An interactive visualization and data portal tool (PALTIDE) for relative sea level and palaeotidal simulations of the northwest European shelf seas since the Last Glacial Maximum

Relative sea level (RSL) predictions based on glacial isostatic adjustment (GIA) simulations and palaeotidal predictions generated by hydrodynamic models using GIA‐generated palaeotopographies are available in the published literature, and datasets are available via data repositories. However, these data are often difficult to extract for specific locations or timeslices, requiring users to request datasets from corresponding authors. To overcome the intractability of these data and to enable users to interrogate datasets themselves without requiring offline requests, we have developed PALTIDE, an online visualization tool with intuitive user interface accessible at https://shiny.bangor.ac.uk/paleotidal/. The model domain for this interactive visualization tool is the northwest European continental shelf, covering the period from the Last Glacial Maximum (LGM) to the present day, and is based on previous GIA simulations by Bradley and colleagues and hydrodynamic simulations using Regional Ocean Modelling System (ROMS) published by Ward and colleagues. The tool is developed in R and utilizes a number of packages including shiny and bslib for the frontend, and arrow, raster and the tidyverse for backend data processing. The tool enables visualizations and data downloads for RSL, tidal amplitude and tide‐dependent parameters for any location within the model domain over 1000‐year timesteps from the LGM to the present.


Introduction
Since the Last Glacial Maximum (LGM;26.5-19 ka;Clark et al., 2009), the changes in the surface distribution of the oceans, ice sheets and landdriven by changes in orbitally modulated insolation and carbon cycle feedbackshave fundamentally influenced all components of the Earth system.Ice sheets control the position of coastlines through both glacio-eustasy and glacio-isostasy and, in so doing, modulate ocean circulation and dynamics.The combined influences of glacio-eustasy and glacio-isostasy on palaeotopographic evolution and relative sea level (RSL) through both space and time can be simulated using glacial isostatic adjustment (GIA) models (Lambeck, 1995(Lambeck, , 1996;;Peltier, 1994;Bradley et al., 2023).GIA models integrate the time-dependent controls (e.g.deformation of the solid Earth) of RSL with input data from numerical ice sheet and solid Earth models and observations (Shennan et al., 2006;Bradley et al., 2023).Sea-level index points (SLIPs) provide the fundamental observational data by which GIA simulations are constrained (Bradley et al., 2023), and an iterative approach is usually adopted to improve the goodness-of-fit between the GIA simulations and the SLIP observations of RSL change.GIA simulations have become fundamental tools in Quaternary science over the past few decades.The integrative nature of GIA modelling means that GIA simulations are now central to both the sea-level and palaeoglaciological research communities, providing a structured and reasoned basis for defining hypotheses for field/ observational testing (Scourse, 2013).
Since they provide simulations of coastline and bathymetric change, palaeotopographies generated by GIA simulations are, in turn, fundamental inputs for 'palaeotidal' models.Palaeotidal simulations of shelf sea and coastal tidal amplitude are reconstructed using hydrodynamic models (e.g.POM, POLCOMS, OTIS, ROMS) that incorporate the major tidal forcings with input from global tidal models, with a boundary usually set at the shelf break.Early palaeotidal model simulations used a fixed topography with sea level defined by only eustatic change (e.g.Austin, 1991).Later palaeotidal modelling efforts included GIA simulations, which provide dynamic palaeotopography (i.e.includes RSL changes) and which more closely approximates geological observational data used to constrain palaeotidal model simulations (Scourse et al., 2002;Uehara et al., 2006;Scourse, 2013).Sensitivity tests using palaeotidal model simulations that integrate GIA topography for northwest Europe (Uehara et al., 2006;Ward et al., 2016) indicate that the response of the shelf tides during deglaciation are more sensitive to the ocean tide input than they are to inputs derived from different generations of GIA model inputs.Global tidal model inputs have improved significantly in recent years, particularly for the period since the LGM through the subsequent period of deglaciation and the Holocene (e.g.Egbert et al., 2004;Green, 2010;Wilmes and Green, 2014;Schmittner et al., 2015;Wang et al., 2020;Lee et al., 2022;Sulzbach et al., 2023) with ongoing advances in computational and modelling capacity.The output from these global palaeotidal models provide key inputs to regional simulations by supplying tidal conditions at model boundaries, such as palaeotidal elevation amplitude and tidal current conditions.
Palaeotidal model simulations have become a powerful tool in Earth systems science since they hindcast the evolution of tidal amplitudes and tide-dependent parameters (bed stress, shelf sea stratification, tidal currents, dissipation of tidal energy) as coastlines and bathymetry change in response to RSL.Palaeotidal model simulations have a number of predictive/hindcasting applications.Simulated palaeotidal amplitudes are important for constraining SLIPs (Shennan et al., 2000;Neill et al., 2010;Ward et al., 2016), which rely on accurate assessment of vertical reference datums, such as mean high water spring tide; palaeotidal amplitudes (18-16 ka BP) from Ward et al. (2016) were used to constrain SLIPs within isolation basins in southwest Norway, in the construction of a revised RSL of the region (Vasskog et al., 2019).In turn, SLIPs are integral to GIA models of vertical crustal motion.Reconstructions of the spatial distribution and timing of seasonal stratification (and the associated tidal mixing fronts) in shelf sea environments are important for understanding fluxes of organic material to the seabed and hence for constraining the evolution of the role of shelf sea environments in the global carbon cycle (e.g.Rippeth et al., 2008;Scourse, 2013).For example, reconstructions of the timing of seasonal stratification in the western Irish Sea (Ward et al., 2016) were compared by Woods et al. (2019) with an age-depth model for a data point within the region, and the authors highlighted the importance of data points for validating and/or constraining palaeotidal model output.Assessments of the dissipation of tidal energy in the global ocean have implications for deep ocean circulation (Green et al., 2009;Wilmes and Green, 2014;Wilmes et al., 2021).Palaeotidal simulations of changes in the extent of the inter-tidal zone have archaeological implications (Mortimer et al., 2013;Barnett et al., 2020).Tidal current and bed shear stress predictions from palaeotidal simulations provide a means of hindcasting shelf sea sediment dynamics (e.g.van der Molen and de Swart, 2001;Scourse et al., 2009;Van Landeghem et al., 2009), with some of the inherent limitations and challenges discussed in Ward et al. (2020).Such large-scale distribution of shelf sea sediments by hydrodynamic processes has implications for coastal and geological basin evolution, and for understanding the contribution that shelf seas play in blue carbon sediment dynamics/habitats and carbon burial on continental shelves; it is this application that is the focus of the Convex Seascape Survey (https://convexseascapesurvey.com).
We have developed an open access online interactive visualization tool (PALTIDE) that enables users to interrogate and download RSL and palaeotidal simulation output via a user-friendly portal.Hitherto these data have been restricted to the palaeotidal community(ies) responsible for developing the simulations and therefore have been inaccessible unless through direct request.The tool enables users to visualize and download data for any location within the model domain in 1000-year timesteps from the LGM (taken here as 21 ka BP) to the present.These data can then be cited in any subsequent publication or outlet with reference to this paper which provides the technical details underpinning the tool.The tool can be accessed at: https://shiny.bangor.ac.uk/paleotidal/.

PALTIDE online visualization tool: development, source code and data
The PALTIDE tool (https://shiny.bangor.ac.uk/paleotidal/) takes output from regional GIA and palaeotidal models and presents these data in a series of online visualizations.The tool is designed to be a straightforward, user-friendly dashboard that allows users to explore palaeotidal simulations via custom data visualizations and provide access to specific subsets of simulation data based on user-specified inputs.All datasets visualized through the web app (RSL and palaeotidal model output) were in XYZ data format (further details below).The tool is developed in R (R Core Team, 2023), and utilizes a number of packages including shiny (Chang et al., 2023) and bslib (Sievert et al., 2023) for the frontend, and arrow (Richardson et al., 2023), raster (Hijmans and van Etten, 2012) and the tidyverse (Wickham et al., 2019) for backend data processing.The archived source code associated with the initial release associated with this paper can be found at https://doi.org/10.5281/zenodo.10020155and the full data shown in simulations can be found at https://doi.org/10.5281/zenodo.10020210.The app is designed to work on most modern web-browsers and has layout optimization for mobile devices.

Relative sea level dataset
The RSL data made available through PALTIDE are from the GIA model of Bradley et al. (2011).This GIA model (specifically constrained for the British Isles) incorporates an ice sheet model developed by Bassett et al. (2005) with constraints on regional ice distribution by Shennan et al. (2006) and Brooks et al. (2008); full descriptions of the GIA model inputs and set-up are described in these source papers.The Bradley et al. (2011) GIA model integrates an ice model that underestimates British-Irish Ice Sheet ice volume and extent, as published by the BRITICE-CHRONO Project (http:// www.britice-chrono.group.shef.ac.uk;Clark et al., 2022).Work is ongoing to incorporate revised GIA simulations, based on the BRITICE-CHRONO data on ice sheet thickness, extent and timings (Bradley et al., 2023), into new palaeotidal model simulations; this will result in an updated version of the online visualization tool (hereafter referred to as the 'tool') in due course.The palaeotopographies of the palaeotidal model (the latter is described below) combine the modern shelf bathymetry with these changes in RSL output by the Bradley et al. (2011) GIA model.

Hydrodynamic model set-up
The hydrodynamic model used is the three-dimensional Regional Ocean Modelling System (ROMS) (Shchepetkin and Mc Williams, 2005) as applied and described by Ward et al. (2016).The model iteration applied generates simulations based on the M 2 principal lunar semi-diurnal constituent, plus S 2 and N 2 constituents.The model has been used to generate simulations for 1000-year timesteps from the LGM, defined here as 21 ka BP, to the present; the timescales used are based on calibrated radiocarbon ages and so approximate the calendrical timescale.Output from a global ocean tidal model based on the Princeton Ocean Model (POM, Uehara et al., 2006) is used to force the shelf tides at the model boundaries.The palaeobathymetries used in the global model were prepared as described in Uehara et al. (2006) and integrate the global GIA simulations based on the ICE-5G (VM2) model (Peltier, 2004).
In the tool, individual datasets are all presented on the same ocean model grid, at ~1/24 degree spatial resolution (~2-3-km grid spacing).This resulted in 625 grid points from 15°W to 11°E, and 861 grid points in latitude from 45°N to 65°N (note that ROMS grids have varying spatial resolution with latitude).For consistency, the RSL datasets of Bradley et al. (2011) which were used within the palaeotidal modelling and which are visualized within this web application were linearly interpolated to the same ocean model grid.

Palaeotidal model output
The ROMS model outputs user-specified variables within a NetCDF file.Here, we use model outputs of tidal elevation amplitudes, depth-averaged (two-dimensional) tidal current speeds and near-bed tidal induced bed shear stress, and simulated tidal current speeds and model water depth are used in the calculation of seasonal stratification.Further details on how these model variables are computed are given below.The relevant variables were extracted from the raw NetCDF model output files and were saved as separate ASCII files, in XYZ data format, with each entry representing a variable value at a model grid point.Each visualization layer (velocity, bed shear stress, etc.) has its own set of ASCII files, with one datafile for each timeslice, 0-21 ka BP.

Simulated bed shear stress
Shelf sea sediment transport is driven by frictional forces exerted on the seabed, referred to as bed shear stress (τ 0 , Equation 1).These bed shear stresses can be exerted by tides, waves, or combined tide plus wave motion, and are expressed as the force exerted by the flow per unit area of bed in terms of the density of water (ρ) and the frictional velocity (u * ) such that: (1) Sediment transport (of non-cohesive sediments) occurs when the bed shear stress exceeds the threshold of motion.Changes in the current regime, such as through changes in sea level, thus directly impact on seabed sediment transport.Simulations of bed shear stress changes over time can help us understand the evolution of large-scale sediment patterns and features.For example, in some areas with large sand banks such as in the East China Sea (e.g.Uehara et al., 2002) and in the Celtic Sea (e.g.Belderson et al., 1986;Scourse et al., 2009), modern hydrodynamic conditions do not appear to be sufficiently energetic for their generation, indicating that they are a product of past current regimes.As such, the threedimensional hydrodynamic model presented here was set to output 'near-bed' bed-shear stress (BSS), computed at the middepth of the bottom computational cell (as opposed to being calculated from depth-averaged tidal current speeds).The equations for computing the eastwards (τ x , Equation 2) and northwards (τ y , Equation 3) components of BSS are: (2) (3) where τ is the BSS, C D is the user-defined drag coefficient, and u and v are the simulated tidal current velocities in the east and north directions, respectively.The quadratic bottom drag scheme implemented, using a bottom drag coefficient of 0.003, was in line with other ROMS modelling studies of the region (e.g.Hashemi and Neill, 2014;Lewis et al., 2015;Robins et al., 2015).Note that no morphodynamic bed level changes (e.g.erosion, sedimentation) are implemented in the simulations as a feedback response to simulated bed shear stresses.

Calculation of seasonal stratification
Tidal mixing fronts are an important feature of many shelf seas that delineate seasonally stratified and well-mixed (or sporadically stratified) waters.This seasonal stratification is a key driver in biological, ecological and biogeochemical characteristics of shelf sea waters, and plays a key role in mediating the primary productivity of a region.Vertical stratification of the water column is driven by heating of surface waters, and where the vertical mixing of the water column is strong enough (predominantly by tidal stirring), this vertical stratification cannot occur.Tidal mixing fronts reside within the zone where the input of kinetic energy from the tides balances the heat input from solar radiation (Simpson and Hunter, 1974).As such, the positions of shelf sea tidal mixing fronts vary both seasonally and with the spring-neap tidal cycle.
Seasonally stratified continental shelf seas can act as net sinks for atmospheric carbon dioxide (CO 2 ).The flooding of the northwest European shelf seas during the last deglacial increased the areal extents of seasonally stratified continental shelf waters.This increase in seasonally stratified waters will in turn have contributed to increased drawdown of atmospheric CO 2 (during the summer months) on the modern northwest European shelf seas relative to the early deglacial period (Rippeth et al., 2008).
Much of the northwest European shelf seas are characterized by strong tidal currents, which are closely linked to seasonal stratification.Simpson and Hunter (1974) determined that the approximate location of the tidal mixing front in the Irish Sea is dependent upon water depth and tidal current speed.Bowers and Simpson (1987) then inferred that the locations of the tidal mixing fronts (on European seas) are consistent with a critical contour (or 'stratification parameter') at χ = 250 m −2 s −3 , using the simulated depth-averaged M 2 tidal current speed (u, Equation 4).It is common to use the log 10 value, and thus the equation becomes: where h is water depth.It is this log 10 value of the stratification parameter which is used here to approximate the position of the tidal mixing front, with a critical contour plotted at χ = 2.4 (Bowers and Simpson, 1987).Areas characterized by χ < 1.9 can be expected to remain well-mixed throughout the year, whereas vertically stratified waters can be expected where χ > 2.9.So-called 'transition zones' are characterized by 1.9 < χ < 2.9, where this represents modulation in the position of the tidal mixing front within this zone due to seasonal heating and the spring-neap cycle.

PALTIDE: description
The online visualization tool, PALTIDE, is constructed around two pages 1.The landing page, which includes brief information on the tool, funder information and contact details, and explains how users are to cite downloaded data.2. The data visualizations page, which allows the user to explore, visualize and download the full suite of palaeotidal model output and RSL datasets upon which the app is based.
The landing page is self-explanatory; here, we explain the main functions of the data visualizations page (Figure 1) and provide additional metadata on each of the downloadable datasets.

Data visualizations
From the landing page, the user can access the full functionality by clicking on the 'Explore Data Visualisations' tab.On this second page, within the 'Maps' section the user may visualize two-dimensional colour (raster) plots (hereafter referred to as 'maps', for ease) of various datasets (Figure 2), as well as download point-location data (Figures 3 and 4).Once on this page, the user must first select an ocean model output to view, with the options being: 1. Tidal amplitude: tidal elevation amplitude of the M 2 tidal constituent.2. Stratification: with categorical data for mixed/frontal/stratified. 3. Peak Bed Stress: simulated magnitude and direction of nearbed peak tide-induced bed shear stress, output directly from the model, i.e. based on M 2 , S 2 and N 2 tidal constituents (in N m −2 ). 4. Tidal Current: simulated peak current speed of the M 2 tidal constituent, as an absolute magnitude (in m s −1 ).
The user may then select whether to interrogate the maps (which is the default option) or whether to view a pregenerated animation of the loaded variable, by switching between the 'Interactive' or 'Animated' tabs [Figure 1,label (ii)].An animation is available for each of the four variables listed above, and illustrates the maps one at a time, at 1000year time-steps, from 21 ka BP forwards in time to the present (0 ka BP).The user may view the different animations by changing the variable within the drop-down menu called 'Data Selection'.There is a slight delay when moving between different model parameters, or when changing the period being visualized.All efforts were taken to minimize this delay, but we have prioritized high-resolution data over run speed.
The user may zoom in on the raster map by using either the +/− sign at the top left of the map panel, or by using the scrolling function on a mouse (scroll wheel).To move the map, simply click and drag the image.For each map, light grey colours indicate land (the ocean model 'land mask'), whereas white areas illustrate the 'ice mask' within the ocean model (the latter visible from 9 ka BP and earlier, Figure 1).For peak bed stress, the colour map illustrates the absolute magnitude of the bed stress (N m −2 ) and the white vector arrows show the associated direction of peak bed stress.For app run speed, it was necessary to downscale and filter the full suite of bed shear stress vectors in the map to show only those vectors representing bed shear stress >0.5 N m −2 and spatially downscaled to only plot every 100 of those (note this does not affect downloaded data).

Additional user-defined options
To the top right of the visualization page is a slider, where the user can choose the time period/year to be visualized in the colour-plot (in 1-ka timeslices).The period to view can be changed by clicking and dragging the slider, or by clicking on discrete points on the scale.Below the timeline is a checkbox option for including the modern coastline ('show modern coastline') on the maps (black line).The contemporary coastline is a shapefile from NOAA's global coastline (Wessel and Smith, 1996) and the 'low-resolution' coastline is used here for app runtime.

Timeseries plots of RSL and tidal amplitude
The user may click on any point within the raster map [Figure 1, label (iii)], using the cursor (a hand), which brings up a 'pin' at the selected location.For any user-defined point location the corresponding time-dependent RSL and tidal elevation amplitude data will be illustrated in the double y-axis line graph to the bottom right of the visualization page (Figure 3), with the title of the plot corresponding to the coordinates of that point location.The x-axis on the line graph is time, from 21 to 0 ka BP.No tidal amplitude points are plotted for timeslices when a point is not sea (referred to as 'water' throughout the app) within the ocean model (i.e. is land/under ice) and, as such, some datasets appear truncated in these plots.Note that no point data are available to visualize or download (described below) for points which have remined dry (i.e.land and/or ice) throughout all simulation timesteps.The user can hover the mouse over the datapoints and further quantitative information pops up (e.g.amplitude/rsl + year + landtype).The so-called 'landtype', i.e. whether a point is water/land/ice at each timeslice, is provided within the downloaded data (described in more detail below).

Data download
The data for a point location may be downloaded using the dark grey 'Download Data' button to the bottom right of the Data Visualisation page [Figure 1, label (vii)].The data which are downloaded (Figure 4) are determined by the variable (model output) loaded in the map [label (a) in Figure 1].Data available to download for point locations are: 1. Relative sea level (in metres below contemporary level, where present-day RSL = 0).2. Stratification.3. Bed shear stress (u-and v-components as well as absolute magnitude, in N m −2 ). 4. Tidal current (simulated peak current speed of the M 2 tidal constituent, as an absolute magnitude, in m s −1 ).
The default file download names are self-explanatory but can easily be overwritten: Tidal Amplitude.csv,Stratification.csv,Peak Bed Stress.csv and Tidal Current.csv.The format of each.csvdata table is latitude*longitude*variable for each 22-ka timeslice.

Summary
The PALTIDE tool enables users to interrogate, download and visualize RSL and palaeotidal data for any location on the northwest European continental shelf for the period since the LGM based on the GIA simulations of Bradley et al. (2011) and the palaeotidal simulations of Ward et al. (2016).Because the data include site-and time-specific simulations of RSL as well as palaeotidal simulations of tidal amplitude, seasonal stratification, peak bed stress vectors and surface tidal currents, we anticipate that this tool will be of interest and value to a very wide range of user disciplines comprising Quaternary and marine geology, geophysics, Earth system science, sedimentology, marine ecology/ biology, carbon cycle biogeochemistry, geomorphology, palaeoclimatology, palaeoceanography, sedimentology and archaeology.Later editions of the tool will include revised simulations for the northwest European continental shelf region based on GIA simulations integrating the BRITICE-CHRONO project ice sheet  observations (Bradley et al., 2023) and extension of the tool to all the global continental shelves using updated global GIA simulations.This work is ongoing funded by the Convex Seascape Survey (https://convexseascapesurvey.com/).Any data deriving from this first version of PALTIDE should cite this paper alongside Bradley et al. (2011) and Ward et al. (2016).

Figure 1 .
Figure 1.Data visualizations page showing (i) choice of model variable to view and (ii) an option to explore the interactive map or load an animation of the selected variable.While on the interactive maps (iii), further user-defined options include (iv) simulation timeslice to load and view.By clicking on the map and selecting a point location (v) the timeseries data for RSL and tidal elevation amplitude are plotted for that location (vi).Using the data download button (vii) the user may download the data associated with the variable loaded in the map.[Color figure can be viewed at wileyonlinelibrary.com]

Figure 2 .
Figure 2. Example two-dimensional raster plots (maps) of (a) tidal elevation amplitude, (b) seasonal stratification, (c) tidal current speeds, and (d) bed shear stress speed (colour-scale) and direction (white vector arrows).(e) A zoomed-in illustration of the bed shear stress vectors, for the area indicated by the white bounding box in (d).All maps are for 10 ka BP.Labels (i)-(iv) on (a) are the approximate locations of the point data plotted in Figure 3. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3 .
Figure 3. Example plots of changes in RSL (left y-axes, blue lines) and tidal elevation amplitudes (right y-axes, green lines) with time (x-axes).The approximate point locations (i-iv) for which these data are plotted are given in Figure 2(a).[Color figure can be viewed at wileyonlinelibrary.com]

Figure 4 .
Figure 4. Format of downloaded data for (a) tidal amplitude and (b) bed shear stress.In each, where ocean model outputs are not available (NA), the land_type column indicates whether the point was land or under ice at that timeslice.The tidal elevation amplitude and RSL are provided in all downloaded files.