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Since the mid-1990s, a series of FES (finite element solution) global ocean tidal atlases has been produced and released with the primary objective to provide altimetry missions with tidal de-aliasing correction at the best possible accuracy. We describe the underlying hydrodynamic and data assimilation design and accuracy assessments for the latest FES2014 release (finalized in early 2016), especially for the altimetry de-aliasing purposes. The FES2014 atlas shows extremely significant improvements compared to the standard FES2004 and (intermediary) FES2012 atlases, in all ocean compartments, especially in shelf and coastal seas, thanks to the unstructured grid flexible resolution, recent progress in the (prior to assimilation) hydrodynamic tidal solutions, and use of ensemble data assimilation technique. Compared to earlier releases, the available tidal constituent's spectrum has been significantly extended, the overall resolution has been augmented, and additional scientific byproducts such as loading and self-attraction, energy diagnostics, or lowest astronomical tides have been derived from the atlas and are available. Compared to the other available global ocean tidal atlases, FES2014 clearly shows improved de-aliasing performance in most of the global ocean areas and has consequently been integrated in satellite altimetry geophysical data records (GDRs) and gravimetric data processing and adopted in recently renewed ITRF standards (International Terrestrial Reference System, 2020). It also provides very accurate open-boundary tidal conditions for regional and coastal modelling.

The deformation radius is widely used as an indication of the eddy length scale at different latitudes. The radius is usually calculated assuming a flat ocean bottom. However, bathymetry alters the baroclinic modes and hence their deformation radii. In a linear quasigeostrophic two-layer model with realistic parameters, the deep flow for a 100-km wave approaches zero with a bottom ridge roughly 10 m high, leaving a baroclinic mode that is mostly surface trapped. This is in line with published current meter studies showing a primary EOF that is surface intensified and has nearly zero flow at the bottom. The deformation radius associated with this “surface mode” is significantly larger than that of the flat bottom baroclinic mode. Using World Ocean Atlas data, the surface radius is found to be 20%–50% larger over much of the globe, and 100% larger in some regions. This in turn alters the long Rossby wave speed, which is shown to be 1.5–2 times faster than over a flat bottom. In addition, the larger deformation radius is easier to resolve in ocean models.

The Surface Ocean CO2 Atlas (SOCAT) is a synthesis of quality-controlled fCO2 (fugacity of carbon dioxide) values for the global surface oceans and coastal seas with regular updates. Version 3 of SOCAT has 14.7 million fCO2 values from 3646 data sets covering the years 1957 to 2014. This latest version has an additional 4.6 millionfCO2 values relative to version 2 and extends the record from 2011 to 2014. Version 3 also significantly increases the data availability for 2005 to 2013. SOCAT has an average of approximately 1.2 million surface waterfCO2 values per year for the years 2006 to 2012. Quality and documentation of the data has improved. A new feature is the data set quality control (QC) flag of E for data from alternative sensors and platforms. The accuracy of surface water fCO2 has been defined for all data set QC flags. Automated range checking has been carried out for all data sets during their upload into SOCAT. The upgrade of the interactive Data Set Viewer (previously known as the Cruise Data Viewer) allows better interrogation of the SOCAT data collection and rapid creation of high-quality figures for scientific presentations. Automated data upload has been launched for version 4 and will enable more frequent SOCAT releases in the future. High-profile scientific applications of SOCAT include quantification of the ocean sink for atmospheric carbon dioxide and its long-term variation, detection of ocean acidification, as well as evaluation of coupled-climate and ocean-only biogeochemical models. Users of SOCAT data products are urged to acknowledge the contribution of data providers, as stated in the SOCAT Fair Data Use Statement. This ESSD (Earth System Science Data) “living data” publication documents the methods and data sets used for the assembly of this new version of the SOCAT data collection and compares these with those used for earlier versions of the data collection (Pfeil et al., 2013; Sabine et al., 2013; Bakker et al., 2014). Individual data set files, included in the synthesis product, can be downloaded here: 10.1594/PANGAEA.849770. The gridded products are available here: 10.3334/CDIAC/OTG.SOCAT_V3_GRID.

In this study, we present the first combined open- and coastal-ocean pCO2 mapped monthly climatology (, 10.25921/qb25-f418, https://www.nodc.noaa.gov/ocads/oceans/MPI-ULB-SOM_FFN_clim.html, last access: 8 April 2020) constructed from observations collected between 1998 and 2015 extracted from the Surface Ocean CO2 Atlas (SOCAT) database. We combine two neural network-based pCO2 products, one from the open ocean and the other from the coastal ocean, and investigate their consistency along their common overlap areas. While the difference between open- and coastal-ocean estimates along the overlap area increases with latitude, it remains close to 0 µatm globally. Stronger discrepancies, however, exist on the regional level resulting in differences that exceed 10 % of the climatological mean pCO2, or an order of magnitude larger than the uncertainty from state-of-the-art measurements. This also illustrates the potential of such an analysis to highlight where we lack a good representation of the aquatic continuum and future research should be dedicated. A regional analysis further shows that the seasonal carbon dynamics at the coast–open interface are well represented in our climatology. While our combined product is only a first step towards a true representation of both the open-ocean and the coastal-ocean air–sea CO2 flux in marine carbon budgets, we show it is a feasible task and the present data product already constitutes a valuable tool to investigate and quantify the dynamics of the air–sea CO2 exchange consistently for oceanic regions regardless of its distance to the coast.

Ocean acidification has profoundly altered the ocean's carbonate chemistry since preindustrial times, with potentially serious consequences for marine life. Yet, no long-term, global observation-based data set exists that allows us to study changes in ocean acidification for all carbonate system parameters over the last few decades. Here, we fill this gap and present a methodologically consistent global data set of all relevant surface ocean parameters, i.e., dissolved inorganic carbon (DIC), total alkalinity (TA), partial pressure of CO2 (pCO2), pH, and the saturation state with respect to mineral CaCO3 (Ω) at a monthly resolution over the period 1985 through 2018 at a spatial resolution of 1∘×1∘. This data set, named OceanSODA-ETHZ, was created by extrapolating in time and space the surface ocean observations of pCO2 (from the Surface Ocean CO2 Atlas, SOCAT) and total alkalinity (TA; from the Global Ocean Data Analysis Project, GLODAP) using the newly developed Geospatial Random Cluster Ensemble Regression (GRaCER) method (code available at https://doi.org/10.5281/zenodo.4455354, Gregor, 2021). This method is based on a two-step (cluster-regression) approach but extends it by considering an ensemble of such cluster regressions, leading to improved robustness. Surface ocean DIC, pH, and Ω were then computed from the globally mapped pCO2 and TA using the thermodynamic equations of the carbonate system. For the open ocean, the cluster-regression method estimates pCO2 and TA with global near-zero biases and root mean squared errors of 12 µatm and 13 µmol kg−1, respectively. Taking into account also the measurement and representation errors, the total uncertainty increases to 14 µatm and 21 µmol kg−1, respectively. We assess the fidelity of the computed parameters by comparing them to direct observations from GLODAP, finding surface ocean pH and DIC global biases of near zero, as well as root mean squared errors of 0.023 and 16 µmol kg−1, respectively. These uncertainties are very comparable to those expected by propagating the total uncertainty from pCO2 and TA through the thermodynamic computations, indicating a robust and conservative assessment of the uncertainties. We illustrate the potential of this new data set by analyzing the climatological mean seasonal cycles of the different parameters of the surface ocean carbonate system, highlighting their commonalities and differences. Further, this data set provides a novel constraint on the global- and basin-scale trends in ocean acidification for all parameters. Concretely, we find for the period 1990 through 2018 global mean trends of 8.6 ± 0.1 µmol kg−1 per decade for DIC, −0.016 ± 0.000 per decade for pH, 16.5 ± 0.1 µatm per decade for pCO2, and −0.07 ± 0.00 per decade for Ω. The OceanSODA-ETHZ data can be downloaded from https://doi.org/10.25921/m5wx-ja34 (Gregor and Gruber, 2020).

A new feed-forward neural network (FFNN) model is presented to reconstruct surface ocean partial pressure of carbon dioxide (pCO2) over the global ocean. The model consists of two steps: (1) the reconstruction ofpCO2 climatology, and (2) the reconstruction ofpCO2 anomalies with respect to the climatology. For the first step, a gridded climatology was used as the target, along with sea surface salinity (SSS), sea surface temperature (SST), sea surface height (SSH), chlorophyll a (Chl a), mixed layer depth (MLD), as well as latitude and longitude as predictors. For the second step, data from the Surface Ocean CO2 Atlas (SOCAT) provided the target. The same set of predictors was used during step (2) augmented by their anomalies. During each step, the FFNN model reconstructs the nonlinear relationships between pCO2 and the ocean predictors. It provides monthly surface ocean pCO2 distributions on a 1∘×1∘ grid for the period from 2001 to 2016. Global ocean pCO2 was reconstructed with satisfying accuracy compared with independent observational data from SOCAT. However, errors were larger in regions with poor data coverage (e.g., the Indian Ocean, the Southern Ocean and the subpolar Pacific). The model captured the strong interannual variability of surface oceanpCO2 with reasonable skill over the equatorial Pacific associated with ENSO (the El Niño–Southern Oscillation). Our model was compared to three pCO2 mapping methods that participated in the Surface Ocean pCO2 Mapping intercomparison (SOCOM) initiative. We found a good agreement in seasonal and interannual variability between the models over the global ocean. However, important differences still exist at the regional scale, especially in the Southern Hemisphere and, in particular, in the southern Pacific and the Indian Ocean, as these regions suffer from poor data coverage. Large regional uncertainties in reconstructed surface ocean pCO2 and sea–air CO2 fluxes have a strong influence on global estimates of CO2 fluxes and trends.

We report global long-term trends in surface ocean pH using a new pH data set computed by combining fCO2 observations from the Surface Ocean CO2 Atlas (SOCAT) version 2 with surface alkalinity estimates based on temperature and salinity. Trends were determined over the periods 1981–2011 and 1991–2011 for a set of 17 biomes using a weighted linear least squares method. We observe significant decreases in surface ocean pH in ~70% of all biomes and a mean rate of decrease of 0.0018 ± 0.0004 yr−1 for 1991–2011. We are not able to calculate a global trend for 1981–2011 because too few biomes have enough data for this. In half the biomes, the rate of change is commensurate with the trends expected based on the assumption that the surface ocean pH change is only driven by the surface ocean CO2 chemistry remaining in a transient equilibrium with the increase in atmospheric CO2. In the remaining biomes, deviations from such equilibrium may reflect that the trend of surface ocean fCO2 is not equal to that of the atmosphere, most notably in the equatorial Pacific Ocean, or may reflect changes in the oceanic buffer (Revelle) factor. We conclude that well-planned and long-term sustained observational networks are key to reliably document the ongoing and future changes in ocean carbon chemistry due to anthropogenic forcing.

Seawater absorption of anthropogenic atmospheric carbon dioxide (CO2) has led to a range of changes in carbonate chemistry, collectively referred to as ocean acidification. Stoichiometric dissociation constants used to convert measured carbonate system variables (pH,pCO2, dissolved inorganic carbon, total alkalinity) into globally comparable parameters are crucial for accurately quantifying these changes. The temperature and salinity coefficients of these constants have generally been experimentally derived under controlled laboratory conditions. Here, we use field measurements of carbonate system variables taken from the Global Ocean Data Analysis Project version 2 and the Surface Ocean CO2 Atlas data products to evaluate the temperature dependence of the carbonic acid stoichiometric dissociation constants. By applying a novel iterative procedure to a large dataset of 948 surface-water, quality-controlled samples where four carbonate system variables were independently measured, we show that the set of equations published by Lueker et al. (2000), currently preferred by the ocean acidification community, overestimates the stoichiometric dissociation constants at temperatures below about 8 ∘C. We apply these newly derived temperature coefficients to high-latitude Argo float and cruise data to quantify the effects on surface-water pCO2 and calcite saturation states. These findings highlight the critical implications of uncertainty in stoichiometric dissociation constants for future projections of ocean acidification in polar regions and the need to improve knowledge of what causes the CO2 system inconsistencies in cold waters.

We developed a simple method to refine existing open-ocean maps and extend them towards different coastal seas. Using a multi-linear regression we produced monthly maps of surface ocean fCO2 in the northern European coastal seas (the North Sea, the Baltic Sea, the Norwegian Coast and the Barents Sea) covering a time period from 1998 to 2016. A comparison with gridded Surface OceanCO2 Atlas (SOCAT) v5 data revealed mean biases and standard deviations of 0 ± 26 µatm in the North Sea, 0 ± 16 µatm along the Norwegian Coast, 0 ± 19 µatm in the Barents Sea and 2 ± 42 µatm in the Baltic Sea. We used these maps to investigate trends in fCO2, pH and air–seaCO2 flux. The surface ocean fCO2 trends are smaller than the atmospheric trend in most of the studied regions. The only exception to this is the western part of the North Sea, where sea surface fCO2 increases by 2 µatmyr-1, which is similar to the atmospheric trend. The Baltic Sea does not show a significant trend. Here, the variability was much larger than the expected trends. Consistently, the pH trends were smaller than expected for an increase in fCO2 in pace with the rise of atmosphericCO2 levels. The calculated air–sea CO2 fluxes revealed that most regions were net sinks for CO2. Only the southern North Sea and the Baltic Sea emitted CO2 to the atmosphere. Especially in the northern regions the sink strength increased during the studied period.

The seasonal variability of mode-1 M 2 internal tides is investigated using 25 years of multi-satellite altimeter data from 1992–2017. Four seasonal internal tide models are constructed using seasonally-subsetted altimeter data and World Ocean Atlas seasonal climatologies. This work is made possible by a newly-developed mapping procedure that can significantly suppress model errors. Seasonal-mean and seasonally-variable internal tide models are derived from the four seasonal models. All the models are inter-compared and evaluated using independent CryoSat-2 data. The seasonal-mean model is overall the best model because averaging the four seasonal models further reduces model errors. The seasonally-variable models are better in the tropical zone, where large seasonal signals may overcome model errors. Each seasonal model works best in its own season and worst in its opposite season. These internal tide models reveal that mode-1 M 2 internal tides are subject to significant seasonal variability and their seasonal variations are a function of location. Large seasonal variations dominantly occur in the tropical zone, where the World Ocean Atlas climatology shows strong seasonal variations in ocean stratification. Seasonal phase variations are obtained from the directionally-decomposed internal tide components. They are dominantly ±60° at the equator and up to ±120° in the central Arabian Sea. Incoherence caused by seasonal phase variations is usually <10%, but may be up to 40–50% in the tropical zone.