Effects of wave-induced vertical Reynolds stress on upper-ocean momentum transfer over the Scotian Shelf during extreme weather events

Journal Pre-proof Effects of wave-induced vertical Reynolds stress on upper-ocean momentum transfer over the Scotian Shelf during extreme weather events Pengcheng Wang, Jinyu Sheng

PII: DOI: Reference:

S2352-4855(19)30503-1 https://doi.org/10.1016/j.rsma.2019.100954 RSMA 100954

To appear in:

Regional Studies in Marine Science

Received date : 8 July 2019 Revised date : 20 October 2019 Accepted date : 9 November 2019 Please cite this article as: P. Wang and J. Sheng, Effects of wave-induced vertical Reynolds stress on upper-ocean momentum transfer over the Scotian Shelf during extreme weather events. Regional Studies in Marine Science (2019), doi: https://doi.org/10.1016/j.rsma.2019.100954. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Journal Pre-proof Confidential manuscript submitted to Regional Studies in Marine Science

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Effects of wave-induced vertical Reynolds stress on upper-ocean

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momentum transfer over the Scotian Shelf during extreme

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weather events

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Pengcheng Wang1,2 and Jinyu Sheng1,3

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Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada Now at Environment and Climate Change Canada

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Ocean Division, International Graduate School at Shenzhen, Tsinghua University, Shenzhen, 518055, Guangdong, China (visiting Pengcheng Scholar)

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Corresponding authors: ([email protected], [email protected])

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Abstract The effects of wave-induced vertical Reynolds stress (WIVRS) on the upper-ocean momentum

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transfer over the Scotian Shelf (ScS) are examined using a coupled wave-circulation modelling

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system during two extreme storm events: Hurricane Earl and Winter Storm Echo. The effects of

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WIVRS are specified in the circulation model using the wave pressure-slope stress (𝛕𝐏 ) suggested

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by Mellor (2013). The inclusion of 𝛕𝐏 enhances the downward momentum transfer within the

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surface layer when the storm passes overhead associated with strong vertical gradients of 𝛕𝐏 ,

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leading to relatively weak vertical shears of horizontal currents and thus weak turbulent Reynolds

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stress (𝛕𝐓 ) in the upper-ocean layer. This in turn weakens the vertical momentum transfer to deeper

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water through 𝛕𝐓 just after the storm passage. The reduced downward momentum transfer after

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the storm due to the inclusion of 𝛕𝐏 is found to be in better agreements with both the ADCP

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observations and the HF-radar observations. The ADCP observations show a relatively slow decay

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of upper-ocean currents, and the HF-radar observations show relatively strong clockwise-rotating

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near-inertial surface currents over the offshore area of the ScS just after the storm passage. The

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model results also demonstrate that the effects of 𝛕𝐏 are more pronounced during Hurricane Earl

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due to deeper penetration depths of 𝛕𝐏 associated with stronger winds (up to 33 m/s) than those

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during Winter Storm Echo (wind speeds up to 25 m/s).

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1. Introduction Ocean surface gravity waves play a very important role in transferring momentum and energy

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from the atmosphere to ocean. Accurate predictions of ocean currents require proper

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representations of wave-related processes, which are typically neglected in many numerical

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simulations of ocean currents. For example, the wind stress (i.e., momentum flux) at the sea surface

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used to drive an ocean circulation model is usually parameterized in terms of wind speeds with the

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wind-dependent drag coefficient 𝐶𝐷 . The presence of surface waves (sea states) can, however,

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strongly modify the sea surface roughness and thus 𝐶𝐷 (Donelan et al., 2004; Holthuijsen et al.,

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2012). Takagaki et al. (2012, 2016) showed that intense wave breaking can cause the saturation of

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𝐶𝐷 for strong wind speeds above 35 m/s. Donelan (2018) found that surface waves can induce a

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flow separation leading to a minimum in 𝐶𝐷 at very high wind speeds above 56 m/s. Surface waves

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can also mediate the momentum flux transferred to the ocean through the wave growth and

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dissipation (e.g., Perrie et al., 2003; Fan et al., 2010). Perrie et al. (2003) found that reductions or

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enhancements in the momentum transfer from the atmosphere to the ocean due to the surface wave

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growth or dissipation can each reach about 20%-30%. The inclusion of the momentum transfer

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from surface waves to ocean currents due to the wave dissipation was found to significantly

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improve the simulated nearshore currents during extreme weather events such as hurricanes and

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tropical storms (Staneva et al. 2017; Wang et al. 2017).

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From the sea surface to the subsurface water, surface waves can affect the vertical momentum

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transfer through the wave-enhanced turbulent mixing. For example, the breaking waves can 3

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enhance the surface turbulence through the input of the turbulent kinetic energy (TKE) at the

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surface (Craig & Banner, 1994). The nonbreaking waves can enhance the production of turbulence

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through an interaction between the wave orbital velocity and turbulence velocity (e.g., Qiao et al.,

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2004). The Langmuir circulation, which involves an interaction of the Stokes drift with the mean

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flow (Craik & Leibovich, 1976), is another important wave process that can strongly enhance the

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mixing of upper ocean (e.g., Fan et al., 2014; Wu et al., 2015). A recent study by Takagaki et al.

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(2015) found, however, that the effect of the Langmuir circulation on the scalar transfer across the

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air-sea interface is relatively small in comparison with turbulent eddies.

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Surface gravity waves can also affect the vertical momentum transfer through the wave-

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̅̅̅̅ induced vertical Reynolds stress components defined as ̅̅̅̅ 𝑣̃𝑤 ̃ and 𝑢 ̃𝑤 ̃ (where 𝑢̃, 𝑣̃, 𝑤 ̃ are the wave

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orbital velocities in a Cartesian coordinate system (𝑥, 𝑦, 𝑧), 𝑥 is taken to be the wave propagation

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direction, 𝑦 is parallel with wave crests, and 𝑧 is vertically upward from the mean sea level). Here,

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̅̅̅̅ 𝑣̃𝑤 ̃ is equivalent to an interaction between the Coriolis force and the Stokes drift (𝐟 × 𝐔𝒔 ), known

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as the Coriolis-Stokes force. Polton et al. (2005) showed that the Coriolis-Stokes force can

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substantially change the mean current profile over the wind-driven surface mixed layer. However,

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̅̅̅̅ ̅̅̅̅ 𝑢 ̃𝑤 ̃ has usually been neglected in ocean circulation models since 𝑢 ̃𝑤 ̃ = 0 based on the linear wave

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solution with 𝑢̃ and 𝑤 ̃ in quadrature. In reality, 𝑢̃ and 𝑤 ̃ can be out of quadrature for growing

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waves (Mellor, 2013; Nielsen et al., 2011) and dissipative waves (Phillips, 1977; Deigaard &

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̅̅̅̅ Fredsoe, 1989), resulting in non-zero 𝑢 ̃𝑤 ̃ . Recent laboratory experiments made by Olfateh et al

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̅̅̅̅ ̅̅̅̅ (2017) also provided reasonable measurements of non-zero 𝑢 ̃𝑤 ̃ under wind waves. Thus, 𝑢 ̃𝑤 ̃ is

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potentially significant as it provides an additional mechanism for the vertical momentum transfer

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̅̅̅̅ in addition to the turbulent Reynolds stress. Mellor (2013) recently found that 𝑢 ̃𝑤 ̃ is equivalent to

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a subsurface projection of the wind pressure correlated with the wave slope. Mellor (2013) treated

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̅̅̅̅ 𝑢 ̃𝑤 ̃ as a pressure-slope momentum transfer term in an ocean circulation model, and demonstrated

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improved agreements between simulated and measured temperatures in a simple one-dimensional

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case. Gao et al. (2018) used the approach of Mellor (2013) in their study and found that the

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̅̅̅̅ inclusion of 𝑢 ̃𝑤 ̃ can enhance the vertical mixing by 30% in the middle layers in Jiaozhou Bay.

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̅̅̅̅ Nonetheless, the effects of 𝑢 ̃𝑤 ̃ on the momentum transfer in the oceanic water column require

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further studies.

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The main objective of this study is to examine the effects of wave-induced vertical Reynolds

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̅̅̅̅ stress (𝑢 ̃𝑤 ̃ , hereinafter WIVRS) on the upper-ocean momentum transfer using a coupled wave-

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circulation model. The study region is the Scotian Shelf (ScS), which is a rugged open shelf

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bounded by the Laurentian Channel to the east, the Northeast Channel to the west, and deep waters

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to the south (Figure 1). The ScS is socially and economically important since it supports

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commercial and recreational fisheries, marine recreation and tourism, aquaculture, shipping and

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transportation, and other economic activities that directly contribute to the economic health of the

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province of Nova Scotia. This region is affected frequently by winter storms and occasionally by

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hurricanes. A two-way coupled wave-circulation model has been developed for this region to study

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the effects of different wave-current interaction mechanisms under extreme weather conditions

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(Wang & Sheng, 2016). For the present study, the WIVRS is included in the coupled wave-

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circulation model to study its effects on ocean currents over the ScS during two extreme weather

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events: Hurricane Earl in September 2010 and Winter Storm Echo in December 2015. During both

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storm events, high-quality ADCP measurements were available on the inner ScS. During Echo,

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high frequency (HF) radar observations were also available over this study region. These

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observations are used in this study to assess the model performance in simulating the storm-

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induced ocean currents. The effects of WIVRS are derived from the comparison of model results

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with and without the inclusion of WIVRS.

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The structure of the paper is organized as follows. The observational data provided by the

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ADCP, HF-radar and wave buoys are described in section 2. The coupled wave-circulation model

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is described in section 3. The model results during the two storm events are presented in section 4.

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The summary and discussion are given in section 5.

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2. Observation

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As part of the Ocean Tracking Network, bottom-mounted, upward-looking ADCPs were

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deployed at three locations on the inner part of the ScS to monitor the Nova Scotia Current from

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2008 to 2016 (Dever et al., 2016). The ADCP currents were averaged over 30 min time windows

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and 4 m vertical bins. The shallowest bin was centered at 10 m from the sea surface and the deepest

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bin was 10 m above the bottom. It should be noted that, in this study, two ADCPs at locations T1

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and T2 were functional during Hurricane Earl, while one ADCP at location T2 was functional

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during Winter Storm Echo (Figure 1).

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In addition, during Winter Storm Echo, high-quality surface current observations on the inner

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ScS were collected by a HF-radar system deployed off Halifax Harbor by the Marine

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Environmental Observation Prediction and Response (MEOPAR) network. The HF-radar system

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consists of two long-range CODAR-Seasonde radars located at Sandy Cove and Clam Harbor

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(Figure 2). Each radar operates at a central frequency of 4.8 MHz and provides hourly radial

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surface currents with 6 km resolution and coverage up to 200 km off the coastal radar site. HF-

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radar measurements can be used to infer ocean currents averaged from the surface to a depth of

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the order of λ/4π where λ is the Bragg wavelength (Stewart & Joy, 1974). This depth corresponds

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to approximately 2.5 m at the transmit frequency of 4.8 MHz. The HF-radar data were found to

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have good quality in comparison with moored ADCP data during three winter months from

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December 2015 to February 2016 (Wang et al., 2018). More details on the processing of the HF-

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radar data can be found in Wang et al. (2018).

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The HF-radar data had, however, some data gaps due to the radio interference experienced by

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both radar units. The hourly data at grid points with more than 50% temporal coverage (Figure 2)

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from 1200Z 15 December to 1800Z 16 December 2015 during Winter Storm Echo are used in this

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study. During this period, the HF-radar data coverage is relatively good.

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During the two storm events, in-situ wind and wave observations at four buoys on the ScS and

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in the Gulf of Maine (Figures 1 and 2) are also used to validate model results. Buoy 44024 has

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been operated by the Northeastern Regional Association of Coastal Ocean Observing Systems.

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Buoys 44137 and 44258 have been operated by Environmental Canada. The Halifax buoy has been

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maintained by the SmartAtlantic (http://www.smartatlantic.ca).

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3. A coupled wave-circulation modelling system The two-way coupled wave-circulation model developed by Wang and Sheng (2016) is used

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in this study. The coupled model consists of a three-dimensional (3D) ocean circulation model

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known as DalCoast, and a third-generation spectral ocean surface wave model known as

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WAVEWATCH III (WW3). The wave effects on the 3D circulation are specified in the circulation

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model using the vortex force formalism (Bennis et al., 2011) and the breaking wave-induced

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mixing (Craig & Banner, 1994). In the wave model, the effects of ocean surface currents on surface

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waves include the relative wind effect, current-induced convergence, wavenumber shift and

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refraction (Tolman et al., 2014). The importance of these wave-current interaction mechanisms in

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the eastern Canadian waters was investigated in several previous studies (Wang & Sheng, 2016,

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2018; Wang et al., 2017).

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3.1. Ocean circulation model

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DalCoast is a regional ocean circulation model based on the Princeton Ocean Model (POM)

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(Mellor, 2004). The latter is a 3D, sigma coordinate, primitive-equation ocean circulation model.

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DalCoast uses the spectral nudging technique (Thompson et al., 2007) and the semi-prognostic

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method (Sheng et al., 2001) to reduce the seasonal bias in the model circulation and hydrography.

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DalCoast has been validated extensively in the past using observations of hydrography, sea level,

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and currents (Ohashi & Sheng, 2013, 2015; Ohashi et al., 2009a, 2009b; Wang et al., 2018).

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3.1.1 Pressure-slope momentum transfer The momentum equations that incorporate the vortex force formalism (Bennis et al., 2011) are written as, ̂ 𝜕𝑢 𝜕𝑡

+ 𝑢̂

̂ 𝜕𝑢 𝜕𝑥

+ 𝑣̂

̂ 𝜕𝑢 𝜕𝑦

+𝑤 ̂

̂ 𝜕𝑢 𝜕z

− 𝑓𝑣̂ +

𝜌 𝜕𝑥

= 𝜕𝑣̂

[𝑓 + (

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1 𝜕𝑝

𝜕𝑥

𝜕𝑣̂ 𝜕𝑡

+ 𝑢̂

𝜕𝑣̂ 𝜕𝑥

+ 𝑣̂

𝜕𝑣̂ 𝜕𝑦

+𝑤 ̂

𝜕𝑣̂ 𝜕z

+ 𝑓𝑢̂ +

1 𝜕𝑝 𝜌 𝜕𝑥

= 𝜕𝑣̂

− [𝑓 + (

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−

−

̂ 𝜕𝑢 𝜕𝑦

̂ 𝜕𝑢 𝜕𝑦

)] 𝑉𝑠 − 𝑊𝑠

)] 𝑈𝑠 − 𝑊𝑠

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𝜕𝑥

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̂ 𝜕𝑢 𝜕𝑧

̂ 𝜕𝑢 𝜕𝑧

−

−

𝜕𝐽

𝜕𝑥

𝜕𝐽

𝜕𝑦

+

+

𝜕𝜏𝑇,𝑥 𝜕𝑧

𝜕𝜏𝑇,𝑦 𝜕𝑧

+

+

𝜕𝜏𝑃,𝑥 𝜕𝑧

𝜕𝜏𝑃,𝑦 𝜕𝑧

(1)

(2)

where (𝑢̂, 𝑣̂, 𝑤 ̂) are components of the quasi-Eulerian velocity and (𝑈𝑠 , 𝑉𝑠 , 𝑊𝑠 ) are components of

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the Stokes drift velocity in the horizontal (𝑥, 𝑦) and vertical (𝑧) directions, respectively, 𝑓 is the

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Coriolis parameter, 𝜌 is a reference density, 𝑝 is the hydrostatic pressure, and 𝐽 is the Bernoulli-

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head or wave-induced mean pressure. The first two terms on the right side of (1-2) are the vortex

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force which incorporates the Coriolis-Stokes force. The turbulent stress vector 𝛕𝐓 = (𝜏 𝑇,𝑥 , 𝜏 𝑇,𝑦 ) is

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given as

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𝛕𝐓 (𝑧) = (𝐾𝑀

̂ 𝜕𝑢 𝜕𝑧

, 𝐾𝑀

𝜕𝑣̂ 𝜕𝑧

)

(3)

where 𝐾𝑀 is the mixing coefficient, and 𝛕𝐓 (0) at the sea surface is the friction drag which

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represents the direct molecular interaction at the air-sea interface.

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To study the effects of WIVRS, we follow Mellor (2013) and incorporate the WIVRS in the

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circulation model by adding the pressure-slope stress vector 𝛕𝐏 = (𝜏𝑃,𝑥 , 𝜏𝑃,𝑦 ) to the right side of 9

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Eqs. (1-2), ̅̅̅̅̅̅̅ 𝜕𝜂 ̅̅̅̅̅̅̅ 𝜕𝜂 𝛕𝐏 (𝑧) = (𝑝𝑤 , 𝑝𝑤 ) 𝐹𝑆𝑆 𝐹𝐶𝐶

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𝜕x

with

𝐹𝑆𝑆 =

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sinh(𝑘(𝑧+ℎ)) sinh 𝑘𝑑

𝜕y

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; 𝐹𝐶𝐶 =

cosh(𝑘(𝑧+ℎ)) cosh 𝑘𝑑

(4a)

(4b)

where 𝑝𝑤 is the surface wind pressure, 𝜂 is the surface elevation, 𝑘 is the wavenumber, and 𝑑 =

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ℎ + 𝜂 is the total water depth. It is noted that, 𝐹𝑆𝑆 𝐹𝐶𝐶 = 1 at the sea surface, and 𝛕𝐏 (0) is the

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correlation of wind pressure and wave slope, known as the wave or “form” drag which arises from

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a greater integrated pressure on the backward face of a wave than on the forward face (e.g., Buckles

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et al. 1984). It should be noted that

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(Mellor, 2003). Mellor (2013) showed that 𝛕𝐏 dominates over 𝛕𝐓 near the surface, while below the

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surface these two stresses are comparable.

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3.1.2 Wind stress

𝜕𝛕𝐏

has the same vertical structure as the Stokes drift velocity

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The surface wind stress has two components, namely: the friction drag 𝛕𝐓 (0) and the form

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drag 𝛕𝐏 (0), which asymptotically apply to cases of low and high wind speeds, respectively (e.g.,

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Donelan, 1990; Mellor 2018). In the transition case associated with moderate wind speeds (5-12

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m/s), both stress components are important. In this study, we consider these two components

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separately since the subsurface responses to these two components of surface stress are different

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as shown in Eqs. (1-2). We follow Mellor (2018) and use separate formulas for the two stress

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components defined as:

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̅̅̅̅̅̅̅ ̅̅̅̅̅̅̅ 𝜕𝜂 𝜕𝜂 𝛕𝐏 (0) = (𝑝𝑤 , 𝑝𝑤 ) = 𝜌𝑎 𝐶𝐷𝑃 |𝐔10𝑟 |𝑼10𝑟 ,

(5a)

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𝛕𝐓 (0) = 𝜌𝑎 𝐶𝐷𝑇 |𝐔10𝑟 |𝑼10𝑟

(5b)

𝜕y

pro of

𝜕x

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where 𝜌𝑎 is the density of the air, 𝐔10𝑟 is the vector difference between the 10-m wind vector and

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the ocean surface current vector. The form drag coefficient 𝐶𝐷𝑃 is defined in terms of the

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significant wave height 𝐻𝑠 (in units of m) and inverse wave age

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at the peak frequency (in same units of 𝑈10 ) :

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𝑧0𝑃 = 1.38 × 10−4 𝐻𝑠 (

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(6a)

] (1 − 𝛼),

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ln (𝑧10 /𝑧0𝑃 )

𝑈10 𝑐𝑝

2.66

(6b)

)

The friction drag coefficient 𝐶𝐷𝑇 is calculated from the law of the smooth wall, resulting in (Schlicting, 1978):

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, with 𝑐𝑝 to be the phase speed

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𝐶𝐷𝑃 = [

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𝑐𝑝

2

𝜅

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𝑈10

𝐶𝐷𝑇 = [

𝜅

2

(7a)

] 𝛼,

ln (𝑧10 /𝑧0𝑇 )

𝑧0𝑇 = 𝛾

𝜈

(7b)

𝑢∗

𝜏𝑎

where, 𝜅 = 0.41 is the von Karman constant, 𝜈 is the kinematic viscosity, 𝑢∗ = √

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velocity, and 𝛾 = 0.11 (Edson et al., 2013) is the roughness Reynolds number for smooth flow.

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An empirical coefficient 𝛼 in Eqs. (6a) and (7a) is used to combine the two drag coefficients:

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𝜌𝑎

is the friction

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𝛼 = exp [−3.0 × 10−5

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(

𝜈

𝑐𝑝

0.9

) ]

(8)

Thus, the combined stress vector and the corresponding drag coefficient are:

pro of

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𝐻𝑠 𝑢∗ 𝑈10

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𝛕 = 𝛕𝐏 (0) + 𝛕𝐓 (0)

(9a)

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𝐶𝐷 = 𝐶𝐷𝑃 + 𝐶𝐷𝑇

(9b)

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3.2. Surface wave model

WW3 is a third-generation spectral surface wave model developed at the NOAA/National

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Centers for Environmental Prediction. WW3 solves the wave action balance equation, with the

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wave action density spectrum (𝑁 = 𝐸/𝜎) defined as a function of (𝑘, 𝜃), where E, 𝜎, 𝑘, and 𝜃

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are respectively wave energy, relatively frequency, wave number, and wave direction. The wave

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action balance equation in WW3 can be written as,

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+ 𝛻𝑥 ∙ (𝐱̇ 𝑁) +

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𝜕𝑁 𝜕𝑡

𝜕

𝜕𝑘

(𝑘̇𝑁) +

𝜕 𝜕𝜃

𝑆 (𝜃̇ 𝑁) = 𝑡𝑜𝑡 𝜎

𝜕𝜎 𝜕𝐷 𝜕𝐔 𝑘̇ = − −𝐤∙ 𝜕𝐷 𝜕𝑠

(12)

𝜕𝑠

1 𝜕𝜎 𝜕𝐷 𝜃̇ = − ( +𝐤∙ 𝑘 𝜕𝐷 𝜕𝑚

(10) (11)

𝐱̇ = 𝐜𝑔 + 𝐔

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𝜕𝐔 𝜕𝑚

)

(13)

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where 𝐜𝑔 is the group velocity of waves, 𝑼 is the surface ocean current vector, 𝒌 is the

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wavenumber vector, 𝑠 is a coordinate in the direction 𝜃, and 𝑚 is a coordinate perpendicular to 𝑠. 12

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The left-hand side of (10) represents the local rate of change of the action density (the first term),

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the wave propagation in spatial (second term) and spectral (third and fourth terms) space. The

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right-hand side of (10) contains the net source term 𝑆𝑡𝑜𝑡 , which includes all physical processes that

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generate, dissipate and redistribute the wave energy.

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Equations (10-13) indicate that ocean circulation affects the wave action density spectrum in

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four ways. Firstly, ocean currents modify the speed of the wave action flux in the spatial space.

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Secondly, in the spectral space, the horizontal variation of ocean currents causes wavenumber shift

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and wave refraction in the way similar to effects of the bathymetry variation. Thirdly, in the source

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term, the surface wind velocity vector 𝑼𝟏𝟎 used to calculate the wave growth is replaced by (𝑼𝟏𝟎 −

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𝜖𝑼). Here 𝜖 = 0.7 (Wang & Sheng, 2016) is a tuning coefficient for the relative wind effect in

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WW3. Lastly, the sea surface elevation modifies the total water depth used in the wave model,

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although this effect is only large in the very shallow water regions where waves could feel the

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ocean bottom.

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3.3. Model setup

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The model domain of DalCoast (Figure 1) covers the Gulf of St. Lawrence, the Scotian Shelf,

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the Gulf of Maine and adjacent deep waters of the North Atlantic Ocean (71.5°W-56°W, 38.5°N-

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52°N), with a horizontal resolution of (1/16)° (~7 km) in both the longitudinal and latitudinal

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directions. There are 40 sigma levels in the vertical direction, which are concentrated near the

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surface and bottom and are equally distributed in the interior. The model topography is based on

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the General Bathymetric Chart of the Oceans (GEBCO) bathymetry data (http://www.gebco.net/).

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The external forcing for the model includes hourly surface winds and atmospheric pressures at the

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sea level (SLP) extracted from the Climate Forecast System Reanalysis (CFSR) (Saha et al., 2010).

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DalCoast is also driven by the net heat and freshwater fluxes at the sea surface and the freshwater

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runoff from major rivers in the region. At the model lateral open boundaries, the circulation model

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is driven by (a) storm-induced hourly sea level and depth averaged currents simulated by a

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barotropic model covering the northwest Atlantic Ocean (72°W-42°W, 38°N-60°N) with a

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resolution of (1/12)°; (b) tidal forcing specified in terms of hourly sea levels and depth averaged

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currents predicted by the OSU Tidal Inversion System (OTIS) including 8 tidal constituents (M2,

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S2, N2, K2, K1, O1, P1, and Q1); and (c) daily values of the 3D temperature, salinity and large-scale

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density-driven currents provided by an ocean-ice numerical model of the northwest Atlantic

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(Urrego-Blanco & Sheng, 2012).

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WW3 uses the same horizontal model grid and bathymetry as DalCoast. To account for the

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effect of swells generated outside of the study area, a coarser-resolution wave model based also on

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WW3 is applied to a larger domain (84°W-10°W, 10°N-65°N) with a horizontal resolution of (1/4)°.

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The wave model results over this larger domain are used to provide boundary conditions for the

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wave model of the eastern Canadian shelf. The spectral domain consists of 36 directional bins with

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10° of resolution and 29 frequencies 𝑓𝑛 ranging from 0.04 to 0.6 Hz with a logarithmic increment

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of 𝑓𝑛+1 = 1.1𝑓𝑛 . The source package known as ST6 (Tolman et al., 2014) is applied to compute

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the wind input and dissipation source terms.

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3.4. Design of numerical experiments Two numerical experiments were designed to examine the effects of WIVRS: (a) the coupled

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wave-circulation model run with both 𝝉𝑷 and 𝝉𝑻 (the control run, Run 1), (b) the coupled model

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run with only 𝝉𝑻 in Eqs. (1-2) (Run 2). It should be noted that the coupled wave-circulation model

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in both runs uses the total wind stress calculated based on Eq. (9a). The main difference between

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these two runs is that the vertical momentum transfer associated with vertical mixing in Run 1

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depends on the combination of 𝝉𝑷 and 𝝉𝑻 , while that in Run 2 depends entirely on 𝝉𝑻 .

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4. Model results during two storm events

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Two extreme weather events are considered in this study: (a) Hurricane Earl and (b) Winter

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Storm Echo. Hurricane Earl translated northeastward to the ScS (Figure 1) and made a landfall as

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a 120 km/h category-1 hurricane (Saffir-Simpson hurricane scale) on the south coast of Nova

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Scotia on 4 September 2010. This storm generated a maximum storm surge of about 1.2 m in

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Halifax Harbor and huge surface waves with significant wave heights of up to 10 m and peak

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waves up to 23 m at a marine buoy outside of the Harbor. Different from the pathway of Hurricane

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Earl, Winter Storm Echo swept the ScS from west to east (Figure 1) on 15-16 December 2015.

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Echo was a typical winter storm and had a storm diameter of 3-4 times larger with weaker winds

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(up to 25 m/s) than typical hurricanes.

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4.1. Hurricane Earl

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As mentioned above, Hurricane Earl is a weak category-1 hurricane (wind speeds up to 33 m/s) 15

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that translated northeastward and passed through the ScS in early September 2010 (Figure 1).

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Figures 3a-3d present time series of observed and reanalysis winds (speed and direction) at the

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two buoys (44258 and 44024) located close to the storm track. The CFSR reanalysis winds at the

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two buoys agree reasonably well with observations, due in part to the fact that the meteorological

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observations made at these two buoys were assimilated into the atmospheric circulation model in

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generating the CFSR winds. It should also be noted that the size of the storm expanded

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significantly (with the radius of maximum winds of ~111 km) when Earl moved northeast on 4

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September, indicating that the horizontal resolution (~0.3o, which is relatively coarse) of the CFSR

303

is reasonable to represent the general structure of the storm during Hurricane Earl.

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Figures 3e-3h present time series of observed and simulated significant wave heights (𝐻𝑠 ) and

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peak wave periods (𝑇𝑝 ) at buoys 44258 and 44024 during Earl. As the winds of this storm reached

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the peak at about 25m/s, the observed 𝐻𝑠 reached about 9-10 m, and the observed 𝑇𝑝 were about

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7-17 s at the two buoys. The relatively long peak wave periods at these two buoys indicate that the

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surface gravity waves over the western Scotian Shelf and adjacent waters during Hurricane Earl

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were strongly affected by remotely-generated swells propagating along with the storm. The

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coupled model in the control run (Run 1) reproduces reasonably well the observed 𝐻𝑠 and 𝑇𝑝 at

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the two buoys, except that the coupled model overestimates the observed maximum 𝐻𝑠 at buoy

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44024, presumably due to the overestimated reanalysis winds used to drive the model. After the

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peak winds, the observed 𝐻𝑠 at the two buoys exhibit oscillation patterns with periods close to the

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local inertial period (~17 h). These near-inertial oscillations in the significant water heights were

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also observed during other hurricane cases on the eastern Canadian Shelf (Wang and Sheng, 2016),

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and they are caused by the strong near-inertial currents in the wake of the hurricane. The coupled

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model in Run 1 performs reasonably well in reproducing the observed near-inertial oscillation of

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𝐻𝑠 at buoy 44024, but less well at buoy 44258 presumably due to the relative coarse model

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resolution at this nearshore location.

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Figure 4a presents model-calculated values of the combined drag coefficient 𝐶𝐷 (defined in Eq.

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(9b)) in terms of the 10-m wind speeds (𝑈10 ) over the inner ScS, which were sampled at 3-h

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intervals on 4-5 September 2010 during Hurricane Earl. For 𝑈10 > 10 m/s, the data points for 𝐶𝐷

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at a given 𝑈10 are highly scattered, indicating the important role of the form drag given by Eq. (6).

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For 𝑈10 < 5 m/s, by contrast, the data points of 𝐶𝐷 at a given 𝑈10 are much less scattered and

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approximately equal to the values for the friction drag coefficient given by Eq. (7). Also shown in

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Figure 4a are two wind-speed-dependent 𝐶𝐷 values calculated using the classic Large and Pond

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(1981, hereafter LP81) method and a recent comprehensive drag coefficient parameterization,

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namely the COARE 3.5 algorithm (Edson et al., 2013). Figure 4a demonstrates that most of the

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data points for 𝐶𝐷 are scattered around the solid line given by LP81 but far from the line given by

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the COARE 3.5 algorithm for 12 m/s < 𝑈10 < 25 m/s.

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Figure 5 presents observed and simulated currents (demeaned, detided) as a function of time

332

and depth at the two ADCP locations (T1 and T2, Figure 1) on the inner ScS during Hurricane Earl.

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To examine the storm-induced currents, we detided and demeaned the currents to eliminate both

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the tidal components and the background mean flow known as the Nova Scotia Current over this

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region. It should be noted that the tidal currents on the inner ScS are generally weak with

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magnitudes of ~0.10 m/s or less (see Appendix), and the Nova Scotia Current flows southwestward

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with peak surface speeds reaching 0.30 m/s centered at approximately 45 km from the coast (Wang

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et al., 2018). Figures 5a-d show that intense ocean currents (up to 0.9 m/s) in the upper-ocean

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mixed layer (~35 m) were observed by both ADCPs during the peak winds when the storm passed

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overhead around 1600Z on 4 September 2010. After Earl passed by, these currents underwent

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“Rossby adjustment” and near-inertial currents (NICs) were generated. These NICs had

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magnitudes of ~0.5 m/s with the e-folding decay timescales of 8-9 inertial cycles (~6 days) at both

343

ADCP locations, based on an analysis of near-inertial band-passed currents (not shown). In the

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lower layer, the NICs had a phase difference of about 180o from those in the upper layer, due to

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the superposition of the initial upper layer response and the barotropic response felt throughout the

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water column (e.g., Pettigrew, 1981; Shearman, 2005).

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Figures 5e-h demonstrate that the coupled model in Run 1 (with 𝝉𝑷 ) generally reproduces the

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observed vertical structure of (demeaned and detided) currents and its temporal evolution at

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location T1 during Earl, except that the magnitudes are underestimated. The model deficiency in

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generating amplitudes of observed currents could be attributed mostly to underestimations of

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upper-ocean stratifications and frontal structure of coastal currents by the coupled model. In

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comparison with Run 1, the model results in Run 2 (without 𝝉𝑷 , Figures 5i-l) have stronger vertical

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current shears near the surface during the peak winds. As soon as the storm passed by, the upper-

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ocean momentum simulated by the coupled model in Run 2 propagates downward (around 0300Z

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September 5 for the along-shore current and around 0800Z September 5 for the cross-shore

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current), while the upper-ocean momentum in Run 1 mostly remains in the surface layer.

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Furthermore, during the subsequent near-inertial cycles, the upper-ocean currents simulated in Run

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2 decay more quickly than those in Run 1, due to the large downward momentum leakage. Overall,

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in comparison with Run 2, model results in Run 1 are in better agreements with the ADCP

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observations with a relatively slow decay of the upper-ocean currents during Hurricane Earl.

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To explain the above differences between two model runs, we examine the time-depth

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distributions of 𝝉𝑷 and 𝝉𝑻 calculated by the coupled model at location T1 shown in Figure 6. As

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mentioned earlier, the vertical momentum transfer associated with vertical mixing depends on the

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combined effect of 𝝉𝑷 and 𝝉𝑻 in Run 1, and entirely on 𝝉𝑻 in Run 2. Figures 6a-b and 6e-f

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demonstrate that, in Run 1, the form drag 𝝉𝑷 (0) dominates over the skin drag 𝝉𝑻 (0) at the surface

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during the peak winds. Below the surface, 𝛕𝐏 decreases exponentially with depth as indicated in

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Eq. (4), while non-zero 𝝉𝑻 also evolves due to the local current shear. By comparison, the

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simulated 𝝉𝑻 in Run 2 features smaller vertical gradients than 𝛕𝐏 + 𝛕𝐓 in Run 1 in the surface layer

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(~11 m) during the peak winds (Figures 6c-d and 6g-h), leading to stronger vertical current shears

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near the surface in Run 2 than in Run 1 as discussed in Figure 5. These stronger vertical shears in

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Run 2 further result in relatively large 𝝉𝑻 beneath the surface layer, which is responsible for the

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faster decay of the upper-ocean currents in Run 2 than in Run 1.

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4.2. Winter Storm Echo

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Echo was an intense winter storm sweeping across the ScS from west to east (Figure 1) on 15-

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16 December 2015. Figures 7a-7d present time series of observed and CFSR reanalysis winds

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(speed and direction) at the buoy in Halifax Harbor and buoy 44137. The reanalysis winds at buoy

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44137 agree very well with observations due again to data assimilation used in generating the

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CFSR reanalysis winds (Figures 7b,d). The reanalysis winds at the Halifax buoy also agree

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reasonably well with observations except around 23:00 on 15 December, during which the

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reanalysis wind speed shows a double-peak pattern associated with the passage of the storm’s

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“eye”, while the observed wind speeds remained strong (Figure 7a). This discrepancy can be due

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to an unrealistic simulated “storm eye” or/and errors in the position of the storm center in the

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reanalysis winds. It should be noted that wind observations at the Halifax buoy were not used in

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generating the reanalysis winds.

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Figures 7e-7h present time series of observed and simulated 𝐻𝑠 and 𝑇𝑝 at Halifax buoy and

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buoy 44137 during Winter Storm Echo. The observed 𝐻𝑠 reached ~4 m at the nearshore location

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(Halifax buoy) and ~8 m at the offshore location (44137). The observed 𝑇𝑝 increased from 3 s to

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11 s during the storm. In comparison, the observed 𝑇𝑝 during Echo are shorter than those during

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Hurricane Earl, indicating that the wave field during Echo was younger than that during Earl. The

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coupled wave-circulation model in the control run (Run 1) reproduces reasonably well the

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observed 𝐻𝑠 and 𝑇𝑝 at the two buoys, except that the model underestimates the observed 𝐻𝑠 at the

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Halifax buoy around 00:00 on 16 December due in part to the underestimated reanalysis winds

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used by the model.

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We next examine the model-calculated values of the combined drag coefficient 𝐶𝐷 in terms of

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the 10-m wind speeds (𝑈10 ) over the inner ScS at 3-h intervals on 15-16 December 2015 for Winter

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Storm Echo (Figure 4b). Similar to Hurricane Earl, the data points for 𝐶𝐷 during Echo are highly

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scattered for 𝑈10 > 7 m/s. One of main differences between these two storms is that most of these

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data points for 𝐶𝐷 are associated with relatively low values of wave ages during Winter Storm

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Echo, and they are scattered around the solid line given by the COARE 3.5 algorithm (Figure 4b),

400

instead of that given by LP81 during Hurricane Earl (Figure 4a). In the literature, there are no

401

specific explanations regarding the differences between COARE3.5 and LP81. However, Edson et

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al. (2013) showed that the composite dataset used to derive COARE3.5 are mostly under young

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wave conditions, which is consistent with the relatively young wave conditions during winter

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storm Echo. Although wave conditions in the dataset used for LP81 are not available, based on the

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results in this study, we speculate that the different wave conditions could contribute to the

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differences between these two schemes.

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Figure 8 presents observed and simulated currents (demeaned and detided) as a function of

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time and depth at the two ADCP locations (T1 and T2, Figure 1) on the inner ScS during Winter

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Storm Echo. The observed subsurface ocean responses to Echo at location T2 (Figures 8a-b)

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demonstrate similar features to those during Hurricane Earl (Figure 6), expect for smaller

411

magnitudes due to weaker winds and deeper mixed layer (~50 m) in winter. The storm-induced

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NICs during Echo had magnitudes of ~0.25 m/s with the e-folding decay timescales of 3 inertial

413

cycles, which were half of those during Earl. The coupled model in Run 1 and 2 (Figures 8e-f and

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8i-j) reproduces reasonably well the observed vertical distributions of currents at location T2. By

415

comparison, the major differences in results between the two runs at both locations T1 and T2

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occur near the surface (~6 m) during and just after the peak winds, which are similar but weaker

417

than those found during Hurricane Earl. During the subsequent near-inertial cycles, the differences

418

between the two runs are much smaller than those during Earl.

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The above-discussed differences in model results between Winter Storm Echo and Hurricane

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Earl can be explained partially by differences in 𝝉𝑷 and 𝝉𝑻 between the two storm cases. Figures

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9a and e present the time-depth distributions of simulated 𝝉𝑷 during Echo at location T1. During

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Winter storm Echo, the large amplitudes of 𝝉𝑷 occur near the surface (~6 m), with its penetration

423

depths to be only about half of those during Earl (Figures 6a,e). Below this thin surface layer, the

424

simulated 𝛕𝐏 + 𝛕𝐓 in Run 1 are similar to 𝝉𝑻 in Run 2 for Winter Storm Echo (Figures 9c-d and

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9g-h). As a result, the major effects of 𝝉𝑷 during Echo are restricted in the thin surface layer (~6

426

m).

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We next examine the model performance in simulating surface ocean currents by comparing

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model results with the HF-radar observations during Echo. Figures 10a-c present time series of

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wind stress, observed and simulated surface currents (detided, demeaned) spatially-averaged over

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the HF-radar grid points (marked in Figure 2). To be consistent with the HF-radar observations,

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the vertically integrated currents within the upper 2.5 m depth simulated by the model are used for

432

comparison. Following the passage of the storm, the wind stress rotated clockwise in time, and the

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observed surface currents feature an oscillation behavior with a period close to the local inertial

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period (~17 h), consistent with the ADCP observations at location T2 (Figures 8a-b). The coupled

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model in Run 1 reproduces reasonably well the above observed variations of currents (RMSE<0.2

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m/s, Figures 10d-e), except for around times A and B where the model deficiencies are relatively

437

large in reproducing the observed cross-shore currents (RMSE: 0.22-0.31 m/s, Figure 10e).

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Possible causes for these relatively large discrepancies at times A and B will be discussed in the

439

later part of the paper. By comparison, model results in Run 2 generally agree less well with

440

observations, with larger RMSE values than those in Run 1.

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It should be noted that the above comparison was made for the spatially-averaged currents,

442

using the RMSE to represent the error averaged over the spatial grids. The RMSE value is not

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sufficient if the observations have relatively strong spatial variability. To further quantify the model

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performance in simulating the spatial variability of currents, we use the spatial version of the 𝛾 2

445

statistic of Thompson and Sheng (1997) defined as

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𝑉𝑎𝑟(𝑂−𝑀) 𝑉𝑎𝑟(𝑂)

(13)

where 𝑉𝑎𝑟 denotes the spatial variance, and 𝑂 and 𝑀 denote observational and simulated values

448

respectively. Small values of 𝛾 2 indicate the good model performance. If 𝛾 2 < 1, the observed

449

spatial variance is reduced by subtracting hindcasts from observations. Figures 10f-g show that

450

relatively large values of 𝛾 2 occur in both model runs around time C for the along-shore currents,

451

times B and D for the cross-shore currents. Nonetheless, in comparison with Run 2, the inclusion

452

of 𝜏𝑃 in Run 1 reduces the values of 𝛾 2 during these three periods, indicating the important effects

453

of 𝜏𝑃 . During other periods, both model runs show relatively good performances in simulating the

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spatial variability of currents with 𝛾 2 < 1. To further examine the spatial variability of currents during Echo, we present in Figure 11 the

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observed and simulated instantaneous maps of surface currents on the inner ScS covered by the

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HF radar at four selected specific times (A, B, C, and D, Figure 10) with an 8-h time interval during

458

the storm. At time A, the HF-radar observations (Figure 11a) feature generally an onshore-directed

459

flow, as the eastern periphery of the storm approached the ScS associated with intense

460

northwestward winds (Figure 10a). The coupled wave-circulation model in both runs (Figures

461

11e,i) reproduces reasonably well the observed onshore-directed flow except for overestimated

462

magnitudes due in part to slightly overestimated winds at this time (Figure 10 a). By comparison,

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the model results in Run 2 have larger overestimations of currents. In addition, the model results

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in both runs are more spatially uniform than observations due in part to the relatively coarse-

465

resolution atmospheric forcing.

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At time B, the HF-radar observations (Figure 11b) feature a cyclonic circulation pattern,

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consistent with the passage of the storm center over this region (Figure 10a). The coupled model

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in both runs (Figures 11f,j) also produces reasonably well the cyclonic circulation pattern but with

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some model deficiencies in simulating its observed position. These model discrepancies suggest

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that the CFSR reanalysis winds have errors of ~25 km in terms of the position of the storm center

471

during this period, which in turn can explain the model discrepancy between the observed and

472

reanalysis winds at the Halifax buoy as discussed in Figure 7.

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At time C, the HF-radar observations (Figure 11c) feature the intense southwestward currents

474

(up to 1.0 m/s), as the western periphery of the storm approached the ScS associated with strong

475

offshore winds (Figure 10a). The coupled model in both runs (Figures 11g,k) reproduces the

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observed southwestward flow but with some model deficiencies in simulating the observed spatial

477

variability of currents. The model discrepancies are most likely due to HF-radar observation errors

478

and real small-scale features that are not simulated correctly by the models due to inadequate

479

model resolution and imperfect model physics. Overall, at times A-C when the storm passed

480

overhead, the comparison of model results between Runs 1 and 2 demonstrates that the effects of

481

𝝉𝑷 are mainly to reduce the magnitudes of surface currents. This is consistent with relatively fast

482

downward momentum transfer due to strong vertical gradients of 𝝉𝑷 near the surface, as previously

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discussed at the two ADCP locations.

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At time D, the local winds were weak (Figure 10a), and the storm-induced currents underwent

485

a “Rossby adjustment”, based on the fact that the observed surface currents over the offshore areas

486

(~60 km off the coast) rotated by about 180o in the clockwise direction (comparing Figures 10c

487

and 10d), consistent with the rotation of NICs in nearly half of the local inertial cycle (~17 h).

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Within ~40 km off the coast, the NICs were inhibited presumably due to decreased water depth

489

and increased mixed layer depth (Wang et al., 2016). Model results in Run 1 (Figure 11h) agree

490

reasonably well with observations except for underestimated magnitudes and clockwise rotations

491

of NICs over the offshore area of the domain. By comparison, the coupled model in Run 2 does

492

not generate the observed clockwise rotation (about 180o) of NICs over the offshore areas (Figure

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11l). These results are consistent with reduced turbulent momentum transfer in the upper-ocean

494

layer with the inclusion of 𝝉𝑷 just after the storm passage, as previously discussed at the two ADCP

495

locations.

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5. Summary and discussion

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The effects of wave-induced vertical Reynolds stress (WIVRS) on the upper-ocean momentum

498

transfer were examined based on numerical results produced by a coupled wave-circulation model

499

on the Scotian Shelf (ScS). Two storm events were considered in this study: (a) Hurricane Earl in

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September 2010 and (b) Winter Storm Echo in December 2015. The effects of WIVRS were

501

implemented in a coupled wave-circulation model using the wave pressure-slope stress (𝝉𝑷 )

502

suggested by Mellor (2013). The wind stress at the sea surface specified in the coupled model is

503

sea-state dependent and represented as a combination of two different components, form drag

504

𝝉𝑷 (0) and skin drag 𝝉𝑻 (0), which provide boundary conditions for 𝝉𝑷 and the turbulent Reynolds

505

stress (𝝉𝑻 ), respectively. The combined sea-state-dependent wind stress is found to be more

506

consistent with the drag coefficient given by Large and Pond (1981) during Hurricane Earl, but

507

more consistent with the drag coefficient given by Edson et al. (2013) during Winter Storm Echo.

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The performance of the coupled wave-circulation model was first assessed to be satisfactory

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by comparing model currents with the observed time-varying, vertical profiles of currents made

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by the ADCPs, and surface currents made by the high frequency (HF) radar on the inner ScS.

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Model results in two numerical experiments were analyzed to examine the effects of 𝝉𝑷 . In the 26

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model experiment with 𝝉𝑷 (Run 1), vertical momentum transfer associated with vertical mixing

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depends on the combination of 𝝉𝑷 and 𝝉𝑻 . In the model experiment without 𝝉𝑷 (Run 2), the effect

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of 𝝉𝑷 is compensated by 𝝉𝑻 and vertical momentum transfer associated with vertical mixing

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depends entirely on 𝝉𝑻 . Analyses of model results demonstrate that, during both storm events, the

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inclusion of 𝝉𝑷 accelerates the downward momentum transfer in the upper-ocean layer when the

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storm passes overhead associated with strong vertical gradients of 𝝉𝑷 near the surface, leading to

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relatively weak vertical shears of horizontal currents and thus weak 𝝉𝑻 in the upper-ocean layer,

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which in turn weakens the momentum transfer to deeper water through 𝝉𝑻 just after the storm

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passage. As a result, surface ocean currents simulated in Run 1 are reduced by 𝝉𝑷 during the peak

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winds, which has a better agreement with the HF-radar observations during Echo than model

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results in Run 2. In the vertical direction, by comparison, the reduced downward momentum

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transfer due to the inclusion of 𝝉𝑷 was found to be more consistent with both the ADCP

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observations showing a relatively slow decay of the upper-ocean currents, and the HF-radar

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observations showing relatively strong clockwise-rotating near-inertial currents over the offshore

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area of the inner ScS just after the storm passed by. In addition, the comparison of results between

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the two storm events demonstrates that the effects of 𝝉𝑷 are more pronounced over the vertical

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during Hurricane Earl due to deeper penetration depths of 𝝉𝑷 associated with stronger winds (up

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to 33 m/s) than those during Winter Storm Echo associated with weaker winds (up to 25 m/s).

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Overall, the model results presented in this study demonstrate that, in addition to the turbulence

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transfer, the WIVRS is another important process that transfers the wind momentum at the sea 27

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surface to the water column during storm events. The fact that the wind momentum is partly

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transferred by the surface wave motion should be included in future ocean circulation models.

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Furthermore, changes in momentum transfer induced by WIVRS can affect the transfer of scalar

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quantities such as temperature and salt. It would be a worthwhile endeavor to examine the effects

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of WIVRS on the long-term mixed layer development in the future.

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Acknowledgments and data

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This research was supported in part by the Government of Canada Program World Class

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Prevention, Preparedness and Response for Oil Spills from Ships Initiative, the Marine

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Environmental Observation, Prediction and Response Network (MEOPAR), Ocean Frontier

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Institute (OFI), and Lloyd's Register (LR). JS is supported by the Natural Sciences and Engineering

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Research Council of Canada (NSERC), Ocean Frontier Institute (OFI), and Shenzhen Government

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Research Fund (KQJSCX20170720174016789). The authors thank two anonymous reviewers for

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their constructive comments.

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Appendix: Tidal currents on the inner Scotian Shelf

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Figure A1 presents observed and simulated surface current ellipses of two principle constitutes,

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M2 and K1, calculated based on the HF-radar data and model results over the HF-radar grid on the

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inner Scotian Shelf for three winter months (December 2015 to February 2016). For the observed

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M2 tidal current ellipses, with increasing distance from the shore, the magnitudes of tidal currents

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vary from 2.0 cm/s to 4.0 cm/s, and the direction orientations vary from the cross-shore direction

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to the north-south direction. For the observed K1 tidal current ellipse, the magnitudes increase from

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3.0 cm/s to 8.0 cm/s with increasing distances from the shore, and the direction orientations are

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generally aligned with the along-shore direction except for areas near the west and east edges of

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the grid. By comparison, model results produced by the coupled wave-circulation model are in

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reasonable agreement with observations expect for areas over the southwest and southeast edges

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of the grid for the M2 currents, and areas near the west and east edges of the grid for the K1 currents.

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These model-data discrepancies are due in part to observational errors associated with relatively

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low data availability and high geometric dilution of precision (GDOP, Chapman, 1997) errors near

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the edges of the grid (Wang et al., 2018), and the remaining discrepancy can be due to inadequate

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model resolutions and imperfect model physics.

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Figure 1. Major topographic features of the model domain over the eastern Canadian shelf, HFradar stations (red circles), ADCP stations (blue asterisks), buoy stations (blue triangles), and tracks of two storms considered in this study.

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Figure 2. Map showing the HF-radar grid (colored dots), HF-radar stations (red circles), ADCP stations (blue asterisks), and buoy stations (blue triangles) on the inner part of the Scotian Shelf. The color of the dots indicates the proportion of available data on 15-16 December 2015. The gray solid and dashed contour lines represent the smoothed water depths of 100 and 200 m, respectively. Abbreviations are used for Sandy Cove (SCOV) and Clam Harbour (CLMH)

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Figure 3. (a-d) Time series of observed and reanalysis wind speeds and directions, and (e-h) time series of observed and simulated significant wave heights (𝐻𝑠 ) and peak periods (𝑇𝑝 ) at buoys 44258 and 44024 during a 3-day period in early September 2010 (Hurricane Earl). The model results in the control run (with both 𝛕𝐏 and 𝛕𝐓 ) are used in (e-f).

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Figure 4. Comparison of modelled sea-state-dependent drag coefficient (𝐶𝐷 ) with the wind-speeddependent 𝐶𝐷 given by the Large and Pond (1981) method and the COARE 3.5 algorithm (Edson et al., 2013) during (a) Hurricane Earl, and (b) Winter Storm Echo.

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Figure 5. Hovmoller plots of detided and demeaned currents during a 3-day period in early September 2010 (Hurricane Earl) at locations T1 (top two rows) and T2 (bottom two rows). The left, middle and right columns are for the ADCP observations, and model results in Runs 1 and 2, respectively. The black contour lines delineates the speed of 0.08 m/s.

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Figure 6. Hovmoller plots of modelled wave pressure-slope stress (𝛕𝐏 ) and turbulent Reynolds stress (𝛕𝐓 ) during a 2-day period in early September 2010 (Hurricane Earl) at location T1 in Run 1 (left three columns) and Run 2 (right column).

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Figure 7. (a-d) Time series of observed and reanalysis wind speeds and directions, and (e-h) time series of observed and simulated significant wave heights (𝐻𝑠 ) and peak periods (𝑇𝑝 ) at the Halifax buoy and buoy 44137 during a 2-day period in mid-December 2015 (Winter Storm Echo). The model results in the control run (with both 𝛕𝐏 and 𝛕𝐓 ) are used in (e-f).

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Figure 8. Hovmoller plots of detided and demeaned currents during a 3-day period in midDecember 2015 (Winter Storm Echo) at locations T1 (top two rows) and T2 (bottom two rows). The left, middle and right columns are for the ADCP observations, and model results in Runs 1 and 2, respectively. The black contour lines delineates the speed of 0.06 m/s.

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Figure 9. Hovmoller plots of modelled wave pressure-slope stress (𝛕𝐏 ) and turbulent Reynolds stress (𝛕𝐓 ) during a 2-day period in mid-December 2015 (Winter Storm Echo) at location T1 in Run 1 (left three columns) and Run 2 (right column).

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Figure 10. Time series of (a) reanalysis wind stress, (b, c) observed and simulated currents (detided, demeaned) spatially-averaged over the HF-radar grid, (d, e) spatial RMSEs, and (f, g) spatial 𝛾 2 for two different model runs during Winter Storm Echo on 15 and 16 December 2015. The dashed lines mark the selected four specific times (A, B, C and D) at which the results are shown in Figure 11.

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Figure 11. Instantaneous distributions of (a-d) observed and (e-l) simulated surface current vectors (detided, demeaned) at four specific times A (1500Z Dec 15), B (2300Z Dec 15), C (0700Z Dec 16) and D (1200Z Dec 16) shown in Figure 10 during Winter Storm Echo in December 2015. The gray solid and dashed contour lines represent the smoothed 100 and 200 m depths, respectively.

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Figure A1. Observed (red) and simulated (blue) surface current ellipses of two principle constitutes, (a) M2 and (b) K1, calculated based on the HF-radar data and model results over the HF-radar grid on the inner Scotian Shelf for three winter months (December 2015 to February 2016). The gray solid and dashed contour lines represent the smoothed 100 and 200 m depths, respectively.

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Declaration of interests

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☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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