# Persistent Coastal Temperature Biases in km-Scale Climate Models Due To Unresolved Oceanic Tidal Mixing

Audrey Delpech, Anne-marie Tréguier, Louis Marié, Rohit Ghosh, Malcolm Roberts

► To cite this version:

Audrey Delpech, Anne-marie Tréguier, Louis Marié, Rohit Ghosh, Malcolm Roberts. Persistent Coastal Temperature Biases in km-Scale Climate Models Due To Unresolved Oceanic Tidal Mixing. Geophysical Research Letters, 2025, 52 (19), 10.1029/2025GL118014. http://dx.doi.org/10.1029/2025GL118014

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# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2025GL118014

**Key Points:**

* Systematic warm sea surface temperature biases are identified in summer on oceanic continental shelves in climate models

* The biases correspond to the location of tidal mixing fronts induced by barotropic tidal dissipation

* These oceanic biases also induce atmospheric temperature biases over sea and land

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

A. Delpech,
audrey.delpech@cnrs.fr

**Citation:**

Delpech, A., Tréguier, A.-M., Marié, L., Ghosh, R., & Roberts, M. J. (2025). Persistent coastal temperature biases in km-scale climate models due to unresolved oceanic tidal mixing. *Geophysical Research Letters*, *52*, e2025GL118014.
https://doi.org/10.1029/2025GL118014

Received 9 JUL 2025
Accepted 15 SEP 2025

© 2025. The Author(s).
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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## Persistent Coastal Temperature Biases in km-Scale Climate Models Due To Unresolved Oceanic Tidal Mixing

Audrey Delpech¹ ID, Anne-Marie Tréguier¹ ID, Louis Marié¹ ID, Rohit Ghosh², and Malcolm J. Roberts³ ID

¹Laboratoire d'Océanographie Physique et Spatiale, CNRS, Ifremer, IRD, University of Brest, Plouzané, France, ²Alfred Wegner Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, ³Met Office Hadley Center, Exeter, UK

**Abstract** Recent advances in numerical modeling have enabled km-scale climate simulations, improving global climate representation and local-scale projections, critical to climate adaptation strategies. In this context, the present study assesses the performance of such models over coastal shelf seas—key climate-sensitive regions—in their ability to represent the sea surface temperature (SST) and air temperature. Compared to satellite and reanalysis data, the models exhibit systematic warm biases (~3°C in SST, ~1.5°C in air temperature) in summer across several shelf seas: the European shelf, the Gulf of Maine, the Yellow sea, the Arctic and Patagonian shelves. These biases strongly correlate with tidal mixing fronts, driven by the dissipation of the barotropic tide and identified by the Simpson-Hunter parameter. These findings suggest that missing tidal mixing is a significant error source on coastal shelves, highlighting the need for improved ocean mixing representations to enhance model accuracy.

**Plain Language Summary** The latest climate models can now provide more detailed information about local climates, which is important for helping populations prepare for climate change. This study looks at how well these models perform in shallow coastal seas around the world. We found that these models often overestimate temperatures in certain coastal areas, especially in the summer. The study shows that the warm temperature errors are linked to strong tidal currents, that can affect how the heat is mixed in the ocean. The current models do not include this mixing process well, which leads to errors in the representation of oceanic temperature. These errors also affect air temperatures over the sea and nearby land. Improving how tides and ocean mixing are represented in climate models could make local climate predictions more accurate.

## 1. Introduction

Coastal oceans are crucial for the climate system and provide major ecosystem services. Among other, they account for ~20% of total oceanic carbon sequestration (DeVries et al., 2023; Roobaert et al., 2024) and harbor 90% of aquaculture and fisheries areas on which 600 million people live worldwide (FAO, 2024). Despite the crucial importance of coastal and shelf seas, they are very often poorly represented in global ocean and climate models (Holt et al., 2017). However, recently developed high-resolution (ocean resolution <20 km) climate models from the High Resolution Model Intercomparison Project (HighResMIP) (Haarsma et al., 2016; M. J. Roberts et al., 2025) offer new capabilities for downscaling climate information at the scale needed for climate adaptation policies and climate services (M. Roberts et al., 2018). At the same time, this brings up the necessity to evaluate the accuracy of these models not only globally but also at a regional scale, and in particular in coastal regions.

In this study, we propose to evaluate the representation of the SST in the coastal ocean in 8 high-resolution coupled climate models participating in HighResMIP. We will in particular address the following questions: (a) What are the dominant processes underlying SST biases on the shelf in climate models?; and (b) What are the implications for the local ocean-atmosphere coupled system?

Sea surface temperature (SST) in coastal oceans is governed by a variety of multiscale processes (Simpson & Sharples, 2012): currents and eddies, setting up the horizontal SST structures; wind-driven upwelling and downwelling, modulating the SST on daily to seasonal timescales; rivers, inducing changes in surface stratification and therefore in the penetration of the atmospheric radiative fluxes; and tides, inducing mixing in the bottom boundary layer that can decrease the SST if it reaches the surface. SST cooling due to tidal mixing
generally occurs onshore of tidal mixing fronts, which delineate the boundary between regions where the tidal mixing dominate the seasonal stratification and regions where the seasonal stratification dominates the tidal mixing. Previously reported locations of tidal mixing fronts include: the Northwestern European Shelf (Pingree & Griffiths, 1978; Simpson & Hunter, 1974), the Northeastern American Shelf: Gulf of Maine and Gulf of Saint Laurent (Garrett et al., 1978), the Hudson Bay (Canadian Arctic) (Griffiths et al., 1981), the Patagonian Shelf (Glorioso, 1987), the Northeastern Australian Shelf (Timko et al., 2019), the China Shelf Seas: Yellow Sea and South China Sea (Hu et al., 2003; Lie, 1989), the Sea of Okhotsk (Zhabin & Dubina, 2012), the East Bering Sea (Schumacher et al., 1979). See also Belkin et al. (2009) and Timko et al. (2019) for a review. These fronts generally emerge in late spring and summer, when the setup of the seasonal stratification offshore of the front increases the cross-front gradient and disappear in winter (Belkin et al., 2009).

Using twin global hindcasts forced with an atmospheric reanalysis, Timko et al. (2019) have shown significant SST differences on the continental shelves between simulations with and without tides. Subsequently, focusing on the Northwestern European shelf and using an ocean-atmosphere coupled hindcast, Arnold et al. (2021) have quantified the surface temperature differences over Great Britain and the British seas, with and without tides. They found a decrease in summer SST of 6°C with tides compared to without tides, a decrease in air surface temperature of 3°C above the sea, 1.5°C above the coastal land and 0.3°C on average over Great Britain. To a lesser extent, they also found a decrease in winds and precipitations over Great Britain in the simulation with tides. This is the first study to show the link between oceanic tides and meteorological conditions. However, this study has two main limitations: First, the influence of oceanic tides on atmospheric conditions has been investigated for a single year (2018), with a particularly warm summer, that could overestimate the observed differences. Second, the study does not evaluate the potential impact of oceanic tides on the oceanic and atmospheric temperatures on a global scale, and it is unclear whether this retroaction is specific to the British seas or can also be found in other shelf seas.

To our knowledge, the accuracy of SST representation on the continental shelves and its impact on the atmospheric temperature has never been assessed in climate models on a global scale, and is therefore the focus of this paper.

The remainder of this paper is organized as follows: Section 2 describes the set of high-resolution climate models used for this study and the observations chosen for bias computation. Section 3 describes the SST biases in the global coastal ocean, their correlation with tidal mixing fronts and their relation to atmospheric temperature biases. Finally, Section 4 discusses some future pathways for improving the representation of coastal temperatures in climate models.

## 2. Data and Method

### 2.1. Climate Models and Simulations

The analyses conducted in this study are based on HighResMIP climate simulations. HighResMIP is a protocol designed to investigate the impact of increased resolution in global climate models on the representation of climate processes. It includes coupled ocean-atmosphere simulations, with horizontal resolutions ranging from standard (~100 km) to high (<25 km), enabling improved representation of phenomena such as tropical cyclones or ocean eddies, with a common experimental protocol to facilitate inter-model comparisons (Haarsma et al., 2016). HighResMIP protocol provides a control simulation with constant 1950 forcing from 1950 until 2050, a historical simulation including anthropogenic forcing from 1950 until 2014 and future scenarios from 2015 to 2050. Here we evaluate the SST and the 2m-air temperature from the historical simulations of 8 high-resolution coupled climate models following the HighResMIP protocol (Table S1 in Supporting Information S1). This set of models ensures a diversity in dynamical core components, set up and parameterization. It includes standard HighResMIP eddy permitting (~20 km) models like EC-Earth3P-HR (Haarsma et al., 2020), CNRM-CM6-1-HR (Voldoire et al., 2019), BCC-CSM2-HR (Wu et al., 2021), CMCC-CM2-VHR4 (Scocchi-marro et al., 2022) and ECMWF-IFS-HR (C. D. Roberts et al., 2018), and a few more recent and higher resolution eddy-rich models, up to 6 km horizontal resolution on the mid-latitude shelves: HadGEM-GC31-HH (M. J. Roberts et al., 2019), CESM1-CAM5-SE-HR (Chang et al., 2020), AWI-IFS-FESOM-ER (Ghosh et al., 2025).
## 2.2. Observations

The climate models SST and 2 m air temperature are evaluated against observations. Sea surface temperature observations are taken from the Climate Change Initiative Sea Surface Temperature data set from the European Space Agency (ESA-CCI SST), which provides a consistent, long-term record of global SST derived from satellite observations. The product merges data from multiple satellites including three series of infrared sensors and two series of microwave sensors. The data set provides daily-averaged SST on a 0.05° grid from 1981 to the present (Merchant et al., 2019). A sensitivity analysis of the results of this study has been conducted and shows that the results are not sensitive to the choice of the observation product. As an example, Figure S1 in Supporting Information S1 shows the bias of another SST data set (EN4, Good et al. (2013)) relative to ESA-CCI SST. The inter-product biases are very small and uniform and cannot be responsible for the biases discussed in the next sections. Air surface temperatures (at 2 m) are taken from ERA5. ERA5 is the fifth-generation global atmospheric reanalysis produced by the European Center for Medium-Range Weather Forecasts (ECMWF). It provides hourly estimates of a wide range of atmosphere, ocean, and land variables, from 1940 to the present, on a 31 km grid. ERA5 integrates observations from satellites, weather stations, radiosondes, and other platforms using advanced data assimilation and modeling techniques (Hersbach et al., 2020).

## 2.3. Bias Computation

Model temperatures and observations are regridded on a common 0.25° grid using a bilinear interpolation. This ensures that the same observation field is subtracted for all models. The biases are computed as: model temperature - observations. Mean biases are computed over a period of 30 years (1985–2014), corresponding to the last 30 years of the historical simulation. These mean biases are computed for two different seasons: winter, corresponding to the mean of January, February and March in the northern hemisphere and to the months of July, August and September in the southern hemisphere, and summer, with the reversed definition.

Note that the bias computations have also been tested for different averaging periods (10, 20 and 30 years) and for different season definitions: December, January, February and June, July, August for winter and summer in the northern hemisphere respectively (not shown). Our results have proven insensitive to the length of the period and to the definition of the winter and summer seasons.

## 2.4. $S_h$ Computation

The local balance between tidal mixing and stratification on a shallow shelf sea can be measured with the ratio (Pingree & Griffiths, 1978):

$$R = \frac{g\alpha Q h (2C_p)^{-1}}{\rho C_d |\mathbf{u}|^3} \quad (1)$$

where $g$ is the gravitational acceleration, $\alpha$ is the thermosteric expansion coefficient, $Q$ is the net downward surface heat flux, $h$ is the depth of the water column, $C_p$ is the specific heat at constant pressure, $\rho$ is the density of sea water, $C_d$ is the bottom drag coefficient and $|\mathbf{u}|$ is the depth-averaged (barotropic) velocity. $R \gg 1$ represents stratified conditions, $R \ll 1$ represents mixed conditions, and mixing fronts are found near $R \sim 1$. Assuming that $g, \alpha, C_p, C_d, \rho, Q$ are uniform on a regional scale, the ratio can be approximated by the Simpson-Hunter parameter (Simpson & Hunter, 1974):

$$S_h = \log_{10} \left( \frac{h}{|\mathbf{u}|^3} \right) \quad (2)$$

which is often used to predict the location of tidal mixing fronts. Note that, as it includes only the barotropic tidal currents, this coefficient scales only the barotropic tidal mixing to the local stratification and does not account for the baroclinic tidal mixing associated with the shoaling and breaking of tidal internal waves.

In this paper, $h$ is taken from GEBCO (Weatherall et al., 2024)—a global terrain model providing land and seabed elevation data on a 30 arc-second (1/120°) grid from a combination of ship-based soundings and satellite altimetry; and $|\mathbf{u}|$ is taken from FES2014 (Lyard et al., 2021)—a global ocean tide model developed by
assimilating satellite altimetry into an hydrodynamic model. It provides an estimation of tidal elevations (amplitude and phase), tidal currents (u and v) and tidal loading on a 1/16° grid for 34 tidal constituents (including M₂, S₂, O₁, K₁, etc.). Here we take |u| as the module of the sum of all tidal constituents velocity, |u| = (Σₙ(uₙ² + vₙ²))¹/² where n ∈ {M₂, S₂, O₁, K₁...}.

3. Results

3.1. Sea Surface Temperature Biases on the Shelves

In summer, the SST bias patterns present striking similarities on the continental shelves from one model to another (Figure 1), leading to persistent warm biases in the multi-model mean at specific locations on the shelves. In the Gulf of Maine and bay of Fundy on the Northeastern American shelf, the biases are the largest, exceeding 6°C in some models like the AWI model (Figure 1b, Table S1 in Supporting Information S1) and 4°C in the multi-model mean (Figure 1e). Strong warm biases of 3°C in the multi-model mean can also be found on the North-western European Shelf, in the Channel Sea between France and Great Britain, in the Irish Sea between Ireland and Great Britain and in the North Sea, east of Great Britain (Figures 1a–1e, middle). In the Yellow Sea warm biases can be found along the coast of China, North and South Korea (Figures 1a–1e, right). Other warm biases can be found in the Eastern Bering Sea, in the Foxe basin (Canadian Arctic), with amplitude exceeding 3°C, on the Patagonian shelf, in the White Sea (Russian Arctic) and to a lesser extent on the Northern Australian shelf.

In winter, the SST biases are quite different from one model to another, leading to a small residual in the multi-model mean. However, some small amplitude cold biases (1.5–2°C) appear around Great Britain, on the Northwestern European Shelf; in the Gulf of Maine on the Northeastern American Shelf and along the coast of South Korea in the Yellow Sea, up to 3°C (Figure S2 in Supporting Information S1). Overall, these cold winter shelf biases are found roughly at the same locations as the warm summer biases.

These persistent biases point toward a missing physical process. Indeed, the errors and biases in models that are associated with the chaotic nature of climate variability, generally have a random phase across models (Raäi-sänen, 2007). These biases are averaged out by the 30-year and the multi-model means. The only reasonable explanation for such different models with different set-up and parameterization to exhibit a common bias pattern is therefore a missing physical process (e.g., Bock et al. (2020)). This is investigated in the next section.

3.2. Correlation With Tidal Mixing Fronts

Barotropic tides are not included in climate models; hence, the tidal mixing associated with their dissipation is also overlooked. The dissipation of barotropic tides occurs mostly in coastal regions and increases mixing in the bottom boundary layer. In specific regions where the tidal currents are strong and/or the water depth is small, it can dominate over the local stratification and mix the whole water column (Simpson & Sharples, 2012). The local balance between tidal mixing and stratification can be inferred from the S<sub>h</sub> parameter (Section 2.4). Regions where tidal mixing dominates over seasonal stratification correspond to low S<sub>h</sub> values. Such low S<sub>h</sub> values can be found in the Northwestern European shelf, in the Foxe Basin, the Northeastern American shelf, the Amazon and Patagonian shelves, the Yellow Sea, the Northwestern Australian shelf and the East Bering Sea (Figure 2), consistent with the location of the main tidal mixing fronts previously reported (Section 1, and Belkin et al. (2009); Timko et al. (2019)).

These regions are also where persistent warm SST biases are found in summer across the different climate models (Figure 1). Figure 2c further emphasizes the statistical relationship between low S_h values and warm SST biases by showing the scatterplot of the grid cells in the (SST bias, S_h) plane for the three example regions. For each region, a k-means clustering analysis (Kanungo et al., 2002) reveals two clusters of points (see Table S2 in Supporting Information S1 for the Silhouette score (Shahapure & Nicholas, 2020) selecting the optimal number of clusters): a first one (Cluster 1) with low S_h values and large positive SST biases (centers at 2.2°C, 1.1°C and 0.7°C for the Northeastern American shelf, the Northwestern European shelf and the Yellow Sea respectively), and a second cluster (Cluster 2) with large S_h values and nearly zero or negative SST biases (centers at -0.7°C, 0.1°C and 0.2°C respectively). The distributions of SST bias for the two clusters have a distinct mode in each region, with Cluster 1 having a much larger positive tail (Figure 2d). Finally, the Pearson correlation coefficients between S_h and the SST bias are one or two order of magnitude higher for Clusters 1 than for Clusters 2 (Table S3
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Sea surface temperature (SST) bias on the continental shelves in summer averaged over 1985–2014, (a) multi-model mean global; (b) AWI model, (c) CMCC model; (d) NCAR model and (e) multi-model mean (see Table S1 in Supporting Information S1) for three example shelves: the Northeastern American shelf (left), the Northwestern European shelf (middle), and the Yellow Sea (right). The black contours correspond to the isobaths (200, 500 and 1,000 m) and delineate the shelf break. Squared regions correspond to regions with consistently warm summer SST biases. The hatches correspond to biases < ±0.5°C.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** (a) Simpson-Hunter parameter *S*<sub>*h*</sub> over the global continental shelf. Regions with low *S*<sub>*h*</sub> values, in which tidal mixing dominates the seasonal stratification, are highlighted in square boxes. (b) Zoom in example regions (from left to right): the Northeastern American Shelf, the Northwestern European Shelf and the Yellow Sea. (c) Scatter plot of the grid cells of the region in the plane (SST bias, *S*<sub>*h*</sub>) colored by their cluster belonging as determined by the *k*-means method, the center of each cluster in indicated in the legend. (d) Normalized histogram of binned SST bias for each cluster.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 3.** 2 m air temperature bias in summer averaged over 1985–2014, (a) multi-model mean global over the continental shelves; (b) multi-model mean, regional.</figcaption></figure>

in Supporting Information S1). This shows the strong correlation between low $S_h$ values (i.e., high barotropic tidal mixing regions) and warm SST biases.

These results support the idea that the unresolved tidal mixing is responsible for these persistent SST biases. Indeed, on the continental shelves in summer, the net air-sea heat flux is generally positive for the ocean (the ocean is warmed up by the atmosphere) and increases the thermal stratification near the surface. Mixing inside tidal mixing fronts therefore has a cooling effect (mixing up warm surface water with cooler bottom water). Hence, the absence of tidal mixing will result in warm SST biases. In contrast, in winter, the net air-sea heat flux is generally negative for the ocean (the atmosphere is warmed up by the ocean), tidal mixing therefore has a warming effect (mixing up cool surface water with warmer bottom water). Hence, the absence of tidal mixing will result in cold SST biases. In winter however, the water column is generally well mixed due to stronger winds, storms and waves, reducing the effect of tidal mixing on the thermal stratification and SST, as seen from Figure S2 in Supporting Information S1.

### 3.3. Impact on the Atmospheric Temperature Biases

Tidal mixing fronts not only induce oceanic temperature biases but also atmospheric temperature biases. The 2 m air temperature summer bias shows that most coastal regions exhibiting a warm SST bias due to the missing tidal mixing also exhibit a warm air temperature bias above, up to 2°C (Figure 3a). This warm temperature bias can extend over land in some regions. For example, over the Northwestern European Shelf, a positive (warm) air temperature bias of 1.2°C is found over sea (Channel sea, Irish sea and North Sea along the Eastern shore of England), and a smaller but significant positive bias of 0.6°C is also found in the Southern part of England and in the Northwestern part of France, extending a few hundred kilometers inland from the shore (Figure 3b, middle). This is consistent with Arnold et al. (2021) who showed that the SST cooling induced by tidal mixing around Great Britain also impacts the temperature, wind and precipitation over land. For the Northeastern America
region, the warm air temperature bias is quite strong over the ocean, and reaches up to 2.7°C over the bay of Fundy, with only a very small extension inland (Figure 3b, left). The same is true for the Yellow Sea region, where the warm air temperature bias is very small over sea and land and does not exceed 0.4°C (Figure 3b, right).

However, we acknowledge that the biases that can be attributed to the tidal mixing fronts adds to biases from other sources. In particular, climate and atmospheric models are known to have cold biases over mountainous areas (Bock et al., 2020; Boer et al., 1992; Lalande et al., 2021; Mao & Robock, 1998), particularly in areas with topography and permanent snow or ice and can be partially attributed to a misrepresentation of snow-ice albedo and snow cover parameterization in models (Lalande et al., 2023). This is visible in Figure 3b, where cold biases are found over Newfoundland, Norway and Scotland, South Korea and Southeastern China. These cold biases can lead to an underestimation of the warm biases caused by the missing tidal mixing.

## 4. Discussion and Conclusions

The results presented here have shown a correlation between surface temperature biases (both oceanic and atmospheric) in climate models and regions marked by tidal fronts (Simpson Hunter parameter ≪1). These biases are systematic in all the models considered here, although they present a regional disparity: from 1°C to 4°C for SST, and from 1 to 2°C for 2 m air temperature. They are the dominant bias feature on the continental shelves in the multi-model mean, although air temperature biases are possibly underestimated due to a general cold bias over continental topography. Note that this study has been conducted using HighResMIP simulations only, with resolution <20 km in the ocean. However, the same biases are observed for CMIP-like simulations of resolution generally >20 km in the ocean (Figure S3 in Supporting Information S1). In these lower-resolution simulations, coastal areas are less well represented due to a simplified coastline and land-sea mask, making them less suitable for coastal climate studies. In addition, other sources of error have a larger imprint on coastal temperature in these simulations, making this bias less important relatively to others.

Overall, this study points toward the necessity of including barotropic tidal mixing in climate models for an accurate representation of oceanic and atmospheric temperatures in coastal regions. This can be achieved by explicitly representing the tides or parameterizing the barotropic tidal mixing. The explicit representation of tides is generally limited by the computational costs. Indeed, the fast tidal motions constrain the time step of the model (Müller et al., 2010; Song et al., 2023), which can become a limitation for climate simulations integrated over centuries. Moreover, an energetically consistent representation of tides requires to resolve tidal internal waves, which necessitates a spatial and temporal resolution that is too costly to achieve in climate simulations (Song et al., 2023). A useful compromise consist in downscaling climate projections using regional coupled models that resolve tides as in Chaigneau et al. (2022). Another solution would be to achieve a parameterization through the modification of the vertical eddy viscosity and diffusivity coefficients, that will act as an injection of turbulent kinetic energy in the water column. This approach has already been used to parameterize multiple unresolved mixing sources in the ocean, for example, the mixing associated with the dissipation of internal tides (de Lavergne et al., 2020). However, two main difficulties arise for the formulation of such a parameterization: The first difficulty is to define the spatial extent on which to apply the modification of the coefficients. A first avenue would be to rely on the Simpson-Hunter parameter, but as underlined by Timko et al. (2019), there is no universal threshold of this parameter that would describe the position of all fronts. In some regions, the fronts have been extensively sampled and empirical relationships allow to determine a local parameter threshold for the position of the fronts, but complementary approaches, such as satellite SST observations should be used for undersampled regions. The second difficulty is to define the magnitude of the added viscosity and diffusivity in an energetically consistent way (Lee et al., 2006). In situ microstructure turbulence measurements exist across these tidal mixing fronts (Palmer et al., 2008; Yoshida & Oakey, 1996) and should help dimensioning the parameterization, but such observations are scarce in space and time, while tidal mixing is most likely not uniform. This approach should certainly be complemented with dedicated simulation experiments to test and adjust the parameterized coefficients.

Finally, this paper has focused on the impact of the missing barotropic tidal mixing on the representation of the mean oceanic and atmospheric surface temperatures in climate models. Future perspectives include understanding these impacts on the representation of the temperature variance and extremes. Beyond the issue of the missing barotropic tidal mixing in climate models, this calls for a mechanistic understanding of tides and tidal mixing, including tidal internal waves dissipation on the shelf (McSweeney et al., 2020; Palóczy et al., 2021;
Siyanbola et al., 2024), and the impact of these processes on SST, regional heat budget and their variability. Their study could be achieved in twin coupled simulations with and without tidal forcing, such as the experimental framework proposed by Arnold et al. (2021).

## Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

## Data Availability Statement

All HighResMIP simulations used in this study are available on the Earth System Grid Federation platform and on the World Data Center for Climate catalogue under the following references. HadGEM-GC31-HH (Coward & Roberts, 2023); CESM1-CAM5-SE-HR (Hurrel et al., 2023); EC-Earth3P-HR (EC-Earth, 2023); BCC-CSM2-HR (Jie et al., 2023); CNRM-CM6-1-HR (Voldoire, 2023); CMCC-CM2-VHR4 (Scoccimarro et al., 2023); ECMWF-IFS-HR (C. D. Roberts et al., 2023). The observation data sets used are also freely available: ESA SST CCI can be downloaded from the CEDA archive (Good & Embury, 2024). And ERA5 can be downloaded from the Copernicus Climate Data Store (Hersbach et al., 2023).

## Acknowledgments

This publication is part of the EERIE project. This project has received funding from the European Union's Horizon Europe research and innovation program under Grant Agreement number 101081383. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Climate Infrastructure and Environment Executive Agency (CINEA). Neither the European Union nor the granting authority can be held responsible for them. All UK partners are funded by UK Research and Innovation (UKRI) under the UK government's Horizon Europe funding guarantee (Grant 10057890).

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