostatic adjustment processes (Wehmiller et al., 2004); therefore, outcrops of this age might have been eroded by later highstands. However, there are reports of MIS 5e successions scattered along the coast (Wehmiller et al., 2010, 2012; O'Neal and McGeary, 2002; Wright et al., 2009), which should be screened for insertion in WALIS. Also, as already mentioned in the previous sections, the Last Interglacial amino acid racemization data obtained from samples of the US Atlantic coast (Wehmiller et al., 2021) should be included in future versions of WALIS. In Bermuda, data from corals (Chutcharavan and Dutton, 2021a) and cave deposits (Dumitru et al., 2021) are included in WALIS 1.0. Still, more sites and dated samples are reported in a recent review by Muhs et al. (2020). Their inclusion in the subsequent versions of WALIS must be considered a priority, given the importance of this area for unraveling land motion changes driven by glacial isostatic adjustment in the North Atlantic.

On the East Atlantic, Pedoja et al. (2014) report that Last Interglacial sea-level proxies were mapped in Ireland by Orme (1966). While it seems unlikely that this study contains enough metadata to be considered for WALIS, some of the Quaternary deposits presented in this early study might have been the subject of successive dating (e.g., Gallagher and Thorp, 1997), thereby meeting the standard for their inclusion in subsequent versions of WALIS. Last Interglacial data missing from WALIS 1.0 may also be present on the Atlantic coasts of the Iberian Peninsula (Alonso and Pagés, 2007; Meireles and Texier, 2000; Benedetti et al., 2009). In the Azores islands, Last Interglacial deposits have also been reported (Ávila et al., 2009, 2015) but are not included in WALIS 1.0. Only U-series ages with no indication of paleo sea level are reported in WALIS 1.0 from the Canary and Cabo Verde archipelagos. However, enough metadata might be present in some papers (Zazo et al., 2010, 2007; Muhs et al., 2014) to upgrade these points to sea-level proxies in the subsequent versions of WALIS.

Within the Mediterranean Sea, data from several studies were inserted in WALIS 1.0. However, some areas lack records, mainly in the eastern part of the basin. For example, there seem to be little to no studies on the coastal Quaternary of Libya, except for one site near Alexandria inserted in WALIS 1.0 (Mauz and Elmejdoub, 2021). While sites in Israel and Cyprus have been inserted in WALIS 1.0 (Sivan and Galili, 2020; Zomeni, 2021), there are no sites in WALIS for Lebanon, Syria, Turkey, and Greece. In these areas, Last Interglacial sea-level proxies are reported in the literature (e.g., Sanlaville, 1974; Dodonov et al., 2008; Tarıet al., 2018; Gaki-Papanastassiou et al., 2009) and should be screened to gauge whether enough metadata are available for their insertion in the following versions of WALIS. Also, Last Interglacial sea-level proxies from the Black Sea are reported by Pedoja et al. (2014) but are not yet present in WALIS 1.0. The published records in these areas need to be evaluated and eventually included in the subsequent versions of WALIS.

There is a substantial lack of data in WALIS 1.0 along the Atlantic coasts of northern and central Africa. However, there are several recent studies detailing Last Interglacial marine and coastal sequences in Morocco (Barton et al., 2009; Plaziat et al., 2008, 2006; Rhodes et al., 2006), Mauritania, and Senegal (Giresse et al., 2000), where data might be gathered for subsequent WALIS versions. There are only a few other reports of Last Interglacial shorelines (e.g., Gregory, 1962) south of Senegal, the first southwards being those in Angola inserted in WALIS 1.0 by Cooper and Green (2021).

Another area where more data could be added to WALIS is the Red Sea. Here, several U-series ages on corals have been reviewed by Chutcharavan and Dutton (2021a), some of which were identified as “sea-level index points from corals”. Further sea-level index points might be retrieved from studies reporting on Last Interglacial shorelines in Saudi Arabia (Dullo, 1990) and the Gulf of Suez (Parker et al., 2012; Bosworth and Taviani, 1996). On the other side of the Arabian Peninsula, in the Gulf of Oman and the Persian Gulf, the only data inserted in WALIS 1.0 are those related to MIS 5a/5c proxies (Thompson and Creveling, 2021b). However, potential MIS 5e sea-level proxies are reported in the literature from Oman (Falkenroth et al., 2020, 2019), United Arab Emirates, Qatar (Williams and Walkden, 2002), and Iran (Oveisi et al., 2007; Pirazzoli et al., 2004). These studies must be screened to gauge whether valid sea-level index points can be inserted in the subsequent versions of WALIS.

There are no data in WALIS 1.0 for India and the Chagos–Laccadive ridge. Key references from which data might be retrieved are Bhatt and Bhonde (2006), Banerjee (2000) (for India), Woodroffe (2005), and Gischler et al. (2008) (for the Chagos–Laccadive Ridge). Unfortunately, we could not find publications reporting data for Last Interglacial successions in Thailand, Malaysia, and the islands of Sumatra and Java. WALIS 1.0 also lacks data from the South China Sea; however, some potentially Last Interglacial sites were reported by Pedoja et al. (2008).

In Australia, the Last Interglacial data included in WALIS 1.0 are mainly derived from corals (Chutcharavan and Dutton, 2021a) along the western coast and the Great Barrier Reef. Thompson and Creveling (2021b) report MIS 5a/5c in South Australia. Further data on MIS 5e shorelines from strand plains in South Australia are available from several studies (Murray-Wallace and Belperio, 1991; Murray-Wallace, 2002; Murray-Wallace et al., 2016; Pan et al., 2018) and should be included in the subsequent versions of WALIS.

While WALIS 1.0 represents a concrete result, we know there are several ways in which the WALIS database and infrastructure could be improved. We discuss the main avenues for improvement below. These emerged during the compilation of WALIS 1.0, and more will likely be identified as the database starts to be used by more end users.

As mentioned above, the database structure is now a collection of tables with no links defined in MySQL. Creating such a connection would imply a partial restructuring of the PHP interface. However, this would improve the overall structure of the WALIS database. Another technical improvement would consist in allowing bulk uploads, which at the current stage is not possible.