The influence of different turbulence schemes on modelling primary production in a 1D coupled physical–biological model

A one-dimensional (1D) coupled physical–microbiological model has been applied to a site in the central North Sea. The impact of the choice of the turbulence closure scheme on the modelling the primary production has been investigated.The model was run with four different parameterisations of vertical mixing of heat, momentum and dissolved and suspended matters, using M2 tidal forcing and the hourly mean meteorological forcing of 1989 to reproduce the annual thermal structure and primary production. The four mixing parameterisations are: Level 2 turbulence closure scheme [Mellor, G.L., Yamada, T., 1974. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791–1806; Mellor, G.L., Yamada, T., 1982. Development of a turbulence closure model for geophysical Fluid problems. Rev. Geophys. Space Phys. 20 (4) 851–875] using an explicit numerical scheme [Sharples, J., Tett, P., 1994. Modelling the effect of physical variability on the midwater chlorophyll maximum. J. Mar. Res. 52, 219–238]; a version of the Level 2.5 turbulence closure scheme [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55–62; Ruddick, K.G., Deleersnijder, E., Luyten, P.J., Ozer, J., 1995. Haline stratification in the rhine/meuse freshwater plume: a 3D model sensitivity analysis. Cont. Shelf Res. 15 (13) 1597–1630] simplified to use an algebraic mixing length by Sharples and Simpson [Sharples, J., Simpson, J.H., 1995. Semidiurnal and longer period stability cycles in the Liverpool Bay region of freshwater influence. Cont. Shelf Res. 15, 295–313], also solved explicitly; the same simplified L2.5 scheme with an implicit numerical solution and modified vertical discretisation scheme [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206]; and another version of the same scheme (but using a different algebraic mixing length) as described by Xing and Davies [Xing, J., Davies, A.M., 1996a. Application of turbulence energy models to the computation of tidal currents and mixing intensities in the shelf edge regions. J. Phys. Oceanogr. 26, 417–447; Xing, J., Davies, A.M., 1996b. Application of a range of turbulence models to the computation of tidal currents and mixing intensities in shelf edge regions. Cont. Shelf. Res. 16, 517–547; Xing, J., Davies, A.M., 1998. Application of a range of turbulence energy models to the computation of the internal tide. Int. J. Numer. Methods Fluids 26, 1055–1084]. Various model outputs at the sea surface and in depth profiles have been compared with data collected in 1989 as part of the North Sea Project [Huthnance, J.M., 1990. Progress on North Sea Project. NERC News, vol. 12, pp. 25–29, UK]. It is shown that the biological results are extremely sensitive to the small changes in the physical conditions, which arise due to the different turbulence schemes tested. The timing of the spring bloom and the maintenance of the midwater chlorophyll maximum all differ greatly between model runs, and the gross primary production varies by a factor of two from the highest to lowest results. The simplified Level 2.5 scheme, implemented using the numerical methods of Annan [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206], produces results, which give the best agreement with the available data.     

Physical processes in the ROFI regime

The distinctive feature of all ROFI (Regions Of Freshwater Influence) systems is the input of significant amounts of buoyancy as freshwater from river sources. If the spatial scale is unrestricted by coastal topography and stirring is weak, this input tends to drive a coast-parallel flow in which the Coriolis force constrains a wedge of low density water against the coastal boundary. Without frictional effects, this flow is subject to baroclinic instability which induces large meanders and eddies in the flow but in, many ROFIs, the tidal flow induces frictional effects which stabilise the density driven flow.In the absence of the effects of rotation and stirring, the buoyancy input tends to induce stratification through an estuarine circulation in the direction of the gradient. When stirring is applied, by the action of wind, waves or tidal flow, the density current is suppressed but is rapidly re-established when stirring ceases, as in the Linden-Simpson (1988) laboratory tank experiments. In real ROFI systems, a combination of all these processes operates so that the structure of the water column and the flow is the result of a competition between the stratifying influence of buoyancy input and the net stirring effect of the wind, waves and the tides. This competition is more difficult to analyse than the heating-stirring competition, because freshwater buoyancy input is not spatially uniform but enters at discrete sources along the coast and its subsequent spreading has to be determined.While the springs-neaps cycle in tidal stirring imposes a regular fortnightly modulation on vertical mixing, the influence of the wind is irregular and depends, not just on the magnitude of the stress, but also on the direction in which it acts. In some exposed shallow water situations there may also be significant stirring due to waves generated by non-local winds.ROFI systems are further complicated by the action of tidal straining in which differential advection, due to vertical shear in the tide, interacts with the density gradient to generate fluctuations in vertical stability at the tidal frequency which, in some cases, are of sufficient amplitude to switch the water column between stable stratification and vertical density homogeneity each tidal cycle. This straining along with the other ROFI processes have been incorporated into a series of 1-D models to provide a more objective test of the hypotheses about the mechanisms involved. Comparison of model hindcasts with observations indicate that we now have a first-order understanding of the complex behaviour of ROFIs.On a global scale it is clear that ROFIs represent an important component of the shelf-sea environment of particular concern in relation to the impact of pollutant discharges. To date, most studies of ROFI's have concentrated on systems in temperate latitudes but attention needs to be focused on the very extensive ROFIs in tropical regions where most of the world's river discharge enters the ocean. In monsoonal regions, these inputs exhibit strong seasonal modulation which may, in competition with tidal stirring, result in an annual cycle of stratification and the formation of fronts.