Elsevier

Ocean Modelling

Volume 136, April 2019, Pages 66-84
Ocean Modelling

Assessment of shelf sea tides and tidal mixing fronts in a global ocean model

https://doi.org/10.1016/j.ocemod.2019.02.008Get rights and content

Highlights

  • We perform a first order assessment of the skill of HYCOM tides in the coastal and shelf seas.

  • RMSE for tidal heights represents 23–35% of the RMS amplitude in the coastal and shelf seas of global HYCOM.

  • Inclusion of tides in global HYCOM has a visible impact on SST in coastal and shelf seas.

  • HYCOM with embedded tides reproduces known seasonal tidal mixing fronts in their expected location.

  • We provide evidence for the existence of tidal mixing fronts on the North West Australian Shelf.

Abstract

Tidal mixing fronts, which represent boundaries between stratified and tidally mixed waters, are locations of enhanced biological activity. They occur in summer shelf seas when, in the presence of strong tidal currents, mixing due to bottom friction balances buoyancy production due to seasonal heat flux. In this paper we examine the occurrence and fidelity of tidal mixing fronts in shelf seas generated within a global 3-dimensional simulation of the HYbrid Coordinate Ocean Model (HYCOM) that is simultaneously forced by atmospheric fields and the astronomical tidal potential. We perform a first order assessment of shelf sea tides in global HYCOM through comparison of sea surface temperature, sea surface tidal elevations, and tidal currents with observations. HYCOM was tuned to minimize errors in M2 sea surface heights in deep water. Over the global coastal and shelf seas (depths <200 m) the area-weighted root mean square error of the M2 sea surface amplitude in HYCOM represents 35% of the 50 cm root mean squared M2 sea surface amplitude when compared to satellite constrained models TPXO8 and FES2014. HYCOM and the altimeter constrained tidal models TPXO8 and FES2014 exhibit similar skill in reproducing barotropic tidal currents estimated from in-situ current meter observations. Through comparison of a global HYCOM simulation with tidal forcing to a global HYCOM simulation with no tides, and also to previous regional studies of tidal mixing fronts in shelf seas, we demonstrate that HYCOM with embedded tides exhibits quite high skill in reproducing known tidal mixing fronts in shelf seas. Our results indicate that the amount of variability in the location of the tidal mixing fronts in HYCOM, estimated using the Simpson-Hunter parameter, is consistent with previous studies when the differences in the net downward heat flux, on a global scale, are taken into account. We also provide evidence of tidal mixing fronts on the North West Australian Shelf for which we have been unable to find references in the existing scientific literature.

Introduction

The coastal and shelf seas represent less than 10% of the world's oceans yet have an important role in primary production and the global carbon cycle. This role, however, is poorly understood (Bauer et al., 2013). On a regional scale there are many different factors, such as riverine input, sediment transport, nutrient availability, coastal geometry and bathymetry that may affect the local biogeochemical cycle. Local mixing rates within the water column impact pelagic ecosystems and may enhance or inhibit growth rates. Within coastal and shelf seas the boundary between mixed and stratified waters is represented by persistent seasonal mixing fronts that occur when mixing due to tidal and wind forcing balances buoyancy production due to surface heat flux. Such fronts are regions of high biological activity and hence can be expected to play a role in the biogeochemical cycle. Belkin et al. (2009) provides a comprehensive review of the location of known oceanic fronts based upon satellite sea surface temperature observations in selected large marine ecosystems.

Coastal and shelf seas are also regions of large tidal energy dissipation. Egbert and Ray (2003) estimated that about 2/3 of the total M2 tidal dissipation occurs in shallow seas. Tidal mixing also influences coastal sea surface temperatures, which impact regional climates. Hence the accuracy of tides in the coastal regions of global tide models needs to be assessed.

Most modelling studies of coastal and shelf seas are conducted using limited area regional models. Very few modelling studies (e.g. Holt et al., 2009) have been conducted to model the global coastal ocean. Recent developments of the global version of the HYbrid Coordinate Ocean Model (HYCOM: Chassignet et al., 2009) include the implementation of a forward tide algorithm based upon astronomical arguments (Arbic et al., 2010, Arbic et al., 2012, Arbic et al., 2018). At current horizontal grid resolutions of 1/12.5° and 1/25° global HYCOM is able to resolve the continental margins and hence is able to resolve features such as mixing fronts in the coastal and shelf seas. Previous studies of the skill of global HYCOM with embedded tides have examined the sea surface elevation signature of surface and internal tides (Ansong et al., 2015; Ngodock et al., 2016; Savage et al., 2017; Shriver et al., 2012, Shriver et al., 2014; Stammer et al., 2014), tidal currents (Timko et al., 2012, Timko et al., 2013), and barotropic and baroclinic tidal energetics (Ansong et al., 2017; Buijsman et al., 2015, Buijsman et al., 2016). Most of the aforementioned HYCOM studies have focussed on model performance in deep waters, where water column depth exceeds 1000 m or 1500 m. Stammer et al. (2014) briefly discussed HYCOM tidal elevation errors over the shelf seas. Savage et al. (2017) compared tidal elevation variances in HYCOM vs. tide gauges. In this paper we focus on a comparison of HYCOM tidal elevations and currents vs. observations on the shelf, and we investigate the occurrence and location of tidal mixing fronts in a global HYCOM simulation.

Accurate simulation of tides in coastal and shelf regions requires accurate tidal forcing at the shelf edge and good representation of shallow water processes such as bottom friction and features such as coastline geometry and bathymetry. Such factors influence the propagation and superposition of tidal constituents on the shelf as well as mixing in the continental margins. Within these shallow regions the dissipation of tidal energy is primarily due to bottom friction. As discussed in Arbic et al. (2010) and Buijsman et al. (2016) HYCOM uses an internal wave drag scheme applied in the bottom 500 m of the water column to improve the accuracy of sea surface M2 tidal heights over deep water (>1500 m). The wave drag scheme is not applied when the water column is <500 m depth. In this paper we examine HYCOM skill in replicating observed tides in regional and shelf seas where water column depth is, typically, 200 m or less.

A mixing front represents the location where the water column changes from being stratified to well-mixed. A simple measure of stratification is the difference, ΔT = SST − SBT, between the sea surface temperature (SST) and seabed temperature (SBT). Wind driven mixing can be expected to maintain well-mixed waters (ΔT ≤ 0.5 °C) when the water column depth is <30 m (Bowers and Simpson, 1987). Strong currents produce bottom friction that results in additional mixing (Simpson, 1981). Tidal mixing fronts form in water column depths between 50 and 100 m when mixing due to dissipation of tidal currents balances buoyancy production due to incoming solar radiation (Simpson and Hunter, 1974). The ΔT = 0.5 °C degree contour may be somewhat ambiguous for determination of the mixing front locations. Another measure of the stratification, based upon the potential energy anomaly,φ=1hh0ρρ¯gzdzρ¯=1hh0ρdzmay be used to define the location of a mixing front whereby |∇φ| exceeds a threshold value as φ → 0 (J. Simpson, personal communication). Within this paper we identify mixing front locations using the ΔT = 0.5 °C degree contour and also define fronts as those regions for which |∇φ| > 2.5 ⋅ 10−4 and φ < 10 J m−3. In general, we find that the ΔT = 0.5 °C degree contour provides a reasonable proxy for the location of mixing fronts identified using the potential energy anomaly. Identification of mixing front locations using the ΔT = 0.5 °C contour is useful as the potential energy anomaly and its gradient are more computationally expensive to estimate.

The balance between tidal dissipation and buoyancy production may be defined by the ratio, R, (Pingree and Griffiths, 1978):R=gαQh/2CpρCdu3,where g is the acceleration due to gravity, α is the volume coefficient of expansion, Q is the net downward surface heat flux, h is the depth of the water column, Cp is the specific heat at constant pressure, ρ is the density of seawater, Cd is the bottom drag coefficient, and u is the depth averaged velocity. On a regional scale g, α, Cp, ρ, Cd may be assumed constant so that:RQhu3.R is non-dimensional hence we can rewrite Eq. (2a) as:log10R=log10gαQh/2CpρCdu3=log102CpρCd+log10Qhu3.

Assuming that g, α, Cp, ρ, Cd are constant (locally) then:log10R=C+log10Qhu3=C+SQ,where: C=log102CpρCd and:SQ=log10Qhu3.

Assuming: g ~ 9.81 ms−2, α ~ 2.1 · 10−4 °C−1 (when S = 34 PSU, T = 15 °C at zero pressure), Cp ~4000 J kg−1 °C−1, ρ ~ 1025 kg m−3, Cd ~ 0.0025 we have, C ~ −7.0. So that, to leading order, SQ ~ log10(R) - C = log10(R) + 7.0 represents the logarithm of the non-dimensional quantity, R. For temperatures between 5 and 25 °C and salinities between 30 and 35 PSU, the thermal heat flux, α, may vary between 1 · 10−4 and 3 · 10−4 which may also contribute to the global variation of log10(R). However, along an individual front the variation in α is expected to be small.

The Simpson-Hunter parameter, S = log10(hu−3) is often used to predict the location of tidal mixing fronts for constant heat flux, Q. Based upon over 13,000 historical observations of ΔT, Bowers and Simpson (1987) estimated that observed fronts on the Northwest European shelf (NWES) occur at a critical value S = 2.7 ± 0.4, with h and u measured in m and m s−1, respectively. Holt and Umlauf (2008) compared the output from a regional model of the NWES to the observed location of seasonal tidal mixing fronts based upon ~80,000 ΔT observations from the International Council for the Exploration of the Sea (ICES, 2014, http://geo.ices.dk) and found that the mean frontal position occurred at a critical value of the Simpson-Hunter parameter, S = 3.0 ± 0.3.

Eq. (3) represents the Simpson-Hunter parameter with the net downward surface heat flux, Q, included so that the predicted location of tidal mixing fronts accounts for the differences in heat flux at different locations. The net downward heat flux, Q, is estimated from satellite observations and reanalysis (Liu et al., 2015).

There have been numerous studies of tidal mixing fronts in shelf seas using regional models and infrared satellite images. Studies examining tidal mixing fronts on the NWES include: Simpson and Hunter (1974), Simpson et al. (1978), Pingree and Griffiths (1978), Simpson and Bowers (1981), Bowers and Simpson (1987), Holt and Umlauf (2008), and O'Dea et al. (2012). Mixing fronts have also been studied in the Canadian arctic: Griffiths et al. (1981) studied tidal mixing fronts in Hudson Bay and Foxe Basin; Hannah et al. (2009) studied fronts in the Canadian Arctic Archipelago. Other studies of tidal mixing fronts have been conducted for the Gulf of St. Lawrence (Pingree and Griffiths, 1980; Lu et al., 2001); Gulf of Maine (Garrett et al., 1978; Loder and Greenberg, 1986); Patagonian shelf (Glorioso, 1987; Glorioso and Simpson, 1994; Glorioso and Flather, 1995; Acha et al., 2004; Luz Clara et al., 2015); South China Sea (Tong et al., 2010); Bungo Channel, Japan (Takeoka et al., 1997); and Sea of Okhotsk (Zhabin and Dubina, 2012). The above list is non-exhaustive but illustrates the prevalence of tidal mixing fronts within shelf seas around the globe.

In this paper we provide a first order assessment of HYCOM skill in replicating shelf sea tides. We compare sea surface heights to tide gauges, and to the altimeter constrained models TPXO8 (Egbert et al., 1994; Egbert and Erofeeva, 2002) and FES2014 (Carrere et al., 2016; Lyard et al., 2017 (in prep); http://www.aviso.altimetry.fr). Where velocity records are available we also compare the model barotropic tidal currents to tidal currents estimated from velocity records.

In order to provide an estimate of model bias and anomalies from climatological means HYCOM SST for the arctic and austral summers is compared to the 30 year seasonal averages between 1982 and 2011 of the Objectively Interpolated Sea Surface Temperatures estimated from satellite data (OISST; Reynolds et al., 2002) and also to the Multi-scale Ultra-high Resolution foundation SST (MUR SSTfnd; Chin et al., 2017) estimated from satellite observations between December 2011–February 2012 and June 2012–August 2012 which coincide with the period of time simulated by HYCOM.

The location of tidal mixing fronts in HYCOM is estimated in terms of the potential energy anomaly and its gradient as well as the sea surface to seabed temperature gradient. Observations of the global potential energy anomaly and global seabed temperature are difficult to obtain and for that reason the locations of the tidal mixing fronts in HYCOM are compared to horizontal gradients of the MUR SSTfnd to provide observational evidence of mixing front locations for the period of time simulated by HYCOM. We also compare tidal mixing fronts in the HYCOM simulation with tides to tidal mixing fronts reported in previous studies. Our identification of tidal mixing fronts, based upon differences in stratification and vertical temperature gradients, assumes that they result from the influx of solar radiation and from changes in stratification due to changes in the temperature field. While sea ice dynamics, including ice-melt, and freshwater influx from major rivers are included in the model we do not attempt to identify mixing fronts associated with differences in salinity. Much of our manuscript focuses on the NWES where large amounts of data, as well as a regional simulation using the Nucleus for European Modelling of the Ocean (NEMO; Madec, 2008), are available for comparison. We also provide evidence of tidal mixing fronts on the North West Australian Shelf (NWAS) which we have not been able to identify in the existing scientific literature.

In Section 2 we describe the HYCOM simulations and NEMO simulation as well as the selection of observations and data products used for comparison to the model simulations. In Section 3 we compare global HYCOM output to observations to provide an overall assessment of HYCOM skill in coastal and shelf seas. In Section 4 we take a closer look at the NWES, where we compare HYCOM skill to the skill of a regional NEMO simulation. In Section 5 we extend our study to other shelf and coastal seas to assess HYCOM skill focussing on regions with large amplitude tides where tidal mixing fronts have previously been studied. Section 5 also examines the NWAS where large amplitude tides are known to occur and yet previous studies of tidal mixing fronts over the NWAS are difficult to identify in the literature. In Section 6 we discuss our results on the skill of global HYCOM in replicating the tides and tidal mixing fronts in coastal and shelf seas.

Section snippets

Model configuration and data selection

The global HYCOM simulations used in this study (Ngodock et al., 2016) are configured on a tripolar grid with 41 hybrid vertical layers and 1/12.5° horizontal resolution (approximately 8.9 km at the equator). Fig. 1 shows the bathymetry, but on a uniform cylindrical projection, rather than the tripole grid. HYCOM employs a time-varying vertical coordinate which consists of z-layers to represent the near surface mixed layer, terrain following coordinates in shallow water, and isopycnal

HYCOM performance in global shelf seas

For this study we define the global coastal and shelf seas as those regions of the global ocean with a depth <200 m. Fig. 1 shows the global HYCOM bathymetry with the 200 m bathymetric contour depicted by a gray line. The locations of the current meters and the regional study areas discussed in this paper are also displayed on Fig. 1.

The Root Mean Square Error (RMSE) between model values and tide gauge observations of SSH may be calculated using tidal amplitude and phase:RMSESSHgaugemodel=n=1N1

HYCOM skill on the Northwest European Shelf (NWES)

The NWES is a region of the world's oceans for which comprehensive observations, and numerous modelling studies, exist. As such it is possibly the best location to assess HYCOM performance in a specific shelf sea. Egbert and Ray (2001) estimated total M2 tidal energy dissipation on the NWES to be D = 203–208 GW and we find that between depths of 10 and 200 m the dissipation due to bottom friction is D = 212 GW in TPXO8.1 compared to D = 254 GW in HYCOM.

Compared to the tide gauges used in

Hudson Bay and Hudson Strait (HBS)

Arbic et al. (2007) showed that the resonance response in the Ungava Bay and Hudson Strait is large enough to influence tides throughout the North Atlantic; Arbic et al. (2009) showed that the impact of Hudson Strait tides extends globally. Griffiths et al. (1981) previously studied the location of tidal mixing fronts in the Hudson Bay system and identified tidal mixing fronts in Foxe Basin, James Bay and Ungava Bay. The region of Hudson Bay, Hudson Strait, and the Labrador Sea dissipates 261

Discussion and conclusions

We have compared two HYCOM simulations, with and without embedded tides, to assess the impact of adding tides on shelf sea mixing in a global 3-dimensional ocean general circulation model. The global HYCOM ASEnKF experiment with tides is forced by 5 tidal constituents (M2, S2, N2, K1, and O1) and includes an improved bathymetry under the ice shelves in Antarctica but otherwise the grid and model forcing for HYCOM simulations with and without tides are identical.

Our comparison indicates that the

Acknowledgements

The authors would like to thank Prof. John Simpson of Bangor University in Wales, three anonymous reviewers, and the editors of Ocean Modelling for providing many useful comments and suggestions on earlier drafts of this manuscript. We would also like to thank Jeff Book, Naval Research Laboratory, for providing insight and advice on the study of the North West Australian Shelf. Most of BKA's contributions to this paper took place while he was on sabbatical in France. BKA thanks many French

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