Bed shear stress in the southern North Sea as an important driver for suspended sediment dynamics

Abstract

This paper addresses the spatial and temporal patterns of drivers for sediment dynamics in coastal areas. The basic assumption is that local processes are dominating. The focus is put on the bed shear stress in the southern part of North Sea giving the basic control for deposition–sedimentation and resuspension–erosion. The wave-induced bed shear stress is formulated using a model based on the concept that the turbulent kinetic energy associated with surface waves is a function of orbital velocity, the latter depending on the wave height and period, as well as on the water depth. Parameters of surface waves are taken from simulations with the wave spectrum model WAM (wave model). Bed shear stress associated with currents is simulated with a 3D primitive equation model, Hamburg Shelf Ocean Model. Significant wave height, bed shear stress due to waves and currents, is subjected to empirical orthogonal functions (EOF) analysis. It has been found that the EOF-1 of significant wave height represents the decrease of significant wave height over the shallows and, due to fetch limitation, along the coastlines. Higher order modes are seesaw-like and, in combination, display a basin-scale rotational pattern centred approximately in the middle of the basin. Similar types of variability is also observed in the second and third EOF of bed shear stress. Surface concentrations of suspended matter derived from MERIS satellite data are analysed and compared against statistical characteristics of bed shear stress. The results show convincingly that the horizontal distribution of sediment can, to a larger extent, be explained by the local shear stress. However, availability of resuspendable sediments on the bottom is quite important in some areas like the Dogger Bank.

Appendices

Appendix 1 Models used

The bed shear stress components due to currents and waves are calculated using the ocean currents simulated by HAMSOM and waves estimated with the ocean wave spectrum model WAM. Waves are represented by significant wave height, wave period and wave direction.

The region of interest is the southern North Sea from 50.87° N to 57.17° N and from 3.40° W to 9.10° E. Both models are integrated on the same grid with a horizontal resolution of 1.5′ in the north–south direction and 2.5′ in the east–west direction (corresponding to 2.5–3 km).

Meteorological forcing for the models HAMSOM and WAM is based on hourly data provided by the regional model of atmosphere (Feser et al. 2001). It includes the two wind components, atmospheric pressure, air temperature, relative humidity and cloudiness. The model runs were performed for the year 2003.

In the setup described above, HAMSOM is coupled with a SPM transport model. Results from these simulations will be addressed in a separate paper. In the present study, we analyse only outputs from the circulation model and WAM.

1.1 HAMSOM model

The 3D ocean circulation model HAMSOM is a baroclinic, primitive equation model described by Backhaus (1985) and Pohlmann (1996). It has been widely applied and validated for many other shelf areas worldwide. It includes the equations of momentum, continuity and seawater state, as well as transport equations for temperature and salinity. The model uses a semi-implicit numerical scheme. It is one-way nested into a large-scale HAMSOM model domain for the North Atlantic and uses sea level elevation and climatic averages of temperature and salinity at the open boundaries. HAMSOM uses z-coordinates and, in the present setup, includes 21 vertical layers variable from 5.0 m in the upper layers and up to 10 m in the lower layers and a time step of 5 min. The fresh water sources are represented in the model by the rivers Weser, Ems and Rhine (DOD 2006), the Ijssel, Nordzeekanaal and Scheldt (Pätsch and Lenhart 2004), the Thames, Welland, Humber, Tees, Tyne and Forth (GRDC 2006). The fresh water discharges data were linearly interpolated to fit the temporal resolution of the model.

1.2 WAM model

WAM is a third-generation wave spectral model, which solves the wave transport equation explicitly without any a priori assumptions on the shape of the wave energy spectrum. A detailed description of the WAM model is given by Günther et al. (1992) and Komen et al. (1994). WAM is a state-of-the-art spectral wave model specifically designed for global and shelf sea applications. It can run in deep or shallow waters and includes depth and current refraction (steady depth and current field only). It can be set up for any local or global grid with a prescribed data set, and grids may be nested for fine scale applications. The WAM was applied first to the North Atlantic on a coarse grid and then to the southern North Sea (shallow water mode) using the boundary conditions (wave spectra) from the WAM run for the North Atlantic. The forcing of the coarse model uses the wind filed from the NCEP re-analysis.

Appendix 2 Description of major parameters

We parameterise current-only bed shear stress $\tau _{\text{b}}^{\text{c}}$ as

$$\tau ^{{\text{c}}}_{{\text{b}}} = \rho C_{{\text{D}}} \ifmmode\expandafter\bar\else\expandafter\=\fi{U}^{2}_{{\text{b}}} ,$$

(9)

where ρ = 1,000 kg m⁻³ is the water density, ${\overline U _{\text{b}} }$ is the averaged current speed at the lowest model level and C _D is the drag coefficient. The value of C _D is determined by the bed roughness length Z ₀ and the thickness of the lowest water layer H _b:

$$C_{\text{D}} = {\text{0}}{\text{.16}}\left( {{\text{1}} + {\text{ln}}\left( {\frac{{Z_{\text{0}} }}{{H_{\text{b}} }}} \right)} \right)^{ - {\text{2}}} $$

(10)

where Z ₀ = d ₅₀/12, and d ₅₀ is the mean sand grain size, for which we take d ₅₀ = 0.25 mm.

In Eq. 5 for bed shear stress due to waves, $\tau _{\text{b}}^{\text{w}}$, we parameterise the wave friction factor f _w as

$$f_{\text{w}} = \max \left\{ {f_{{\text{wr}},} f_{{\text{ws}}} } \right\}.$$

(11)

The rough-bed wave friction factor f _wr is given by:

$$f_{{{\text{wr}}}} = {\text{0}}{\text{.237}}r^{{ - {\text{0}}{\text{.52}}}}$$

(12)

where

$$r = \frac{A}{{k_{\text{s}} }},$$

(13)

is the relative roughness, k _s = 2.5 × d ₅₀ is the Nikuradse roughness length, and A = U _w T/2π is the semi-orbital excursion.

The smooth-bed wave friction factor

$$f_{{{\text{ws}}}} = BR_{{\text{w}}} ^{{ - N}}$$

(14)

is dependent on the Reynolds number $R_{{\text{w}}} = \frac{{U_{{\text{w}}} A}}{\nu }$, where ν = 1.6 × 10⁻⁶ m² s⁻¹ is the kinematic viscosity. In Eq. 14, B = 2 and N = 0.5 if R _w ≤ 5 × 10⁵ (laminar flow). In the case of turbulent flow (R _w > 5 × 10⁵), B = 0.0521 and N = 0.187.

As described in Section 3.1, the value of the friction velocity u* controls the sedimentation and erosion of SPM. In the area of our study, according to Gayer et al. (2006), sedimentation occurs for u* < 0.01 m s⁻¹, for 0.010 ≤ u* < 0.028 m s⁻¹ resuspension of SPM occurs, while erosion occurs when 0.028 m s⁻¹ ≤ u*.