We consider the Norwegian Meteorological Institute’s system regarding the daily forecasts of water level, and warnings of possible dangerous water level events along the Norwegian coast. The system consists of three parts, the production of water level forecasts, a decision support system, and a system for dissemination of warnings to key users and the general public. Included is a brief description of the forecasting model and the parallel ensemble prediction system, and an assessment of the forecasts produced by them. Based on the assessment of the production models for a three year period we find that they provide sufficiently trustworthy forecasts of water levels for the purpose at hand. Also included is a description of the web based decision support system for issuing warnings. The decision support system was for instance used during the extreme weather event “Elsa” in February 2020, and was found to be an efficient tool both to monitor the event in its early stages and to expedite warnings to key users and the general public.

This chapter investigates the effect of including more than one dimension in space. In particular, it discusses the impact on numerical stability and the stability criterion. Extension to three dimensions is then straightforward.

The purpose of this chapter is to learn how to solve a simple subset of the momentum equations ( 1.1 ) numerically. The focus is on the shallow water equations, and in particular their depth integrated versions ( 1.33 ) and ( 1.34 ). Despite their simplicity, the shallow water equations include the essence of the momentum equations. For instance, we retain the possibility of a geostrophic balance and the impact of nonlinear terms on the dynamics.

In this chapter, we discuss the fundamentals of how to cast a PDE into finite difference form. More specifically, the reader will learn how to discretize the diffusion equation, and learn why some discretizations work and some do not. This will be the opportunity to introduce concepts such as numerical stability, convergence, and consistency. It will be explained how to check whether a discretization is stable and consistent, and the reader will learn about explicit and implicit schemes, the rudiments of elliptic solvers, and the concept of numerical dissipation or artificial damping inherent in our discretizations.

So far, we have only used the Cartesian geopotential coordinate system consisting of three orthogonal spatial coordinates x, y, z. Relaxing the orthogonality between the vertical coordinate z and the two horizontal coordinates x, y can make it much easier to analyze phenomena in atmospheres and oceans, and devise compelling models of them. The development of such non-orthogonal coordinate systems remains at the forefront of research in numerical modeling. The purpose of this chapter is, therefore, to present the salient issues relating to these generalized vertical coordinates.

The aim of this chapter is to discuss open boundaries and some of the techniques used to deal with them. An open boundary is defined as a computational boundary at which disturbances originating in the interior of the computational domain are allowed to leave without disturbing or deteriorating the interior solution (Røed and Cooper, Advanced physical oceanographic numerical modelling. D. Reidel Publishing Co, Dordrecht, 1986). Even though the governing equations are still valid at these boundaries, they nonetheless constitute a boundary in a numerical sense. Hence, we focus on how to construct conditions, or open boundary conditions (OBCs), in such a way that disturbances originating in the interior of the computational domain are indeed allowed to leave without disturbing or deteriorating the interior solution.

The aim here is to summarize a set of sound procedures for establishing what is referred to below as a “good” model. The text is based on earlier reports by the author on the subject, in particular McClimans et al. (1992) and Røed (1993). For more extensive reading on the subject, the reader is referred to the in-depth analysis documented in the GESAMP report (GESAMP 1991), or the review Lynch and Davies 1995.

The purpose of this chapter is to use the knowledge acquired in the previous chapters to learn about some slightly more advanced topics. For instance, we sketch ways to construct schemes of higher order accuracy, and ways to solve problems when advection and diffusion are equally important. Furthermore, we consider ways to treat nonlinearities numerically, and ask whether they harbor implications for instability. Since two-way nesting is becoming more and more popular, we also say a few words about smoothing and filtering, and give a detailed presentation of two-way nesting itself. Since the spectral method mentioned in the preface is rather common in global atmospheric models, the chapter ends with a brief description of a one-dimensional application of this method.

To model currents in a fjord accurate tidal forcing is of extreme importance. Due to complex topography with narrow and shallow straits, the tides in the innermost parts of a fjord are both shifted in phase and altered in amplitude compared to the tides in the open water outside the fjord. Commonly, coastal tide information extracted from global or regional models is used on the boundary of the fjord model. Since tides vary over short distances in shallower waters close to the coast, the global and regional tidal forcings are usually too coarse to achieve sufficiently accurate tides in fjords. We present a straightforward method to remedy this problem by simply adjusting the tides to fit the observed tides at the entrance of the fjord. To evaluate the method, we present results from the Oslofjord, Norway. A model for the fjord is first run using raw tidal forcing on its open boundary. By comparing modelled and observed time series of water level at a tidal gauge station close to the open boundary of the model, a factor for the amplitude and a shift in phase are computed. The amplitude factor and the phase shift are then applied to produce adjusted tidal forcing at the open boundary. Next, we rerun the fjord model using the adjusted tidal forcing. The results from the two runs are then compared to independent observations inside the fjord in terms of amplitude and phases of the various tidal components, the total tidal water level, and the depth integrated tidal currents. The results show improvements in the modelled tides in both the outer, and more importantly, the inner parts of the fjord.

We consider the distribution and level of local vertical mixing inside of the Drøbak Sill in the Oslofjord, Norway. The work is motivated by observations of long periods (∼years) of hypoxic or even anoxic conditions in the innermost basin, episodes attributed to weak vertical mixing. In line with earlier work on the subject we assume that the local vertical mixing level inside of the sill is predominantly determined by the loss of energy of propagating, tidally-induced internal waves whose source is the sill region. To investigate possible differences in vertical mixing we estimate the eddy diffusivity in the various basins based on model simulations and observations using three methods whereby the eddy diffusion coefficient is estimated. The model we use is an ultra high-resolution version of the three-dimensional, hydrostatic ocean model ROMS forced solely by barotropic tide well outside of the sill. To evaluate the sensitivity of the model results we perform sensitivity experiments in which the mesh size and various parameters and parameterizations are varied. We find indeed that the internal waves lose most of their energy before they reach the innermost basin, and hence set the scene for long periods of no deep water renewal. The sensitivity experiments reveal that it is important that the model's mesh size is small enough to resolve the dominant wavelengths of the topography. Moreover, we find that the strength of the turbulence production and hence the mixing depends on the initially chosen stratification. The method we use is generic and may be applied to any sill fjord.

This study examined sex differences in furniture assembly performance by manipulating the availability of instructions. Two groups of participants with an equal number of men and women assembled a kitchen trolley from IKEA. One group received step-by-step instructions, and the other group a diagram of the finished product. In addition, individual spatial ability was measured with the mental rotation test (MRT) and added to the analyses. Our results showed that men assembled the furniture faster (d=0.78) and more accurately (d=0.65) than women. Overall, participants performed better with step-by-step instructions than without (d=0.61), and the time spent on instructions was negatively related to MRT scores, r=-.428, p=.006. Aside from the time spent on instructions, women assembled the furniture nearly as fast as men did, and the sex difference in assembly score could be explained by differences in individual spatial ability. Copyright (c) 2015 John Wiley & Sons, Ltd.