Non-linear interactions between tides and storm surges during extreme weather events over the eastern Canadian shelf

Abstract

In this study, the non-linear tide-surge interactions (NTSIs) over the eastern Canadian shelf (ECS) are examined numerically during two extreme weather events. A three-dimensional ocean circulation model for the ECS based on the Regional Ocean Modeling System (ROMS-ECS) is used. The model is driven by tides and atmospheric forcing in a barotropic mode by neglecting baroclinic effects on NTSIs in this study. The atmospheric forcing is based on the hourly atmospheric reanalysis known as ERA5 produced by the European Centre for Medium-Range Weather Forecasts. The performance of ROMS-ECS in simulating tides and storm surge is assessed using observed sea levels and previous numerical results over the ECS. Analyses of model results during Hurricanes Bill (2009) and Dorian (2019) demonstrate that relatively strong NTSIs occur over regions with strong tidal and wind-driven currents. The relatively intense NTSIs also modulate the magnitudes and timings of maximum storm surges as well as the amplitudes and phases of tides during the storm. In addition, the three-dimensional (3D) currents are modulated greatly by the NTSIs over the shelf break region. It is found that the non-linear friction and advection are the dominant factors in the NTSIs during the two storms. Relatively strong NTSIs also occur after the passage of the storm due to shelf waves generated by non-local storm winds.

Appendices

Appendix A: Error statistics for model comparisons

The root mean square error (RMSE), correlation coefficient (R), and γ² (Thompson and Sheng 1997) are used in this study to quantitatively assess the model performance.

$$\mathrm{RMSE}={\left(\frac{1}{N}{\sum }_{i=1}^{N}{\left({M}_{i}-{O}_{i}\right)}^{2}\right)}^{1/2}$$

(A-1)

$$R=\frac{{\sum }_{i=1}^{N}\left({M}_{i}-\overline{M }\right)\left({O}_{i}-\overline{O }\right)}{{\left({\sum }_{i=1}^{N}{\left({M}_{i}-\overline{M }\right)}^{2}{\sum }_{i=1}^{N}{\left({O}_{i}-\overline{O }\right)}^{2}\right)}^{1/2}}$$

(A-2)

$${\gamma }^{2}=\frac{Var \left(O-M\right)}{Var\left(O\right)}$$

(A-3)

where N is the total number of observations, M and O denote respectively the modeled and observed values, and the overbar in Eq. (A-2) represents temporal averaging. Var represents the variance operator. Physically, the γ² value in Eq. (A-3) represents the ratio between the variance of the model hindcast errors and the variance of the observations. The smaller γ² is, the better is the model performance. Empirically, the threshold value of γ² is chosen to be 1.

Appendix B: Co-amplitudes and Co-phases of M2 and K1 tides in baroclinic run

The baroclinic effect is not considered in this study. Past studies suggested that the tidal circulation over the ECS is affected by the hydrography and its seasonal variability (Ohashi et al. 2009; Wang et al. 2020). To demonstrate the effect of stratification and associated seasonal variability on the tidal elevations, the ROMS-ECS is run in baroclinic mode, with external forcing described in Section 3 and additional forcing associated with the net heat and freshwater fluxes at the sea surface and freshwater discharges from major rivers. From the hourly sea levels produced by the ROMS-ECS in February and August 2019, co-amplitudes and co-phases of tidal sea levels for the two major constituents M₂ and K₁ are calculated.

Co-amplitudes and co-phases of M₂ tidal sea levels in the baroclinic run (Fig. 

Fig. B1

Co-amplitudes (color image) and co-phases (contours) of a, c M₂ and b, d K₁ tidal elevations calculated from hourly sea levels produced by the ROMS-ECS in baroclinic mode in a, b February and c, d August

B1a, c) in February and August 2019 have large-scale features almost identical to their counterparts in the barotropic run (Fig. 3a). The amplitudes of the M₂ tides in the baroclinic run are slightly larger than their barotropic counterparts in the LC (thought to be due to the influence of baroclinic pressure gradient), while the phase of M₂ tides leads its counterpart in the barotropic run over LS.

Co-amplitudes and co-phases of K₁ tidal sea levels in the baroclinic run (Fig. B1b, d) in February and August 2019 also have features almost identical to their counterparts in the barotropic run (Fig. 3b) over the deep ocean waters of the northern North Atlantic and Labrador Sea, except for the noticeable differences over BB and ESL. Over these regions, the simulated amplitudes of K₁ produced by the ROMS-ECS in baroclinic mode are larger than in barotropic mode due to the baroclinic effect of stratification in the former.

In the baroclinic run, the co-amplitudes and co-phases of the M₂ tide in February (Fig. B1a) over the LC is smaller than in August (Fig. B1c). The differences in the co-amplitudes and co-phases of the K₁ tide between February (Fig. B1b) and August (Fig. B1d) show that the K₁ tidal elevations have larger amplitudes in BB and ESL in summer than winter. The comparisons of the M₂ and K₁ tides in the baroclinic run between February and August indicate that the tides are affected by the seasonal variability in stratification (Ohashi et al. 2009).